A review of evolutionary graph theory with applications to game theory

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the “fixation probability” - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.     

A new sociobiological theory of homosexuality applicable to societies with universal marriage

Several sociobiological theories have tried to explain human homosexuality. Adaptationally orthodox theories view it as a specific instance of reproductive altruism, in which the homosexual orientation in combination with a cross-gender identity is the emotional motivator of a nonreproductive role, leading to higher inclusive fitness for the individual displaying the trait in a particular environment. The nonreproduction is typically assumed to be plete—a large reproductive sacrifice. A new model is proposed in which human homosexuality remains a reproductively altruistic, trait, but in which the magnitude of the altruism is much reduced, and so presumably is more likely to result in a net increase in inclusive fitness. The theory applies to societies in which social pressures require marriage of essentially all reproductively able individuals, and does not require gender nonconformity. Hence, the new theoy fills some of the gaps left by the earlier orthodox theories, and in combination with them offers a consolidated set of hypothesis for testing.     

A practical method for calculating evolutionary trees from sequence data

In a previous paper (Klotz et a1., 1979) we described a method for determining evolutionary trees from sequence data when rates of evolution of the sequences might differ greatly. It was shown theoretically that the method always gave the correct topology and root when the exact number of mutation differences between sequences and from their common ancestor was known. However, the method is impractical to use in most situations because it requires some knowledge of the ancestor. In this present paper we describe another method, related to the previous one, in which a present-day sequence can serve temporarily as an ancestor for purposes of determining the evolutionary tree regardless of the rates of evolution of the sequences involved. This new method can be carried out with high precision without the aid of a computer, and it does not increase in difficulty rapidly as the number of sequences involved in the study increases, unlike other methods.     

The effect of sex-allocation biasing on the evolution of worker policing in hymenopteran societies

Mutual policing is thought to be important in conflict suppression at all levels of biological organization. In hymenopteran societies (bees, ants, and wasps), multiple mating by queens favors mutual policing of male production among workers (worker policing). However, worker policing of male production is proving to be more widespread than predicted by relatedness patterns, occurring in societies headed by single-mated queens in which, paradoxically, workers are more related to the workers' sons that they kill than the queen's sons that they spare. Here we develop an inclusive-fitness model to show that a second reproductive conflict, the conflict over sex allocation, can explain the evolution of worker policing contrary to relatedness predictions. Among ants, and probably other social Hymenoptera, workers kill males to favor their more related sisters. Importantly, males are killed at the larval stage, presumably because workers cannot determine the sex of queen-laid eggs. Sex-allocation biasing favors worker policing because policing removes some males (the workers' sons) at low cost at the egg stage rather than at higher cost at the larval stage. Our model reveals an important interaction between two reproductive conflicts in which the presence of one conflict (sex allocation) favors the suppression of the other (male production by workers).     

Cercopithecine Y-chromosome data provide a test of competing morphological evolutionary hypotheses

We report here the results of the first molecular evolutionary analysis to include members of all 10 extant genera of cercopithecine monkeys. A total of 44 individuals were surveyed for approximately 2.2 kb of the testis-specific protein, Y-chromosome (TSPY). The TSPY sequences were subjected to parsimony analyses in PAUP 4.0, followed by tree comparison tests designed to assess existing morphological hypotheses of cercopithecine evolution. The results of these tests show that the present Y-chromosome dataset unambiguously supports: (1) monophyly of Macaca, (2) polyphyly of the mangabeys (Cercocebus and Lophocebus), (3) paraphyly of Cercopithecus, and (4) inclusion of Allenopithecus and Miopithecus in the tribe Cercopithecini. A number of unexpected Y-chromosome relationships are also discussed, including a pattern suggesting resurrection of the genus Chlorocebus for the guenons currently identified as Erythrocebus patas, Cercopithecus aethiops, and Cercopithecus lhoesti. Relative rate tests reveal significant difference in the TSPY substitution rate across numerous lineages in the tribe Cercopithecini. Because the rate differences follow no obvious phylogenetic pattern, "local" molecular clocks were not employed and divergence dates were not estimated for this tribe. In contrast, similar analysis of the Papionini reveals rate heterogeneity between a single pair of taxonomic groups: Macaca vs. the "African papionins." Divergence dates were therefore calculated for the tribe by calibrating TSPY clocks specific to each of these two clades.     

