Joint phenotypes,evolutionary conflict and the fundamental theorem of natural selection

Multiple organisms can sometimes affect a common phenotype. For example, the portion of a leaf eaten by an insect is a joint phenotype of the plant and insect and the amount of food obtained by an offspring can be a joint trait with its mother. Here, I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species. Selective conflict between the interactants occurs when selection takes opposite signs on the joint phenotype. The mean fitness of a population changes not just through its own genetic variance but also through the genetic variance for its fitness that resides in other species, an update of Fisher''s fundamental theorem of natural selection. Some similar results, using inclusive fitness, apply to within-species interactions. The models provide a framework for understanding evolutionary conflicts at all levels.     

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.     

Fisher'S geometrical model of fitness landscape and variance in fitness within a changing environment

The fitness of an individual can be simply defined as the number of its offspring in the next generation. However, it is not well understood how selection on the phenotype determines fitness. In accordance with Fisher's fundamental theorem, fitness should have no or very little genetic variance, whereas empirical data suggest that is not the case. To bridge these knowledge gaps, we follow Fisher's geometrical model and assume that fitness is determined by multivariate stabilizing selection toward an optimum that may vary among generations. We assume random mating, free recombination, additive genes, and uncorrelated stabilizing selection and mutational effects on traits. In a constant environment, we find that genetic variance in fitness under mutation-selection balance is a U-shaped function of the number of traits (i.e., of the so-called "organismal complexity"). Because the variance can be high if the organism is of either low or high complexity, this suggests that complexity has little direct costs. Under a temporally varying optimum, genetic variance increases relative to a constant optimum and increasingly so when the mutation rate is small. Therefore, mutation and changing environment together can maintain high genetic variance. These results therefore lend support to Fisher's geometric model of a fitness landscape.     

Fundamental theorem of natural selection and frequency-dependent selection: analysis of the matrix game diploid model

Following Ewens' interpretation about Fisher's fundamental theorem of natural selection, the matrix game model for diploid populations undergoing non-overlapping, discrete generations is investigated. The total genetic variance is decomposed and it is shown that the partial change in the mean fitness, which is equal to the additive genetic variance over the mean fitness, can be thought of as a change due only to the partial changes in the phenotypic frequencies.     

ON THE LOW HERITABILITY OF LIFE-HISTORY TRAITS

Life-history traits such as longevity and fecundity often show low heritability. This is usually interpreted in terms of Fisher's fundamental theorem to mean that populations are near evolutionary equilibrium and genetic variance in total fitness is low. We develop the causal relationship between metric traits and life-history traits to show that a life-history trait is expected to have a low heritability whether or not the population is at equilibrium. This is because it is subject to all the environmental variation in the metric traits that affect it plus additional environmental variation. There is no simple prediction regarding levels of additive genetic variance in life-history traits, which may be high at equilibrium. Several other patterns in the inheritance of life-history traits are readily predicted from the causal model. These include the strength of genetic correlations between life-history traits, levels of nonadditive genetic variance, and the inevitability of genotype-environment interaction.     

Niche construction and the environmental term of the price equation: How natural selection changes when organisms alter their environments

Organisms construct their own environments and phenotypes through the adaptive processes of habitat choice, habitat construction, and phenotypic plasticity. We examine how these processes affect the dynamics of mean fitness change through the environmental change term of the Price Equation. This tends to be ignored in evolutionary theory, owing to the emphasis on the first term describing the effect of natural selection on mean fitness (the additive genetic variance for fitness of Fisher's Fundamental Theorem). Using population genetic models and the Price Equation, we show how adaptive niche constructing traits favorably alter the distribution of environments that organisms encounter and thereby increase population mean fitness. Because niche-constructing traits increase the frequency of higher-fitness environments, selection favors their evolution. Furthermore, their alteration of the actual or experienced environmental distribution creates selective feedback between niche constructing traits and other traits, especially those with genotype-by-environment interaction for fitness. By altering the distribution of experienced environments, niche constructing traits can increase the additive genetic variance for such traits. This effect accelerates the process of overall adaption to the niche-constructed environmental distribution and can contribute to the rapid refinement of alternative phenotypic adaptations to different environments. Our findings suggest that evolutionary biologists revisit and reevaluate the environmental term of the Price Equation: owing to adaptive niche construction, it contributes directly to positive change in mean fitness; its magnitude can be comparable to that of natural selection; and, when there is fitness G × E, it increases the additive genetic variance for fitness, the much-celebrated first term.     

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.     

Perspective: Here's to Fisher,additive genetic variance,and the fundamental theorem of natural selection

Fisher's fundamental theorem of natural selection, that the rate of change of fitness is given by the additive genetic variance of fitness, has generated much discussion since its appearance in 1930. Fisher tried to capture in the formula the change in population fitness attributable to changes of allele frequencies, when all else is not included. Lessard's formulation comes closest to Fisher's intention, as well as this can be judged. Additional terms can be added to account for other changes. The "theorem" as stated by Fisher is not exact, and therefore not a theorem, but it does encapsulate a great deal of evolutionary meaning in a simple statement. I also discuss the effectiveness of reproductive-value weighting and the theorem in integrated form. Finally, an optimum principle, analogous to least action and Hamilton's principle in physics, is discussed.     

Natural Selection and Age-Structured Populations

This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reproductive potential. This result is an information theoretic analog of Fisher''s fundamental theorem of natural selection.     

Evolution of total net fitness in thermal lines: Drosophila subobscura likes it 'warm'

Fisher's fundamental theorem states that heritable variation for net fitness sets a limit to the rate of response to natural selection. How will temperate (i.e. cold‐tolerant) species cope with contemporary rapid global warming? Using three‐fold replicated lines of Drosophila subobscura that had been allowed to evolve for 4 years (between 32 and 59 generations) at 13 °C (cold), 18 °C (the supposed optimum temperature), and 22 °C (warm) I assess here how net fitness changes according to thermal environments. Net fitness was estimated following the classical approach in population genetics of competing over a number of generation in outbred experimental populations multiple wild‐type O chromosomes (homologous to arm 3R in D. melanogaster) independently derived from each base thermal stock in an otherwise homogeneous genetic background against a balancer chromosome. Warm‐adapted populations (‘warm‐adapted O chromosomes’) performed comparatively well at all tested temperatures. However, net fitness was severely reduced in cold‐adapted populations when transferred to warmer conditions. It seems, therefore, that thermal fitness breath for D. subobscura flies is positively associated to temperature. These findings are discussed in relation to the fast world‐wide clinal shifts in the frequency of genetic markers correlated with current climate change.     

Natural selection and the maximization of fitness

The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. Here I critically appraise the prospects for reconciliation. I first distinguish four varieties of fitness maximization. I then examine two recent developments that may appear to vindicate at least one of these varieties. The first is the ‘new’ interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions. The second is the Formal Darwinism project, which forges links between gene frequency change and optimal strategy choice. In both cases, I argue that the results fail to establish a biologically significant maximization principle. I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. A more promising approach may be to find maximization principles that apply conditionally and to show that the conditions were satisfied in the evolution of particular traits.     

LONG-TERM EXPERIMENTAL EVOLUTION IN ESCHERICHIA COLI. VII. MECHANISMS MAINTAINING GENETIC VARIABILITY WITHIN POPULATIONS

Six replicate populations of the bacterium Escherichia coli were propagated for more than 10,000 generations in a defined environment. We sought to quantify the variation among clones within these populations with respect to their relative fitness, and to evaluate the roles of three distinct population genetic processes in maintaining this variation. On average, a pair of clones from the same population differed from one another in their relative fitness by approximately 4%. This within-population variation was small compared with the average fitness gain relative to the common ancestor, but it was statistically significant. According to one hypothesis, the variation in fitness is transient and reflects the ongoing substitution of beneficial alleles. We used Fisher's fundamental theorem to compare the observed rate of each population's change in mean fitness with the extent of variation for fitness within that population, but we failed to discern any correspondence between these quantities. A second hypothesis supposes that the variation in fitness is maintained by recurrent deleterious mutations that give rise to a mutation-selection balance. To test this hypothesis, we made use of the fact that two of the six replicate populations had evolved mutator phenotypes, which gave them a genomic mutation rate approximately 100-fold higher than that of the other populations. There was a marginally significant correlation between a population's mutation rate and the extent of its within-population variance for fitness, but this correlation was driven by only one population (whereas two of the populations had elevated mutation rates). Under a third hypothesis, this variation is maintained by frequency-dependent selection, whereby genotypes have an advantage when they are rare relative to when they are common. In all six populations, clones were more fit, on average, when they were rare than when they were common, although the magnitude of the advantage when rare was usually small (~1% in five populations and ~5% in the other). These three hypotheses are not mutually exclusive, but frequency-dependent selection appears to be the primary force maintaining the fitness variation within these experimental populations.     

Joint effects of pleiotropic selection and stabilizing selection on the maintenance of quantitative genetic variation at mutation-selection balance

In quantitative genetics, there are two basic "conflicting" observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (V(G)) and the observed strength of total stabilizing selection (V(s,t)) are analyzed with a rare-alleles model. Both kinds of selection reduce V(G) but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, V(G) increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, V(G) decreases with increasing leptokurtosis of mutational effects on the trait. The V(G) and V(s,t) are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.     

