Peter D. Taylor

Queen's University | QueensU · Department of Mathematics & Statistics

Much debate has appeared in the literature over the generality of the inclusive fitness approach in the modeling of evolutionary behaviour. Here I focus on the capacity of the inclusive fitness approach to effectively handle non-additive or synergistic interactions. I work with a binary interaction with the matrix game [abcd] and I restrict attenti...

The persistence of altruism and spite remains an enduring problem of social evolution. It is well known that selection for these actions depends on the structure of the population-that is, on actors' genetic relationships to recipients and to the 'neighbourhood' upon which the effects of their actions redound. Less appreciated, however, is that pop...

Abstract How should we measure the relative selective advantage of different behavioral strategies? The various approaches to this question have fallen into one of the following categories: the fixation probability of a mutant allele in a wild type population, some measures of gene frequency and gene frequency change, and a formulation of the inclu...

The local mate competition model from sex ratio theory predicts female-biased sex ratios in populations that are highly subdivided during mating, and is thought to accord well with the population structure of malaria parasites. However, the selective advantage of female-biased sex ratios comes from the resulting increase in total reproductive outpu...

Hamilton's formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We...

Abstract Kin recognition systems enable organisms to predict genetic relatedness. In so doing, they help to maximize the fitness consequences of social actions. Recognition based on phenotypic similarity-a process known as phenotype matching-is thought to depend upon information about one's own phenotype and the phenotypes of one's partners. We pro...

I study the evolution of a pair of competing behavioural alleles in a finite graph-structured population when there are non-additive or "synergistic" fitness effects. I begin with the Price equation and extend it to both a personal-fitness and an inclusive-fitness formulation. I thereby obtain an extension of "Hamilton's Rule" to synergistic effect...

In the simple version of Skunk, a pair of dice is rolled again and again until either you choose to sit or at least one 1 comes up. If you sit, your payoff is the dice sum of all your previous rolls. If at least one 1 comes up while you are still standing, your payoff is zero. Here we look at an extension of the game in which you must also choose t...

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or 'synergistic' fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the othe...

Considerable recent work on the evolution of behaviour has been set in structured populations. An interesting “cancellation” result is known for structures, such as lattices, cycles and island models, which are homogeneous in the sense that the population “looks the same” from every site. In such populations all proximate or immediate fitness effec...

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. Nowak et al. argue that inclusive fitness theory has been of little value in explaining the natural world, and that it has led to negligible progress in explaining the evolution of eusociality. However, we believe that their arguments are based upon a...

We reason that natural selection acting under conditions imposed by physical factors (e.g., geometric constraints on growth rate) and community organization (e.g., persistent finite population sizes, equal total biomass of organisms in proportionately equal size ranges) should lead to certain life history features. The initial size of resource-capt...

Studies of the evolution of a social trait often make ecological assumptions (of population structure, life history), and thus a trait can be studied many different times with different assumptions. Here, I consider a Moran model of continuous reproduction and use an inclusive fitness analysis to investigate the relationships between fecundity or s...

Recent work on the evolution of behaviour is set in a structured population, providing a systematic way to describe gene flow and behavioural interactions. To obtain analytical results one needs a structure with considerable regularity. Our results apply to such "homogeneous" structures (e.g., lattices, cycles, and island models). This regularity h...

This conversation was spearheaded by some research we conducted, as mathematics educators interested in learning from elementary teachers, particularly those we judged as experts in their field. In this research, we were interested in unpacking and reflecting upon the mathematical thinking teachers found themselves enacting as they negotiated their...

General models of the evolution of cooperation, altruism and other social behaviours have focused almost entirely on single traits, whereas it is clear that social traits commonly interact. We develop a general kin-selection framework for the evolution of social behaviours in multiple dimensions. We show that whenever there are interactions among s...

In an inclusive fitness model of social behaviour, a key concept is that of the relatedness between two interactants. This is typically calculated with reference to a "focal" actor taken to be representative of all actors, but when there are different interaction configurations, relatedness must be constructed as an average over all such configurat...

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well mixed in the sense that everyone is equal...

The central tool for the study of allele frequency change due to selection is the remarkably simple but powerful formula of Price [Nature227 (1970) 520]. Here, I provide what might be called a structural analysis of this formula. The formula essentially accumulates the average allele frequency change over many instances of a fitness-determining int...

Spatial structure has been shown to promote altruistic behavior, however, it also increases the intensity of competition among relatives. Our purpose here is to develop a model in which this competition is minimized, more precisely a local increase in fecundity has a minimal competitive effect on the fitness of nearby individuals. We work with an i...

Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of space to evolutionary game dynamics: phenotype space. The population is well-mixed in the sense that everyone...

The methods of inclusive fitness provide a powerful analysis of the action of selection on social behaviour. The key component of this analysis is the concept of relatedness R. In infinite populations, a standard method of calculating relatedness coefficients is through coefficients of consanguinity using the notion of genetic identity by descent....

Recent theoretical studies of selection in finite structured populations have worked with one of two measures of selective advantage of an allele: fixation probability and inclusive fitness. Each approach has its own analytical strengths, but given certain assumptions they provide equivalent results. In most instances the structure of the populatio...

The existence of spiteful behaviors remains controversial. Spiteful behaviors are those that are harmful to both the actor and the recipient, and they represent one of the four fundamental types of social behavior (alongside selfishness, altruism, and mutual benefit). It has generally been assumed that the conditions required for spite to evolve ar...

Two standard mathematical formulations of kin-selection models can be found. Inclusive fitness is an actor-centred approach, which calculates the fitness effect on a number of recipients of the behaviour of a single actor. Direct fitness is a recipient-centred approach, which calculates the fitness effect on the recipient of the behaviour of a numb...

We investigate the evolution of sex allocation and dispersal in a two-habitat environment using a game theoretic analysis. One habitat is of better quality than the other and increased habitat quality influences the competitive ability of offspring in a sex-specific manner. Unlike previous work, we allow incomplete mixing of the population during m...

Interactions between individuals such as hosts and pathogens are often characterized by substantial phenotypic plasticity. Pathogens sometimes alter their exploitation strategies in response to defensive strategies adopted by their host and vice versa. Nevertheless, most game-theoretic models developed to explain the evolution of pathogen and host...

We investigate the conflict between queen and worker over sex allocation, specifically the allocation of the queen's eggs between workers and reproductives and the allocation of the reproductive eggs between male and female. In contrast to previous models, we allow workers to observe and use information about the strategy of the queen. We consider...

We investigate an instance of conflict between mates over the sex ratio of their brood. We construct a kin-selection model for the evolution of the sex ratio assuming local resource competition (LRC) among females. We explore two basic scenarios: (a) the case where parents make simultaneous sex-ratio decisions (the simultaneous allocation model); a...

We investigate two methods of measuring fitness in evolutionary games played among members of a finite population. Classical notions of stability account for the action of selection only, and use immediate reproductive gains as a measure of fitness. This classical interpretation of fitness is what we call reproductive fitness (RF), and is found in...

We investigate the co-evolutionary relationship between sex-ratio bias and sex-specific dispersal behaviour using an inclusive fitness approach. We consider two models: (i) DDM, in which dispersal of both sexes occurs before mating; and (ii) DMD, in which male dispersal precedes mating and female dispersal follows mating. Under DDM, at equilibrium,...

Consider a two-player game in which each player contributes a costly resource to the common good of the pair. For such contests, the Nash equilibrium contribution, x*, is one for which neither player can increase its pay-off by unilaterally altering its contribution from x*. We study an elaboration of this game, which allows the players to exchange...

What gives cooperation an evolutionary edge? Two features of a population — spatial structure and finite size — are factors in the success of any strategy, although more subtle than we thought.

We will talk here about teaching, but at the centre of our discussion must be mathematics, because without the subject, there is nothing to teach. We must go beyond mathematics, of course, because the task of the teacher is not so much to work with the subject as to bring it into the classroom, and this requires a particular kind of intimacy with a...

We investigate the correspondence between discrete-trait games (for example, matrix games) and continuous-trait games, paying particular attention to the standard criteria for evolution-ary stability. We show that the standard evolutionarily stable strategy conditions for discrete-trait games can be seen as a special case of the conditions employed...