A statistical test of phylogenies estimated from sequence data

A simple approach to testing the significance of the branching order, estimated from protein or DNA sequence data, of three taxa is proposed. The branching order is inferred by the transformed-distance method, under the assumption that one or two outgroups are available, and the branch lengths are estimated by the least-squares method. The inferred branching order is considered significant if the estimated internodal distance is significantly greater than zero. To test this, a formula for the variance of the internodal distance has been developed. The statistical test proposed has been checked by computer simulation. The same test also applies to the case of four taxa with no outgroup, if one considers an unrooted tree. Formulas for the variances of internodal distances have also been developed for the case of five taxa. Conditions are given under which it is more efficient to add the sequence of a fifth taxon than to do 25% more nucleotide sequencing in each of the original four. A method is presented for combining analyses of disparate data to get a single P value. Finally, the test, applied to the human-chimpanzee-gorilla problem, shows that the issue is not yet resolved.     

The inference of evolutionary trees from molecular data.

1. Procedures for multiple alignment of sequence data, subsequent phylogenetic inference, and testing of the trees derived are presented. 2. The assumptions underlying different approaches and the extent to which they are valid are discussed.     

Reproductive bribing and policing as evolutionary mechanisms for the suppression of within-group selfishness

We show that a new, simple, and robust general mechanism for the social suppression of within-group selfishness follows from Hamilton's rule applied in a multilevel selection approach to asymmetrical, two-person groups: If it pays a group member to behave selfishly (i.e., increase its share of the group's reproduction, at the expense of group productivity), then its partner will virtually always be favored to provide a reproductive "bribe" sufficient to remove the incentive for the selfish behavior. The magnitude of the bribe will vary directly with the number of offspring (or other close kin) potentially gained by the selfish individual and inversely with both the relatedness r between the interactants and the loss in group productivity because of selfishness. This bribe principle greatly extends the scope for cooperation within groups. Reproductive bribing is more likely to be favored over social policing for dominants rather than subordinates and as intragroup relatedness increases. Finally, analysis of the difference between the group optimum for an individual's behavior and the individual's inclusive fitness optimum reveals a paradoxical feedback loop by which bribing and policing, while nullifying particular selfish acts, automatically widen the separation of individual and group optima for other behaviors (i.e., resolution of one conflict intensifies others).     

A nonparametric test for association with censored data

A nonparametric procedure is proposed for the problem of testing association between two continuous variables when one is subject to arbitrary censoring. The motivation for the procedure derives from our finding that Cox's likelihood procedure may not adequately control the size of the test. The proposed procedure allows the censoring mechanism to depend on the independent variable, is simple computationally, and provides accurate control over the size of the test even for quite small samples. Asymptotic results suggest that it may provide a sensitive alternative to Cox's procedure. An example dealing with survival following operation for myasthenia gravis is provided, wherein a method for testing after adjustment for covariate information is described.     

A general theory for the evolutionary dynamics of virulence

Most theory on the evolution of virulence is based on a game-theoretic approach. One potential shortcoming of this approach is that it does not allow the prediction of the evolutionary dynamics of virulence. Such dynamics are of interest for several reasons: for experimental tests of theory, for the development of useful virulence management protocols, and for understanding virulence evolution in situations where the epidemiological dynamics never reach equilibrium and/or when evolutionary change occurs on a timescale comparable to that of the epidemiological dynamics. Here we present a general theory similar to that of quantitative genetics in evolutionary biology that allows for the easy construction of models that include both within-host mutation as well as superinfection and that is capable of predicting both the short- and long-term evolution of virulence. We illustrate the generality and intuitive appeal of the theory through a series of examples showing how it can lead to transparent interpretations of the selective forces governing virulence evolution. It also leads to novel predictions that are not possible using the game-theoretic approach. The general theory can be used to model the evolution of other pathogen traits as well.     

