Cultural Evolution and Demography - Investigating the Emergence of Modern Human Culture

Complex MRes Summer Project Cultural Evolution and Demography - Investigating the Emergence of Modern Human Culture

Tom Sumner

Supervisors - Prof. Stephen Shennan and Dr. Mark Thomas Approx Word Count - 9000 Contents

1 Introduction 3

2 Archaeological Evidence of Cultural Change 4 2.1 The Upper Paleolithic Transition ...... 4 2.2 The African Stone Age ...... 5 2.3 Sahul ...... 5 2.4 Explaining the Archaeological Data ...... 5 2.5 Past Population Dynamics ...... 7

3 The Process of Cultural Evolution 8 3.1 The Transmission of Culture ...... 8 3.2 The Generation of Cultural Variation ...... 9 3.3 The Forces of Cultural Evolution ...... 10 3.4 Cultural Evolution in Pleistocene Societies ...... 12

4 Modelling Cultural Evolution 13 4.1 An Analytical Model of a Continuous Trait ...... 14 4.1.1 Specifying the Model ...... 14 4.1.2 Analysing the Model ...... 15 4.1.3 Problems with the Analytical Model ...... 19 4.2 Cultural Transmission in a Fragmented Population ...... 19 4.2.1 Vertical Transmission ...... 20 4.2.2 Oblique Transmission ...... 20 4.2.3 Migration ...... 21 4.2.4 Updating the Adult Population ...... 22 4.3 Parameter values ...... 22 4.3.1 Group Size, Ng,o ...... 22 4.3.2 Migration Rate, mg ...... 23 4.3.3 Number of Groups, G ...... 23 4.3.4 Oblique Transmission Parameter, Pob ...... 24 4.4 Initialisation and Data Collection ...... 24

5 Results 24 5.1 Simulation of a Single Group ...... 24 5.2 Simulation of Multiple Groups ...... 25

1 6 Discussion 30 6.1 Further Work ...... 31

7 Conclusion 32

8 Acknowledgements 34

A Technical Details for the Analytical Model 38 A.1 The Price Equation ...... 38 A.2 Application to the Model ...... 39

B Generating Random Deviates from a Gumbel Distribution 41

C Simulation Code 42

2 1 Introduction

“Modern humans are characterised by an unusual set of qualities: a capacity for abstract thought and communication, a remarkable degree of behavioural ﬂexibility and signiﬁcant innovative capabilities notably in the realm of technology. The interesting evolutionary questions are when, where, how and why these characteristics developed.” [23]

The archaeological record is our primary source of information about the behaviour of our earliest ancestors. Attempts to understand the evolution of modern humans usually focus on trying to explain the patterns observed in these material remains. One of the most intriguing questions raised by the archaeological evidence concerns the nature and causes of the rapid expansions in human culture in the last 50,000 years. It has been proposed that human culture is an inheritance system anal- ogous in some ways to genetic evolution [3],[5]. This view is strongly sup- ported by the evidence that social learning plays an important role in the determination of much of our behaviour [34]. It is therefore reasonable to assume that the patterns of emerging cultural complexity observed in the archaeological record may be explained, at least in part, by the theories of cultural transmission and evolution [31]. The processes of cultural evolution are strongly affected by the size and structure of the human populations in which they are operating. We now have strong evidence that rather than being static and unchanging, past populations experienced a number of expansions and crashes. It is also apparent that these population fluctuations were in part a result of climatic change. If we wish to explain the patterns of cultural change via the mechanisms of cultural evolution theory we must consider the influence of demography on those mechanisms. Various quantitative models of the relationship between population size and cultural evolution have been proposed [16],[32] but have only been ex- plored in the simplest terms. The aim of this project is to develop a simple model to investigate the effects of demography on the process of cultural evolution in the context of the Late Pleistocene (from approximately 120 ka BP (kilo annum before present)). In particular, we are interested in the effects of population size, population fragmentation and migration rate on the appearance of modern human behaviour. I will begin by describing the archaeological background to the project including evidence for demographic changes throughout the Pleistocene. In section 3 I outline the main processes of cultural evolution before discussing

3 which of these are likely to have been important in early human societies. I will then discuss a model of cultural transmission ﬁrst introduced by Henrich and Boyd [17] which forms the basis of my own simulation of cultural evolution in a fragmented population. The report will conclude by discussing the key results of this simulation and possible further work.

2 Archaeological Evidence of Cultural Change

While there is some debate about the exact dating it is typically agreed that anatomically modern humans (Homo sapiens) evolved between 200,000 and 150,000 years ago in Africa and the Levant (a region encompassing the modern countries of Cyprus, Israel, Jordan, Palestine, Lebanon and Syria) [21]. After undergoing a series of population bottlenecks it is believed that the initial population split leading to an expansion out of Africa around 80,000 years ago [35]. During this period, evidence of cultural complexity as indicated by material remains is sparse. When markers of modernity do occur they appear at different times in different places and are often inconsistently maintained until approximately 50,000 years ago. At this point there is a rapid increase in cultural complexity marked by improved blade technology, the increased use of bone in tool manufacture, greater exploitation of resources and a sudden appearance of personal ornaments and other art forms [22]. These markers are typically used to characterise modern human behaviour. In the following sections I briefly describe the patterns of cultural expansion in various geographical locations before highlighting the problems these patterns cause for the most common explanation of the emergence of modern human behaviour, that it is a result of the advent of modern biological and cognitive capacities.

2.1 The Upper Paleolithic Transition In Europe the term Paleolithic is used to describe the period from 2.5 mil- lion years ago until 10 ka BP. It is conventionally divided into three sub periods: the Lower, Middle and Upper Paleolithics. The Lower Paleolithic (LP) extends until approximately 120 ka BP and is asscoiated with early hominid species such as Homo habilis. The transition from the Middle Pa- leolithic (MP) to the Upper Paleolithic (UP) occurred around 40,000 years ago and marked a dramatic change in human culture [1],[22]. This transition is characterised by a rapid increase in technological complexity and the appearance of symbolic culture such as art and personal decoration.

4 2.2 The African Stone Age In Africa the same time period is divided into the Early, Middle and Late Stone Age. The transition from the Middle Stone Age (MSA) to the Late Stone Age (LSA) is often seen as another example of a rapid switch to more sophisticated behaviour. There is also growing evidence that many of the characteristics commonly associated with the LSA can also be found in MSA contexts although it appears these are inconsistently maintained. Examples include bone tools, use of aquatic resources and the processing and use of pigments [21]. The African archaeological record seems therefore to reﬂect a gradual accumulation of skills and behaviours which culminated in a rapid expansion at the start of the LSA.

