arXiv subjects

Steven A. Frank

Publications and source records attributed to Steven A. Frank.

50 records · Page 3Linked to original sources

arXiv2012

Natural selection. IV. The Price equation

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection, and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen.

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arXiv2011

Demography and the tragedy of the commons

Individual success in group-structured populations has two components. First, an individual gains by outcompeting its neighbors for local resources. Second, an individual's share of group success must be weighted by the total productivity of the group. The essence of sociality arises from the tension between selfish gains against neighbors and the associated loss that selfishness imposes by degrading the efficiency of the group. Without some force to modulate selfishness, the natural tendencies of self interest typically degrade group performance to the detriment of all. This is the tragedy of the commons. Kin selection provides the most widely discussed way in which the tragedy is overcome in biology. Kin selection arises from behavioral associations within groups caused either by genetical kinship or by other processes that correlate the behaviors of group members. Here, I emphasize demography as a second factor that may also modulate the tragedy of the commons and favor cooperative integration of groups. Each act of selfishness or cooperation in a group often influences group survival and fecundity over many subsequent generations. For example, a cooperative act early in the growth cycle of a colony may enhance the future size and survival of the colony. This time-dependent benefit can greatly increase the degree of cooperation favored by natural selection, providing another way in which to overcome the tragedy of the commons and enhance the integration of group behavior. I conclude that analyses of sociality must account for both the behavioral associations of kin selection theory and the demographic consequences of life history theory.

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arXiv2011

A general model of the public goods dilemma

An individually costly act that benefits all group members is a public good. Natural selection favors individual contribution to public goods only when some benefit to the individual offsets the cost of contribution. Problems of sex ratio, parasite virulence, microbial metabolism, punishment of noncooperators, and nearly all aspects of sociality have been analyzed as public goods shaped by kin and group selection. Here, I develop two general aspects of the public goods problem that have received relatively little attention. First, variation in individual resources favors selfish individuals to vary their allocation to public goods. Those individuals better endowed contribute their excess resources to public benefit, whereas those individuals with fewer resources contribute less to the public good. Thus, purely selfish behavior causes individuals to stratify into upper classes that contribute greatly to public benefit and social cohesion and to lower classes that contribute little to the public good. Second, if group success absolutely requires production of the public good, then the pressure favoring production is relatively high. By contrast, if group success depends weakly on the public good, then the pressure favoring production is relatively weak. Stated in this way, it is obvious that the role of baseline success is important. However, discussions of public goods problems sometimes fail to emphasize this point sufficiently. The models here suggest simple tests for the roles of resource variation and baseline success. Given the widespread importance of public goods, better models and tests would greatly deepen our understanding of many processes in biology and sociality.

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arXiv2011

Evolutionary foundations of cooperation and group cohesion

In biology, the evolution of increasingly cooperative groups has shaped the history of life. Genes collaborate in the control of cells; cells efficiently divide tasks to produce cohesive multicellular individuals; individual members of insect colonies cooperate in integrated societies. Biological cooperation provides a foundation on which to understand human behavior. Conceptually, the economics of efficient allocation and the game-like processes of strategy are well understood in biology; we find the same essential processes in many successful theories of human sociality. Historically, the trace of biological evolution informs in two ways. First, the evolutionary transformations in biological cooperation provide insight into how economic and strategic processes play out over time--a source of analogy that, when applied thoughtfully, aids analysis of human sociality. Second, humans arose from biological history--a factual account of the past that tells us much about the material basis of human behavior.

