THE MEASUREMENT THEORY OF FITNESS

In this article, an approach to measure fitness is proposed that considers fitness as a measure of competitive ability among phenotypes or genotypes. This approach is based on pairwise competition tests and is related to measures of “utility” in mathematical economics. Extending the results from utility theory it is possible to recover the classical Wrightian fitness measure without reference to models of population growth. A condition, quasi‐BTL, similar to the Bradley–Terry–Luce condition of classical utility theory is shown to be necessary for the existence of frequency and context‐independent fitness measures. Testing for violations of this quasi‐BTL condition can be used to the detect genotype‐by‐genotype interactions and frequency‐dependent fitness. A method for the detection of genotype by environment interactions is proposed that avoids potential scaling artifacts. Furthermore the measurement theoretical approach allows one to derive Wright's selection equation. This shows that classical selection equations are entirely general and exact. It is concluded that measurement theory is able to give definite answers to a number theoretical and practical questions. For instance, this theory identifies the correct scale for measuring gene interaction with respect to fitness and shows that different scales may lead to wrong conclusions.     

Natural selection on age-specific fertilities in human females: comparison of individual-level fitness measures.

Lifetime reproductive success and timing of reproduction are key components of life-history evolution. To understand the evolution of reproductive schedules, it is important to use a measure of fitness that is sensitive both to reproductive quantity and reproductive timing. There is a contradiction between the theory, which mainly focuses on the rate measures of fitness (r and lambda), and empirical studies, which mainly use lifetime reproductive success (LRS), or some of its correlates, as a fitness measure. We measured phenotypic selection on age-specific fertilities in three pre-modern human populations using individually estimated finite rate of increase, er (lambda). We found that lambda and lifetime reproductive success ranked individuals differently according to their fitness: for example, a female giving birth to four children at a young age may actually have a higher fitness than a female giving birth to six children at a greater age. Increase in fertility at the young age classes (15-19 years) was favoured by selection, but the intensity of selection on fertility was higher in the older age classes (20-30 years), where the variance in fertility was highest. Hence, variation in fertility in the older age classes (20-30) was actually responsible for most of the observed variation in fitness among the individuals. Additionally, more than 90% of variation in fitness (lambda) was attributable to individual differences in LRS, whereas only about 5% of all variation in fitness was due to differences in the reproductive schedule. The rate-sensitive fitness measure did not significantly challenge the importance of total fertility as a component of fitness in humans. However, the rate-sensitive measure clearly allowed more accurate estimation of individual fitness, which may be important for answering some more specific questions.     

Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics

The measure dynamics approach to modelling single-species coevolution with a one-dimensional trait space is developed and compared to more traditional methods of adaptive dynamics and the Maximum Principle. It is assumed that individual fitness results from pairwise interactions together with a background fitness that depends only on total population size. When fitness functions are quadratic in the real variables parameterizing the one-dimensional traits of interacting individuals, the following results are derived. It is shown that among monomorphisms (i.e. measures supported on a single trait value), the continuously stable strategy (CSS) characterize those that are Lyapunov stable and attract all initial measures supported in an interval containing this trait value. In the cases where adaptive dynamics predicts evolutionary branching, convergence to a dimorphism is established. Extensions of these results to general fitness functions and/or multi-dimensional trait space are discussed.     

Variance and variability,uncovering an underappreciated component of reproductive isolation

Estimating the fitness of line crosses has been a key element in studies of inbreeding depression, hybridization, and speciation. Fitness values are typically compared using differences in the arithmetic mean of a fitness component between types of crosses. One aspect of fitness that is often overlooked is variance in offspring fitness over time. In the majority of studies, ignoring this aspect of fitness is unavoidable because it is impossible to estimate variance in offspring fitness over long time periods. Here, I describe a method of estimating variance in offspring fitness by substituting spatial variation for temporal variation and provide an empirical example. The method is based on Levene's test of homogeneity of variances. It is implemented by quantifying differences in residual variation among cross types. In a previous study, I performed crosses between populations of the annual plant Diodia teres and quantified hybrid fitness. In this study, another component of isolation and heterosis was revealed when considering variance in offspring fitness. When taking into account variance in offspring fitness using geometric mean fitness as the measure of performance, hybrids between populations from different habitats showed less heterosis than when calculating fitness based on arithmetic mean. This study demonstrates that variance in offspring fitness can be an important aspect of fitness that should be measured more frequently.     

