Direct fitness or inclusive fitness: how shall we model kin selection?

Two standard mathematical formulations of kin-selection models can be found. Inclusive fitness is an actor-centred approach, which calculates the fitness effect on a number of recipients of the behaviour of a single actor. Direct fitness is a recipient-centred approach, which calculates the fitness effect on the recipient of the behaviour of a number of actors. Inclusive fitness offers us a powerful heuristic, of choosing behaviour to maximize fitness, but direct fitness can be mathematically easier to work with and has recently emerged as the preferred approach of theoreticians. In this paper, we explore the fundamental connection between these two approaches in both homogeneous and class-structured populations, and we show that under simple assumptions (mainly fair meiosis and weak selection) they provide equivalent formulations, which correspond to the predictions of Price's equation for allele frequency change. We use a couple of examples to highlight differences in their conception and formulation, and we briefly discuss a two-species example in which we have a class of 'actor' that is never a 'recipient', which the standard direct fitness method can handle but the usual inclusive fitness cannot.     

Evolution in alternating environments with tunable interlandscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, although understanding the effects of varying selection pressures remains challenging. Here, we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the interlandscape correlation, can either increase or decrease steady‐state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anticorrelated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub‐optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anticorrelated paired landscapes leads to ergodic‐like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady‐state fitness in comparison to single landscape evolution.     

Predation Determines Different Selective Pressure on Pea Aphid Host Races in a Complex Agricultural Mosaic

Field assessments were conducted to examine the interplay between host plant and predation in complex agricultural mosaic on pea aphid clover and alfalfa races. In one experiment, we examined the relative fitness on clover race (CR) and alfalfa race (AR) pea aphids on broad bean, red clover and alfalfa alone. But because clover is typically grown in a more complex agricultural mosaic with alfalfa and broad bean, a second experiment was conducted to assess the fitness consequences under predation in a more complex agricultural field setting that also included potential apparent competition with AR pea aphids. In a third experiment we tested for the effect of differential host race density on the fitness of the other host race mediated by a predator effect. CR pea aphids always had fitness losses when on broad bean (had lower fitness on broad bean relative to red clover) and fitness benefits when on red clover (higher fitness on red clover relative to broad bean), whether or not in apparent competition with alfalfa race aphids on bean and alfalfa. AR suffered fitness loss on both alfalfa and bean in apparent competition with CR on clover. Therefore we can conclude that the predation rate between host races was highly asymmetrical. The complexity of the agricultural mosaic thus can influence prey selection by predators on different host plants. These may have evolutionary consequences through context dependent fitness benefits on particular host plants.     

Alterations of the gut microbiome are associated with epigenetic age acceleration and physical fitness

Epigenetic clocks can measure aging and predict the incidence of diseases and mortality. Higher levels of physical fitness are associated with a slower aging process and a healthier lifespan. Microbiome alterations occur in various diseases and during the aging process, yet their relation to epigenetic clocks is not explored. To fill this gap, we collected metagenomic (from stool), epigenetic (from blood), and exercise-related data from physically active individuals and, by applying epigenetic clocks, we examined the relationship between gut flora, blood-based epigenetic age acceleration, and physical fitness. We revealed that an increased entropy in the gut microbiome of physically active middle-aged/old individuals is associated with accelerated epigenetic aging, decreased fitness, or impaired health status. We also observed that a slower epigenetic aging and higher fitness level can be linked to altered abundance of some bacterial species often linked to anti-inflammatory effects. Overall our data suggest that alterations in the microbiome can be associated with epigenetic age acceleration and physical fitness.     