We develop a general inclusive fitness model for genetic evolution at an imprinted locus – one at which selection is allowed to act conditionally upon parental origin of the gene. In many cases of interest, such genes affect the fitness of relatives, particularly sibs. We formulate a matrilineal and patrilineal inclusive fitness and show that these...

We study the evolution of altruism in one- and two-dimensional stepping-stone populations with discrete overlapping generations. We find that increasing survival probability facilitates the evolution of altruism, in agreement with recent results for a patch-structured population. We allow the altruistic behaviour to affect either fecundity or survi...

We consider the evolution of dispersal in an environment that varies spatially but that is con-stant in time. We allow an age structure with dispersal possible in all life-stages. We suppose that demes are large enough that kin effects can be ignored. It has previously been shown that cost-free dispersal can persist over evolutionary time. However,...

We use Hamilton's inclusive fitness method to calculate the evolutionarily stable dispersal rate in 1- and 2-dimensional stepping-stone populations. This extends previous results by introducing a positive probability for adults to survive into the next generation and breed again. Relatedness between nearby individuals generally decreases with incre...

Very little attention has been given in the literature to the interesting question of how to handle relatedness in finite populations. The main problem is that a finite population is never really "at equilibrium" in that it represents just one realization of an infinite assemblage of possible allelic distributions. A recent paper of Rousset and Bil...

We use an inclusive fitness model to study the evolution of altruism in a patch-structured population in which there is positive probability of breeder survival from one generation to the next. We find first that breeder survival promotes altruism and second that there is a marked difference between benefits of fecundity and benefits of survival. U...

We use an inclusive fitness model to study the evolution of altruism in a patch-structured population in which there is positive probability of breeder survival from one generation to the next. We find first that breeder survival promotes altruism and second that there is a marked difference between benefits of fecundity and benefits of survival. U...

We present two theorems that generalize Pontryagin's maximum principle to the setting of dynamic evolutionary games between genetically related individuals. The two theorems correspond to two types of interactions among individuals: patch-structured populations in which individuals locally “play the field” and pairwise interactions. These generaliz...

The evolution of a gene for female choice of mates with heterozygous advantage at a single locus is discussed. Recent analyses of this problem have been mathematically unclear and misleading. A genetic calculation for a hypothetical one-locus, diallelic species shows that the choice gene is not favoured in a static environment. Computations are pre...

A framework is presented for unifying single locus genetic and game theoretic models of continuous traits under frequency-dependent selection when there are interactions among relatives. This framework serves two purposes. First, it is used to determine how "games between relatives" must be modeled to be genetically valid. There are two commonly em...

In intrademic selection models, individuals interact in groups, and this interaction phase is usually treated as a point in time. It is likely, however, that interactions take place over some time period. If selfishness is treated as a quantitative trait and this time period is explicitly considered, how does the evolutionarily stable strategy (ESS...

Trisomy is a genetic abnormality of considerable medical importance. The most familiar example is trisomy 21, which causes Down Syndrome [Cummings, M. R. (1988) Human Heredity: Principles and Issues (West Publishing Company, New York)]. In a classic paper, Axelrod and Hamilton [Axelrod, R. & Hamilton, W. D. (1981) Science 211, 1390-1396] offered a...

We unite two general models for evolutionary change under the forces of selection, mutation and reproduction, a genetic model (replicator dynamics) and a cultural model (gradient dynamics). Under the assumption of normality, we find that the mean and variance dynamics are essentially identical under the two models and we relate these to the ESS and...

Many biological characters of interest are temporal sequences of decisions. The evolution of such characters is often modelled using dynamic optimization methods such as the maximum principle. A quantity central to these analyses is the 'Hamiltonian' function, named after the mathematician William R. Hamilton. On the other hand, evolutionary models...

Kin selection arguments, based on Hamilton's (1964) concept of inclusive fitness, provide a powerful heuristic and can therefore give us valuable insights into the different pathways through which natural selection acts. But their formulation can be quite tricky, requiring as they do, a close accounting of all the fitness effects of a particular it...

There has been recent interest in using the techniques of quantitative genetics to study optimal life histories under frequency-dependent selection, but a search of the literature has revealed no clear quantitative genetics recursion that incorporates both frequency dependence and overlapping generations. This may be due in part to the historical t...

My purpose here is to provide a coherent account of inclusive fitness techniques, accessible to a mathematically literate graduate student in evolutionary biology, and to relate these to standard one-locus genetic models. I begin in Sect. 2 with a general formulation of evolutionary stability; in Sect. 3 and Sect. 4 I interpret the basic stability...

In a patch of hermaphroditic plants, with a low level of pollen migration between patches, a prevailing wind creates a gradient, within the patch, in the strength of local competition among pollen for reproductive success. This leads to a sex ratio gradient, with a male (pollen) bias in downwind individuals, which can be quite strong even for large...

We construct an inclusive fitness model to find the evolutionarily stable sex ratios in a partially sibmating diploid or haplodiploid population. We assume a constant rate of sibmating with inbred offspring incurring a fitness penalty which, under haplodiploidy, is only suffered by females. We construct a one-locus genetic model for the same proble...

The theoretical hypothesis that the sex-ratio should be biased towards the sex with the wider and/or more even dispersal pattern is tested and confirmed with an inclusive fitness model in a one-dimensional diploid stepping-stone population in which offspring can remain on their home site or disperse one site to the right or left. Two models are exa...

In a structured population, with partial dispersal of offspring, there will be competition among related offspring for reproductive resources, or local resource competition (LRC), and, when the strength of this competition differs between the sexes, this will generate a sex ratio bias in favor of the sex with the least LRC. Standard models assume t...

We construct an inclusive fitness model of the relative selective advantage of sibmating and outbreeding behaviour, under the assumption that inbred offspring pay a fitness penalty. We are particularly interested in the question of whether such inbreeding depression is enough to generate a stable phenotypic polymorphism, with both kinds of breeding...

Experimental work of Nadel and Luck (1992) on a chalcidoid wasp provides a confirmation of sex ratio theory under local mate competition.

A general formulation of inclusive fitness is proposed which specifically accounts for competitive effects between relatives. As an example, for an asexual population in a homogeneous inelastic environment, such as is found in a stepping-stone model of dispersal, the inclusive fitness of a breeding female, under weak selection, is independent of he...

A viscous population (Hamilton, 1964) is one in which the movement of organisms from their place of birth is relatively slow. This viscosity has two important effects: one is that local interactions tend to be among relatives, and the other is that competition for resources tends to be among relatives. The first effect tends to promote and the seco...

We present a theoretical framework in order to understand how the relationship between male parental care and paternity is dependent on the relationship between male parental care and offspring recruitment. When there is an S-shaped relationship between offspring recruitment and the parental care of a single male, we predict a threshold relationshi...

Following the approach of Schaffer (1974, Ecology 55, 291-303.) and Charlesworth & Leon (1976, Am. Nat. 110, 449-459.) the tradeoff between fecundity and survival/growth is investigated in an age-structured population with density independent life history parameters. The results of the above authors are generalized by allowing the tradeoff curve to...

Price and Liou (1989; see 90L/11771) suggested that directional selection operates on a correlated, environmentally determined trait (nutritional state). In their model, the genetic component of clutch size could also be subject to selection, but, if clutch size is not evolving, this selection must be nondirectional (eg normalizing). The authors he...

Presents an inclusive-fitness model for the evolution of dispersal rates in subdivided populations where patches vary in the density of resources available for breeding and relatedness among patch mates of the same sex. If male and female relatednesses and male immigration rate are independent of patch density, then the model predicts that the mean...

A general notion of evolutionary stability is formulated in models in which the possible behaviours are parameterized by a continuous variable, and selection is assumed to be weak. Two local stability conditions are formulated, m-stability and (δ-stability, the former being first-order and the latter second-order in the mutant behavioural deviation...

A model of seed provisioning is used to illustrate the relationship between an inclusive fitness and a one locus genetic model, with particular attention to the two basic local stability conditions: δ-stability and m-stability The model is able to illustrate the difference between these two conditions, and provide an example in which the first hold...

Much recent work has focused on the transition from G. R. Price's (1970, Nature 227, 520-521) formula for allele frequency change to an inclusive fitness condition for the selective advantage of a certain behaviour. In case there is any kind of asymmetry between the sexes, the analysis must keep track of the two sexes separately, and this leads to...

A series of papers, Hamilton & May (1977), [16] and [17] and Frank (1986) have developed and generalized a model of dispersal of offspring to random sites in a stable environment. I present an inclusive fitness model for such dispersal behaviour, applicable in diploid or haplodiploid populations with dispersal under offspring or maternal control....

From the standpoint of most people’s interests and perspectives, little need be added to the simple and elegant statement above. From the special perspective of a student of evolution, the statement seems a trifle parochial, and some qualifications and additions seem justified. It seems parochial in three respects, which we will call the dimensiona...

The quality of parental care appears to correlate positively with egg size, both among and within species of fishes. A model to explain continuous covariation between the quality of parental care and egg size contains 3 major assumptions about the dependence of offspring survival on egg size: offspring from larger eggs develop more slowly and take...

A cryptographic scheme for controlling access to information within a group of users organized in a hierarchy was proposed by Akl and Taylor (1983). The scheme enables a user at some level to compute from his own cryptographic key the keys of the users below him in the organization. In such a system there exists the possibility of two users collabo...

A general equation for equilibrium sex allocation is provided which models asymmetries between son and daughter in the costs of offspring production, the genetic relatedness to the controlling genotype and the amount of competition for mating opportunities and reproductive resources. A genetic proof is given which is valid for diploid and haplodipl...

A general matrix equation for evolutionary equilibrium of sex allocation is derived. The equation allows calculation of ESS values of behavioural parameters in sex allocation models, and provides a conceptual framework in which such models can be viewed. A careful discussion is given of a number of examples from the literature. An attempt is made t...

A number of papers, for example Heuch (1979a, 1979b), have studied type frequencies of heterostylous plant populations at equilibrium. Barrett et al. (1983) have adapted Heuch's (1979a) analysis to a system, such as that in P. cordata, in which pollen is type-specific and each flower produces pollen for all types other than its own. I adopt this as...

An experimental approach, a data handling set-up and a mathematical model for the interpretation of product distributions in Fischer–Tropsch synthesis is presented, together with a description of how the necessary data are obtained by analyzing all product streams and combining the various analyses into a complete and detailed overall product distr...

A generalized scheme for product distribution in Fischer Tropsch synthesis in the absence of non-kinetic effects due to diffusion, shape selectivity, catalyst bifunctionality (e.g. synthesis-cracking catalysts), etc. is presented. The derivations reproduce the Schulz-Flory distribution in one limit and go on to generalize the work of Anderson in pr...

Many authors (Williams, 1966; Gadgil and Bossert, 1970; Taylor et al., 1974; Schaffer, 1979) have considered models of optimal life history strategies. Most generally an organism at any particular age or size has a quantity of available resources which he can spend on maintenance, growth and/or reproduction, and his problem is to allocate these res...

In a population at equilibrium in a stable environment under natural selection there can be very little heritability of fitness. In some species, for example, those with leks, females exhibit strong preferences for certain characteristics in their mates, though all they obtain are his genes and these cannot contribute much to the fitness of their o...

A scheme based on cryptography is proposed for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set (or poset). Straightforward implementation of the scheme requires users highly placed in the hierarchy to store a large number of cryptographic keys. A time-versus-storage trade-off is then described for...

There is a conflict of interest between the queen and her worker-daughters in social hymenoptera over the ratio of investment in male and female reproductives. In the absence of worker-laying and inbreeding, the queen prefers a 1:1 (male : female) investment ratio, whereas the workers prefer a 1:3 ratio. Trivers and Hare (1976) suggest that the wor...

Fisher1 produced the first general argument that a random-mating sexually-reproducing population should devote equal reproductive resources to the production of male and female offspring, while Hamilton2 considered several unusual situations in which the expenditure of reproductive resources should be biased towards one sex or the other. His ‘host’...

Hamilton (1967) pointed out that Fisher's (1930) argument predicting an equality of the sex ratio may break down when there is local competition for mates. He considered in particular a model in which the environment consists of a number of isolated patches, each of which is colonized by a number of inseminated females; the offspring breed within t...

This paper investigates the evolution of the sex ratio under an extension of the haystack model of Maynard Smith (1964). At the beginning of each season a stack is colonized by a number of fertilized females, and their offspring breed there for several generations until new haystacks are available for colonization. We intend this as a model for pop...