Natural selection without survival of the fittest

Susan Mills and John Beatty proposed a propensity interpretation of fitness (1979) to show that Darwinian explanations are not circular, but they did not address the critics' chief complaint that the principle of the survival of the fittest is either tautological or untestable. I show that the propensity interpretation cannot rescue the principle from the critics' charges. The critics, however, incorrectly assume that there is nothing more to Darwin's theory than the survival of the fittest. While Darwinians all scoff at this assumption, they do not agree about what role, if any, this principle plays in Darwin's theory of natural selection. I argue that the principle has no place in Darwin's theory. His theory does include the idea that some organisms are fitter than others. But greater reproductive success is simply inferred from higher fitness. There is no reason to embody this inference in the form of a special principle of the survival of the fittest.I would like to thank John Beatty, Ron Giere, Philip Kitcher and John Winnie for detailed and helpful criticisms of an earlier draft of this paper.     

Multilocus Behavior in Random Environments I. Random Levene Models

In this paper the consequences of natural selection acting on several loci simultaneously in a spatially fluctuating environment are described. The fitnesses of the genotypes are assumed to be additive both within and between loci. The environment is assumed to be made up of a very large (effectively infinite) number of patches in which fitnesses are assigned at random. The resulting deterministic model is called a Random Levene Model and its properties are approximate by a system of differential equations. The main equilibrium properites are that (1) the linkage disequilibrium is zero and (2) the correlations in fitness between alleles at different loci are the principle determinants of the dynamic inter-locus interactions. Although there is no epistasis as conventionally defined, the equilibrium state at the two loci are highly interdependent, the governing principle being that two alleles at different loci whose fitness are negatively correlated across environments have a higher overall fitness due to the reduction in their variance in fitness through the negative correlation. When a large number of loci are considered, they naturally fall into correlation groupings which lead to an enhanced likelihood for polymorphism over that predicted by single-locus theory.     

Remarks on the Evolutionary Effect of Natural Selection

The so-called "Fundamental Theorem of Natural Selection", that the mean fitness of a population increases with time under natural selection, is known not to be true, as a mathematical theorem, when fitnesses depend on more than one locus. Although this observation may not have particular biological relevance, (so that mean fitness may well increase in the great majority of interesting situations), it does suggest that it is of interest to find an evolutionary result which is correct as a mathematical theorem, no matter how many loci are involved. The aim of the present note is to prove an evolutionary theorem relating to the variance in fitness, rather than the mean: this theorem is true for an arbitrary number of loci, as well as for arbitrary (fixed) fitness parameters and arbitrary linkage between loci. Connections are briefly discussed between this theorem and the principle of quasi-linkage equilibrium.     

The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa

Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.     

Deducing implications of fitness maximization when a trade-off exists among alternative currencies

While the theory of natural selection posits that those behaviorsmaximizing reproductive success ("fitness") tend to survive,behavioral ecologists more frequently explain observed behaviorsas maximizing some "currency" on which fitness depends. In thecase of optimal foraging theory, for example, the currency isthe long-term rate of energy intake. This currency approachis adopted because little is known about the form of the fitnessfunction itself. A weakness of the approach is that reproductivesuccess often depends on more than one currency and behaviorswhich augment one currency may reduce another. We explain howto deduce from the hypothesis of fitness maximization testablequalitative and quantitative predictions about behavior whensuch trade-offs exist among currencies and little is known aboutthe fitness function. The methodology we describe is centralto microeconomic theory, and its usefulness explains the centralrole accorded "efficiency conditions" in that theory. We expoundthe approach entirely in terms of two biological examples: apreliminary example involving flower replacement by a perennialand a more elaborate one involving over-winter hoarding by afemale mammal.     

The evolutionary consequences of niche construction: a theoretical investigation using two-locus theory

This paper addresses the joint evolution of environment-altering (niche constructing) traits, and traits whose fitness depends on alterable sources of natural selection in environments. We explore the evolutionary consequences of this niche construction using a two-locus population genetic model. The novel conclusions are that niche construction can (1) cause evolutionary inertia and momentum, (2) lead to the fixation of otherwise deleterious alleles, (3) support stable polymorphisms where none are expected, (4) eliminate what would otherwise be stable polymorphisms, and (5) influence disequilibrium. The results suggest that the changes that organisms bring about in their niche can themselves be an important source of natural selection pressures, and imply that evolution may proceed in cycles of selection and niche construction.     

The evolution of premature reproductive senescence and menopause in human females

Reproductive senescence in human females takes place long before other body functions senesce. This fact presents an evolutionary dilemma since continued reproduction should generally be favored by natural selection. Two commonly proposed hypotheses to account for human menopause are (a) a recent increase in the human lifespan and (b) a switch to investment in close kin rather than direct reproduction. No support is found for the proposition that human lifespans have only recently increased. Data from Ache hunter-gatherers are used to test the kin selection hypothesis. Ache data do not support the proposition that females can gain greater fitness benefits in old age by helping kin rather than continuing to reproduce. Nevertheless, one crucial parameter in the model, when adjusted to the highest value within the measured 95% confidence interval, would lead to the evolution of reproductive senescence at about 53 years of age. Further investigation is necessary to determine whether the kin selection hypothesis of menopause can account for its current maintenance in most populations.     

Fisher’s fundamental theorem of inclusive fitness and the change in fitness due to natural selection when conspecifics interact

Competition and cooperation is fundamental to evolution by natural selection, both in animals and plants. Here, I investigate the consequences of such interactions for response in fitness due to natural selection. I provide quantitative genetic expressions for heritable variance and response in fitness due to natural selection when conspecifics interact. Results show that interactions among conspecifics generate extra heritable variance in fitness, and that interacting with kin is the key to evolutionary success because it translates the extra heritable variance into response in fitness. This work also unifies Fisher’s fundamental theorem of natural selection (FTNS) and Hamilton’s inclusive fitness (IF). The FTNS implies that natural selection maximizes fitness, whereas Hamilton proposed maximization of IF. This work shows that the FTNS describes the increase in IF, rather than direct fitness, at a rate equal to the additive genetic variance in fitness. Thus, Hamilton’s IF and Fisher’s FTNS both describe the maximization of IF.     

Modeling Complex Phenotypes: Generalized Linear Models Using Spectrogram Predictors of Animal Communication Signals

Summary A major goal of evolutionary biology is to understand the dynamics of natural selection within populations. The strength and direction of selection can be described by regressing relative fitness measurements on organismal traits of ecological significance. However, many important evolutionary characteristics of organisms are complex, and have correspondingly complex relationships to fitness. Secondary sexual characteristics such as mating displays are prime examples of complex traits with important consequences for reproductive success. Typically, researchers atomize sexual traits such as mating signals into a set of measurements including pitch and duration, in order to include them in a statistical analysis. However, these researcher‐defined measurements are unlikely to capture all of the relevant phenotypic variation, especially when the sources of selection are incompletely known. In order to accommodate this complexity we propose a Bayesian dimension‐reduced spectrogram generalized linear model that directly incorporates representations of the entire phenotype (one‐dimensional acoustic signal) into the model as a predictor while accounting for multiple sources of uncertainty. The first stage of dimension reduction is achieved by treating the spectrogram as an “image” and finding its corresponding empirical orthogonal functions. Subsequently, further dimension reduction is accomplished through model selection using stochastic search variable selection. Thus, the model we develop characterizes key aspects of the acoustic signal that influence sexual selection while alleviating the need to extract higher‐level signal traits a priori. This facet of our approach is fundamental and has the potential to provide additional biological insight, as is illustrated in our analysis.     

Distributions of beneficial fitness effects in RNA

Beneficial mutations are the driving force of evolution by natural selection. Yet, relatively little is known about the distribution of the fitness effects of beneficial mutations in populations. Recent work of Gillespie and Orr suggested some of the first generalizations for the distributions of beneficial fitness effects and, surprisingly, they depend only weakly on biological details. In particular, the theory suggests that beneficial mutations obey an exponential distribution of fitness effects, with the same exponential parameter across different regions of genotype space, provided only that few possible beneficial mutations are available to that genotype. Here we tested this hypothesis with a quasi-empirical model of RNA evolution in which fitness is based on the secondary structures of molecules and their thermodynamic stabilities. The fitnesses of randomly selected genotypes appeared to follow a Gumbel-type distribution and thus conform to a basic assumption of adaptation theory. However, the observed distributions of beneficial fitness effects conflict with specific predictions of the theory. In particular, the distributions of beneficial fitness effects appeared exponential only when the vast majority of small-effect beneficial mutations were ignored. Additionally, the distribution of beneficial fitness effects varied with the fitness of the parent genotype. We believe that correlation of the fitness values among similar genotypes is likely the cause of the departure from the predictions of recent adaptation theory. Although in conflict with the current theory, these results suggest that more complex statistical generalizations about beneficial mutations may be possible.     

An optimizing principle of natural selection in evolutionary population genetics

This paper brings together two themes in evolutionary population genetics theory. The first concerns Fisher's Fundamental Theorem of Natural Selection: a recent interpretation of this theorem claims that it is an exact result, relating to the so-called "partial" increase in mean fitness. The second theme concerns the desire to find an optimality principle in genetic evolution. Such a principle is found here: of all gene frequency changes which lead to the same partial increase in mean fitness as the natural selection gene frequency changes, the natural selection values minimize a generalized distance measure between parent and daughter generation gene frequency values.     

Molecular spandrels: tests of adaptation at the genetic level

Although much progress has been made in identifying the genes (and, in rare cases, mutations) that contribute to phenotypic variation, less is known about the effects that these genes have on fitness. Nonetheless, genes are commonly labelled as 'adaptive' if an allele has been shown to affect a phenotype with known or suspected functional importance or if patterns of nucleotide variation at the locus are consistent with positive selection. In these cases, the 'adaptive' designation may be premature and may lead to incorrect conclusions about the relationships between gene function and fitness. Experiments to test targets and agents of natural selection within a genomic context are necessary for identifying the adaptive consequences of individual alleles.     

Allozymes and fitness: Evolution of a problem

It was expected that studies of electrophoretic variability in natural populations would resolve longstanding controversies concerning the form of natural selection and its effect on genetic variance in fitness. Recent studies of fitness components for allozymes in E. coli and Drosophila, where genetic backgrounds have been rigidly controlled, and experiments designed to detect small selection coefficients, suggest that selection is much weaker than earlier investigations would indicate. However, perturbing the metabolic background associated with specific loci often allows functional differences to be amplified to an experimentally measurable level. Frequencies of null activity variants in natural populations indicate that the fitness consequences of reduced activity in heterozygoles are probably very small. These results are supported by recent theoretical considerations suggesting that the activity variation associated with electrophoretic variation will have little effect on overall flux in many pathways.     

Altruism and organism: disentangling the themes of multilevel selection theory

The evolution of groups into adaptive units, similar to single organisms in the coordination of their parts, is one major theme of multilevel selection theory. Another major theme is the evolution of altruistic behaviors that benefit others at the expense of self. These themes are often assumed to be strongly linked, such that altruism is required for group-level adaptation. Multilevel selection theory reveals a more complex relationship between the themes of altruism and organism. Adaptation at every level of the biological hierarchy requires a corresponding process of natural selection, which includes the fundamental ingredients of phenotypic variation, heritability, and fitness consequences. These ingredients can exist for many kinds of groups and do not require the extreme genetic variation among groups that is usually associated with the evolution of altruism. Thus, it is reasonable to expect higher-level units to evolve into adaptive units with respect to specific traits, even when their members are not genealogically related and do not behave in ways that are obviously altruistic. As one example, the concept of a group mind, which has been well documented in the social insects, may be applicable to other species.     

Natural selection on body size is mediated by multiple interacting factors: a comparison of beetle populations varying naturally and experimentally in body size

Body size varies considerably among species and among populations within species, exhibiting many repeatable patterns. However, which sources of selection generate geographic patterns, and which components of fitness mediate evolution of body size, are not well understood. For many animals, resource quality and intraspecific competition may mediate selection on body size producing large-scale geographic patterns. In two sequential experiments, we examine how variation in larval competition and resource quality (seed size) affects the fitness consequences of variation in body size in a scramble-competing seed-feeding beetle, Stator limbatus. Specifically, we compared fitness components among three natural populations of S. limbatus that vary in body size, and then among three lineages of beetles derived from a single base population artificially selected to vary in size, all reared on three sizes of seeds at variable larval density. The effects of larval competition and seed size on larval survival and development time were similar for larger versus smaller beetles. However, larger-bodied beetles suffered a greater reduction in adult body mass with decreasing seed size and increasing larval density; the relative advantage of being large decreased with decreasing seed size and increasing larval density. There were highly significant interactions between the effects of seed size and larval density on body size, and a significant three-way interaction (population-by-density-by-seed size), indicating that environmental effects on the fitness consequences of being large are nonadditive. Our study demonstrates how multiple ecological variables (resource availability and resource competition) interact to affect organismal fitness components, and that such interactions can mediate natural selection on body size. Studying individual factors influencing selection on body size may lead to misleading results given the potential for nonlinear interactions among selective agents.     

Cultural transmission and the evolution of human behaviour: a general approach based on the Price equation

Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes.     

Grafen,the Price equations,fitness maximization,optimisation and the fundamental theorem of natural selection

This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory.     

Mirror imagery and biological selection

Lake Tanganiyka has lefty and righty cichlid fish that show there can be natural selection for a trait over its mirror image counterpart.This raises the question ‘Can there be biological selection of a whole organism over its mirror image counterpart?’ That is, could the fitness of a fish be altered by simply changing it into its own enantaniomorph? My answer is no. I present Flatlander thought experiment to demonstrate that mirror imagecounterparts are duplicates because they only differ in how they happen to be oriented in space. The counterparts have the same intrinsic properties and are in the same environment,so there can be no difference in fitness.     

Formalizing Darwinism and inclusive fitness theory

Inclusive fitness maximization is a basic building block for biological contributions to any theory of the evolution of society. There is a view in mathematical population genetics that nothing is caused to be maximized in the process of natural selection, but this is explained as arising from a misunderstanding about the meaning of fitness maximization. Current theoretical work on inclusive fitness is discussed, with emphasis on the author''s ‘formal Darwinism project’. Generally, favourable conclusions are drawn about the validity of assuming fitness maximization, but the need for continuing work is emphasized, along with the possibility that substantive exceptions may be uncovered. The formal Darwinism project aims more ambitiously to represent in a formal mathematical framework the central point of Darwin''s Origin of Species, that the mechanical processes of inheritance and reproduction can give rise to the appearance of design, and it is a fitting ambition in Darwin''s bicentenary year to capture his most profound discovery in the lingua franca of science.     

Genomic imprinting and the units of adaptation

Two guiding principles identify which biological entities are able to evolve adaptations. Williams'' principle holds that, in order for an entity to evolve adaptations, there must be selection between such entities. Maynard Smith''s principle holds that, in order for an entity to evolve adaptations, selection within such entities must be absent or negligible. However, although the kinship theory of genomic imprinting suggests that parent-of-origin-specific gene expression evolves as a consequence of natural selection acting between—rather than within—individuals, it evades adaptive interpretation at the individual level and is instead viewed as an outcome of an intragenomic conflict of interest between an individual''s genes. Here, I formalize the idea that natural selection drives intragenomic conflicts of interest between genes originating from different parents. Specifically, I establish mathematical links between the dynamics of natural selection and the idea of the gene as an intentional, inclusive-fitness-maximizing agent, and I clarify the role that information about parent of origin plays in mediating conflicts of interest between genes residing in the same genome. These results highlight that the suppression of divisive information may be as important as the suppression of lower levels of selection in maintaining the integrity of units of adaptation.