Correctly estimating how environmental stochasticity influences fitness and population growth

Increased temporal variance in life-history traits is generally predicted to decrease individual fitness and population growth. We show that a widely used result of stochastic sensitivity analysis that bolsters this generality is flawed because it ignores the effects of correlations between vital rates. Considering the effects of these correlations (although ignoring autocorrelations), we show that the apparently simple relationship between vital rate variance and fitness can be considerably more complex than previously thought. In particular, the previously estimated negative sensitivities of fitness or population growth to variance in a vital rate can be either enhanced by positive correlations between rates or reversed by negative correlations, even to the point that variability in a rate can increase fitness or population growth. We apply this new sensitivity calculation to data from the desert tortoise and discuss its interpretation in light of the factors generating vital rate correlations.     

Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2(n). The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations.     

Reciprocal sign epistasis between frequently experimentally evolved adaptive mutations causes a rugged fitness landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.     

Molecular basis for a lack of correlation between viral fitness and cell killing capacity

The relationship between parasite fitness and virulence has been the object of experimental and theoretical studies often with conflicting conclusions. Here, we provide direct experimental evidence that viral fitness and virulence, both measured in the same biological environment provided by host cells in culture, can be two unrelated traits. A biological clone of foot-and-mouth disease virus acquired high fitness and virulence (cell killing capacity) upon large population passages in cell culture. However, subsequent plaque-to-plaque transfers resulted in profound fitness loss, but only a minimal decrease of virulence. While fitness-decreasing mutations have been mapped throughout the genome, virulence determinants-studied here with mutant and chimeric viruses-were multigenic, but concentrated on some genomic regions. Therefore, we propose a model in which viral virulence is more robust to mutation than viral fitness. As a consequence, depending on the passage regime, viral fitness and virulence can follow different evolutionary trajectories. This lack of correlation is relevant to current models of attenuation and virulence in that virus de-adaptation need not entail a decrease of virulence.     

Environmental change exposes beneficial epistatic interactions in a catalytic RNA

Natural selection drives populations of individuals towards local peaks in a fitness landscape. These peaks are created by the interactions between individual mutations. Fitness landscapes may change as an environment changes. In a previous contribution, we discovered a variant of the Azoarcus group I ribozyme that represents a local peak in the RNA fitness landscape. The genotype at this peak is distinguished from the wild-type by four point mutations. We here report ribozyme fitness data derived from constructing all possible combinations of these point mutations. We find that these mutations interact epistatically. Importantly, we show that these epistatic interactions change qualitatively in the three different environments that we studied. We find examples where the relative fitness of a ribozyme can change from neutral or negative in one environment, to positive in another. We also show that the fitness effect of a specific GC-AU base pair switch is dependent on both the environment and the genetic context. Moreover, the mutations that we study improve activity at the cost of decreased structural stability. Environmental change is ubiquitous in nature. Our results suggest that such change can facilitate adaptive evolution by exposing new peaks of a fitness landscape. They highlight a prominent role for genotype-environment interactions in doing so.     

Body mass and individual fitness in female ungulates: bigger is not always better

In female vertebrates, differences in fitness often correspond to differences in phenotypic quality, suggesting that larger females have greater fitness. Variation in individual fitness can result from variation in life span and/or variation in yearly reproductive success, but no study has yet assessed the relationships between the components of fitness and phenotypic quality while controlling for life span. We tried to fill this gap using data from long-term monitoring (23 years) of marked roe deer and bighorn sheep, two ungulates with very different life histories. In both species, we found a strong positive relationship between an adult female's mass and her probability of reaching old age: over the long term, bigger is indeed better for ungulate females. On the other hand, we found no evidence in either species that heavier females had higher fitness when differences in life span were accounted for: over the short term, bigger is not necessarily better. Our results indicate that, while broad differences in phenotypic quality affect individual fitness, when differences in life span are accounted for phenotypic quality has no residual effect on fitness. Therefore, within a given range of phenotypic quality, bigger is not always better, for reasons which may differ between species.     

