Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Predicting population genetic change in an autocorrelated random environment: Insights from a large automated experiment

Most natural environments exhibit a substantial component of random variation, with a degree of temporal autocorrelation that defines the color of environmental noise. Such environmental fluctuations cause random fluctuations in natural selection, affecting the predictability of evolution. But despite long-standing theoretical interest in population genetics in stochastic environments, there is a dearth of empirical estimation of underlying parameters of this theory. More importantly, it is still an open question whether evolution in fluctuating environments can be predicted indirectly using simpler measures, which combine environmental time series with population estimates in constant environments. Here we address these questions by using an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga Dunaliella salina to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequencies of two competing strains through amplicon sequencing of nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (determined by their variance), but also their predictability (determined by their autocorrelation), had large impacts on the average selection coefficient. The variance in frequency change, which quantifies randomness in population genetics, was substantially higher in a fluctuating environment. The reaction norm of selection coefficients against constant salinity yielded accurate predictions for the mean selection coefficient in a fluctuating environment. This selection reaction norm was in turn well predicted by environmental tolerance curves, with population growth rate against salinity. However, both the selection reaction norm and tolerance curves underestimated the variance in selection caused by random environmental fluctuations. Overall, our results provide exceptional insights into the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.     

An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment

The evolution of population dynamics in a stochastic environment is analysed under a general form of density-dependence with genetic variation in r and K, the intrinsic rate of increase and carrying capacity in the average environment, and in σ_e², the environmental variance of population growth rate. The continuous-time model assumes a large population size and a stationary distribution of environments with no autocorrelation. For a given population density, N, and genotype frequency, p, the expected selection gradient is always towards an increased population growth rate, and the expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Long-term evolution maximizes the expected value of the density-dependence function, averaged over the stationary distribution of N. In the θ-logistic model, where density dependence of population growth is a function of N^θ, long-term evolution maximizes E[N^θ]=[1−σ_e²/(2r)]K^θ. While σ_e² is always selected to decrease, r and K are always selected to increase, implying a genetic trade-off among them. By contrast, given the other parameters, θ has an intermediate optimum between 1.781 and 2 corresponding to the limits of high or low stochasticity.     

On measuring selection in experimental evolution

Distributions of mutation fitness effects from evolution experiments are available in an increasing number of species, opening the way for a vast array of applications in evolutionary biology. However, comparison of estimated distributions among studies is hampered by inconsistencies in the definitions of fitness effects and selection coefficients. In particular, the use of ratios of Malthusian growth rates as ‘relative fitnesses’ leads to wrong inference of the strength of selection. Scaling Malthusian fitness by the generation time may help overcome this shortcoming, and allow accurate comparison of selection coefficients across species. For species reproducing by binary fission (neglecting cellular death), ln2 can be used as a correction factor, but in general, the growth rate and generation time of the wild-type should be provided in studies reporting distribution of mutation fitness effects. I also discuss how density and frequency dependence of population growth affect selection and its measurement in evolution experiments.     

Does environmental stochasticity matter? Analysis of red deer life-histories on Rum

Summary Most life-history theory assumes that short-term variation in an organism's environment does not affect the survivorships and fecundities of the organisms. This assumption is rarely met. Here we investigate the population and evolutionary biology of red deer,Cervus elephas, to see if relaxation of this assumption is likely to make significant differences to the predicted evolutionary biology of this species. To do this we used 21 years of data from a population of deer on Rum, Western Isles, Scotland. Population growth rates in a stochastic environment were estimated using Tuljapurkar's small noise approximation, confirmed by bootstrap simulation. Numerical differentiation was used to see if the selection pressures (i.e. sensitivities of population growth rate to changes in the vital rates) differ between the stochastic and deterministic cases. The data also allow the costs of reproduction to be estimated. These costs, incorporated as trade-offs into the sensitivity analysis, allow investigation of evolutionary benefits of different life-history tactics. Environmentally induced stochastic variation in the red deer vital rates causes a slight reduction ( 1%) in the predicted population growth rate and has little impact on the estimated selection pressures on the deer's life-history. We thus conclude that, even though density-independent stochastic effects on the population are marked, the deer's fitness is not markedly affected by these and they are adapted to the average conditions they experience. However, the selected life-history is sensitive to the trade-offs between current fecundity, survivorship and future fecundity and it is likely that the environmental variance will affect these trade-offs and, thus, affect the life-history favoured by selection. We also show that the current average life-history is non-optimal and suggest this is a result of selection pressures exerted by culling and predation, now much reduced. As the use of stochastic or deterministic methods provide similar estimates in this case, the use of the latter is justified. Thus,r (the annual per capita rate of population growth) is an appropriate measure of fitness in a population with stochastic numerical fluctuations. In a population of constant size lifetime reproductive success is the obvious measure of fitness to use.     