2.3 Sahul Australia and New Guinea, often referred to as Sahul, is thought to have been colonised by humans by 45,000 years ago. Sahul is separated from South East Asia by the Wallacean archipelago (see figure 1) and despite reduced sea levels the islands of Wallacea would have presented a significant barrier to the dispersal of terrestrial vertebrates. This implies that the humans who colonised Sahul must have had the technology to undertake significant sea crossings, suggesting they possessed modern cognitive capacities. However the archaeological record contains limited examples of the markers of modern behaviour described above [4],[23]. Examples of complex lithic techniques (the production of stone tools and technologies) and evidence of symbolic art forms do not become common until the last glacial maximum (LGM) at 20 ka BP.

2.4 Explaining the Archaeological Data A commonly held view of the appearance of modern human culture is that it is a simple consequence of the development of modern human biological and cognitive capacities. However this explanation is not compatible with the delay between the appearance of anatomically modern humans and modern behaviour as recorded in the archaeological record or with the lack of cultural complexity reported from the early occupation of Sahul. A modiﬁed form of the ”cognitive” view is that some subsequent neurological mutation occurred later in human evolution [20]. To account for the delay this mutation must have occurred between 50-60 ka BP. However by this stage it is believed that modern humans had already split into separate

5 JOC-FJA Cambridge 06 d.3a: 28

Figure 1: Map of Sahul, (Reproduced from [23])

6 populations (see above). Therefore the proposed neurological change must have occurred independently in multiple human lineages. In search of an alternative explanation several authors have turned to demographic considerations. In particular, Shennan [31] has argued that past population dynamics are key to understanding culture change. He argues that if we view culture as an inheritance system (see section 3), the impact of population dynamics on the processes of cultural transmission may help explain the emergence of modern human behaviour.

2.5 Past Population Dynamics Archaeological explanations have often been based on the assumption that past populations were largely static and unchanging entities [31]. However, there is now evidence that this is not the case and that Pleistocene populations probably fluctuated much more than previously thought. Evidence for population change comes from two main sources, genetics and climatic data. Analysis of mitochondrial DNA sequences has led to the suggestion that Pleistocene populations passed through a series of bottlenecks between 100,000 and 70,000 years ago resulting in repeated reduction in population size. After this period, Rogers [30] suggests there was a major expansion of the human population in the late Pleistocene. The most likely cause for the variation in early human populations is climate. The last major bottleneck at 70 ka BP coincides with the paleocli- matic period of oxygen isotope stage (OIS) 4. In Europe the severe glacial conditions of this period would have lead to major population fragmentation and local extinctions over a period of some 10,000 years. The warmer conditions of OIS 3 were far more favourable for population growth [1]. In Sahul most of the last glacial cycle was marked by significant short term temper- ature changes of 5 − 10oC and by high aridity and low CO2 levels. These conditions would have had major impacts on the availability of resources and consequently on human population growth. Following the LGM the climate is believed to have been much less variable. Warmer, moister conditions would have been much more amenable to steady population growth. The archaeological record can also provide indications of population change at a local level. Patterns of site occupation often show that the area was occupied for short periods of time followed by much longer inter- vals of abandonment. It is plausible that such cycles are evidence of local population extinction. In summary the pattern is probably one of large fluctuations followed by a smoother period of population increase. In Europe and Africa this growth

7 appears to commence at around 60,000 years ago and continue through the MSA/LSA and MP/UP transitions. In Sahul population growth begins to occur after the end of the LGM and continue throughout the early Holocene (the period from 10,000 years ago until the present day). Thus the growth of human populations appears to approximately coincide with the appearance of modern culture across the world.

3 The Process of Cultural Evolution

In the context of the archaeological record when we refer to culture, we predominantly mean evidence of craft skills such as tool manufacture. However we can also see signs of more symbolic culture such as cave art and the use of ornaments for personal decoration. The form of these artefacts is a result of a set of rules or instructions followed by the individuals who created them. It is the way in which these rules are spread and modified which governs how human culture changes. It has been recognized for some time that culture is an inheritance system [3],[5] which satisfies the three main requirements for evolution. Firstly, skills and behaviours (which we will also refer to as traits) are transmitted between individuals; humans are a very social species and the majority of our behaviour is socially learned, either via formal teaching or through day to day interactions with other members of society. Secondly, cultural variation can be generated either through deliberate modification or through random processes such as copying error. Finally there is differential success between cultural variants; those individuals who possess certain forms of a trait are more likely to occupy roles where they can transmit them and certain cultural variants are more likely to be adopted by other members of society.

3.1 The Transmission of Culture Cultural traits can be transmitted between models (the person who already possesses the trait) and imitators (the individual inheriting the behaviour) via a number of structures or pathways. Cavalli-Sforza and Feldman [5] adopt the terminology used in epidemiology to describe two distinct mechanisms of transmission; vertical transmission from parents to genetic oﬀspring and horizontal transmission between any two unrelated individuals. In the case of cultural inheritance, the term horizontal transmission is restricted to the transfer of traits between members of the same generation. These could be siblings or age group peers. A third term, oblique transmission is

8 Process of Generation Location of Varia- Copying Errors Cognitive Processes tion Transmission of in- Error in learning Recombination of instructions structions Execution of instruc- Error in implementa- Innovation tions tion Medium of execution Material heterogeneity Translation

Table 1: The sources of cultural variation (Reproduced from [9]) introduced to refer to inheritance of a trait from a non-parental member of a previous generation. Models for oblique transmission can occupy a number of roles including grandparents and other non-parental relatives. However members of the population other than the family may also act as models for oblique transmission. The importance of extra-familial oblique transmission is likely to increase as populations become larger and more structured. In these circumstances individuals are more likely to be influenced by people who hold certain roles in society such as teachers or religious figures. Individuals may inherit traits from a single person or combine information from multiple models to form their own set of instructions for a given behaviour or skill. Vertically inherited traits may be learnt from one parent or result from the combined influence of both mother and father. In the case of horizontal and oblique transmission, much larger numbers of “cultural parents” may be involved in the transmission process. In many cases inheritance may be “sex linked” in that males only pass on skills to other males and females transmit their skills to their cultural daughters. This is likely to be the case in societies where there is a sexual division of labour.