Laboratory relationships between adult lifetime reproductive success and fitness surrogates in a Drosophila littoralis population

The difficulties in measuring total fitness of individuals necessitate the use of fitness surrogates in ecological and evolutionary studies. These surrogates can be different components of fitness (e.g. survival or fecundity), or proxies more uncertainly related to fitness (e.g. body size or growth rate). Ideally, fitness would be measured over the lifetime of individuals; however, more convenient short-time measures are often used. Adult lifetime reproductive success (adult LRS) is closely related to the total fitness of individuals, but it is difficult to measure and rarely included in fitness estimation in experimental studies. We explored phenotypic correlations between female adult LRS and various commonly used fitness components and proxies in a recently founded laboratory population of Drosophila littoralis. Noting that survival is usually higher in laboratory conditions than in nature, we also calculated adjusted adult LRS measures that give more weight to early reproduction. The lifetime measures of fecundity, longevity, and offspring viability were all relatively highly correlated with adult LRS. However, correlations with short-time measures of fecundity and offspring production varied greatly depending on the time of measurement, and the optimal time for measurement was different for unadjusted compared to adjusted adult LRS measures. Correlations between size measures and adult LRS varied from weak to modest, leg size and female weight having the highest correlations. Our results stress the importance of well-founded choice of fitness surrogates in empirical research.     

Characterising the searchability of continuous optimisation problems for PSO

The focus of research in swarm intelligence has been largely on the algorithmic side with relatively little attention being paid to the study of problems and the behaviour of algorithms in relation to problems. When a new algorithm or variation on an existing algorithm is proposed in the literature, there is seldom any discussion or analysis of algorithm weaknesses and on what kinds of problems the algorithm is expected to fail. Fitness landscape analysis is an approach that can be used to analyse optimisation problems. By characterising problems in terms of fitness landscape features, the link between problem types and algorithm performance can be studied. This article investigates a number of measures for analysing the ability of a search process to improve fitness on a particular problem (called evolvability in literature but referred to as searchability in this study to broaden the scope to non-evolutionary-based search techniques). A number of existing fitness landscape analysis techniques originally proposed for discrete problems are adapted to work in continuous search spaces. For a range of benchmark problems, the proposed searchability measures are viewed alongside performance measures for a traditional global best particle swarm optimisation (PSO) algorithm. Empirical results show that no single measure can be used as a predictor of PSO performance, but that multiple measures of different fitness landscape features can be used together to predict PSO failure.     

Two fitness measures for clonal plants and the importance of spatial aspects

The capability of clonal plants to reproduce both sexually and vegetatively and their resulting hierarchical organisation into ramets and genets pose problems for the determination of fitness. We develop ramet-based measures of clonal plant fitness including both modes of reproduction. To this end we use simple population-dynamic equations accounting for limited space, limited dispersal, and disturbance. Neglecting interactions among ramets (r-selection regime) we derive an expression for initial growth rate r as a fitness measure. At higher densities interactions among ramets lead to density control (K-selection regime) and competitive exclusion of genotypes or species may occur. In this case we apply an invasibility criterion to derive an abundance fitness measure: competitiveness C. The optimum of C corresponds to an evolutionary stable strategy. C increases with the proportion of reproductive adults, with inverse module mortality, and with the sum of sexual and vegetative reproduction. The latter are defined as the product of the rate of module production and two correction factors accounting for juvenile mortality before establishment and for the efficiency of space exploitation by propagules. Thus C is equivalent to potential life-time offspring production, in contrast to realized life-time offspring production R₀. Because the correction factor for space exploitation cannot be expressed analytically we obtain it from complementary spatially-explicit individual-based simulations. To illustrate an application of the fitness measure C we predict optimal allocation to vegetative and sexual reproduction. In a homogeneous habitat an intermediate allocation may maximize fitness only if there is a non-linear trade-off between the modes of reproduction. However even if this trade-off is linear, spatially heterogenous disturbances can lead to an intermediate optimum of allocation because seed dispersal with subsequent vegetative spread improves the utilization of available space for recruitment if the spatial extent of single disturbances is much larger than the distance of vegetative dispersal. Thus, our study underlines the importance of spatial features for fitness measures especially of clonal plants.     

Fitness analyses of all possible point mutations for regions of genes in yeast

Deep sequencing can accurately measure the relative abundance of hundreds of mutations in a single bulk competition experiment, which can give a direct readout of the fitness of each mutant. Here we describe a protocol that we previously developed and optimized to measure the fitness effects of all possible individual codon substitutions for 10-aa regions of essential genes in yeast. Starting with a conditional strain (i.e., a temperature-sensitive strain), we describe how to efficiently generate plasmid libraries of point mutants that can then be transformed to generate libraries of yeast. The yeast libraries are competed under conditions that select for mutant function. Deep-sequencing analyses are used to determine the relative fitness of all mutants. This approach is faster and cheaper per mutant compared with analyzing individually isolated mutants. The protocol can be performed in ～4 weeks and many 10-aa regions can be analyzed in parallel.     

Culture theory: The developing synthesis from biology

Conclusions We believe that a useful, complete theory of culture is simpler than the dichotomies promoted by the coevolutionary approach suggest. Culture can be regarded as an aspect of the environment into which each human is born and must succeed or fail, developed gradually by the succession of humans who have lived throughout history. We hypothesize that culture results from the inclusive-fitness-maximizing efforts of all humans who have lived. We think the evidence suggests that cultural traits are, in general, vehicles of genic survival, and that the heritability of cultural traits depends on the judgments (conscious and unconscious) of individuals with regard to their effects on the individual's inclusive fitness.The challenge now before students of culture is to understand the proximate mechanisms, especially the ontogeny of learning biases, that result in the acquisition and transmission of cultural traits. How, for example, do we learn what constitutes an appropriate return on a social investment in different circumstances; i.e., what causes us to feel rewarded by, say, helping offspring who do not help us back, yet consistently to begrudge lesser expenditures to most others, or to feel cheated if we are not compensated for such expenditures immediately? We suggest that the answers to such questions lie in a few basic evolved learning tendencies.     

物种多维生态位宽度测度

经典的生态位宽度测度式基于物种在单一生态位维上各资源状态的分布比例量,而难以应用于物种在多维生态位空间的宽度测度,本文在Ｎ维生态位空间分割为分室的基础上,定义物种生态位宽度为物种在分室上分布与样本在分室的频率分布之间的吻合度,根据最小差别信息统计量,推导出一可基于物种分布比例量也可基于实测值的生态位宽测度式,并以华南鼎湖山自然保护区的厚壳桂群落中物种与土壤因子数据为例加以说明,结果表明优势树种具较     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Voice and handgrip strength predict reproductive success in a group of indigenous african females

Evolutionary accounts of human traits are often based on proxies for genetic fitness (e.g., number of sex partners, facial attractiveness). Instead of using proxies, actual differences in reproductive success is a more direct measure of Darwinian fitness. Certain voice acoustics such as fundamental frequency and measures of health such as handgrip strength correlate with proxies of fitness, yet there are few studies showing the relation of these traits to reproduction. Here, we explore whether the fundamental frequency of the voice and handgrip strength account for differences in actual reproduction among a population of natural fertility humans. Our results show that both fundamental frequency and handgrip strength predict several measures of reproductive success among a group of indigenous Namibian females, particularly amongst the elderly, with weight also predicting reproductive outcomes among males. These findings demonstrate that both hormonally regulated and phenotypic quality markers can be used as measures of Darwinian fitness among humans living under conditions that resemble the evolutionary environment of Homo sapiens. We also argue that these findings provide support for the Grandmother Hypothesis.     

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.     