THE EVOLUTION OF FITNESS

In every generation, the mean fitness of populations increases because of natural selection and decreases because of mutations and changes in the environment. The magnitudes of these effects can be measured in two ways: either directly, by comparing the fitnesses of selected and unselected populations, or indirectly, by measuring the additive variance of fitness and making use of the fundamental theorem of natural selection. The available data suggest that the amount by which natural selection increases mean fitness each generation (or degradation decreases mean fitness) will usually be between 0.1% and 30%; more tentatively, it is suggested that values will typically fall between 1% and 10%. These values can be used to set an upper limit of 5%–10% on the genetic advantage of mate choice.     

GENETIC AND ENVIRONMENTAL VARIATION IN LIFE-HISTORY TRAITS OF A MONOCARPIC PERENNIAL: A DECADE-LONG FIELD EXPERIMENT

Directional and stabilizing selection tend to deplete additive genetic variance. On the other hand, genetic variance in traits related to fitness could be retained through polygenic mutation, spatially varying selection, genotype-environment interaction, or antagonistic pleiotropy. Most estimates of genetic variance in fitness-related traits have come from laboratory studies, with few estimates of heritability made under natural conditions, particularly for longer lived organisms. Here I estimated additive genetic variance in life-history characters of a monocarpic herb, Ipomopsis aggregata, that lives for up to a decade. Experimental crosses yielded 229 full-sibships nested within 32 paternal half-sibships. More than 5000 offspring were planted as seeds into natural field sites and were followed in most cases through their entire life cycle. Survival showed substantial additive genetic variance (genetic coefficient of variation ≈ 54%). Small differences at seedling emergence were magnified over time, such that the genetic variability in survival was only detectable by tracking the success of offspring for several years starting from seed. In contrast to survival, reproductive traits such as flower number, seeds per flower, and age at flowering showed little or no genetic variability. Despite relatively high levels of additive genetic variation for some life-history characters, high environmental variance in survival resulted in very low heritabilities (0–9%) for all of these characters. Maternal effects were evident in seed mass and remained strong throughout the lengthy vegetative period. No negative genetic correlations between major components of female fitness were detected. Mean corolla width for a paternal family was, however, negatively correlated with the finite rate of increase based on female fitness. That negative correlation could help to maintain additive genetic variance in the face of strong selection through male function for wide corollas.     

The nature of nurture in a wild mammal's fitness

Genetic variation in fitness is required for the adaptive evolution of any trait but natural selection is thought to erode genetic variance in fitness. This paradox has motivated the search for mechanisms that might maintain a population''s adaptive potential. Mothers make many contributions to the attributes of their developing offspring and these maternal effects can influence responses to natural selection if maternal effects are themselves heritable. Maternal genetic effects (MGEs) on fitness might, therefore, represent an underappreciated source of adaptive potential in wild populations. Here we used two decades of data from a pedigreed wild population of North American red squirrels to show that MGEs on offspring fitness increased the population''s evolvability by over two orders of magnitude relative to expectations from direct genetic effects alone. MGEs are predicted to maintain more variation than direct genetic effects in the face of selection, but we also found evidence of maternal effect trade-offs. Mothers that raised high-fitness offspring in one environment raised low-fitness offspring in another environment. Such a fitness trade-off is expected to maintain maternal genetic variation in fitness, which provided additional capacity for adaptive evolution beyond that provided by direct genetic effects on fitness.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Simultaneous Estimation of Additive and Mutational Genetic Variance in an Outbred Population of Drosophila serrata

How new mutations contribute to genetic variation is a key question in biology. Although the evolutionary fate of an allele is largely determined by its heterozygous effect, most estimates of mutational variance and mutational effects derive from highly inbred lines, where new mutations are present in homozygous form. In an attempt to overcome this limitation, middle-class neighborhood (MCN) experiments have been used to assess the fitness effect of new mutations in heterozygous form. However, because MCN populations harbor substantial standing genetic variance, estimates of mutational variance have not typically been available from such experiments. Here we employ a modification of the animal model to analyze data from 22 generations of Drosophila serrata bred in an MCN design. Mutational heritability, measured for eight cuticular hydrocarbons, 10 wing-shape traits, and wing size in this outbred genetic background, ranged from 0.0006 to 0.006 (with one exception), a similar range to that reported from studies employing inbred lines. Simultaneously partitioning the additive and mutational variance in the same outbred population allowed us to quantitatively test the ability of mutation-selection balance models to explain the observed levels of additive and mutational genetic variance. The Gaussian allelic approximation and house-of-cards models, which assume real stabilizing selection on single traits, both overestimated the genetic variance maintained at equilibrium, but the house-of-cards model was a closer fit to the data. This analytical approach has the potential to be broadly applied, expanding our understanding of the dynamics of genetic variance in natural populations.