Life histories as adaptive strategies

Optimal control theory is used to produce a general model of life history evolution in a stationary environment. Several disparate trends in current theorizing on life histories are thereby unified. An optimal life history (OLH) is defined as one which maximizes individual fitness (the Malthusian parameter in density-independent populations, the carrying capacity in density-dependent ones). Since the components of fitness depend on the phenotype, the search for an OLH is accomplished in phenotypic space. The optimization is controlled by apportioning the energy obtained at any age between conflicting processes of growth, survival and reproduction. The methods of dynamic optimization which pertain to this problem are reviewed briefly, and its results interpreted biologically. Of these, Pontryagin's method is selected and used to examine some simple models. This method leads one to define a dual variable matched to each phenotypic variable, the prospective value. This provides an indicator of the selective pressures acting at any age on a phenotypic feature to push it towards coincidence with the OLH. This also suggests that at ages in which these dual variables are low (i.e. late ages) there will be greater phenotypic variability around the OLH in any population. The problem of the optimal distribution of reproductive effort over the life history is discussed as well.     

Defining fitness in evolutionary models

The analysis of evolutionary models requires an appropriate definition for fitness. In this paper, I review such definitions in relation to the five major dimensions by which models may be described, namely (i) finite versus infinite (or very large) population size, (ii) type of environment (constant, fixed length, temporally stochastic, temporally predictable, spatially stochastic, spatially predictable and social environment), (iii) density-independent or density-dependent, (iv) inherent population dynamics (equilibrium, cyclical and chaotic), and (v) frequency-dependent or independent. In simple models, the Malthusian parameter ‘r’ or the net reproductive rate R ₀ may be satisfactory, but once density-dependence or complex population dynamics is introduced the invasion exponent should be used. Defining fitness in a social environment or when there is frequency-dependence requires special consideration.     

Selection in a fluctuating environment leads to decreased genetic variation and facilitates the evolution of phenotypic plasticity

Changes in the environment are expected to induce changes in the quantitative genetic variation, which influences the ability of a population to adapt to environmental change. Furthermore, environmental changes are not constant in time, but fluctuate. Here, we investigate the effect of rapid, continuous and/or fluctuating temperature changes in the seed beetle Callosobruchus maculatus, using an evolution experiment followed by a split-brood experiment. In line with expectations, individuals responded in a plastic way and had an overall higher potential to respond to selection after a rapid change in the environment. After selection in an environment with increasing temperature, plasticity remained unchanged (or decreased) and environmental variation decreased, especially when fluctuations were added; these results were unexpected. As expected, the genetic variation decreased after fluctuating selection. Our results suggest that fluctuations in the environment have major impact on the response of a population to environmental change; in a highly variable environment with low predictability, a plastic response might not be beneficial and the response is genetically and environmentally canalized resulting in a low potential to respond to selection and low environmental sensitivity. Interestingly, we found greater variation for phenotypic plasticity after selection, suggesting that the potential for plasticity to evolve is facilitated after exposure to environmental fluctuations. Our study highlights that environmental fluctuations should be considered when investigating the response of a population to environmental change.     

Environmental heterogeneity generates fluctuating selection on a secondary sexual trait

In any population in which resources are limiting, the allocation of resources toward increased reproductive success may generate costs to survival [1-8]. The relationship between a sexually selected trait and fitness will therefore represent a balance between its relative associations with fecundity versus viability [3, 6, 7]. Because the risk of mortality in a population is likely to be heavily determined by ecological conditions, survival costs may vary as a function of the prevailing environment [7]. As a result, for populations experiencing heterogeneous ecological conditions, there may not be a single optimal level of allocation toward reproduction versus survival [9]. Here, we show that early viability and fecundity selection act in opposing directions on a secondary sexual trait and that their relative magnitude depends upon ecological conditions, generating fluctuating selection. In a wild population of Soay sheep (Ovis aries), phenotypic and genetic associations between male horn growth and lifetime reproductive success were positive under good environmental conditions (because of increased breeding success) and negative under poor environmental conditions (because of reduced survival). In an unpredictable environment, high allocation to early horn growth is a gamble that will only pay off if ensuing conditions are favorable. Such fluctuating selection may play an important role in preventing the erosion of genetic variance in secondary sexual traits.     