Direct fitness of group living mammals varies with breeding strategy, climate and fitness estimates

1. Understanding how variation in fitness relates to variation in group living remains critical to determine whether this major aspect of social behaviour is currently adaptive. 2. Available evidence in social mammals aimed to examine this issue remains controversial. Studies show positive (i.e. potentially adaptive), neutral or even negative fitness effects of group living. 3. Attempts to explain this variation rely on intrinsic and extrinsic factors to social groups. Thus, relatively more positive fitness effects are predicted in singularly breeding as opposed to plural breeding species. Fitness effects of sociality in turn may depend on ecological conditions (i.e. extrinsic factors) that influence associated benefits and costs. 4. We used meta-analytic tools to review how breeding strategy or ecological conditions influence the effect size associated with direct fitness-sociality relationships reported in the mammalian literature. Additionally, we determined how taxonomic affiliation of species studied, different fitness and sociality measures used, and major climatic conditions of study sites explained any variation in direct fitness effect size. 5. We found group living had modest, yet positive effects on direct fitness. This generally adaptive scenario was contingent not only upon breeding strategy and climate of study sites, but also on fitness measures examined. Thus, positive and significant effects characterized singular as opposed to plural breeding strategies. 6. We found more positive fitness effects on studies conducted in tropical as opposed to temperate or arid climates. More positive and significant effects were noted on studies that relied on group fecundity, male fecundity and offspring survival as measures of fitness. 7. To conclude, direct fitness consequences of mammalian group living are driven by interspecific differences in breeding strategy and climate conditions. Other factors not examined in this study, namely individual variation in direct and indirect fitness benefits and potential interactions between social and ecological conditions, may be important and require further studies.     

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.     

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.     

Integrating cooperative breeding into theoretical concepts of cooperation

In cooperative breeding systems, some individuals help to raise offspring that are not their own. While early explanations for such altruistic behaviour were predominantly based on kin selection, recent evidence suggests that direct benefits may be important in the maintenance of cooperation. To date, however, discussions of cooperative breeding have made little reference to more general theories of cooperation between unrelated individuals (while these theories rarely address cooperative breeding). Here, we attempt to integrate the two fields. We identify four key questions that can be used to categorise different mechanisms for the maintenance of cooperative behaviour: (1) whether or not individuals invest in others; (2) whether or not this initial investment elicits a return investment by the beneficiary; (3) whether the interaction is direct, i.e. between two partners, or indirect (involving third parties) and (4) whether only actions that increase the fitness of the partner or also fitness reducing actions (punishment) are involved in the interaction. Asking these questions with regards to concepts in the literature on cooperative breeding, we found that (a) it is often straightforward to relate these concepts to general mechanisms of cooperation, but that (b) a single term (such as 'pay-to-stay', 'group augmentation' or 'prestige') may sometimes subsume two or more distinct mechanisms, and that (c) at least some mechanisms that are thought to be important in cooperative breeding systems have remained largely unexplored in the theoretical literature on the evolution of cooperation. Future theoretical models should incorporate asymmetries in power and pay off structure caused for instance by dominance hierarchies or partner choice, and the use of N-player games. The key challenges for both theoreticians and empiricists will be to integrate the hitherto disparate fields and to disentangle the parallel effects of kin and non-kin based mechanisms of cooperation.     

Correlation of co-ordinated amino acid changes at the two-domain interface of cysteine proteases with protein stability.

The engineering of a protein containing an alternative local residue packing for a set of side-chains has proven to be a major challenge because compositional, volumetric and steric constraints must be respected. Homologous proteins should provide examples of alternative groups of residues leading to a similar functional result. The functional significance of a pair of co-ordinated changes that are observed in the cysteine proteases family has been investigated by comparing the effect of individual or double changes on secretion, stability and activity of papain. The two changes are not independent. Detrimental effects of single mutations at one of the two positions can be partly suppressed by the co-ordinated mutation that reproduces naturally occurring contacts, indicating that these changes are concerted. Single mutations at the other position produce milder effects, suggesting a pathway for evolution.     

Potential impacts of multiple partners on mycorrhizal community dynamics

The significance of arbuscular mycorrhizal (AM) fungi in terrestrial ecosystems is widely acknowledged, but the causes and consequences of diversity in these fungi are not well understood. A recent frequency-dependent model suggests that dynamics within mycorrhizal mutualisms could promote the coexistence of at least two competing plant species and two competing fungal species within a community. Models are developed here in which simultaneous association with multiple partners may result in elevated or depressed fitness relative to association with either partner alone. This increases the range of conditions under which negative feedback occurs and coexistence of all four species is possible. Differences between plants in the relative proportions of fungi at which maximum fitness occurs may facilitate coexistence, as may differences between fungi in their abilities to establish interplant connections. These models suggest additional mechanisms by which mutualistic interactions could promote local diversity of plants and AM fungi.