Yalding Population in 1336

Yalding Population in 1336

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John Giffardfreehead35estate bailiff
Lucia Giffardfree34
Tibia Giffardfree8
Millicentia Giffardfree7
Thomas Giffardfree6
Richard Giffardfree4
Gilbert Hughesfree32vicar
1Benedict Dunnfreehead38carpenter
Elena Dunnfreewife37field worker
Katerina Dunnfreedaughter14field worker
Gilbert Dunnfreeson7field worker
William Dunnfreeson5field worker
2Aymer Walterfreehead35thatcher
Agnes Walterfreewife33field worker
Gilbert Walterfreeson15field worker
Ralph Walterfreeson13field worker
Elizabeth Walterfreedaughter11reeve
3John Nashserfhead36brewer
Alice Nashserfwife34field worker
Richard Nashserfson18field worker
Edith Nashserfdaughter9field worker
Thomas Nashserfson7field worker
4Henry Furnerserfhead35cowman
Elena Furnerserfwife32field worker
Edith Furnerserfdaughter13field worker
Richard Furnerserfson12field worker
5Walter Herendenserfhead34shepherd
Agnes Herendenserfwife34field worker
Hugh Herendenserfson10field worker
6Gilbert Paynefreehead41swineherd
Rosa Paynefreewife40baker
John Paynefreeson18field worker
Adam Paynefreeson16field worker
Mariota Paynefreedaughter14field worker
7John Haleserfhead37field worker
Edeline Haleserfwife35brewer
Matilda Haleserfdaughter12field worker
William Haleserfson8field worker
8Henry Rolfeserfhead39blacksmith
Mariota Rolfeserfwife37field worker
Richard Rolfeserfson16field worker
Ralph Rolfeserfson10field worker
9Thomas Brookerserfhead29woodward
Juliana Brookerserfwife28field worker
Henry Brookerserfson7field worker
Simon Brookerserfson3
10Stephen Webbserfhead32hayward
Ivette Webbserfwife31baker
Simon Webbserfson9field worker
11Geoffrey Fletcherserfhead43field worker
Margaret Fletcherserfwife41baker
Osbert Fletcherserfson17field worker
Ralph Fletcherserfson10field worker
12Thomas Woodfreehead45mason
Emma Woodfreewife42field worker
Rosamond Woodfreedaughter16field worker
Daniel Woodfreeson12field worker
13John Brickendenserfhead35miller
Agneta Brickendenserfwife34field worker
Thomas Brickendenserfson14field worker
Edmund Brickendenserfson13field worker
Ralph Brickendenserfson9field worker
14Emma Ashdownserfhead38field worker
Isabella Ashdownserfdaughter15field worker
Edmund Ashdownserfson13field worker
15Robert Goldingfreehead41pedlar
Edith Goldingfreewife40field worker
Simon Goldingfreeson17field worker
Geoffrey Goldingfreeson11field worker
16Rosamond Kyntonserfhead39field worker
Richard Kyntonserfson16field worker
Edith Kyntonserfdaughter10field worker
17Juliana Foremanserfhead39field worker
Rosa Foremanserfmother67blind
Robert Foremanserfson15field worker
Margaret Foremanserfdaughter9field worker
18Margaret Chowringserfhead42field worker
Elena Chowringserfdaughter20field worker
Henry Chowringserfson15field worker
Rosa Chowringserfgranddaughter1
19Elizabeth Clarkefreehead35field worker
Elena Clarkefreedaughter18field worker
Alice Clarkefreedaughter14field worker
Agnes Clarkefreedaughter9field worker
Luke Clarkefreeson5
20Elicia Godfreyfreehead42field worker
Isabella Godfreyfreedaughter16servant
Arnold Godfreyfreeson7field worker
John Godfreyfreeson6field worker
21Richard Bennettfreehead35plasterer
Elena Bennettfreewife33field worker
Agnes Bennettfreemother68disabled
Margery Bennettfreedaughter15servant
Edmund Bennettfreeson11field worker
William Bennettfreeson7field worker
Christina Bennettfreedaughter4
22Agnes Singyardserfhead22field worker
Juliana Singyardserfsister15field worker
John Singyardserfbrother14field worker
23Gilbert Bakerfreehead39messor
Rosa Bakerfreewife36field worker
Alice Bakerfreedaughter16sevant
Thomas Bakerfreeson11field worker
Katerina Bakerfreedaughter10field worker
Edith Bakerfreedaughter8field worker
24Adam Fleeteserfhead33pinder
Johanna Fleeteserfwife31cook
Roger Fleeteserfson9field worker
Simon Fleeteserfson2
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Walter Barfootserfson14field worker
Alice Barfootserfdaughter8field worker
27Margaret Manneringserfhead22field worker
Agnes Manneringserfsister18servant
Cecilia Manneringserfsister15field worker
28Alice Taylorfreehead36field worker
Emma Taylorfreedaughter15field worker
Nicholas Taylorfreeson15field worker
Edith Taylorfreedaughter7field worker
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Johanna Wardserfmother72disabled
Cecilia Wardserfdaughter16field worker
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Matilda Brattleserfsister14servant
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32Mariota Cooperserfhead32field worker
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Alice Cooperserfdaughter9field worker
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Margery Cheesemanserfdaughter7field worker
34Cristina Carpenterserfhead34field worker
Samuel Carpenterserfson13field worker
Alice Carpenterserfdaughter8field worker
35Alice Minchenserfhead23field worker
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Matilda Minchenserfsister14cook
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The importance of life history and population regulation for the evolution of social learning

Social learning and life history interact in human adaptation, but nearly all models of the evolution of social learning omit age structure and population regulation. Further progress is hindered by a poor appreciation of how life history affects selection on learning. We discuss why life history and age structure are important for social learning and present an exemplary model of the evolution of social learning in which demographic properties of the population arise endogenously from assumptions about per capita vital rates and different forms of population regulation. We find that, counterintuitively, a stronger reliance on social learning is favoured in organisms characterized by ‘fast’ life histories with high mortality and fertility rates compared to ‘slower’ life histories typical of primates. Long lifespans make early investment in learning more profitable and increase the probability that the environment switches within generations. Both effects favour more individual learning. Additionally, under fertility regulation (as opposed to mortality regulation), more juveniles are born shortly after switches in the environment when many adults are not adapted, creating selection for more individual learning. To explain the empirical association between social learning and long life spans and to appreciate the implications for human evolution, we need further modelling frameworks allowing strategic learning and cumulative culture.

This article is part of the theme issue ‘Life history and learning: how childhood, caregiving and old age shape cognition and culture in humans and other animals’.

1. Introduction

Humans are exceptionally reliant on culture. Theoretical models of the evolution of learning have brought considerable insight into the adaptive logic of culture and the conditions under which it can evolve [1–4]. But humans are exceptional in many ways, and this constellation of unusual traits must be explained in a unified framework. In particular, human adaptation is integrated with our special life history [5,6]. We owe our ecological success to a highly developed ability to learn from others, but we also exhibit a prolonged juvenile period, shorter inter-birth intervals, and an extended post-reproductive lifespan [7,8]. Human children are dependent on an extended network of carers and develop more slowly than other apes, but we nonetheless can have more of them, in shorter intervals. These traits are arguably unique to the genus Homo [9] and might have coevolved with our extensive reliance on cultural adaptations that allow adults to produce enough energy surplus to fuel this long and expensive development [10–12]. It is still unclear how and when a fully modern life history first appeared. Apes, in general, are characterized by long, slow life histories that are most likely an adaptation for dealing with uncertainty in juvenile recruitment [8]. It has been argued that a fully modern life history was certainly not present in Australopithecus [9] but evolved more recently as a mosaic of different features [13]. The high fertility of long-lived humans supported by our skill-intensive, socially learned foraging niche and substantial allomaternal care allows our species to have multiple dependent offspring at the same time resulting in a much greater potential for population growth and territorial expansion [14].

To understand the integrated role of culture in human adaptation, we need theoretical work that includes age structure and explicitly deals with different life-history dynamics. Age structure is not only an undeniable feature of human (and other animal) populations, it also has profound and often unforeseeable consequences for evolutionary dynamics. Lifetime reproductive success, for instance, is not an adequate measure of fitness anymore as soon as there is age structure, because timing of reproduction and other age-dependent strategies become important determinants of lineage growth rate [15,16]. The age structure and life-history system of a population is also expected to profoundly shape the informational environment learning strategies are responding to. Optimal learning strategies are expected to be age-dependent and we still need a formal life-history theory of learning that includes cultural transmission. How should individuals combine different sorts of information over the course of their lifetime and how does that affect the population distribution of cultural variants? Researchers have used dynamic optimization approaches to compute optimal learning schedules in response to a fixed set of environmental challenges [17,18], but including cultural transmission makes learning strategies inherently frequency-dependent, complicating the use of optimality approaches. Important first steps in this direction are the models by Aoki et al. [19,20] who solve for evolutionarily stable learning schedules and investigate which conditions result in cumulative cultural evolution. Similarly, Fogarty et al. [21] modelled how different sequences of dominant transmission modes throughout an individual’s lifetime affect evolutionary dynamics.

While including age-dependent learning is crucial in understanding how culture and life-history interact, there are also very basic open questions about the adaptive value of culture and of different social learning strategies in age-structured populations. Including age structure in models of social learning requires assumptions about vital rate parameters and the way population growth is regulated. What regulates population size has been described as ‘the fundamental question of population ecology’ [22]. Any population surviving and reproducing at a constant per capita rate will either go extinct or grow exponentially. Growth in natural populations is instead density dependent. Vital rates are said to be density dependent if they change depending on the density of conspecifics, owing to resource depletion or competition for territory [23,24]. Density-dependent population regulation acts as a negative feedback mechanism that keeps a population within the carrying capacity of its environment. Based on a large abundance time-series database covering 1198 species, Brook & Bradshaw [25] demonstrated that density dependence is indeed a pervasive feature of population dynamics in the wild that holds across widely different taxa. Density-independent factors, by contrast, such as natural disasters, weather or pollution, exert their influences on population size regardless of the population’s density and, thus, cannot keep a population at constant levels.