A macro-equation of natural selection

The deterministic dynamical theory of biological populations, developed widely on the basis of the classical work of Fisher and Volterra, in most cases deals with characteristics which cannot be measured directly, e.g. frequencies of various genotypes within a population, their fitness values, competition coefficients, etc. Thus, a theory dealing with a small number of simple averaged macro-characteristics, easily accessible to a direct measurement, would be of great importance. The present paper contains an attempt to establish an equation contributing to such a would-be macrotheory. It is a relationship begween the average fitness of a population (the Malthusian growth parameter), the selective delay (a new concept, introduction in section 3) and the entropy of the equilibrium structure which the population tends to under the natural selection process. A possible method of checking the proposed relationship experimentally is indicated.     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

Darwinian fitness

The term Darwinian fitness refers to the capacity of a variant type to invade and displace the resident population in competition for available resources. Classical models of this dynamical process claim that competitive outcome is a deterministic event which is regulated by the population growth rate, called the Malthusian parameter. Recent analytic studies of the dynamics of competition in terms of diffusion processes show that growth rate predicts invasion success only in populations of infinite size. In populations of finite size, competitive outcome is a stochastic process--contingent on resource constraints--which is determined by the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates. This return rate, a measure of robustness or population stability, is analytically characterized by the demographic parameter, evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. This article appeals to computational and numerical methods to contrast the predictive power of the Malthusian and the entropic principles. The computational analysis rejects the Malthusian model and is consistent with of the entropic principle. These studies thus provide support for the general claim that entropy is the appropriate measure of Darwinian fitness and constitutes an evolutionary parameter with broad predictive and explanatory powers.     

Habitat selection and the value of information in heterogenous landscapes

Despite the wide usage of the term information in evolutionary ecology, there is no general treatise between fitness (i.e. density‐dependent population growth) and selection of the environment sensu lato. Here we 1) initiate the building of a quantitative framework with which to examine the relationship between information use in spatially heterogeneous landscapes and density‐dependent population growth, and 2) illustrate its utility by applying the framework to an existing model of breeding habitat selection. We begin by linking information, as a process of narrowing choice, to population growth/fitness. Second, we define a measure of a population's penalty of ignorance based on the Kullback–Leibler index that combines the contributions of resource selection (i.e. biased use of breeding sites) and density‐dependent depletion. Third, we quantify the extent to which environmental heterogeneity (i.e. mean and variance within a landscape) constrains sustainable population growth of unbiased agents. We call this the heterogeneity‐based fitness deficit, and combine this with population simulations to quantify the independent contribution of information‐use strategies to the total population growth rate. We further capitalize on this example to highlight the interactive effects of information between ecological scales when fear affects individual fitness through phenotypic plasticity. Informed breeding habitat selection moderates the demographic cost of fear commensurate with density‐dependent information use. Thus, future work should attempt to differentiate between phenotypic plasticity (i.e. acute fear) and demographic responses (i.e. chronic changes in population size). We conclude with a broader discussion of information in alternative contexts, and explore some evolutionary considerations for information use. We note how competition among individuals may constrain the information state among individuals, and the implications of this constraint under environmental change.     

Coinfecting parasites can modify fluctuating selection dynamics in host–parasite coevolution

Genetically specific interactions between hosts and parasites can lead to coevolutionary fluctuations in their genotype frequencies over time. Such fluctuating selection dynamics are, however, expected to occur only under specific circumstances (e.g., high fitness costs of infection to the hosts). The outcomes of host–parasite interactions are typically affected by environmental/ecological factors, which could modify coevolutionary dynamics. For instance, individual hosts are often infected with more than one parasite species and interactions between them can alter host and parasite performance. We examined the potential effects of coinfections by genetically specific (i.e., coevolving) and nonspecific (i.e., generalist) parasite species on fluctuating selection dynamics using numerical simulations. We modeled coevolution (a) when hosts are exposed to a single parasite species that must genetically match the host to infect, (b) when hosts are also exposed to a generalist parasite that increases fitness costs to the hosts, and (c) when coinfecting parasites compete for the shared host resources. Our results show that coinfections can enhance fluctuating selection dynamics when they increase fitness costs to the hosts. Under resource competition, coinfections can either enhance or suppress fluctuating selection dynamics, depending on the characteristics (i.e., fecundity, fitness costs induced to the hosts) of the interacting parasites.     