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arXiv2011

Maladaptation and the paradox of robustness in evolution

Background. Organisms use a variety of mechanisms to protect themselves against perturbations. For example, repair mechanisms fix damage, feedback loops keep homeostatic systems at their setpoints, and biochemical filters distinguish signal from noise. Such buffering mechanisms are often discussed in terms of robustness, which may be measured by reduced sensitivity of performance to perturbations. Methodology/Principal Findings. I use a mathematical model to analyze the evolutionary dynamics of robustness in order to understand aspects of organismal design by natural selection. I focus on two characters: one character performs an adaptive task; the other character buffers the performance of the first character against perturbations. Increased perturbations favor enhanced buffering and robustness, which in turn decreases sensitivity and reduces the intensity of natural selection on the adaptive character. Reduced selective pressure on the adaptive character often leads to a less costly, lower performance trait. Conclusions/Significance. The paradox of robustness arises from evolutionary dynamics: enhanced robustness causes an evolutionary reduction in the adaptive performance of the target character, leading to a degree of maladaptation compared to what could be achieved by natural selection in the absence of robustness mechanisms. Over evolutionary time, buffering traits may become layered on top of each other, while the underlying adaptive traits become replaced by cheaper, lower performance components. The paradox of robustness has widespread implications for understanding organismal design.

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arXiv2011

Natural selection. III. Selection versus transmission and the levels of selection

George Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In this article, I extend Williams' approach to show that the ratio of selection bias to transmission bias provides a unifying framework for diverse biological problems. Specific examples include Haldane and Lande's mutation-selection balance, Eigen's error threshold and quasispecies, Van Valen's clade selection, Price's multilevel formulation of group selection, Szathmary and Demeter's evolutionary origin of primitive cells, Levin and Bull's short-sighted evolution of HIV virulence, Frank's timescale analysis of microbial metabolism, and Maynard Smith and Szathmary's major transitions in evolution. The insights from these diverse applications lead to a deeper understanding of kin selection, group selection, multilevel evolutionary analysis, and the philosophical problems of evolutionary units and individuality.

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arXiv2011

Natural selection. II. Developmental variability and evolutionary rate

In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and learning enhance nonheritable phenotypic variation, which in turn can accelerate evolutionary response. In this paper, I show how developmental variability alters evolutionary dynamics by smoothing the landscape that relates genotype to fitness. In a fitness landscape with multiple peaks and valleys, developmental variability can smooth the landscape to provide a directly increasing path of fitness to the highest peak. Developmental variability also allows initial survival of a genotype in response to novel or extreme environmental challenge, providing an opportunity for subsequent adaptation. This initial survival advantage arises from the way in which developmental variability smooths and broadens the fitness landscape. Ultimately, the synergism between developmental processes and genetic variation sets evolutionary rate.

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arXiv2011

Natural selection. I. Variable environments and uncertain returns on investment

Many studies have analyzed how variability in reproductive success affects fitness. However, each study tends to focus on a particular problem, leaving unclear the overall structure of variability in populations. This fractured conceptual framework often causes particular applications to be incomplete or improperly analyzed. In this paper, I present a concise introduction to the two key aspects of the theory. First, all measures of fitness ultimately arise from the relative comparison of the reproductive success of individuals or genotypes with the average reproductive success in the population. That relative measure creates a diminishing relation between reproductive success and fitness. Diminishing returns reduce fitness in proportion to variability in reproductive success. The relative measurement of success also induces a frequency dependence that favors rare types. Second, variability in populations has a hierarchical structure. Variable success in different traits of an individual affects that individual's variation in reproduction. Correlation between different individuals' reproduction affects variation in the aggregate success of particular alleles across the population. One must consider the hierarchical structure of variability in relation to different consequences of temporal, spatial, and developmental variability. Although a complete analysis of variability has many separate parts, this simple framework allows one to see the structure of the whole and to place particular problems in their proper relation to the general theory. The biological understanding of relative success and the hierarchical structure of variability in populations may also contribute to a deeper economic theory of returns under uncertainty.

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arXiv2011

Wright's adaptive landscape versus Fisher's fundamental theorem

Two giants of evolutionary theory, Sewall Wright and R. A. Fisher, fought bitterly for over thirty years. The Wright-Fisher controversy forms a cornerstone of the history and philosophy of biology. I argue that the standard interpretations of the Wright-Fisher controversy do not accurately represent the ideas and arguments of these two key historical figures. The usual account contrasts the major slogans attached to each name: Wright's adaptive landscape and shifting balance theory of evolution versus Fisher's fundamental theorem of natural selection. These alternative theories are in fact incommensurable. Wright's theory is a detailed dynamical model of evolutionary change in actual populations. Fisher's theory is an abstract invariance and conservation law that, like all physical laws, captures essential features of a system but does not account for all aspects of dynamics in real examples. This key contrast between embodied theories of real cases and abstract laws is missing from prior analyses of Wright versus Fisher. They never argued about this contrast. Instead, the issue at stake in their arguments concerned the actual dynamics of real populations. Both agreed that fluctuations of nonadditive (epistatic) gene combinations play a central role in evolution. Wright emphasized stochastic fluctuations of gene combinations in small, isolated populations. By contrast, Fisher believed that fluctuating selection in large populations was the main cause of fluctuation in nonadditive gene combinations. Close reading shows that widely cited views attributed to Fisher mostly come from what Wright said about Fisher, whereas Fisher's own writings clearly do not support such views.

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arXiv2010

Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.

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arXiv2010

A simple derivation and classification of common probability distributions based on information symmetry and measurement scale

Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His approach was phenomenological: a differential equation that generated common distributions without any underlying conceptual basis for why common distributions have particular forms and what explains the familial relations. Pearson's system and its descendants remain the most popular systematic classification of probability distributions. Here, we unify the disparate forms of common distributions into a single system based on two meaningful and justifiable propositions. First, distributions follow maximum entropy subject to constraints, where maximum entropy is equivalent to minimum information. Second, different problems associate magnitude to information in different ways, an association we describe in terms of the relation between information invariance and measurement scale. Our framework relates the different continuous probability distributions through the variations in measurement scale that change each family of maximum entropy distributions into a distinct family.

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arXiv2010

Measurement Invariance, Entropy, and Probability

We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large magnitudes, leading to observations that often follow Student's probability distribution which has a Gaussian shape for small fluctuations from the mean and a power law shape for large fluctuations from the mean. An inverse scaling often arises in which measures naturally grade from logarithmic to linear as one moves from small to large magnitudes, leading to observations that often follow a gamma probability distribution. A gamma distribution has a power law shape for small magnitudes and an exponential shape for large magnitudes. The two measurement scales are natural inverses connected by the Laplace integral transform. This inversion connects the two major scaling patterns commonly found in nature. We also show that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement. Incorporating information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability.

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arXiv2009

The common patterns of nature

We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased stochastic fluctuations: random connections of network nodes; amino acid substitutions with no effect on fitness; species that arise or disappear from communities randomly. These neutral generative models often match common patterns of nature. In this paper, I present the theoretical background by which we can understand why these neutral generative models are so successful. I show how the classic patterns such as Poisson and Gaussian arise. Each classic pattern was often discovered by a simple neutral generative model. The neutral patterns share a special characteristic: they describe the patterns of nature that follow from simple constraints on information. For example, any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves information only about the geometric mean attracts to the power law pattern. I present an informational framework of the common patterns of nature based on the method of maximum entropy. This framework shows that each neutral generative model is a special case that helps to discover a particular set of informational constraints; those informational constraints define a much wider domain of non-neutral generative processes that attract to the same neutral pattern.

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arXiv2009

Natural selection maximizes Fisher information

In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher information arises as the intrinsic metric of natural selection and evolutionary dynamics. Maximizing the amount of Fisher information about the environment captured by the population leads to Fisher's fundamental theorem of natural selection, the most profound statement about how natural selection influences evolutionary dynamics. I also show a relation between Fisher information and Shannon information (entropy) that may help to unify the correspondence between information and dynamics. Finally, I discuss possible connections between the fundamental role of Fisher information in statistics, biology, and other fields of science.

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