The way a population is regulated through density-dependent factors is known to shape the demographic structure of a population [24] and may change the incentives for copying or innovating even if the equilibrium population size and vital rates are constant. Starting with Henrich’s [26] model, that showed how reduced population sizes might have led to the loss of adaptive cultural knowledge in Tasmania, there is now a considerable literature on the importance of population size for cultural evolution [27–31]. It has also been suggested that connectivity or network structure plays a vital role in cultural dynamics [32–34].

Whatever the importance of population size and connectivity in cultural evolution, these features do not suffice to describe the constitution of a population, once demography and age structure are included. A given population size can result from numerous different constellations of vital rates and population regulation regimes which might exert different selection pressures on learning strategies. Vital rates and population regulation jointly determine the age structure of the population, influence when organisms die, when juveniles are born, and how much adaptive information the population possesses at these times. Importantly, even if researchers do not explicitly consider different vital rate constellations and population regulation regimes, they must make implicit assumptions about the way the population is maintained, the implications of which are poorly understood. With respect to the evolution of human life-history traits, for example, Baldini [35] demonstrated that the conclusions of an influential model do not hold if the implied mechanism of density dependence is changed.

This suggests an important project of reconsidering models of the evolution of social learning under different population-regulation and life-history scenarios. In this paper, we aim to clarify the impact of density-dependent population regulation and different life histories on the adaptive value of culture. We present a model of the evolution of social learning in which demographic properties of the population arise endogenously from assumptions about per capita vital rates and separate forms of population regulation, and compare the extent to which social information use is favoured under different scenarios. We find in even these simplest models—a necessary first step in building this literature—that paradoxical effects may arise, such as social learning evolving more readily when lifespan is short. We are able to explain these paradoxical effects in light of the costs and benefits of learning. We close by discussing limits of these models and future directions.

2. Methods

We constructed two models that differ only in the way population size is regulated, either through reduced chances of survival or through reduced chances of giving birth. First, we formulated analytical expressions of the basic population dynamics assuming only two age classes. These demographic models were then used to derive principled parameter combinations for individual-based simulations that allow comparisons of learning dynamics between different population-regulation and life-history regimes while holding other factors constant.

(a) Population regulation

In the simplest models, populations under density-dependent regulation follow a logistic growth curve. Originally developed to model stock dynamics and recruitment in fisheries, Bill Ricker formulated a discrete-time equivalent to the continuous-time logistic model, commonly known as the Ricker map [36]:

(b) Model definitions

(i) Fertility regulation

In the first model, per capita fertility (probability of giving birth per individual per time unit) decreases as the population grows, whereas per capita survival (probability of survival per individual per time unit) is independent of population size. The population dynamics are captured by the following recursions that describe juvenile (class 0) and adult (class 1) individuals, respectively:

(ii) Mortality regulation

In the second model, per capita survival rates decrease with increasing population size, while fertility remains constant:

Both modes of regulation lead to a similar logistic population growth curve that flattens out at equilibrium population size N ^ (see the electronic supplementary material, figure S1). It can be shown (see the electronic supplementary material for details) that the equilibrium population size under fertility regulation is given by

(c) Derivation of principled parameter values

Based on these analytical expressions, we found principled combinations of vital rate and regulation parameters that allow a direct evaluation of their effect on the evolution of learning while keeping other factors constant. We wanted to cover a broad range of different life histories, represented by distant points on the isoclines in electronic supplementary material, figure S2, to explore how population regulation and vital rate parameters jointly affect selection on social learning.

We chose different values for the equilibrium population size N ^ (200, 350, 500), the expected lifespan L ^ (3, 5, 7.5) and fertility regulation parameter δ ( 1 550 , 1 1000 , 1 1500 ) and derived all other parameter values for both modes of regulation (see the electronic supplementary material for details). We will refer to constellations with relatively high mortality and fertility rates as ‘fast’ life histories and to constellations with relatively low mortality and fertility rates as ‘slow’ life histories [38–40].

(d) Social learning simulations

Building on the demographic models, we constructed individual-based simulations to explore the consequences of different life-history constellations on the evolution of social learning in stochastically changing environments. The simulation tracks the behaviour of each individual in a single age-structured population of varying, but finite, size through the sequence of birth and mutation, learning, mortality and ageing, and environmental stochasticity. We focus on one domain of behaviour for which there is a single adaptive variant for any state of the environment. Possessing this adaptive variant increases individuals’ chance of survival by a factor σ > 1 and their chance of reproduction by a factor β > 1. As explained in the previous section, equilibrium population sizes, N ^ , were calculated based on baseline fertility and survival rates. Thus, actual population sizes in the simulations vary depending on the proportion of adapted individuals and exceed the N ^ from the analytical solutions. We assume an infinite state environment that never reverts to an earlier state. This implies that individuals can acquire the adaptive variant only through learning.

(i) Birth and mutation

We assume asexual, haploid reproduction. At the beginning of each time step, all adult individuals give birth to a single offspring with probability b (non-adapted) and probability βb (adapted), respectively. Under fertility regulation, these rates are multiplied by e − δ N t to make them density dependent. Juveniles inherit a learning parameter ξ that deviates slightly from their parent’s value in a random direction. Specifically, during each mutation event a value drawn from N ( 0 , μ ξ ) is added to the value of their parent while ensuring that the resulting ξ value remains within the interval [0,1].

(ii) Learning

All juveniles have the opportunity to acquire the adaptive variant through learning, either individually or socially. Specifically, a juvenile learns individually with probability ξ and socially with probability 1 − ξ. As learning strategies in nature are most likely influenced by myriads of different genes, ξ can be thought of as their cumulative effect that expresses an individual’s tendency towards individual learning. If an individual learns socially, it copies the variant of a randomly chosen adult. If it learns individually, it has a chance w to invent the adaptive solution. Letting only juveniles learn is clearly unrealistic for any real organism, but making simplifying assumptions is critical for understanding complex systems [41]. Allowing only juveniles to learn represents the extreme case of the exploration–exploitation trade-off organisms face between investing in learning as opposed to allocating their time and energy to reproduction.

(iii) Survival and ageing

After learning occurred, all individuals must survive. For both juveniles and adults, there is a chance s (non-adapted) and σs (adapted), respectively, that they survive until the next time step. Under mortality regulation, these rates are multiplied by e − γ N t . Juveniles that learned individually pay a once-only survival cost c that reduces their chance to survive into adulthood. This reflects the commonly held assumption that individual learning is more costly than copying, as individuals may spend considerable amounts of time and resources independently exploring the environment [1,2].

(iv) Environmental stochasticity

After each time step, there is a probability u that the environment changes. When environmental change occurs, all variants in the population become non-adaptive.

See the electronic supplementary material, table S1 for a summary of all parameters used in the simulations. We compared equilibrium population sizes of 200, 350 or 500 individuals, expected lifespans of 3, 5 and 7.5 years (corresponding to s = 0.6 6 ¯ , 0.8, 0.8 6 ¯ ) and weak ( δ = 1 1500 ), moderate ( δ = 1 1000 ) and strong fertility regulation ( δ = 1 550 ) and derived the respective vital rate and mortality regulation parameters from the expressions introduced in the previous section. These values were chosen to represent the widest possible range of population sizes and life histories that were compatible with the architecture of our analytical model. We also systematically varied the rate of environmental change u (every 10th, 100th or 1000th time step), the cost of individual learning c (1%, 5%, 10% reduced chance of surviving into adulthood) and the success rate of individual learning w (1%, 10%, 50%, 90% and 99%). All simulations were programmed in R [42]. Simulation and plotting code can be found on GitHub:

3. Results

All results reported in the following come from the last 5000 time steps of 10 independent 7000 time-step simulations per parameter combination. This duration was sufficient to reach steady state in all cases. In the main text, we report results for moderate strength of population regulation ( δ = 1 1000 ). Results for stronger or weaker regulation were very similar and can be seen in the electronic supplementary material, figures S6 and S7.

(a) Demographics and adaptation dynamics

Electronic supplementary material, figure S3 illustrates the basic demographics and adaptation dynamics for one exemplary parameter combination. Right after a switch in the environment (indicated by dashed lines), all individuals become non-adapted and the population size declines. As only juveniles learn, adaptation levels start to increase earlier in younger age classes compared to older age classes. Five years after the environment has changed, for instance, only individuals aged 5 or younger might possess the adaptive variant, whereas older individuals have learned before the environment has changed. Long after an environmental change, population size fluctuates around the carrying capacity and the proportion of adapted individuals tends to be higher in older age classes selection functions as a population filter and those possessing the adaptive variant are more likely to survive to old ages.

(b) Lifespan

Figure 1 shows a conceptual diagram of the main demographic forces that influence selection on learning in this model. Slower life histories, characterized by long lifespans and low fertility rates, resulted in more individual learning compared to faster life histories (figure 2b). It is counterintuitive that it is fast life histories that favour more social information use instead of the slow life histories typical of primates. However, by determining how long individuals live, L ^ influences the relative length of generation time and expected time between environmental changes [43]. If lifespans are long, conditions are more likely to change within generations and many adults will not have learned since the last switch in the environment. In this case, it pays for a juvenile to learn individually. Also, longer lifespans make early investments in learning more profitable, as organisms have more opportunities to reproduce later on. As individual learning is assumed to be more costly than copying, it is favoured when organisms live long enough to make up for their early investment in learning. This is confirmed by simulations with different costs of individual learning: lowering the recruitment cost to just 1% (as opposed to 5%) largely removed the effect of lifespan on social information use, whereas increasing it to 10% amplified the difference (electronic supplementary material, figures S4 and S5).

Figure 1. Life history and demographic forces influencing selection on learning.

Figure 2. Average propensity for individual learning ξ as a function of (a) equilibrium population size N ^ (values are based on baseline vital rates and thus correspond to situations when all individuals are not adapted) (b) expected lifespan L ^ (values of 3, 5 and 7.5 years correspond to s = 0.6 6 ¯ , s = 0.8 and s = 0.8 6 ¯ , respectively) (c) expected time between environmental changes Ω ( = 1 u ) and (d) success rate of individual learning w. Transparent lines show results from 10 independent simulations, solid lines represent averages across different simulations. Results are averaged over all values of other parameters (c = 0.95). (Online version in colour.)

(c) Population regulation

Population regulation through increased mortality consistently favoured stronger reliance on social learning compared to regulation through reduced fertility. This effect of population regulation was particularly strong in simulations with long lifespans, intermediate to fast changing environments and relatively high success rates of individual learning (figure 2).

There are two mechanistic pathways that explain the effect of population regulation on learning (figure 1). If baseline vital rates are constant, mortality regulation will necessarily result in shorter lifespans compared to fertility regulation. We have seen before how shorter lifespans result in more social learning in the present model. In line with the reasoning that individual learning involves a trade-off between lower juvenile survival and the potential for higher lifetime reproduction, the cost of individual learning modulates the effect of population regulation on learning. If individual exploration is essentially costless (c = 0.01), the difference between populations that are regulated through mortality and fertility, respectively, is much smaller compared to simulations with higher costs of individual learning (electronic supplementary material, figures S4 and S5).

The second pathway is through the influence of regulation on the timing of reproduction (figure 3). Under mortality regulation, birth numbers (purple) drop after a change in the environment and reach their highest level when almost all adults are adapted. For those juveniles, it is likely to be adaptive to learning socially. Under fertility regulation, by contrast, many juveniles are born relatively shortly after the environment has changed, when a substantial proportion of adults do not possess the adaptive variant and it might be more beneficial to learn individually. The bottom row of figure 3 displays the trajectories for effective vital rates, the actual per-individual probabilities of surviving (green) and reproducing (purple) at any point in time (see the electronic supplementary material for details). Under mortality regulation, effective fertility rises as the proportion of adapted adults increases, resulting in most juveniles being born long after environmental changes, when most adults possess adaptive behaviour. The drop in actual birth numbers after an environmental change is owing to the decline in population size. Under fertility regulation, it is the survival probability that increases with the amount of adaptive knowledge. Fertility first also increases before—owing to density-dependent factors—sharply declining as population size rises. This demographic constellation of relatively many births when the environment has just changed favours more individual learning.

Figure 3. Effect of population regulation on timing of reproduction. The top row shows proportion of adapted individuals in black and number of juveniles in purple the bottom row displays effective fertility rates in purple and effective survival rates in green mortality regulation is shown on the left, fertility regulation on the right. Shaded areas represent variation across means of 10 independent simulations. Plot shown for N ^ = 500 , L ^ = 7.5 , δ = 1 1000 , σ = 1.1 , β = 1.1, u = 0.01,w = 0.9, c = 0.05 and μ ξ = 0.01 . (Online version in colour.)

4. Discussion

Life history and age structure matter for the evolution of social learning and most previous models decided to leave out the complexities of real-world demography. Of course, making simplifying assumptions is critical to understand complex systems [41,44], but if we want to understand how culture evolves in real animals, it is not enough to study the dynamics of learning and cultural information in isolation. Instead, we need modelling frameworks incorporating real life history and demography that will help shed light on the question of how culture and life history interacted in shaping who we are. We are just starting to understand how combined life-history/social learning systems might behave and how they could be modelled. As a first step in this direction, we used a combination of demographic models and social learning simulations to investigate how different life cycles and forms of population regulation affect selection on learning. We found that, counterintuitively, a stronger reliance on social learning is favoured in organisms characterized by ‘fast’ life histories with high mortality and fertility rates compared to ‘slower’ life histories typical of primates. Results also unveiled greater social information use in populations that are regulated through mortality, compared to populations that are regulated through fertility. Vital rates and population regulation jointly influence when most juveniles are born, how long individuals live and when they are more likely to die. These demographic variables then influence the incentives to copy or to innovate.

As in Rogers’ influential model [2], social learning in the present model is parasitic, i.e. social learners scrounge adaptive information from individual learners who paid a cost to produce it [45,46]. We chose this relatively simple form of social learning to establish how population regulation and life-history dynamics can affect selection on learning in a well-understood modelling framework. In order for culture to increase population fitness, however, it must make individual learning either more accurate or less costly [47] and both empirical and theoretical results suggest that organisms usually do not copy indiscriminately but use a diverse set of learning strategies in different ecological and social contexts [4]. In this model, organisms could acquire adaptive behaviour through individual learning or one-shot interactions with a demonstrator at the beginning of their lives. Many essential skills in real animals, however, take generations to evolve and years to develop, which is particularly true for complex and causally opaque human culture [5,48]. If adaptive behaviour takes time and practice to develop, longer lifespans should allow individuals to reach higher skill levels and to fully capitalize on cultural information. Moreover, with cumulative culture, adaptive behaviour typically cannot be invented by single individuals on their own, so social learning should be necessary [6,49].

Although our finding of more social learning in short-lived organisms might appear unintuitive to some readers given the opposite empirical association observed in humans and other animals, our results should not be regarded as ‘negative’. The goal of theoretical modelling is not necessarily to reproduce empirical findings, but to sharpen our questions and clarify the implications of certain assumptions about natural processes [44]. Our model demonstrates that simple Rogers-style social learning can be very successful in short-lived organisms and does not explain the coevolution of long lifespans and social information use providing an important baseline for future studies. Such models should investigate the interplay between learning and life-history dynamics with more elaborate learning strategies that let organisms flexibly respond to different cues throughout ontogeny [47] and allow for cumulative cultural evolution [49], instead of the binary ‘adapted/not-adapted’ proposition used here. Important assumptions of the present model are also that learning only occurs in juveniles and the environment never reverts to an earlier state. If adults could repeatedly update their behaviour based on environmental cues and/or the environment could switch back to conditions only experienced by older individuals, older age classes can serve as a reservoir of adaptive information likely to increase the value of culture in long-lived organisms. The present model can be regarded as a cultural ‘null model’ nominating further analyses that will help us determine which additional aspects of cultural adaptation are necessary or sufficient to create selection for slower life histories. In a recent model without cultural transmission, Ratikainen & Kokko [50] found that plasticity does not only evolve in response to a given life history but that plasticity itself can shift the balance in the trade-off between survival and reproductive effort to favour greater longevity (see [51–53] for other work on life history and value of asocial learning). Similar models incorporating social learning and cumulative culture will be crucial in uncovering the multiple trade-offs involved in cultural adaptation.

Our model also suggests that the human mode of cultural adaptation characterized by slow development and long lifespans might not be the only, and probably not even the most common, form of adaptation through social learning and we should expect to see at least simple forms of social learning in many short-lived organisms. This result is in line with the accumulating empirical evidence for the prevalence of social information use in very short-lived organisms such as fruit flies [54,55] and bumblebees [56,57]. Danchin et al. [54], for example, used a transmission chain experiment to show that neutral traits can indeed become cultural markers of mate quality in Drosophila. Similarly, cephalopod molluscs evolved complex brains and high behavioural flexibility together with fast life histories, challenging the idea that intelligence necessarily coevolves with slow life history [58].

Understanding the coevolutionary relationships between social learning and life history will benefit both sides, cultural evolution and life-history theory. Including age structure and life history into models of social learning profoundly changes the informational landscapes learners are navigating, and social learning, on the other hand, can alter life-history trade-offs in ways that are unintelligible without taking culture into account.

Materials and Methods


We sequenced approximately 6 kb of ALMS1 in DNA samples from 91 individuals representing six populations that were obtained from the Coriell Institute for Medical Research Cell Repositories (Camden, NJ). Coriell repository numbers for these samples are as follows: CEPH (n = 21: NA06990, NA07019, NA07348𠄹, NA10830𠄱, NA10842𠄵, NA10848, NA10850𠄴, NA10857𠄸, NA10860𠄱, and NA17201), Han Chinese of L.A. (n = 21: NA17733–NA17749, NA17752�), Middle East (n = 10: NA17041�), Pygmy (n = 10: NA10469�, NA10492�), South Africa (n = 9: NA17341�), South America (n = 10: NA17301�) and South East Asia (n = 10: NA17081�). In addition, we sequenced the same regions in four nonhuman primate DNA samples from the Coriell Institute for Medical Research Cell Repositories with the following repository numbers: gorilla (Gorilla gorilla AG05251), bonobo (Pan paniscus AG05253), chimpanzee (Pan troglodytes AG06939), and orangutan (Pongo pygmaeus AG12256).

DNA Sequencing

Sequencing primers were designed from published human sequence ( <"type":"entrez-nucleotide","attrs":<"text":"NM_015120","term_id":"110349785">> NM_015120) with primer3 ( for coding and noncoding regions of ALMS1: upstream, intron 2, exon 5, intron 7, exon 8, intron 8, exon 10, and downstream (primer sequences are available upon request). We used standard polymerase chain reaction�sed sequencing reactions using Applied Biosystem's Big Dye sequencing protocol on an ABI 3130xl. Sequence data were assembled using Phred/Phrap (Ewing and Green 1998 Ewing et al. 1998), and the alignments were inspected for accuracy with Consed (Gordon et al. 1998, 2001). Polymorphisms were identified with PolyPhred 4.0 (Bhangale et al. 2006). All polymorphic sites were manually verified and confirmed by sequencing the opposite strand. Genotype data from 210 unrelated individuals were obtained from the HapMap project (Release 22 NCBI Build 36) (International HapMap Consortium 2005).

Linkage Disequilibrium (LD)

We calculated r 2 between all pairwise combinations (Hill 1968) of markers in ALMS1 and approximately 1 Mb of flanking sequences (both 5′ and 3′) using HapMap genotype data. Estimates of r 2 were obtained from Haploview (Barrett et al. 2005) for all markers with a minor allele frequency 𢙕% and used in subsequent analyses. To evaluate and compare the distribution of LD within and between the HapMap CEU, YRI, and ASN samples, and how LD decays as a function of distance from ALMS1, we calculated a statistic related to ZnS (Kelly 1997). Specifically, we calculated the average r 2 between all pairwise comparisons of single nucleotide polymorphisms (SNPs) in bin 1 and bin 2:

where n1 is the number of SNPs in bin 1 and n2 is the number of SNPs in bin 2. Here, n2 represents the number of SNPs in ALMS1 and n1 the number of SNPs in nonoverlapping 50-kb windows up and downstream of ALMS1.

Haplotype Analysis

Haplotypes were reconstructed in the HapMap and sequence data with Phase 2.1.1 (Stephens et al. 2001 Stephens and Scheet 2005) using 10 iterations to confirm consistency among runs, and the run with the best average goodness-of-fit was used. We defined Haplogroup A (ancestral) and Haplogroup D (derived) based on the allelic state of seven nonsynonymous SNPs (nsSNPs) (rs3813227, rs6546837, rs6546838, rs6724782, rs6546839, rs2056486, and rs10193972) and Haplogroup D1 and Haplogroup D2 based on the allelic state of two additional SNPs (rs6730785 and rs7598901). The ancestral allele was determined by the chimpanzee sequence.

We used Neighbor from the software package PHYLIP 3.6 (Felsenstein 1989, 2005) to construct unrooted phylogenetic trees on phased sequence (Dnadist was used to calculate the pairwise distance matrix) and HapMap data (average pairwise distances were calculated for the distance matrix). In both cases, we removed recombinant haplotypes occurring among the seven aforementioned nsSNPs (three unique haplotypes/four total haplotypes from the sequence data and two unique haplotypes/three total haplotypes from the HapMap data). We visualized the Neighbor-Joining trees with the APE package in R (

Time to the Most Recent Common Ancestor (TMRCA) Estimates

We used the method described by Thomson et al. (2000) to estimate the TMRCA on our phased sequenced data as this method does not utilize any particular population model. Analyses were performed both on all haplotypes as well as on only haplotypes with no recombination among the seven nsSNPs, and we found minimal effects on the estimated TMRCA (data not shown). We used the average divergence between chimpanzee and human sequences divided by two times the estimated divergence time of 6 million years, which we calculated to be 36/(2*60,00,000), or 3 × 10 𢄦 for our sequence mutation rate. Briefly, to estimate the TMRCA, we used the simple estimate of T, the time since the MRCA (Thomson et al. 2000 Mekel-Bobrov et al. 2005):

where is the unbiased estimator of T, xi is the number of mutational differences between the ith sequence and the MRCA, n is the total number of sequences in the sample, and μ is the mutation rate. In addition, we used three additional methods to estimate the ALMS1 TMRCA (McPeek and Strahs 1999 Bahlo and Griffiths 2000 Templeton 2002), all of which yielded similarly old dates and were not significantly different from one another (data not shown).

Coalescent Simulations

We calculated three standard neutrality tests of the site frequency spectrum: Tajima's D (Tajima 1989), Fu and Li's F test (Fu and Li 1993), and Fay and Wu's H test (Fay and Wu 2000). We used the nonhuman primate sequence to establish the ancestral allele for Fay and Wu's H test. To interpret summary statistics derived from the resequencing data, we performed additional coalescent simulations with the program ms (Hudson 2002) using previously inferred demographic parameters that were found to best fit genomic patterns of variation in the HapMap YRI, CEU, and ASN samples (Schaffner et al. 2005). The exact parameters can be found in table 1 of Schaffner et al. (2005), and involve multiple bottlenecks, population expansions, population splitting, recombination, and gene conversion. The only exception is that we did not include migration following population splitting as Schaffner et al. (2005) found these parameters resulted in only slightly worse fitting models, but the modest increase in levels of population differentiation resulted in more accepted simulation replicates to analyze. The ms command line argument for this model is available upon request. We used a rejection sampling method (Beaumont et al. 2002) to account for the a priori observation of ALMS1 population structure and a total of 1 × 10 7 simulations were performed. Initially, we attempted to accept data sets if they matched observed levels of differentiation in our resequencing data (five or more SNPs with an FST ≥ 0.80 between African and Han Chinese samples and two or more SNPs with an FST ≥ 0.52 between African and CEPH samples). However, none of the 10 million simulation replicates met these criteria, indicating that such levels of structure are incompatible with a neutral demographic model that is consistent with major features of human genomic variation (Schaffner et al. 2005). Thus, for computational tractability, we relaxed the acceptance criteria to one or more SNPs with a pairwise FST ≥ 0.80 and 0.52 between African and Han Chinese samples and African and CEPH samples, respectively. Using these thresholds, 1,405 data sets of the 10 million simulations were accepted and analyzed further. In particular, we evaluated the probability of observing divergent haplotype lineages, TMRCA, and Tajima's D as or more extreme than that observed for ALMS1. In accepted data sets, we calculated TMRCA as described above, Tajima's D (Tajima 1989), and the average number of nucleotide differences between haplogroups carrying the derived allele at the highly differentiated SNP:

where D1 and D2 denote the set of haplotypes belonging to derived haplogroup lineages 1 and 2, respectively. In the simulated data sets, D1 and D2 were chosen so as to maximize dxy.

Table 1

Summary of Coalescent Simulation Results Conditional on Ascertainment

Sample a dxy b P(dxy|FST) c TMRCA b (kya)P(TMRCA|FST) c Tajima's DP(D|FST) c
Han Chinese (n = 42)6.010.0468100.934𢄠.120.827
CEPH (n = 42)4.980.34923010.0811.340.065

Human Genome Diversity Project�ntre d'Etude du Polymorphisme Humain (HGDP�PH) Analysis

We defined haplogroups in the HGDP�PH data set (Li et al. 2008) with six SNPs, Haplogroups A and D were defined based on alleles of four genotyped nsSNPs (rs3813227, rs6546838, rs2056486, and rs10193972) and Haplogroups D1 and D2 were further defined by two additional genotyped SNPs (rs2037814 and rs3820700). Recombinant haplotypes among Haplogroups A and D were excluded from the haplotype frequency map, whereas recombinants between Haplogroups D1 and D2 were included and defined by the allelic status of rs10193972. In order to avoid any single population sample falling below a sample size of 10, we combined the Bantu SE and SW individuals into one Bantu South population.

We developed a simple heuristic statistic to determine how unusual the geographic distribution of ALMS1 genetic variation is relative to the rest of the genome using all autosomal HGDP�PH data that had less than 10% missing data. Specifically, for the ith SNP, we define the global deviance score, GDi, as follows:

where FSTi 12 , FSTi 13 , and FSTi 23 is the unbiased pairwise FST (Weir 1996) between East Asian and African samples, East Asian and American samples, and African and American samples, respectively, for the ith SNP, and is the average allele frequency across samples weighted by sample size. In words, the global deviance score is large when levels of differentiation between Asian and African and Asian and American samples are greater than the genomewide average and levels of differentiation between African and American samples is less than the genomewide average. We included the Bantu (North and South), Biaka, Mbuti, Mandenka, Yoruba, and San in the African sample the Colombian, Karitiana, Maya, Pima, and Surui in the American sample and the Cambodian, Dai, Daur, Han (North and South), Hezhen, Japanese, Lahu, Miaozu, Mongola, Naxi, Oroqen, She, Tu, Tujia, Xibo, Yakut, and Yizu in the East Asian sample.

We used the expression analysis tool (Thomas et al. 2006) to identify enriched PANTHER Pathways, Biological Processes, and Molecular Functions (Thomas et al. 2003) among genes in the top 0.1% of the distribution of GD scores. Pathways and terms with less than five genes were excluded from further analysis, and Bonferroni corrections were used to correct for multiple testing.

Estimating the Time of the Selective Sweep

We estimated the time since the selective sweep for the derived class of ALMS1 lineages by analyzing the amount of nucleotide diversity that has accumulated on the selected haplotypes as described in Akey et al. (2004) where the time back to the selective sweep, t, can be estimated by S/(), where S is the number of segregating sites, n is the number of haplotypes included and μ is the neutral mutation rate of the locus. For ALMS1 derived haplogroups, n = 120, S = 13, and μ = 1.75 × 10 𢄤 . Note that this calculation should be treated as a rough approximation because it assumes a starlike phylogeny, which ALMS1 violates.

Estimating the Strength of Selection

We used the following simple deterministic formula to estimate the selection coefficient, s (Gillespie 1998):

where w - = 1 − 2 pqhs − q 2 s , p is the frequency of the selected allele, q is the frequency of the nonselected allele, and h is the heterozygous effect. We assumed an initial frequency of 10% (a conservatively high estimate based on current frequencies in African samples) and a final frequency of 95% (a conservatively low estimate based on current frequencies in East Asian samples) for the putatively selected allele. The range of s reported in the main text is based on varying the age of the selective event (from 500 to 1,000 generations) and heterozygous effects (h = 0, 0.5, and 1).

Yalding Population in 1336 - History

Community Area 62, 8 miles SW of the Loop. Before the early twentieth century, the area now designated West Elsdon was a marshy remnant of an ancient lake. The Grand Trunk Railroad tracks gave definition to the eastern boundary of the area in 1880. Among the early settlers were German far- mers and Irish railroad workers.

The area became part of Chicago with the annexation of the town of Lake in 1889. A small hamlet of railroad workers called Elsdon grew up around car shops built by the Grand Trunk Railroad near 51st Street and Central Park, in what is now neighboring Gage Park. The railroad eventually opened passenger stations at 51st, 55th, and 59th Streets, but most residential development remained east of the tracks, as the land in West Elsdon was swampier and unimproved.

By the 1920s, people were settling in the area in greater numbers. Population grew from 855 in 1920 to 2,861 in 1930. The development of the nearby Kenwood and Clearing Industrial Districts and the opening of Chicago Municipal Airport ( Midway Airport ) in 1927 just to the west made the area an attractive place to settle. The new residents were primarily Polish and Czech, with smaller numbers of Italian, Yugoslavian, and Lithuanian immigrants. The Roman Catholic Archdiocese of Chicago established St. Turibius parish in 1927 to serve the growing Catholic population. An elementary school was established with the church, and Lourdes High School was built in 1936.

During the 1920s, Crawford Avenue (Pulaski), 55th Street, and other streets were paved, sewers were installed, and two public schools were built. Though some street improvements were made in the section west of Pulaski during the 1930s, the Great Depression economy suspended growth for a time. The area remained rural, and as late as 1938 cows and goats still grazed along 55th Street.

During World War II growth resumed, and the West Elsdon Civic Association organized itself to lobby for street improvements and other community goals. West Elsdon grew from a population of 3,255 in 1940 to its peak of 14,215 in 1960. Almost all of the new building consisted of detached single-family brick houses, and West Elsdon became an extension of the Bungalow Belt.

Many new residents were second-generation or established first-generation immigrants, sometimes moving from the Back of the Yards or other Southwest Side neighborhoods. They were drawn by the prospect of owning a house in a quiet residential area. Predominately Polish, many were part of the “white flight” from neighborhoods to the east.

West Elsdon residents played a central role in the history of racial segregation in Chicago during the Airport Homes race riots in 1946, the first of a series of public housing riots in Chicago. “Airport Homes” was the name of the site in nearby West Lawn established by the Chicago Housing Authority to provide temporary housing to returning veterans and their families during the postwar housing shortage. Residents of West Lawn and West Elsdon rioted and succeeded in intimidating a few black war veterans and their families from joining white veterans in the homes.

The West Elsdon Civic Association became one of the first vocal political enemies of the CHA and its first executive secretary, Elizabeth Wood. Opposition to public housing remained strong in the area. In the early 1970s the West Elsdon Civic Association was an active participant in the “No-CHA” citywide coalition opposing scattered-site public housing in predominantly middle-class white neighborhoods.

In the half century following World War II, West Elsdon remained a quiet, blue-collar white community with a high rate of homeownership. Several processes brought changes in the 1990s. As the older white ethnic generation aged, new families with young children moved to the area. Mexican residents increasingly settled in the eastern part of West Elsdon. As the number of children classified as Hispanic increased in the public elementary schools in the early 1990s, the number of black children admitted from other communities under a school desegregation consent decree rapidly declined.

In 1993 the Chicago Transit Authority began rapid transit service to the Loop on its Orange Line, with a station at Pulaski on the northern edge of the community. This brought suburban-style retail development on Pulaski, and raised property values nearby.

Montgomery County

Alabama State Capitol Building Located in the south-central part of the state, Montgomery County is the seat of state government. The city of Montgomery, now the state capital, is often referred to as the Cradle of the Confederacy because it briefly served as the first capital of the Confederate States of America in 1861. In the mid-twentieth century, Montgomery became the birthplace of the nation's civil-rights movement when Rosa Parks refused to give up her seat to a white passenger on a city bus. Montgomery County evolved from an economy reliant upon cotton to a modern diversified economy that includes the automotive industry and military bases. Montgomery County is governed by an elected five-member commission and includes two incorporated communities.
  • Founding Date: December 6, 1816
  • Area: 793 square miles
  • Population: 227,392 (2016 Census estimate)
  • Major Waterways: Alabama River, Tallapoosa River
  • Major Highways: I-65, I-85, U.S. Highways 31, 231, 331, 80, and 82
  • County Seat: Montgomery
  • Largest City: Montgomery
Andrew Dexter Montgomery County was created by an act of the Mississippi Territorial Legislature on December 6, 1816. The county was named in honor of Maj. Lemuel Montgomery of Tennessee, who was the first U.S. soldier killed in the Battle of Horseshoe Bend during the Creek War of 1813-14. The city of Montgomery is the county seat and was selected as the state's permanent capital in 1846. The county was carved out of Monroe County and originally encompassed most of central Alabama. It was later subdivided into Elmore, Bullock, and Crenshaw Counties. The act that created Montgomery County provided that its courts were to meet initially at Fort Jackson, located at the confluence of the Coosa and Tallapoosa Rivers and site of the surrender of the Creek Indians to Gen. Andrew Jackson, in present-day Elmore County. The courts met there only until June 1818, after which they met in nearby Alabama Town, founded by Gen. John Scott, who with several other migrants from Georgia founded the town on the bluff of the Alabama River. The men abandoned it when a group from New England, led by Andrew Dexter, founded a nearby town in what is now the downtown area of Montgomery and named it New Philadelphia. Scott and his companions then built a new town they called East Alabama. Seeing themselves as rivals, the citizens of East Alabama contemptuously referred to New Philadelphia as Yankee Town. The bitter rivalry ended, however, when the towns merged on December 3, 1819, and incorporated as the city of Montgomery, just prior to Alabama being admitted as a state. Montgomery County Courthouse The city of Montgomery prospered and became the county seat in 1822 and Alabama's permanent capital in 1846. Although it bears the same name as the county, the city was named in honor of a different person, Maj. Gen. Richard Montgomery, who lost his life in the Revolutionary War in the assault against Quebec. The city and the county of Montgomery have been the site of many firsts, with the distinction of being known as the birthplace of the both the Civil War and the civil-rights movement. On February 18, 1861, Jefferson Davis was sworn in as the president of the Confederate States of America in its initial capital of Montgomery. It was from Montgomery that a telegram was sent to authorize the bombardment of Fort Sumter in Charleston Harbor, thus commencing the Civil War. Ninety-four years later, on December 1, 1955, Montgomery played host to a defining event in the birth of the civil-rights movement when Rosa Parks refused to give up her seat to a white passenger on a Montgomery city bus. Ten years later Martin Luther King Jr. ended the Selma-to-Montgomery March for voting rights with a speech delivered from the state capitol grounds. The Civil Rights Memorial and Memorial Center, located across Washington Avenue from the headquarters of the Southern Poverty Law Center, commemorates people who lost their lives during the civil rights movement. Wright's Field Technological firsts were also achieved in Montgomery County. In 1886, the nation's first electric streetcar system was put into operation in Montgomery, and in 1910 the Wright Brothers founded the first flight school for aviators at a site near the Alabama River that would later become Maxwell Air Force Base. Orville Wright recorded the first powered flight in Alabama's history, the local press reporting that "a strange new bird soared over the cotton fields to the west of Montgomery, on March 26, 1910." This site later became an aviation repair depot and eventually evolved into a full-scale air base that today is home to Air University, the U.S. Air Force's center for professional military education. Lehman, Durr & Co., ca. 1874 The advent of the steamboat, the relocation of the state capital from Tuscaloosa, and the cotton trade spurred Montgomery County's antebellum economy. From the county's earliest days, cotton production was its most important local industry, with the first commercial cotton gin having been installed in the area at the beginning of the nineteenth century. Montgomery soon became an important port for shipping cotton from the region. In 1844, Henry Lehman, an immigrant from Germany, was lured by the potential of this economy and opened a small general store in the city of Montgomery. Six years later, brothers Emanuel and Mayer joined him, and they named the business Lehman Brothers. The Civil War disrupted the Lehmans' business. When the war ended, the brothers moved north and concentrated their operations in New York, where they helped establish the Cotton Exchange. Their thriving business subsequently evolved into today's global financial entity. Other businesses suffered from the effects of the Civil War, but the county's economy began to rebound with the growth of the textile industry and the diversification of agricultural industries. Montgomery became, and still is, an important processing and shipping center for cotton, dairy, and other farm products.
  • Educational services, and health care and social assistance (22.2 percent)
  • Retail trade (11.9 percent)
  • Manufacturing (11.5 percent)
  • Public administration (11.3 percent)
  • Arts, entertainment, recreation, and accommodation and food services (10.5 percent)
  • Professional, scientific, management, and administrative and waste management services (10.2 percent)
  • Finance and insurance, and real estate, rental, and leasing (6.0 percent)
  • Other services, except public administration (5.2 percent)
  • Construction (4.1 percent)
  • Transportation and warehousing, and utilities (3.6 percent)
  • Wholesale trade (1.9 percent)
  • Information (1.3 percent)
  • Agriculture, forestry, fishing and hunting, and extractive (0.4 percent)
Maxwell Air Force Base The county's single leading employer is Maxwell-Gunter Air Force Base, which provides approximately 12,700 jobs. In 2003, Korean-owned Hyundai constructed a $1.1 billion automotive assembly and manufacturing plant just south of the city of Montgomery, bringing another 2,700 jobs to the county. Other leading employers include the state of Alabama, Baptist Health System, Montgomery Public Schools, ALFA Insurance Companies, the city of Montgomery, Jackson Hospital and Clinic, and Rheem Manufacturing Company. Flowers Hall The Montgomery Public School System consists of all public schools in Montgomery County and 35 elementary schools, 11 junior/middle schools, and eight high schools. It is estimated that about 17 percent of school-age children in Montgomery County attend private schools. Montgomery County is also home to a number of institutions of higher education, including Alabama State University, a historically black institution founded in 1867 by former slaves in Marion, Perry County, and relocated to Montgomery in 1887 Auburn University at Montgomery (AUM), a metropolitan campus of Auburn University created by the Alabama Legislature in 1967 Huntingdon College, a Methodist-affiliated liberal-arts college founded in 1854 in Tuskegee and relocated to Montgomery in 1910 Faulkner University, a Christian liberal-arts school founded in 1942 and formerly known as Alabama Christian College and Jones School of Law, founded in 1928 by jurist Walter B. Jones (son of Alabama governor Thomas Goode Jones) and now associated with Faulkner University. Montgomery County Map Montgomery County is located in the south-central part of the state within the Coastal Plain physiographic section and encompasses 793 square miles. The Alabama and Tallapoosa Rivers form its northern boundaries with Autauga and Elmore counties. It is bounded on the east by Macon and Bullock Counties, on the south by Pike and Crenshaw Counties, and on the west by Lowndes County. Alabama Department of Archives and History Montgomery County offers numerous recreational and cultural activities. The city of Montgomery has 19 city parks, including Oak Park, which is home to the W. A. Gayle Planetarium. Lagoon Park Golf Course is a par-72 championship course that is open year-round. Montgomery's Riverwalk Stadium is home to the Montgomery Biscuits, an affiliate of the Tampa Bay Rays baseball team.

The Civil War and the civil-rights movement provide many sites for tourists, from the First White House of the Confederacy to the Dexter Avenue King Memorial Baptist Church. Both Jefferson Davis and Martin Luther King Jr. gave historic speeches from the front of the state capitol building. 1950s Montgomery Bus Other sites of interest in the county include museums dedicated to such diverse figures as Hank Williams Sr., Rosa Parks, and F. Scott and Zelda Fitzgerald. Montgomery County is also home to the Alabama Shakespeare Festival, which draws more than 300,000 visitors annually from all over the world. The Montgomery Museum of Fine Arts is located next to the Shakespeare Festival within the Winton M. Blount Cultural Park and contains paintings from such artists as Rembrandt, Goya, and John Singer Sargent. The Montgomery Zoo features animals from all of the world's continents and also includes a miniature train, a sky lift, a playground, and dining facilities.

The Amarna Period of ancient Egypt was the era of the reign of Akhenaten (1353-1336 BCE), known as 'the heretic king'. In the 5th year of his reign (c. 1348 BCE), he issued sweeping religious reforms which resulted in the suppression of the traditional polytheistic/henotheistic religious beliefs of the culture and the elevation of his personal god Aten to supremacy. According to some scholars, the period is limited to Akhenaten's reign while others claim it extends through the time of Akhenaten's successors and ends with the ascent of the pharaoh Horemheb (1320-1292 BCE). This latter claim is the one most commonly favored by mainstream scholarship, and the era is, therefore, most often designated as between c. 1348-1320 BCE.

Akhenaten's religious reforms are considered the first true expression of monotheism in world history and have been praised and criticized in the modern era by scholars arguing for and against the so-called 'heretic king'. The Amarna Period is, in fact, the era of ancient Egypt's history that has received the most attention because Akhenaten's reign is seen as such a dramatic departure from the standard of the traditional Egyptian monarchy.


Following Akhenaten's reforms, the temples of all the gods except those for Aten were closed, religious observances either banned or severely repressed, and the capital of the country was moved from Thebes to the king's new city of Akhetaten (modern-day Amarna). Akhetaten was essentially a city built for the god, not the people, and this reflects the central focus of Akhenaten's reign.

After embracing his new religious belief and suppressing that of others, Akhenaten more or less retreated to his god's city where he assumed the role of god incarnate and dedicated himself to the worship and adulation of his heavenly father, Aten. The lives of his people, trade contracts and alliances with foreign powers, as well as maintenance of the country's infrastructure and military, all seem to have become secondary concerns to his religious devotions.


The religious reforms he instituted would not last beyond his death. His son and successor Tutankhamun (c. 1336-1327 BCE) reversed his policies and brought back traditional religious practices. Tutankhamun's efforts were cut short by his early death but were continued, with far greater zeal, by one of his successors, Horemheb who destroyed the city of Akhetaten and erased Akhenaten's name from history.

Akhenaten & the Gods of Egypt

Akhenaten was the son of the great Amenhotep III (1386-1353 BCE) whose reign was marked by some of the most impressive temples and monuments of the New Kingdom of Egypt (c. 1570 - c. 1069 BCE) such as his palace, his mortuary complex, the Colossi of Memnon who guarded it, and so many others that later archaeologists believed he must have ruled for an exceptionally long time to have commissioned them all. These grand building projects are evidence of a stable and prosperous reign which allowed Amenhotep III to leave his son a wealthy and powerful kingdom.

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At this time, Akhenaten was known as Amenhotep IV, a name taken by Egyptian monarchs to honor the god Amun and which means 'Amun is Content' (or 'Amun is Pleased'). Amenhotep IV continued his father's policies, was diligent in diplomacy regarding foreign affairs, and encouraged trade. In his fifth year, however, he suddenly reversed all of this behavior, changed his name to Akhenaten ('Effective for Aten'), abolished the traditional belief structure of Egypt, and moved the capital of the country from Thebes (center of the Cult of Amun) to a new city built on virgin ground in middle Egypt which he named Akhetaten ('Horizon of Aten', but also given as 'Place Where Aten Becomes Effective'). Precisely what motivated this sudden change in the king is unknown, and scholars have been writing about and debating this question for the past century.

Akhenaten himself does not give any reason for his religious transformation in any of his inscriptions – even though many remain extant – and seems to have believed that the reason for his sudden devotion to a single god was self-evident: this was the one true god human beings should acknowledge, and all the others were either false or far less potent. However clear he may have felt his reasons to be, however, they were not understood that same way by his court or the people.


The ancient Egyptians – like any polytheistic society – worshipped many gods for a simple reason: common sense, or at least that is how they would have viewed their position. It was easy enough to see that in one's daily life a single person could not meet an individual's every need – one interacted with teachers, doctors, one's spouse, one's boss, co-workers, father, mother, siblings – and each of these people had their own unique abilities and contributions to one's life.

To claim that one person could fulfill an individual's every need – that all one required in life was just this one other person – would have seemed as absurd to an ancient Egyptian as it should to anyone living in the present day. The gods were viewed in this exact same way in that one would not think of asking Hathor for help in writing a letter – that was the area of Thoth's expertise – and one would not pray to the literary goddess Seshat for aid in conceiving a child – one would consult Bes or Hathor or Bastet or others who were divine experts in that area.

The gods were an integral part of the people's lives, and the temple was the center of the city. The temples of ancient Egypt were not houses of worship for the people but the earthly homes of the gods. The priests did not exist to serve a congregation but to care for the statue of the god in its home. These temples were often enormous complexes with their own staff who cooked, cleaned, brewed beer, stored grain and other surplus food, copied manuscripts, taught students, served as doctors, dentists, and nurses, and interpreted dreams, signs, and omens for the people.


The importance of the temples was felt far outside the complexes in that they generated and supported entire industries. The harvest and processing of papyrus depended largely on the temples as did amulet makers, jewelers, those who made shabti dolls, weavers, and a host of others. When Akhenaten decided to close the temples and abolish the traditional religious beliefs, all of these businesses suffered for it.

In the present day, when monotheistic understanding is commonplace, Akhenaten is often regarded as a visionary who saw beyond the confines of his religion and recognized the true nature of God but this far from how he was perceived in his time. Further, it is quite likely that his reforms had less to do with a divine vision and were more an attempt to wrest power from the Cult of Amun and reclaim the wealth and power they had accumulated at the expense of the crown.


The King & the Cult of Amun

The Cult of Amun first gained power in the Old Kingdom of Egypt (c. 2613-2181 BCE) when the kings of the 4th Dynasty rewarded the priests with tax-exempt status in return for their diligence in performing mortuary rituals and maintaining the proper rites at the royal pyramid complex at Giza and elsewhere. Even a cursory study of ancient Egyptian history from this period forward makes clear that this particular cult was a perennial problem for the nobility in that they only grew more wealthy and powerful year after year.

Since they paid no taxes in the form of grain grown on their lands, they were able to sell it as they wished. The kings of the 4th Dynasty had also granted them enormous and fertile tracts of land in perpetuity, and this combination enabled them to accrue incredible wealth, and that wealth translated to power. In every one of the so-called 'intermediate periods' in Egyptian history – those eras in which the central government was weak or divided – the priests of Amun remained as powerful as ever, and in the Third Intermediate Period of Egypt (c. 1069-525 BCE), the Amun priests of Thebes ruled Upper Egypt with a greater display of power than the kings of Tanis (in Lower Egypt) could muster.

There was no way a successive king could reverse the policies of the Old Kingdom without undercutting the authority of the monarchy. A king in the Middle Kingdom of Egypt, for example, could not claim that Khufu of the Old Kingdom had made a mistake regarding the Amun cult without admitting that kings, including himself, were fallible. The king was the mediator between the gods and the people who maintained the most important aspects of the culture, and so the king could not be seen as anything less than perfectly divine. The only way a king would be able to reclaim the wealth given away to the priests was to abolish the priesthood, to make them seem less than worthy of their position and power, and this is the course Akhenaten pursued.

Even in Amenhotep III's prosperous reign there is evidence of conflict between the priests of Amun and the crown and the minor solar deity known as Aten was already venerated by Amenhotep III along with Amun and other gods. It may have been Amenhotep III's wife (and Akhenaten's mother), Tiye (1398-1338 BCE) who suggested the strategy of religious reform to her son.