Reproductive Value and Fluctuating Selection in an Age-Structured Population

Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.THE evolutionary dynamics of age-structured populations were formalized by Charlesworth (1980, 1994) and Lande (1982) on the basis of earlier ideas of Fisher (1930, 1958), Medawar (1946, 1952), and Hamilton (1966), showing that the strength of selection on genes affecting the vital rates of survival or fecundity depends on their age of action (reviewed by de Jong 1994; Charlesworth 2000). Fisher defined the reproductive value of individuals of a given age as their expected contribution to future population growth, determined by the age-specific vital rates. This has the property that in a constant environment the total reproductive value in a population always increases at a constant rate. The total population size, however, undergoes transient fluctuations as the stable age distribution is approached, and the total population size only asymptotically approaches a constant growth rate (Caswell 2001).Environmental stochasticity creates continual fluctuations in age structure, producing temporal autocorrelation in population size and in allele frequencies, which seriously complicate demographic and evolutionary analyses. Fisher (1930, 1958, p. 35) suggested for analysis of genetic evolution that individuals should be weighted by their reproductive value to compensate for deviations from the stable age distribution. Here we apply this suggestion to study weak fluctuating selection in an age-structured population in a stochastic environment.One of the central conceptual paradigms of evolutionary biology was described by Wright (1932). His adaptive topography represents a population as a point on a surface of population mean fitness as a function of allele frequencies. Assuming weak selection, random mating, and loose linkage (implying approximate Hardy–Weinberg equilibrium within loci and linkage eqilibrium among loci), natural selection in a constant environment causes the population to evolve uphill of the mean fitness surface (Wright 1937, 1945, 1969; Arnold et al. 2001; Gavrilets 2004). Evolution by natural selection thus tends to increase the mean fitness of a population in a constant environment.Lande (2007, 2008) generalized Wright''s adaptive topography to a stochastic environment, allowing density-dependent population growth but assuming density-independent selection, showing that the expected evolution maximizes the long-run growth rate of the population at low density, . Here r is population growth rate at low density in the average environment and is the environmental variance in population growth rate among years, which are standard parameters in stochastic demography (Cohen 1977, 1979; Tuljapurkar 1982; Caswell 2001; Lande et al. 2003). In this model of stochastic evolution the adaptive topography describing the expected evolution is derived by expressing r and as functions of allele frequencies with parameters being the mean Malthusian fitnesses of the genotypes and their temporal variances and covariances. These results are based on diffusion approximations for the coupled stochastic processes of population size and allele frequencies in a fluctuating environment.Diffusion approximations are remarkably accurate for many problems in evolution and ecology (Crow and Kimura 1970; Lande et al. 2003). Because a diffusion process is subject to white noise with no temporal autocorrelation, the approximation is most accurate if the noise in the underlying biological process is approximately uncorrelated among years. Despite temporal autocorrelation in total population size produced by age-structure fluctuations, the stochastic demography of age-structured populations over timescales of a generation or more can nevertheless be accurately approximated by a diffusion process (Tuljapurkar 1982; Lande and Orzack 1988; Engen et al. 2005a, 2007). The success of the diffusion approximation for total population size occurs because the noise in the total reproductive value is nearly white, with no temporal autocorrelation to first order, and the log of total population size fluctuates around the log of reproductive value with a return time to equilibrium on the order of a few generations (Engen et al. 2007). Hence the diffusion approximation is well suited to describe the stochastic dynamics of total reproductive value as well as total population size.This article extends Lande''s (2008) model of fluctuating selection without age structure by deriving a diffusion approximation for the evolution of an age-structured population in a stochastic environment. Assuming weak selection at all ages, random mating, and a stationary distribution of environments with no temporal autocorrelation, we show that the main results of the model remain valid, provided that the model parameters are expressed in terms of means, variances, and covariances of age-specific vital rates and that allele frequencies are defined by weighting individuals of different age by their reproductive value, as suggested by Fisher (1930, 1958). We perform simulations to verify the accuracy of the diffusion approximation and outline statistical methods for estimating the expected selection acting on the reproductive value weighted allele frequency.     