青藏高原高寒草甸植物花寿命与花吸引特征的关系及其对雌性繁殖成功的影响

花寿命指花保持开放且具有功能的时间长度, 是开花植物繁殖成功的一个重要功能性状。可塑性延长花寿命是植物在不利的传粉环境中保障繁殖的一种策略, 但延长花寿命也会增加繁殖成本。花寿命的可塑性变异不仅受传粉环境的影响, 而且还受资源分配权衡的影响。花寿命的理论模型指出, 植物的花寿命与花吸引特征之间存在资源分配权衡。为了研究在花粉限制环境中, 植物花寿命与花吸引特征之间的资源权衡及其对雌性适合度的相对重要性。该研究以青藏高原高寒草甸不同海拔(2 900和3 600 m)的11种开花植物为研究对象, 分析了不同植物群落中, 物种水平上: (1)花寿命与花吸引特征(花大小以及开花数目)之间的相关关系; (2)花寿命与花吸引特征对植物雌性适合度的相对贡献。结果表明, 无论是低海拔还是高海拔植物群落, 植物的花寿命与开花数目之间均存在权衡关系, 且长的花寿命增加了植物的雌性适合度。但在高海拔环境中, 植物的雌性适合度只与花寿命有关。这说明相对于低海拔植物, 花寿命对高海拔植物的雌性繁殖成功更为重要。     

Evolution of haploid–diploid life cycles when haploid and diploid fitnesses are not equal

Many organisms spend a significant portion of their life cycle as haploids and as diploids (a haploid–diploid life cycle). However, the evolutionary processes that could maintain this sort of life cycle are unclear. Most previous models of ploidy evolution have assumed that the fitness effects of new mutations are equal in haploids and homozygous diploids, however, this equivalency is not supported by empirical data. With different mutational effects, the overall (intrinsic) fitness of a haploid would not be equal to that of a diploid after a series of substitution events. Intrinsic fitness differences between haploids and diploids can also arise directly, for example because diploids tend to have larger cell sizes than haploids. Here, we incorporate intrinsic fitness differences into genetic models for the evolution of time spent in the haploid versus diploid phases, in which ploidy affects whether new mutations are masked. Life‐cycle evolution can be affected by intrinsic fitness differences between phases, the masking of mutations, or a combination of both. We find parameter ranges where these two selective forces act and show that the balance between them can favor convergence on a haploid–diploid life cycle, which is not observed in the absence of intrinsic fitness differences.     

The value of an egg: resource reallocation in ladybirds (Coleoptera: Coccinellidae) infected with male-killing bacteria

Male-killing bacteria are thought to persist in host populations by vertical transmission and conferring direct and/or indirect fitness benefits to their hosts. Here, we test the role of indirect fitness benefits accrued from resource reallocation in species that engage in sibling egg cannibalism. We found that a single-egg meal significantly increased larval survival in 12 ladybird species, but the value of an egg (to survival) differed substantially between species. Next, we tested the impact of three male-killing bacteria on larval survival in one ladybird species, Adalia bipunctata. Spiroplasma reduced larval survival, whereas Wolbachia and Rickettsia had no effect. However, Spiroplasma-infected larvae showed the greatest response to a single-egg meal. The indirect fitness benefit obtained from a single egg is thus so large that even male-killing bacteria with direct fitness costs can persist in host populations. This study supports the hypothesis that fitness compensation via resource reallocation can explain male-killing bacteria persistence.     

The ecological causes of functional distinctiveness in communities

Recent work has shown that evaluating functional trait distinctiveness, the average trait distance of a species to other species in a community offers promising insights into biodiversity dynamics and ecosystem functioning. However, the ecological mechanisms underlying the emergence and persistence of functionally distinct species are poorly understood. Here, we address the issue by considering a heterogeneous fitness landscape whereby functional dimensions encompass peaks representing trait combinations yielding positive population growth rates in a community. We identify four ecological cases contributing to the emergence and persistence of functionally distinct species. First, environmental heterogeneity or alternative phenotypic designs can drive positive population growth of functionally distinct species. Second, sink populations with negative population growth can deviate from local fitness peaks and be functionally distinct. Third, species found at the margin of the fitness landscape can persist but be functionally distinct. Fourth, biotic interactions (positive or negative) can dynamically alter the fitness landscape. We offer examples of these four cases and guidelines to distinguish between them. In addition to these deterministic processes, we explore how stochastic dispersal limitation can yield functional distinctiveness. Our framework offers a novel perspective on the relationship between fitness landscape heterogeneity and the functional composition of ecological assemblages.     