3.2 The Generation of Cultural Variation Cultural variation can be produced in a number of ways. It may be generated within the population or introduced from external sources. Eerkens and Lipo [9] discuss the generation of variation in material culture and provide a useful categorisation of its sources (see table 1). They deﬁne three diﬀerent “locations” at which variation can be introduced; during the transmission of a trait, during execution of the trait and in the medium used to execute the trait. In addition they distinguish between random errors and those which are the result of cognitive processes by the imitator. Variation is introduced during the transmission of information when the

9 imitator misinterprets or misremembers the information being transmitted. The process is an example of what Eerkens and Lipo term copying error. Imitators may also make a conscious decision to combine information from multiple sources. This is referred to as a cognitive process. Additionally, if skills are inherited by observing the models behaviour the imitator may simply not have sufficient information to accurately infer the instructions being followed. This increases the opportunity for variation to be introduced during the transmission process. Random errors may also be introduced due to imprecision in the way an individual executes a set of instructions. In many examples of material culture such errors will be a result of differences in manual dexterity. The “cognitive” equivalent is when an individual intentionally modifies the way they perform a task despite having acquired accurate information from their model. Such innovations will often be directed towards improving the adap- tiveness of a trait. However there is no reason why innovations need to be successful. The effects of the medium of execution may be particularly important in material culture. As an example, heterogeneity in the material used to produce stone blades may cause different end results even if the same instructions are followed. This source of error may be amplified if information on selecting materials is subject to errors during transmission. Individuals may also make conscious choices to execute a trait in an alternative medium. Cultural variation can also be introduced into a population from external sources. Migration of individuals into a population may result in the introduction of new cultural variants (or even completely new traits). However the introduction of new variants or traits does not require the permanent relocation of people. New skills or behaviours can also be introduced into a population through exchange and interaction.

3.3 The Forces of Cultural Evolution Transmission alone will not lead to cultural evolution. Given that cultural variation exists, for culture to evolve there must be some additional mechanisms via which particular variants are favoured over others. These mechanisms are often referred to as the“forces of cultural evolution” [3],[29] and include cultural selection, biased transmission and cultural drift. Cultural selection will occur if individuals who are characterised by certain cultural variants have a greater chance of becoming models for cultural transmission than those who possess alternative forms. In the case of vertical transmission, it seems reasonable to assume that some cultural traits

10 will have an effect on reproductive success. Individuals who possess forms of these traits which increase their reproductive fitness will be more likely to become parents and transmit their cultural variants to the next generation. However cultural selection can also act on horizontally and obliquely transmitted traits particularly in structured societies where individuals in specific roles play an important part in the enculturation process. If individuals with certain forms of those traits are more likely to occupy those roles then those variants are more likely to be transmitted through the population. The process of biased transmission also involves non-random selection of cultural models, but as a result of the choices made by imitators. The models available to an individual will display a range of variants for a given trait. Biased transmission occurs when individuals make a choice as to which of these variants to adopt rather than selecting their models at random. Boyd and Richerson [3] define three types of bias transmission, direct bias, indirect bias and frequency-dependent bias. Directly biased transmission occurs when individuals select their model for a given skill by assessing the alternatives in the population of possible models and adopting the behaviour which appears most successful. This process can be time consuming as it requires the naive individual to evaluate each variant in the population before making their decision about who to copy. However, it is likely to result in the most reliable choice of the best variant to adopt. Indirect bias results when a second trait is used as an indicator of the attractiveness of an individual as a model for the behaviour to be imitated. Selecting models in this way may shortcut the costly evaluation required in direct biased transmission. For example, it may be easier to evaluate who is the best hunter by their hunting returns, and adopt their method of spear construction, than to evaluate each form of spear independently. It may often be the case that the characteristics being copied have nothing to do with the models attractiveness in the indicator trait [15] and as a result indirect bias will be an unreliable way to select the best model. Frequency dependent or conformist bias refers to situations where a naive individual uses the frequency of a variant among his models to assess the best variant to adopt. This is not the same as assuming that the probability of adopting a variant is proportional to the frequency of that variant in the set of models. Frequency dependent bias requires that “naive individuals be disproportionately likely to acquire the more (or less) common variant” [3]. Selecting cultural variants based on frequency may have a number of benefits. Firstly it allows individuals to benefit from the experience of other members of the population rather than having to evaluate each alterna-

11 tive themselves. Generally this will only be a good approach if some other process has increased the frequency of the most successful variant. Con- formist transmission may also be important in situations where deviating from the norm may have costly consequences. For example failure to follow the accepted rules of co-operation may result in punishment by fellow group members. The final process which may effect the frequency of cultural variants is drift. In finite populations sampling error will cause the frequency of cultural variants to vary randomly and may result in particular variants being lost from the population. This will be particularly important if the forces of selection and biased transmission are weak.

3.4 Cultural Evolution in Pleistocene Societies The processes discussed can combine in multiple ways to produce very different dynamics of cultural change. To investigate the evolution of early modern human culture we need to identify which of these processes are likely to have been important in Pleistocene societies. Unfortunately we have very little archaeological evidence to help an- swer this question. Some studies of Neolithic sites have found that specific forms of artefacts are restricted to certain houses implying that the skills and knowledge for producing those items were vertically transmitted [31]. However this is merely one plausible explanation and is insufficient evidence on which to base our assumptions. An alternative approach is to base our estimates on an ethnographic argument by studying those modern societies whose way of life is most similar to that of Pleistocene humans [10],[28]. It is generally agreed that con- temporary hunter gatherers are the closest examples we have to our early ancestors. There are obvious arguments against making such simple assumptions, not least that “most living hunter gather societies have been seriously disrupted, either directly or indirectly, by contact with modern colonial culture” [8]. However, in the absence of an alternative framework we will follow this approach. Many studies have highlighted the dominant role of vertical and oblique transmission and the relatively insignificant influence of horizontal inheritance on most craft techniques. Shennan and Steele [34] reviewed a range of ethnographic data and concluded that transmission was predominantly vertical and oblique. Guglielmino et al [12] in their study of cultural variation in Africa also concluded that the patterns observed were most consistent with a combination of vertical and oblique transmission. In many cases trans-

12 mission only occurs between members of the same gender, a consequence of the sexual division of labour in many hunter gather societies [34]. Henrich and Gil-White [18] in their analysis of the evolution of prestige present empirical evidence to suggest that children and adults pay particular attention to skilled individuals and preferentially imitate them when learning new skills. It seems likely that together with vertical transmission this would have been the main mechanism operating in Pleistocene society. Frequency biased transmission may well be involved in the transmission of symbolic or ritual traits where conformity may be important in maintaining group structure however for craft skills it seems likely that it would play a lesser role. Drift would probably have inﬂuenced the cultural dynamics of Pleis- tocene populations. Ethnographic comparisons suggest that early Homo sapiens would have lived and interacted in small populations of approximately 150 people (see section 4.3.1). In these circumstances, sampling effects would have played a part in increasing the frequency of certain variants over others.

4 Modelling Cultural Evolution

The first major attempt to develop a quantitative framework for describing cultural evolution was undertaken by Cavalli-Sforza and Feldman in their book Cultural Transmission and Evolution: A Quantitative Approach [5] and was continued by Boyd and Richerson in Culture and the Evolutionary Process [3]. Both sets of authors were primarily concerned with understanding how the structural features of cultural inheritance discussed in section 3 produce the patterns of behaviour observed in humans and in particular how the relative frequencies of the various forms of a cultural trait change over time. Subsequently, various authors have used this framework to develop models of the cultural transmission process in a variety of scenarios. In the rest of this section I discuss a specific model of cultural evolution [17] which is a plausible description of the transmission of craft skills in Pleistocene societies. This model of skill transmission was used as the basis for an in- vestigation into the effects of demography on the maintenance of complex skills.

13 4.1 An Analytical Model of a Continuous Trait In their paper On Modelling Cognition and Culture Henrich and Boyd [17] introduced an analytical model of the transmission of a continuous trait within a population of size N. The use of a continuous description of a trait is appropriate for describing a wide variety of craft based skills where individuals techniques or methods are not limited to one of a set of discrete variants. The model assumes that transmission is oblique and directly biased and that the inheritance process is noisy. Through a combination of copying errors and innovations imitators never achieve trait values equal to their model. Instead the imitator values are drawn from some probability distribution. The authors used this model to show that the more complicated the skill the larger the population that is required to maintain and improve that skill.

4.1.1 Specifying the Model Consider a population of N individuals, labelled i = 1, 2, .....N, each of whom has a certain level of ability in some skill, for example arrow construction, defined by a real number zi. These individuals represent the adult generation. The larger the value of zi the more proficient or successful the individual is at the skill. Associated with each individual is a w-value (wi) which defines the probability that the individual will be selected as a cultural model. Each individual in the subsequent generation (also of size N) attempts to copy the most skilled individual h in the previous generation. Therefore wi = 1 for i = h and zero for all other i. It is assumed that each individual is able to correctly identify the best model but that they do not simply replicate the models behaviour. During transmission variation will be introduced from several sources (see section 3.2). If skills are copied by observing behavioural displays, the imitator must try and infer the instructions or rules used by the model to produce that behaviour. However behavioural displays are often incom- plete meaning not all the information required to replicate the trait is made available by the model. It is also assumed that human inference is rarely perfect and as a result imitators will not be able to accurately reproduce their model’s behaviour. The authors also assume that most copying errors will result in behaviours which are less effective than the model but that on occasion, through a combination of luck and successful experimentation naive indi-

14 viduals will exceed the models skill value. Given that individuals are at- tempting to copy the most skilled member of the group, this bias towards lower skill values seems reasonable. To model this Henrich and Boyd [17] use a Gumbel probability distribution to select the imitators zi values. The probability density function for a Gumbel distribution is given by equation 1 and is shown in ﬁgure 2:

exp(−g)g p(x) = (1) β

x−µ where g = exp(− β ). µ is the location parameter or mode of the distribution and β > 0 is the scale parameter which determines the spread of the distribution. The mean of the Gumbel distribution is given by:

x = µ + β (2) where = 0.57721 is the Euler-Mascheroni constant

In the skill transmission model the mode of the distribution is given by equation 3.

µ = (zh) − α (3) Typically imitators will achieve a skill value which is worse than the model by an amount α (see ﬁgure 2). The value of α is a measure of how complicated the skill is and consequently how diﬃcult it is to learn. The spread parameter β describes the extent to which naive individuals vary in their outcomes.

4.1.2 Analysing the Model To analyse this model, the authors use the Price Equation [26]. This equation can be used to describe the change in some average character in any evolutionary system [11]. The Price Equation (equation 4) separates the change in the average value of that character into two components, the effect of selection and the eﬀects of transmission.

4z = Cov(w, z) + E(w4z) (4)

15 iue2 h itiuino mttrsilvle.Lanr h oythe copy who Learners values. skill imitator of distribution model, The 2: Figure kl au.(erdcdfo [17]) from (Reproduced value. skill by mode α lhuhteei rbblt htiiaoswl xedtemodels the exceed will imitators that probability a is there although z h h − banavledanfo ublpoaiiydsrbto with distribution probability Gumbel a from drawn value a obtain ,

α Probability Imitator Acquires Skill Value, z n spread and β yial hi au ilb os hntemodel the than worse be will value their Typically . " ! Imitator SkillValue,z 16 z h where 4z is the change in the average value of some character z and w is the fitness value associated with that character. The first term is the covariance between w and z and describes the effect of selection. The second term is the expectation of the fitness times the change in the character and models the effects of transmission (for a further explanation see appendix A). Using the Price Equation, it can be shown (see appendix A) that for the assumptions discussed above the change in the average skill value in the population is given by:

4z = −α + β( + ln(N)) (5)

If 4z > 0 then the average value of the skill in the population will increase in the subsequent generation. This is referred to by Henrich [16] as adaptive cultural evolution, the population becomes better at performing the given task. Such skills are likely to be maintained in the population and more importantly, be visible in the archaeological record. If the reverse is true, the population will become worse at the skill and the ability to perform the task will eventually be lost. This process is described as maladaptive loss. By setting 4z = 0 we can solve for the conditions under which transmission will generate adaptive evolution of a skill:

α N ∗ > exp( − ) (6) β For a given ratio of α and β there is a critical population above which the skill will evolve adaptively. This threshold is represented graphically in figure 3. The dependence of this threshold on α and β is also important. Larger values of α increase the population size needed to achieve adaptation. This implies that more complex skills, which are harder to imitate require a larger population to be maintained. In smaller populations these skills will be more likely to be lost than those simpler behaviours which are easier to imitate. Henrich [16] has used this result to try and explain the apparent loss of cultural complexity in Tasmania. Cut off from the Australian mainland some 10,000 years previously by rising sea levels the aborignal Tasmanians remained one of the most isolated populations in the world until contact with Europeans in the 18th Century. When European explorers first landed on Tasmania they found a society that had perhaps the simplest material

17 5000

4000

3000 *

N Cumulative Adaptive Evolution

2000

1000

Maladaptive Loss

0 4 5 6 7 8 9 !/"

Figure 3: Regimes of cumulative adaptation and maladaptive loss. (Repro- duced from [17])

18 culture of any modern humans [6]. Not only that, it appeared that the Tasmanian technology had become simpler during the period of isolation. It has been argued that this was simply a result of local requirements and that the Tasmanians had no need to maintain those skills which seem to have been lost [27]. An alternative argument proposed in light of the model predictions is that a change in population size (as a result of being segregated from the mainland) may have lead to a regime in which the more complex tools and behaviours could not be maintained [16].

4.1.3 Problems with the Analytical Model Read [27] has argued that this model and its application to the Tasmanian data is flawed in several ways. While many of his criticisms are related to the interpretation of the archaeological evidence he does raise one significant problem with the assumptions of the model. Henrich [16] assumes that each individual is copying the most skilled person in the population, but in the case of Tasmania this population was approximately 4000 people. Furthermore, they were spread over a wide geographic area separated by mountainous regions [19]. It seems unlikely that such a large, poorly connected population could have interacted on a sufficiently regular basis to allow the proposed process of social learning to occur. In the remainder of this report I will discuss the implementation of a simple simulation based on this model in which the population is divided into a number of smaller subgroups linked by migration. This is a more plausible description of the demographic conditions during the Pleistocene and also relaxes the assumption that it is possible to identify and copy the most skilled individual in a very large and widely distributed population. The aim of the simulation is to investigate the conditions under which skills will undergo adaptive evolution and hence be maintained.

4.2 Cultural Transmission in a Fragmented Population In the simulation the total population consists of G sub-populations labelled g = 1, 2, ...... G. Each group g has a population of individuals of size Ng,p who each possess a value z for some skill. These individuals transmit their skills to the oﬀspring population, of size Ng,o, of the sub-group of which they are members. The skill transmission process is based on the model described above but incorporates an element of vertical transmission which is likely to have been important in Pleistocene societies (see section 3.4).

19 The simulation proceeds via the following steps which are described in more detail below:

a. Vertical transmission of skills from parents to genetic oﬀspring

b. Oblique transmission of skills from most successful individual to a proportion of the oﬀspring

c. Migration of newly encultured individuals to other groups

d. Replacement of current parent generation by oﬀspring

4.2.1 Vertical Transmission All naive individuals initially learn their behaviour from their genetic parents. For each naive individual a parent, labelled p, is selected at random from the previous generation and the offspring inherits a skill value which is drawn from a Gumbel distribution with mode zp − α and spread β. This introduces copying error and innovation into the transmission process (see section 4.1.1). It is assumed that the skill value of any individual z > 0, z = 0 is equivalent to the individual not being able to perform the skill. To account for this, if a negative value is selected from the Gumbel distribution that individuals skill level is set to zero. It is also assumed that there is a sexual division of labour so that men and women possess different sets of skills. These skills are only transmitted to naive individuals of the same gender. Each sub-population therefore rep- resents either the male or female population of the group and transmission occurs from a single parent to a single offspring [32].

4.2.2 Oblique Transmission

After vertical transmission a fraction of the population, Pob, change their skill value by imitating the most successful individual in the previous generation as described in section 4.1.1. To simulate this, we identify the member of the population with the highest skill value and label this value zh. The imitator skill values are then assigned by generating random variates from a Gumbel distribution with parameters µ = zh − α and spread β using the inverse transformation sampling method (see Appendix B). As in the case of vertical transmission, skill values are prevented from being negative. It is also assumed that once a skill is lost from a sub-group it can only be reintroduced by the arrival of a migrant with a non-zero value for that skill. Therefore if all members of the sub-group have z = 0 (so that

20 zh = 0) all naive individuals also have z = 0. Similarly if a genetic parent’s skill level is zero their oﬀspring will have z = 0.

4.2.3 Migration

Following skill transmission a proportion mg of the oﬀspring population leave each site. This value is truncated to an integer to allow us to move a whole number of people. These migrants are then distributed between the other groups depending on the relative accessibility of those groups. Each group g is deﬁned by its Cartesian co-ordinates (xg, yg) and by its connectivity to the other groups. The x, y co-ordinates can be interpreted as the position of the centre of the region occupied by the group. For a group g = j the connectivity is given by:

X Sj = Cjgexp(−adjg) (7) g6=j where djg is the Euclidian distance between group j and group g and a = 0.01 [13]. This exponential dependence on distance has been shown to be suitable for describing the dispersion of migrants whose movement is governed by a random walk [14]. The term Cjg = 1 if group g is accessible from group j and zero otherwise. This would allow us to simulate the condition where certain groups can not be reached due to geographical barriers such as mountain ranges or oceans. In the current work we assume all sites are accessible so that Cjg = 1 for all g. Individuals leaving patch j are distributed between the possible destination patches g depending on the contribution of patch g to Sj:

exp(−adjg) ψjg = (8) Sj Destinations are selected at random until each migrant has been relo- cated. The probability of selecting a given destination is equal to its ψ value calculated from equation 8. It is assumed that all migrants survive and that none return to their group of origin therefore the total population size remains constant.

21 4.2.4 Updating the Adult Population Once the migrants have been distributed to their destinations, the current oﬀspring population in each group becomes the new adult population. This includes any immigrants to the group. The size of the adult population in group j is therefore given by:

X Nj,p = Nj,o − floor(mgNj,o) + migjg (9) g where migjg is the number of migrants joining group j from group g. This parent population then becomes the models for the subsequent oﬀspring generation of size Nj,o in group j. The oﬀspring population is assumed to be the same in each generation irrespective of the adult population following migration.

4.3 Parameter values

4.3.1 Group Size, Ng,o The values used for group size should represent the size of a Pleistocene social unit whose individuals interacted on a sufficiently regular basis for skill transmission to occur. Unfortunately we can draw very little information on Pleistocene group size from archaeological data. While it may be possible to estimate the occupancy of a given site based on its area and remains it is hard to infer anything about the size of a regularly interacting group from this data. Such a group may encompass those living at any number of proximate sites. To estimate group size parameters we will instead use an ethnographic argument. Studies of hunter gatherer societies suggest that many, including the !Kung San of Southern Africa and Australian aboriginals, have three distinct levels of social structure. The smallest group, commonly referred to as bands, usually consist of 25-50 individuals [2] and often correspond to overnight camps. The largest population unit, the tribe, typically refers to a group related by their dialectal similarity and geographical area. These groups typically consist of upwards of 500 individuals [2]. An intermediate group size of approximately 150 individuals also commonly occurs. These intermediate groups can often be defined in terms of ritual function and constitute “a subset of the population that interacts on a sufficiently regular basis to have strong bonds based on direct personal knowledge” [8].

22 This intermediate group size is remarkably similar to the average group size of human populations predicted by Dunbar [8]. From a study of non- human primates, Dunbar [7] derived a relationship between neocortex ratio (the volume of the neocortex divided by the volume of the rest of the brain) and group size in primates. The implication is that there is a cognitive limit to the number of individuals that any one person can interact with (and hence the total group size) and that this limit is a function of relative neocortex size. Extrapolating this relationship to humans, predicts that the average group size over which stable relationships can be maintained is 147.8 with a 95% confidence interval of 100.2-231.1 [8]. Assuming that our current brain size reflects that of our Pleistocene ancestors we can assume that 150 is a reasonable approximation for the average size of a regularly interacting Pleistocene social unit. The size of the offspring generation in each sub-group would be some fraction of this total group size. If we assume a sexual division of labour (as discussed above) and that at any one time 50% of the population is sub- adults then the effective population size for transmission is one quarter of the total group size. Plausible values for Ng,o therefore range from 5-105 in steps of 5. This is equivalent to total group sizes between 20 and 420. Particular attention will be paid to the region Ng,o = 25 − 50 which corresponds to groups of 100 - 200 individuals, the approximate range predicted by Dunbar.

4.3.2 Migration Rate, mg Values for plausible migration rates can again be estimated from ethnographic data. Studies of Australian aboriginal societies have reported migration rates in the range 0.07 to 0.21 based on intertribal marriage rates while data from the !Kung San indicates that migration rates may be as high as 0.3 [10]. Due to the wide diversity in these estimates and the fact that they may or may not be representative of Pleistocene migration rates I have used a range of values from 0.025 to 0.5 in steps of 0.025. However it seems reasonable to assume that migration rates above 0.1 would be highly unlikely in a landscape where the population is highly fragmented.

4.3.3 Number of Groups, G The number of groups is likely to have varied signiﬁcantly over the Pleis- tocene. The most probable result of a decline in climatic conditions would have been the extinction of local groups. Similarly, in improving conditions increases in population size would have lead to the division of expanding

23 groups into multiple smaller sub populations. The simulation was run for populations of between 1 and 1000 groups to investigate the eﬀects of G on the conditions for adaptation.

4.3.4 Oblique Transmission Parameter, Pob Evidence indicates that oblique transmission is important in the inheritance of craft skills however we do not know to what extent. To investigate the effect of the strength of oblique transmission on the skill evolution process and in particular the threshold for adaptive evolution of a skill each simulation was run with Pob = 0.25, 0.5, 0.75, 1.0.

4.4 Initialisation and Data Collection

The simulation is initialised by creating G groups each of size Ng,o. Here, each group was assumed to be the same size. An initial skill value is then assigned to each individual. Again these were assumed to be the same for all individuals across all groups. I also assumed that the migration rate from each group was the same. We therefore have G identical sub-populations. Each group is randomly assigned a set of (x, y) co-ordinates in a square space of side L. The simulation was then allowed to run for t generations. For all results presented here t = 100. We are primarily interested in the conditions which result in adaptive cultural evolution, when does the average value of a skill increase in a population. It is under these conditions that we are likely to see evidence of a skill in the archaeological record. To measure this, I calculate the average value of the skill after 100 generations across all individuals in all groups. If this value exceeds the initial skill level the “scenario” is said to be adaptive. Due to the stochastic nature of the simulation it is run for multiple iterations for the same parameter set and the number of adaptive runs is calculated. If more than 50% of the iterations are adaptive the parameter set is assumed to be adaptive. Initial tests indicate that 100 iterations is suﬃcient to produce consistent results.

5 Results

5.1 Simulation of a Single Group I began by running the simulation for a single group to see if the behaviour was the same as that of the analytical model. These initial simulations were

24 also used to identify the effect of the initial conditions and the amount of oblique transmission on the results. The simulation was run for multiple group sizes and the threshold population above which a skill is adaptive was plotted against the skill complexity. To simplify the number of parameters, I fixed β = 1 for all runs and used increasing values of α to indicate increasing skill complexity. Figure 4 shows the results for different values of the initial skill level Sinitial = 1, 10, 100 with Pob = 1.0. The data points are fitted to an exponential of the form N = exp(α − n) (where n is a parameter to be de- termined by the fit) using gnuplots implementation of the nonlinear least- squares Marquardt-Levenberg algorithm. This indicates that the results display the same qualitative behaviour as the analytical model. It can also be seen that increasing Sinitial reduces the threshold population required for a given skill to improve. Changing the initial skill value does not affect the qualitative behaviour of the model. Figure 5 shows the threshold group size for a given skill complexity for different amounts of oblique transmission. In each case Sinitial=10. This shows that the amount of oblique transmission is important in determining the threshold for adaptation. Reducing Pob increases the required group size for a given skill. The more complex the skill the greater the effect of oblique transmission on the threshold population. As with varying the initial skill level the qualitative behaviour is not altered by modifying the amount of oblique transmission.

5.2 Simulation of Multiple Groups

The simulation was then run for various combinations of group size, Ng,o, number of groups, G, and migration rate mg. The results of these simulations are presented below. In figure 6, G is fixed at 10. The surface shows the migration rate required to achieve adaptive evolution for skills of varying complexity for a range of group sizes (plotted in the x,y plane). Any combination of migration rate, group size and skill complexity above this surface will result in the skill being maintained. Sub figures a-d show the results for Pob = 0.25, 0.5, 0.75 and 1.0 respectively. The results show some general trends in the conditions for adaptation. Firstly, migration rate is important in determining whether or not a skill will survive. A skill which would be maladaptive in a single isolated group, mg = 0, can be maintained in the same size group if it is connected to other sub-populations by migration. The simpler the skill the lower the

25 S = 1.0 100 initial Sinitial = 10.0 Sinitial = 100.0

60 * N

0 0 1 2 3 4 5 6 !

Figure 4: Threshold for adpative evolution in a single group. The data points correspond to diﬀerent initial skill values as indicated in the legend. In each case, β = 1 and P = 1.0

migration rate required to generate adaptive cultural evolution within the total population. Similarly the larger the group size the lower the migration rate needs to be. An important point to note is that a drop in the migration rate can cause more complex skills to enter the maladaptive regime while allowing simpler traits to be maintained. The results also show that the amount of oblique transmission is important in determining the required migration rate for a given skill and group size. The lower Pob, the greater the threshold migration rate for a given skill and group size. Figure 7 demonstrates the eﬀect of varying the number of groups. The surface shows the number of groups required to achieve adaptive evolution for a given combination of group size and skill complexity (plotted in the x,y plane). As previously, the sub ﬁgures a-d show the results for Pob =

26 P = 0.25 100 P = 0.50 P = 0.75 P = 1.00

60 * N

0 0 1 2 3 4 5 !

Figure 5: Threshold for adpative evolution in a single group. The data points correspond to diﬀerent values of Pob as indicated in the legend. In each case, β = 1 and Sinitial = 10.0

0.25, 0.5, 0.75 and 1.0 respectively. mg is fixed at 0.1. An increase in the number of groups increases the complexity of skill which can be maintained in the population for a fixed group size. The required number of groups for a given skill is a function of group size, the larger the groups the smaller the number of groups required. The number of groups also depends on the skill complexity, more difficult to learn skills require more subgroups to make the skill adaptive. As before, increasing the amount of oblique transmission lowers the adaptive threshold. Figure 7 shows that for a given group size, the number of groups required to make a skill adaptive increases abruptly above a certain complexity such that those skills do not reach an adaptive regime within the range of G shown. For group sizes between 25 and 50, increasing the number of groups to 1000 (with mg = 0.1) does not produce adaptation for α > 5. Extending

27 Migration Rate (M) Migration Rate (M)

0.5 0.5 0.45 0.45 0.4 0.4 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.05 0.05 0 0 5 5 15 15 25 25 35 35 45 6 45 6 55 5 55 5 Group Size (N) 65 Group Size (N) 65 75 4 75 4 85 3 85 3 95 2 Skill Complexity 95 2 Skill Complexity 105 1 105 1

(a) Pob = 0.25 (b) Pob = 0.50

Migration Rate (M) Migration Rate (M)

Figure 6: The threshold migration rate for skills to become adaptive in a population of 10 sub groups of size N. The space above the surface describes the regime in which skills will be maintained.

28 Number of Groups (G) Number of Groups (G)

20 20 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 0 0 5 5 15 15 25 25 35 35 45 6 45 6 55 5 55 5 Group Size (N) 65 Group Size (N) 65 75 4 75 4 85 3 85 3 95 2 Skill Complexity 95 2 Skill Complexity 105 1 105 1

(a) Pob = 0.25 (b) Pob = 0.50

Number of Groups (G) Number of Groups (G)

Figure 7: The minimum number of groups of size N required for a skill to become adaptive. Migration rate mg = 0.1. The space above the surface describes the regime in which skills will be maintained.

29 the range of G values further would show whether an adaptive regime can be reached or if there is a limit on the complexity of skill which can be maintained for a given group size and migration rate.

6 Discussion

The results of the simulation show that the conditions for a given skill to be adaptive are a function of the migration rate, the size of each group, the number of such groups and the amount of oblique transmission. More complex skills require a larger better connected population or a greater dependence on oblique transmission to be maintained. Returning to the question posed at the very beginning of this report, we can ask if these results provide a possible explanation of the emergence of modern human culture. While the amount of oblique transmission is important we have little evidence for suitable values of Pob. In addition we do not know whether the dependence on oblique transmission is likely to have varied over time. It is possible that if populations became more structured, the amount of oblique transmission may have increased with less emphasis being placed on parental teaching. If this were the case the results indicate that more complex skills would have been sustainable within the same demographic conditions. Whether this is applicable during the Pleistocene is debatable but it is clearly important to consider the strength of oblique transmission in any further work. The effects of the demographic parameters provides more insight into the possible causes of the patterns of cultural complexity observed in the archaeological record. From the emergence of modern humans until the sudden appearance of the commonly accepted markers of modern human culture [22] some 100,000 thousand years later human populations were probably small and subject to regular fluctuations as the result of adverse climate change (see section 2.5). Such populations may well have consisted of small sub groups distributed over a wide area. In terms of the simulation, this would have meant low values of G, the number of groups, and low migration rates. Assuming group sizes of between 25 and 50 individuals and a maximum migration rate of 0.1 the results of the simulation indicate that only skills with α < 5 could be maintained. If a more complex skill was “invented” it would be in the maladaptive regime and probably be lost from use. Population fluctuations would have meant transient increases in the num-

30 ber of groups which may have pushed the population into an adaptive regime for more complex skills. The subsequent extinction of local groups could cause those complex skills to begin to decline in sophistication and possi- bly disappear completely. However given the sharp increase in the number of groups required to produce adaptation above a given skill level there would have to be a large shift in the number of groups for this effect to occur. Climate change may also have affected migration rates. As the number of groups in a given area decreased individual populations would have been more isolated. As isolation increases the number of people leaving a group is likely to decrease. Therefore fluctuations in migration rate may also have caused contributed to changes in the types of skills which could be maintained. Such fluctuations could provide a plausible explanation for the irregular appearance of cultural traits more commonly associated with the LSA or UP throughout the Middle Stone Age in Africa. Approximately 60,000 years ago, corresponding with the end of OIS 4 the subsequent improved climatic conditions would have allowed human populations to grow steadily. This would have resulted in an increase in the number of local groups and a greater level of interaction between them, an increase in both G, and mg in terms of the model. If complicated behaviours were introduced into the population either through innovation or from external sources they are more likely to have been maintained. The large increase in the number of groups required to push skills into the adapative regime may explain way there is little evidence of modern human behaviour for a significant period after the end of OIS 4. The population would have had to increase substantially before any effects are observed. Similar conclusions can be made about the data from Sahul. Poor climate would have kept the population size low up until the end of the LGM limiting the complexity of skills which could be maintained. Even if the founding populations brought certain modern skills with them the results of the simulation show that these may have decreased in sophistication and could quickly be abandoned. During the Holocene, population growth as a result of improved environmental conditions would have raised the complexity of skills which could be maintained.

6.1 Further Work The simulation has only been investigated in simple scenarios of homoge- nous group structure and static parameter values. While this provides some useful qualitative insights it would be worthwhile to carry out further simulations to try and establish more precisely the quantitative threshold values

31 for cumulative adaptation of certain skills to occur. Before doing this it would be necessary to identify appropriate values for the skill difficulty α which are representative of specific tasks and behaviours. It would also be interesting to investigate the effects of varying β, which measures the variation in peoples learning ability. In all the results discussed here β = 1. An alternative approach to modelling the complexity of a given skill would be to define α as a percentage of the current skill level so that as a population became better at a skill it was harder to improve on that ability. For example we could say that in producing a stone blade, imitators would on average achieve a product which was 10% worse than their model. This would seem to be a more realistic description of the learning process and may be easier to estimate from either archaeological or ethnographic observations. By dynamically varying the parameters the model could then be used to investigate whether changes in demography would have the impact discussed above. For example what would be the consequences for the evolution of a skill if, due to changes in climate, the number of groups was reduced. The existing model could be easily adapted to investigate such scenarios.

7 Conclusion

The patterns in the archaeological record raise a number of questions about how and why modern human culture evolved. Evidence of population fluctuations supports the view that demography may be an important factor in determining those patterns. Here I have assumed that culture is an inheritance system and investigated whether the effects of demographic changes on the processes of cultural evolution can provide an explanation for the patterns of cultural complexity uncovered by archaeologists. Based on an existing description of skill transmission a simulation of cultural evolution in a population of small sub groups linked by migration was produced . The results of the simulation indicate that the complexity of skill which can be maintained is a function of group size, group number and migration rate. This suggests that the demographics of early humans may have prevented the appearance of “modern” behaviour. Not until the population expansions of the late Pleistocene were demographic conditions suitable to support the development of more advanced skills and practices. While this is clearly a simplistic view of the numerous processes underly- ing the development of modern human culture these results do show that the combination of cultural inheritance and demographic fluctuations may be a

32 part of a more complete explanation of the emergence of modern behaviour amongst our early ancestors.

33 8 Acknowledgements

I would like to thank Professor Stephen Shennan and Dr. Mark Thomas for their helpful comments and suggestions throughout the course of the project.

34 References

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36 [25] N. Porch and J. Allen (1995) Tasmania: archaeological and palaeo- ecological perspectives

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37 A Technical Details for the Analytical Model

A.1 The Price Equation We begin by deriving the Price Equation as in [11].

Consider a population of elements labelled i. The frequency of elements with index i is qi and each element with index i has some character zi. In 0 the descendant population qi is the proportion of the population that inherit their character from parents of index i. If wi is the ﬁtness of index i (the 0 contribution of parents with index i to the next generation) then qi is given by:

0 qi = qiwi/f (10) where w is the mean ﬁtness of the parent population.

If there is some change in z during the transmission process (for example mutation) then the descendants of index i will have a range of character 0 values. If zi is the average character value of the descendants of i then the change in character value for descendants of index i is given by:

0 4zi = zi − zi (11)

We can deﬁne the change in the average character value between the two generations as:

X 0 0 X 4z = qizi − qizi (12) i i and by substituting equations 10 and 11 into equation 12 we can rewrite this as:

X X 4z = qi(wi/w)(zi + 4zi) − qizi (13) i i

38 which using standard deﬁnitions for the covariance (Cov) and expectation (E) results in the Price Equation:

4z = Cov(w, z) + E(w4z) (14)

A.2 Application to the Model From section 4.1 we have the following assumptions:

a. The parent population consists of N individuals

b. Each individual is indexed by a diﬀerent i

qi = 1/N for all i c. Every individual in the subsequent generation is “descended” from the individual, h, with the highest skill value

wi = 1 for i = h and zero otherwise w = 1/N

Using these assumptions, equation 13 becomes:

X 4z = zh + 4zh − qizi (15) i = zh + 4zh − z (16) where z is the mean value of z in the parent population.

If the skills in the adult population are distributed according to a Gum- bel distribution with mode m and spread β then:

z = m + β (17)

zh ≈ m + β( + ln(N)) (18)

Equation 18 is an approximation of the expected value of the maximum value drawn from a sample of size N (see [16]).

Each individual in the descendant generation also draws their skill value

39 from a Gumbel distribution with mode zh −α and spread β. Using equation 11 the change in character value for the descendants of h is then given by:

4zh = ((zh − α) + β) − zh (19) = −α + β (20)

Substituting these expressions into equation 16 gives equation 5 from section 4.1.2:

4z = −α + β( + ln(N)) (21)

40 B Generating Random Deviates from a Gumbel Distribution

The cumulative distribution function (CDF) for a Gumbel distribution with mode µ and spread β is given by:

F (x;µ;β) = exp(−exp(µ − x)/β) (22)

With a known form for the CDF, F we can use the inverse transform sampling method to generate random deviates from the distribrution described by F as follows:

a. Generate a random uniform deviate U in the range [0, 1]

b. Compute the value X such that F (X) = U

c. X is a random deviate drawn from the distribution described by F

For the Gumbel distribution we have:

U = exp(−exp(µ − X)/β) (23) so that:

X = µ − β ln(− ln U) (24) is a random deviate drawn from the Gumbel Distribution.

41 C Simulation Code

The simulation was written in C.

#include #include #include #include

#define Gmax 400 //max number of groups #define Nmax 100 //max size of any group #define Smax 6 //max number of skills #define max_gen 100 //max number of generations

float x[Gmax]; //co-ordinates of each group float y[Gmax]; float L; //max size of world float d[Gmax][Gmax]; //distance between groups int connect[Gmax][Gmax]; //connection matrix float c[Gmax][Gmax]; //connectivity of i to j float a = 0.01; //constant used in calculating c float c_sum[Gmax]; //total connectivity of i float pc[Gmax][Gmax]; //proportional connectivity of j float survival[Gmax]; //prob of surviving migration(not currently used) float mortality = 0.0; //mortality parameter (not currently used)

//function to calculate site map void site_map(int G){

int i,j;

for (i=0; i

int main (void) {

//open I/O data files

FILE *fp6; fp6 = fopen("plot2.txt", "w");

42 FILE *fp7; fp7 = fopen("output2.txt", "w");

//set up the random number generator const gsl_rng_type * T; //initialise gsl_rng * r; T = gsl_rng_mt19937; //use T to set the method to be used r = gsl_rng_alloc (T); gsl_rng_set (r, (unsigned)time( NULL ) ); //seed from the clock

//initialise parameters and variables int i,j,p,o,s,t,h,k,iterations,iG,iN,im,iobv; float max_iterations; //number of iterations to perform float G; //number of groups int tmax; //number of generations int N; //population size int parent_pop_size[Gmax]; int num_emigrants[Gmax]; float migrant_rate; int num_immigrants[Gmax][Gmax]; float destination; int f[Gmax][Smax]; int skill_number; float mode; float parent_skill_level[Gmax][Smax][Nmax]; //parental skill levels float offspring_skill_level[Gmax][Smax][Nmax]; //offspring skill levels float total_skill[Gmax][Smax]; //total value of each skill in each group float average_skill[Gmax][Smax]; //average value of each skill in population float max_skill[Gmax][Smax]; //max value of each skill in each group int parent; float oblique; float world_adaptive[Smax]; float world_average[Smax];

//parameter values int Nv,Gv,mv,obv; skill_number =4; float alpha[] = {4,5,6,7}; float beta[] = {1,1,1,1}; tmax = 100; max_iterations = 100; L = 100; Gv = 6; float G_values[] = {10,50,100,150,200,300}; Nv = 4; int N_values[] = {15,25,35,45,55}; mv = 1; float m_values[] = {0.1}; obv = 1; float ob_values[] = {1.0};

//run the simulation for each combination of parameters

43 for(iN=0; iN

//repeat multiple iterations for(s=0;s

//simulate for (t=0; t

//migration

//calculate migrant numbers for(i=0; i

44 } }

//move migrants for(i=0; i

//calculate new pop sizes and shift skill arrays to zero for(i=0; i

//find max value of each skill in each group in the current generation

for(i=0; i max_skill[i][s]){ max_skill[i][s] = parent_skill_level[i][s][p]; } }

45 } }

//skill assignment

//vertical transmission for(i=0; i

//oblique transmission from most skilled individual in parent generation for(i=0;i

if(max_skill[i][s] == 0.0) continue; mode = max_skill[i][s] - alpha[s]; for(o=0; o

//update generations - offspring become parents for(i=0; i

46 }

//output stats

for(s=0; s

for(i=0; i

for(s=0; s10.0){ world_adaptive[s] ++; } }

}

for(s=0; s

} fprintf(fp7,"\n"); } } } } //tidy up gsl_rng_free (r); //free the memory of the random number generator fclose(fp6); fclose(fp7);

return 0; }