Fixation probabilities depend on life history: fecundity, generation time and survival in a burst-death model

The burst-death model has been developed to describe the life history of organisms with variable generation times and a burst of a fixed number of offspring. The model also includes an optional constant clearance rate, such as washout from a chemostat, and the possibility of sustained periods of population growth followed by severe bottlenecks, as in serial passaging. In this model, a beneficial mutation can either increase the burst rate or the burst size, or reduce the clearance rate, thus increasing survival. In this article we examine the effects of these three possible mechanisms on both the Malthusian fitness and the fixation probability of the lineage. We find that equivalent relative increases in the burst rate or burst size confer equivalent increases in the Malthusian fitness of a lineage, whereas increasing survival typically has a more moderate effect on Malthusian fitness. In contrast, for beneficial mutations that confer the same increase in fitness, mutations that increase survival are the most likely to fix, followed by mutations that increase the burst rate. Mutations that increase the burst size are the least likely to fix. These results imply that mutant lineages with the highest Malthusian fitness are not, in many cases, the most likely to escape extinction.     

GENETIC CONSTRAINTS ON ADAPTATION TO A CHANGING ENVIRONMENT

Genetic correlations between traits can constrain responses to natural selection. To what extent such correlations limit adaptation depends on patterns of directional selection. I derive the expected rate of adaptation (or evolvability) under randomly changing selection gradients. When directional selection gradients have an arbitrary covariance matrix, the average rate of adaptation depends on genetic correlations between traits, contrary to the isotropic case investigated in previous studies. Adaptation may be faster on average with more genetic correlation between traits, if these traits are selected to change jointly more often than the average pair of traits. However, natural selection maximizes the long‐term fitness of a population, not necessarily its rate of adaptation. I therefore derive the average lag load caused by deviations of the mean phenotype from an optimum, under several forms of environmental changes typically experienced by natural populations, both stochastic and deterministic. Simple formulas are produced for how the G matrix affects long‐term fitness in these contexts, and I discuss how their parameters can be estimated empirically.     

Genomics of cellular proliferation in periodic environmental fluctuations

Living systems control cell growth dynamically by processing information from their environment. Although responses to a single environmental change have been intensively studied, little is known about how cells react to fluctuating conditions. Here, we address this question at the genomic scale by measuring the relative proliferation rate (fitness) of 3,568 yeast gene deletion mutants in out‐of‐equilibrium conditions: periodic oscillations between two environmental conditions. In periodic salt stress, fitness and its genetic variance largely depended on the oscillating period. Surprisingly, dozens of mutants displayed pronounced hyperproliferation under short stress periods, revealing unexpected controllers of growth under fast dynamics. We validated the implication of the high‐affinity cAMP phosphodiesterase and of a regulator of protein translocation to mitochondria in this group. Periodic oscillations of extracellular methionine, a factor unrelated to salinity, also altered fitness but to a lesser extent and for different genes. The results illustrate how natural selection acts on mutations in a dynamic environment, highlighting unsuspected genetic vulnerabilities to periodic stress in molecular processes that are conserved across all eukaryotes.     

The units of selection and measures of fitness

This paper presents a unified account of the properties of the measures, Malthusian parameter and entropy in predicting evolutionary change in populations of macromolecules, cells and individuals. The Malthusian parameter describes the intrinsic rate of increase of the population. The entropy describes the intrinsic variability in populations: it characterizes the variability in mutation and replication rates in populations of macromolecules; the rate of decay of synchrony in populations of cells; and the degree of iteroparity in populations of individuals. The Malthusian parameter determines ultimate population numbers: under constant environmental conditions, it is the rate of increase when equilibrium conditions are attained. Entropy determines population stability: the gain in the Malthusian parameter due to small fluctuations in the life-cycle variables is determined by entropy. These properties, which are valid for populations of macromolecules, cells and individuals, show that the Malthusian parameter and entropy act as complimentary fitness indices in understanding evolutionary change in populations.