Tiye exerted significant influence over both her husband and son and, through them, the court and bureaucracy of Egypt. Her support of Akhenaten's reforms is well documented, and as a savvy politician, she would have recognized them as the only means to elevate the power of the pharaoh at the expense of the priests. Some scholars have also suggested Akhenaten's famous queen Nefertiti (c. 1370 - c. 1336 BCE) as the inspiration for the reforms as she also clearly supported and participated in the new faith.

A number of scholars over the years have claimed that Akhenaten's religious reforms were not monotheistic but simply a suppression of the activity of other cults to elevate that of Aten. This claim makes little sense, however, if one is aware of that same kind of initiative in Egypt's past. Amun was elevated to the height of king of the gods, and his temple at Karnak was (and still is) the largest religious building ever constructed in history. Even so, the cults of all the other gods were allowed to flourish just as they always had.

One cannot claim that the religious initiatives of Akhenaten were along the same lines as the earlier one of the priests of Amun they were not. Akhenaten's Great Hymn to the Aten - as well as his religious policies - made clear that there was only one god worth worshipping. The Great Hymn to the Aten, written by the king, describes a god so great and so powerful that he could not be represented in images and could not be experienced in any of the temples or cities across the nation this god needed his own new city with his own new temple, and Akhenaten would build it for him.


The city of Akhetaten was the fullest expression of Akhenaten's new vision. It was constructed c. 1346 BCE on virgin land in the middle of Egypt on the east bank of the Nile River, built midway between the traditional capitals of Memphis to the north and Thebes to the south. Boundary steles were erected at intervals around its perimeter which told the story of its founding. On one of these, Akhenaten tells the story of how he chose the location:

Behold, it is Pharaoh, who found it – not being the property of a god, not being the property of a goddess, not being the property of a male ruler, not being the property of a female ruler, and not being the property of any people. (Snape, 155)

The new city could not belong to anyone prior to Aten. In the same way that the god was to be understood in a new light, so his place of worship had to be entirely novel. Amun, Osiris, Isis, Sobek, Bastet, Hathor, and the many other gods had been worshipped for centuries at different cities sacred to them but Akhenaten's god needed a site where no god had been venerated before.

The four main districts were the North City, Central City, Southern Suburbs, and Outskirts. The North City was laid out around the Northern Palace which was dedicated to Aten. Throughout Egypt's history the king and his family lived in the palace, and Akhenaten himself would have grown up in the enormous and luxurious palace of his father at Malkata. At Akhetaten, however, the royal family lived in apartments to the rear of the palace, and the most opulent rooms, painted with outdoor scenes depicting the fertility of the Delta region, were dedicated to Aten who was thought to inhabit them. In order to welcome Aten to the palace, the roof was open to the sky.

The Central City was designed around the Great Temple of Aten and the Small Temple of Aten. This was the bureaucratic center of the city where the administrators worked and lived. The Southern Suburbs were the residential district for the wealthy elite and featured large estates and monuments. The Outskirts were where the peasant farmers lived who worked the fields and built and maintained the nearby tombs in the necropolis.

Akhetaten was a carefully planned engineering wonder with enormous pylons at its entrance, an awe-inspiring palace and temples, and wide avenues down which Akhenaten and Nefertiti could ride in their chariot in the mornings. It does not seem to have been designed with the comfort or interests of anyone but themselves in mind, however. Since the land had never been developed before, any of the other people who lived and worked there would have had to have been uprooted from other cities and communities and transplanted at Akhetaten.

The Amarna Letters

The area of the Central City has been of greatest interest to archaeologists since the discovery of the so-called Amarna Letters in 1887 CE. A local woman who was digging in the mud for fertilizer uncovered these clay cuneiform tablets and alerted the local authorities. Dating from the reigns of Amenhotep III and Akhenaten, these tablets were found to be records of Mesopotamian rulers as well as correspondence between the kings of Egypt and those of the Near East.

The Amarna Letters have provided scholars with invaluable information on life in Egypt at this time as well as the relationship between Egypt and other nations. These tablets also make clear how little Akhenaten himself cared for the responsibilities of rule once he was ensconced in his new city. The pharaohs of the New Kingdom expanded the borders of the country, formed alliances, and encouraged trade through regular correspondence with other nations. These monarchs were keenly aware of what was happening both beyond and within Egypt's borders. Akhenaten chose to simply ignore whatever happened beyond the borders of Egypt and, it seems, anything beyond the boundaries of Akhetaten.

Foreign rulers' letters and appeals for help went unheeded and unanswered. Egyptologist Barbara Watterson notes that Ribaddi (Rib-Hadda), king of Byblos, who was one of Egypt's most loyal allies, sent over fifty letters to Akhenaten asking for help in fighting off Abdiashirta (also known as Aziru) of Amor (Amurru) but these all went unanswered and Byblos was lost to Egypt (112). Tushratta, the king of Mitanni, who had also been a close ally of Egypt, complained that Amenhotep III had sent him statues of gold while Akhenaten only sent gold-plated statues. There is evidence that Queen Nefertiti stepped in to answer some of these letters while her husband was otherwise engaged with his personal religious rituals.

Amarna Art

The transformative nature of these rituals is reflected in the art of the period. Egyptologists and other scholars have often commented on the realistic nature of Amarna Art and some have even suggested that these depictions are so accurate that the king's physical infirmities can be detected. Amarna art is the most distinctive in all of Egypt's history and its difference in style is often interpreted as realism.

Unlike the images from other dynasties of Egyptian history, works from the Amarna Period depict the royal family with elongated necks and arms and spindly legs. Scholars have theorized that perhaps the king "suffered from a genetic disorder called Marfan's syndrome" (Hawass, 36) which would account for these depictions of him and his family as so lean and seemingly oddly-proportioned.

A much more likely reason for this style of art, however, is the king's religious beliefs. The Aten was seen as the one true god who presided over all and infused all living things through life-giving, transformative rays. Envisioned as a sun disk whose rays ended in hands touching and caressing those on earth, Aten not only gave life but dramatically changed the lives of believers. Perhaps, then, the elongation of the figures in these images was intended to show human transformation when touched by the power of the Aten.

The famous Stele of Akhenaten, depicting the royal family, shows the rays of the Aten touching them all and each of them, even Nefertiti, depicted with the same elongation as the king. To consider these images as realistic depictions of the royal family, afflicted with some disorder, seems to be a mistake in that there would be no reason for Nefertiti to share in the king's supposed syndrome. The claim that realism in ancient Egypt art is an innovation of the Amarna Period is also untenable. The artists of the Middle Kingdom (2040-1782 BCE) initiated realism in art centuries before Akhenaten.

Tutankhamun & Horemheb

These artworks were created to adorn the tomb of the king and his family in the city of Aten. Akhetaten was designed as the god's home in the same way that the gods' individual temples had once been built. Akhetaten was created to be grander than any of these temples and, in fact, more opulent than any other city in Egypt. Akhenaten seems to have attempted to introduce Aten to the great Temple of Amun at Karnak early in his reforms but these attempts were unwelcome and encouraged him to build elsewhere. Every aspect of the city was carefully planned by the king and the architecture was designed to reflect the glory and splendor of his god.

Akhetaten flourished throughout Akhenaten's reign but, after his death, was abandoned by Tutankhamun. There seems to be evidence that the city was still operational through the reign of Horemheb, notably a shrine to that pharaoh found on site, but the capital was moved to Memphis and then back to Thebes.

Tutankhamun in the present day is best known for the discovery of his tomb in 1922 CE but, after the death of his father, he would have been respected as the king who restored the ancient religious beliefs and practices of the land. The temples were reopened and the businesses which depended on them began to operate as they used to. Tutankhamun did not live long enough to see his reforms through, however, and his successor (the former vizier Ay) carried them on.

It was the pharaoh Horemheb, though, who finally restored Egyptian culture fully. Horemheb may have served under Amenhotep III and was commander-in-chief of the army under Akhenaten. When he came to the throne, he made it his life's mission to destroy all trace of the Amarna Period.

Horemheb razed Akhetaten and dumped the ruins of the monuments and stelae into pits as fill for his own monuments. So thorough was Horemheb's work that Akhenaten was wiped from Egyptian history. His name was never mentioned again in any kind of records, and where his reign needed to be cited, he was referred to only as "the heretic of Akhetaten".


Horemheb considered his former king worthy of what has come to be known as the Damnatio Memoriae (Latin for 'condemnation of memory') in which all memory of a person is erased from existence. Although this practice is most commonly associated with the Roman Empire, it was first practiced in Egypt centuries earlier through inscriptions known as Execration Texts. An execration text was a passage inscribed on ostraca (a shard of a clay pot) or sometimes on a figure (along the lines of a voodoo doll) and often on a tomb warning would-be robbers of the horrors which awaited them should they enter uninvited.

In the case of Akhenaten, the execration text took the physical form of completely eradicating his memory from history. He had inscribed his name and that of his god at the Temple of Amun at Karnak these were erased. He had erected other monuments and temples elsewhere these were torn down. He had replaced the name of Amun at the Temple of Hatshepsut with the name of Aten this was changed back. He had built a grand city on the banks of the Nile surrounded by inscriptions which told the story of its building, its builder, and his god this was razed to the ground. Finally, Horemheb backdated his reign in official inscriptions to that of Amenhotep III to completely blot out the memory of Akhenaten, Tutankhamun, and the vizier Ay.

Akhenaten's name was lost to history until the 19th century CE when the Rosetta Stone was deciphered by Jean-Francois Champollion in 1824 CE. Excavations in Egypt had unearthed the ruins of Akhenaten's monuments used as fill, and the site of Akhetaten had been mapped and drawn early in the 18th century CE. The discovery of the Amarna Letters, along with these other finds, told the story of the ancient 'heretic king' of Egypt in the modern age where monotheism has become accepted as a natural, and desirable, evolution in religious understanding.

In this age, Akhenaten has often been hailed as a religious visionary and hero who took the first steps, even before Moses, in trying to enlighten people to the true nature of God. Akhenaten is a staple example of a proto-Christian, according to some understandings, who – centuries before the Christian era – recognized the reality of a deity unlike his creations, one who dwells in "light inaccessible" (Isaiah 55:8-9 and I Timothy 6:16). This respect for the ancient king and his reign, however, should be recognized as a modern development based upon a modern-day understanding of the nature of divinity.

In his day, and for centuries after, Akhenaten and the Amarna Period were unknown to the people of Egypt and for a very good reason: his religious initiatives had thrown the country off balance and disrupted the core cultural value of harmony between the gods, the people, the land they lived in, and the paradise of the afterlife they hoped to enjoy eternally. A present-day understanding might see Akhenaten as a religious hero but to his people he was simply a poor ruler who allowed himself to forget the importance of balance and fell into error.

History [ edit | edit source ]

The site was once used as a storage site for dwarven metals mined from the Desertsmouth Mountains to the east. Ώ] As all cargo heading along the River Tesh needed to be unloaded before the Dagger Falls and reloaded on the other side it wasn't long before humans and other folk began coming to the site to trade with the dwarves. It was here that dwarven fortifications for the shipments sprang up and the beginnings of the village grew. Ε]

Dagger Falls had long been the seat of power for Daggerdale if only by virtue of it being the largest settlement. The Morn family ruled the dale from Dagger Falls for centuries until 1336 DR when the Zhentarim agents deposed them. Ζ] Ώ]

The town was then primarily controlled by series of Zhentilar-nominated constables, who held it until Randal Morn's triumphant retaking of Dagger Falls in 1369 DR. Ώ]

In 1372, it still existed as a frontier town under the authority of Randal Morn, Lord of Daggerdale. Ώ]

The coevolution of age at maturity and investment in survival

I now shift attention to the model of Kaplan et al. [1]. I review the assumptions and claims of the model, and then reanalyze it under various forms of population regulation. My goal is not to discredit Kaplan et al.’s hypothesis (which I think is promising), but to demonstrate that the results they derive fail under many forms of population regulation.

The model

The model in Kaplan et al. ([1], p. 165) treats the coevolution of two life history characteristics: age at maturity and investment in survival. Individuals experience two life stages: a juvenile, pre-reproductive stage, and an adult, reproductive stage, which begins at age t. In both stages, individuals invest some proportion λ of available energy to mortality reduction. Among juveniles, the remaining energy is devoted to the development of embodied capital (growth and learning). Among adults, the remaining energy is devoted to reproduction. Only t and λ evolve in this model.

The instantaneous death rate, μ, is constant across ages for any given strategy. Since λ measures investment in mortality reduction, μ is a decreasing function of λ: strategies with high λ live longer. To allow for external effects on mortality, the parameter θ is introduced to quantify the extrinsic mortality risk. μ is an increasing function of θ.

Kaplan et al. do not provide fertility functions, but they do provide a term that represents the energy invested in fertility. I simply let this equal fertility outright, so that an m function is recovered. Thus, fertility at age t is equal to the embodied capital produced up to that point, multiplied by 1−λ (as the rest of the energy continues to be invested in survival). Let the embodied capital at age t be denoted by P(t,λ,ε). P is an increasing function of t: more time in maturity allows for more embodied capital. It is a decreasing function of λ, as this energy is lost to survival investment. ε is an ecological parameter that measures the ease of the environment with respect to fertility: all other things being equal, greater ε implies higher fertility. Finally, Kaplan et al. assume that energy production grows at an exponential rate g after maturity due to skills and knowledge acquired from experience during the reproductive stage. I translate this energy production directly to fertility.

The claimed results

Kaplan et al. claim six general results with regard to evolution in t and λ. Let t ^ and λ ^ be the optimal values of age at maturity and investment in mortality reduction, respectively. Then Kaplan et al. claim (10) (11) (12)

Inequalities (10) say that, all other things being equal, niches more hospitable to reproduction favor later maturity and greater investment in mortality reduction. Inequalities (11) say that as extrinsic mortality increases, selection favors earlier maturity and lesser investment in mortality reduction. Inequalities (12) say that a greater growth rate of energy production (and therefore fertility) after maturity selects for later maturity and greater investment in mortality reduction.

Kaplan et al. emphasize not only the directional effects of the ecological parameters, but also the positive coevolutionary relationship between age at maturity and investment in survival. For each parameter change, they found that the age at maturity and the investment in survival always increased or decreased together (i.e., for each line, the derivatives have the same sign).


Forms of population regulation.

The main problem with the original analysis in Kaplan et al. is a failure to specify the form of population regulation, precluding identification of the proper maximand. Instead, they claim zero population growth without specifying precisely how this occurs, and then assume that selection maximizes a density-independent R. To reanalyze the model properly, one must first specify forms of population regulation I choose three simple cases here (although two produce identical outcomes, as seen just below). I generalize by allowing one case of nonzero population growth, as well as two forms of density dependence.

  1. Density-independent (exponential) growth
  2. Density-dependent fertility
  3. Density-dependent mortality

In case 1, all fertility and mortality rates are fixed quantities, independent of population density. Selection maximizes r here, whereas it maximizes N ^ for all other cases. This would be reasonable if, over the evolutionary timescale of interest, human populations were largely regulated by density-independent factors.

In case 2, fertility across all ages and strategies depends on population size via the same multiplier. This is precisely the condition under which R happens to be maximized, as discussed above (see equations (5) and (6)). As shown there, I assume that m(x,N) = e −DN m0(x), where m0 is the fertility under zero population density and D quantifies the extent to which fertility is adversely affected by population density. Survival rates are independent of density.

In case 3, the same form of density dependence applies to mortality for each age, rather than fertility. That is, l(x,N) = e −DNx l0(x). Fertility is independent of density. This form, too, was mentioned in the previous section (equations (8) and (9)), but selection does not maximize R here.

Note that in both density-dependent cases, the D parameters are assumed to be fixed. That is, all strategies are affected by density equally. I assume this only for simplicity, as different strategies could realistically vary in their susceptibility to crowding. Fortunately, this assumption also leads to a useful simplification: cases 1 and 3 favor the exact same strategy for l and m. This follows because r and D N ^ , which are respectively maximized in cases 1 and 3, take the same functional form in the Euler-Lotka equation, as is seen by comparing the integral of Equation (1) to those of (9). This simplification implies that we need only consider two cases: cases 1 and 3 together, and case 2. These simple differences in population regulation lead to very different optimal life history strategies.

Cases 1 and 3.

Under density-independent population growth (case 1), we have the following demographic equations: (13) (14) (15) Under density-dependent mortality (case 3), l(x) is multiplied by the term e −DNx as described above. For R to remain finite, we require that g < μ. I assume this throughout, as do Kaplan et al. [1].

Under density-independence, a strategy’s growth rate is found by plugging the functions (13), (14), and (15) into Equation (1). Doing this, integrating, and simplifying produces Solving for r produces (16) W is the product-log function: W[z] solves the equation z = W[z]e W[z] . Though W is a complicated function, it is useful to know that W[z] > 0 for z > 0 and dW/dz > 0, i.e. the product-log is an increasing function of its argument.

An invading strategy will only invade if the r of the invading strategy is greater than that of the resident strategy. If mutant strategies both t and λ tend to differ from their resident values by a small amount, then the direction of evolution is predicted by the derivatives of r with respect to both strategy variables. Furthermore, any internal equilibrium in t and λ must satisfy the condition that both derivatives equal 0. Thus we search for optima via the simultaneous solution of dr/dt = 0 and dr/dλ = 0. Simplifying these gives us (17) (18) where r is given by Equation (16). (We must also check that the solution actually maximizes, rather than minimizes, r.) Note that these differ from equations (2) and (3) in Kaplan et al. [1] (reproduced below in (21) and (22)).

The analogous equations for the case of density-dependent mortality are found by replacing r in the above equations with D N ^ , subject to the constraint that N ^ implies 0 population growth as in Equation (3). These two models favor the same strategy at equilibrium, so all further results apply to both.

Due to the complexity of these equations, I have been unable to derive any general results about parameter effects, leaving claims (10), (11), and (12) difficult to evaluate in general. To proceed I assume explicit functions for P and μ and seek numerical solutions. I assume the functions (19) (20) Equation (19) implies that fertility at maturity is a diminishing-returns function of age at maturity. The parameter α measures the initial rate at which embodied capital is acquired during the juvenile period. β is the diminishing-returns parameter: with higher β, the more quickly returns to learning and growth diminish. In Equation (20), γ determines the rate at which investments in survival (λ) decrease mortality risk. The remaining parameters were defined above and satisfy the assumptions of Kaplan et al. [1].

Equations (19) and (20) can be substituted into Equations (17) and (18), which can then be solved numerically. While this procedure cannot prove general results, contradictions to most of Kaplan et al.’s claims readily arise (see Figs. 1 and 2). Under all parameter values numerically investigated (see supporting text), I find that, contrary to inequalities (10), t ^ and λ ^ both decrease as ε increases niches more hospitable to reproduction prompt earlier maturity and lesser investment in survival. Contrary to inequalities (11), t ^ and λ ^ both increase with θ niches with greater extrinsic mortality risk favor later maturity and greater investment in survival. Finally, while λ ^ does increase with g as Kaplan et al. predicted, t ^ decreases niches in which production continues to grow in adulthood favor earlier maturity. This latter finding also shows that λ and t may not evolve in the same direction.

Watch the video: Dosnuskaimas (July 2022).


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