An evolutionary theory of cuisine

The evolution of human diet is the product of both biological and cultural adaptations to various plants and animals in the environment. This paper develops a new theory for the evolution of cuisine practices which attempts to account for how food processing provided a critical link in enhancing the nutrient balance of major domesticated plants. Dr. Katz is a Professor of Anthropology and Director of the W. M. Krogman Center for Research in Child Growth and Development at the University of Pennsylvania. He first became interested in food and cuisine research as a result of his work with minerals in the diets of Inuit (Eskimo) peoples of the Alaskan Arctic and then with maize in the diets of the Lacandon Maya Indians in the early 1970s. Since then he has published numerous books and papers on developing the theory of cuisine presented in this paper.     

The vicissitudes of evolutionary theory

Conclusion I have referrred to the data-generating capacity of the alternative research program, that it should stimulate fruitful hypotheses. Conversely, static theory (i.e., analysis dependent on mathematical logic to impose regularities on non-linear processes) is vulnerable to serendipitous data which violates its deductive structure. In that spirit, Jerison cautions: Where hints are found in brain structure, for example, of asymmetries in the brain, we can exploit them as a basis for good hypothesis, but we should also recognize that hypotheses created in this way are likely to be weak.Brain asymmetry data, surely among the least linear evidence available — topological irregularities of convoluted space — have been integrated in Holloway's program as but one phenotypic window on the evolution of complex cognitive functioning. There are no a priori methodological nor theoretical exclusions of this kind of data, for they complement an open-ended research program.Furthermore, asymmetry evidence may yet satisfy a test for phyletic evolution (gradualism) demanded by the punctuational model — the provision of data for gradual character change, especially if the character is complex, appears to have functional significance and can be shown to be associated with palaeoenvironmental change. Finally, these new considerations have stimulated additional questions for students of brain evolution. Among the more interesting of these is whether the growing evidence of asymmetry, its sexual dimorphism and other kinds of population distribution, and its functional lateralization in general, suggest ongoing foci for selection pressures in our continuing evolution.Evolutionary study, in its reliance on positivistic technique and conformance to standards of scientific proof, is being assimilated within the general tendency of all science, toward more and more mathematical modeling. Mathematical simulations are not more isomorphic with evolutionary processes than are other kinds of syntheses. In fact, models incorporating extremely limited fossil data mislead us with their inferential chains of necessity. Projected into an inevitable future, they are ironic equations of social processes born in evolutionary times.A science which seeks to manipulate nature nevertheless cannot undo what happened in evolution. The errors and indeterminateness of human evolution are constraints on the species no longer embedded in nature. Their scientific status is not the issue. They can be interpreted, however. We can rationalize an ideological mastery of generalized biological processes which debases our own history. Or we can achieve an authentic understanding of its originality as part of our own making. That would be a beginning, for evolution has not ended, in realizing the creative possibilities of human consciousness. But, then again, over all of these natural constraints and cultural possibilities lies the shadow of genetic engineering. The clash between Western science and universal humanity will be fought on that ground, should we survive the nuclear age.Bernard Belasco is an Associate Professor at Baruch College of the City University of New York.     

A novel analytical method for evolutionary graph theory problems

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.     

The structure of microbial evolutionary theory

The study of microbial phylogeny and evolution has emerged as an interdisciplinary synthesis, divergent in both methods and concepts from the classical evolutionary biology. The deployment of macromolecular sequencing in microbial classification has provided a deep evolutionary taxonomy hitherto deemed impossible. Microbial phylogenetics has greatly transformed the landscape of evolutionary biology, not only in revitalizing the field in the pursuit of life's history over billions of years, but also in transcending the structure of thought that has shaped evolutionary theory since the time of Darwin. A trio of primary phylogenetic lineages, along with the recognition of symbiosis and lateral gene transfer as fundamental processes of evolutionary innovation, are core principles of microbial evolutionary biology today. Their scope and significance remain contentious among evolutionists.