Life-history evolution and the origin of multicellularity

The fitness of an evolutionary individual can be understood in terms of its two basic components: survival and reproduction. As embodied in current theory, trade-offs between these fitness components drive the evolution of life-history traits in extant multicellular organisms. Here, we argue that the evolution of germ-soma specialization and the emergence of individuality at a new higher level during the transition from unicellular to multicellular organisms are also consequences of trade-offs between the two components of fitness-survival and reproduction. The models presented here explore fitness trade-offs at both the cell and group levels during the unicellular-multicellular transition. When the two components of fitness negatively covary at the lower level there is an enhanced fitness at the group level equal to the covariance of components at the lower level. We show that the group fitness trade-offs are initially determined by the cell level trade-offs. However, as the transition proceeds to multicellularity, the group level trade-offs depart from the cell level ones, because certain fitness advantages of cell specialization may be realized only by the group. The curvature of the trade-off between fitness components is a basic issue in life-history theory and we predict that this curvature is concave in single-celled organisms but becomes increasingly convex as group size increases in multicellular organisms. We argue that the increasingly convex curvature of the trade-off function is driven by the initial cost of reproduction to survival which increases as group size increases. To illustrate the principles and conclusions of the model, we consider aspects of the biology of the volvocine green algae, which contain both unicellular and multicellular members.     

The sociobiology of sex: inclusive fitness consequences of inter-sexual interactions

The diversity of social interactions between sexual partners has long captivated biologists, and its evolution has been interpreted largely in terms of 'direct fitness' pay-offs to partners and their descendants. Inter-sexual interactions also have 'indirect effects' by affecting the fitness of relatives, with important consequences for inclusive fitness. However, inclusive fitness arguments have received limited consideration in this context, and definitions of 'direct' and 'indirect' fitness effects in this field are often inconsistent with those of inclusive fitness theory. Here, we use a sociobiology approach based on inclusive fitness theory to distinguish between direct and indirect fitness effects. We first consider direct effects: we review how competition leads to sexual conflict, and discuss the conditions under which repression of competition fosters sexual mutualism. We then clarify indirect effects, and show that greenbeard effects, kin recognition and population viscosity can all lead to episodes of indirect selection on sexual interactions creating potential for sexual altruism and spite. We argue that the integration of direct and indirect fitness effects within a sociobiology approach enables us to consider a more diverse spectrum of evolutionary outcomes of sexual interactions, and may help resolving current debates over sexual selection and sexual conflict.     

The Relationship between Parasite Fitness and Host Condition in an Insect - Virus System

Research in host-parasite evolutionary ecology has demonstrated that environmental variation plays a large role in mediating the outcome of parasite infection. For example, crowding or low food availability can reduce host condition and make them more vulnerable to parasite infection. This observation that poor-condition hosts often suffer more from parasite infection compared to healthy hosts has led to the assumption that parasite productivity is higher in poor-condition hosts. However, the ubiquity of this negative relationship between host condition and parasite fitness is unknown. Moreover, examining the effect of environmental variation on parasite fitness has been largely overlooked in the host-parasite literature. Here we investigate the relationship between parasite fitness and host condition by using a laboratory experiment with the cabbage looper Trichoplusia ni and its viral pathogen, AcMNPV, and by surveying published host-parasite literature. Our experiments demonstrated that virus productivity was positively correlated with host food availability and the literature survey revealed both positive and negative relationships between host condition and parasite fitness. Together these data demonstrate that contrary to previous assumptions, parasite fitness can be positively or negatively correlated with host fitness. We discuss the significance of these findings for host-parasite population biology.     

Epistasis from functional dependence of fitness on underlying traits

Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.     

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory.