The estimation of a bivariate fitness function from two samples taken from a population

Summary The fitness of animals subjected to natural selection can be defined as the probability of surviving selection for a given interval of time, or some convenient multiple of this. If the fitness is related to some measurable variablesX, Y, Z,… then the relationship is expressed mathematically in the fitness functionw(x, y, z,…) and this function can be estimated by comparing the joint distribution ofX, Y, Z,… in samples taken before and after selection. In an earlier paper (Manly, 1975) the problems involved in estimating a fitness function of one variable were discussed. In the present paper various methods for estimating a bivariate fitness function are proposed and compared on some semiartificial sample data. It is concluded that either a generalized version ofO’Donald’s (1968) method of moments or a weighted multiple regression method will be most satisfactory. Alternative methods involving assumptions of normality will need to be used with great care.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Multiple Comparisons of Polynomial Distributions

Asymptotically correct 90 and 95 percentage points are given for multiple comparisons with control and for all pair comparisons of several independent samples of equal size from polynomial distributions. Test statistics are the maxima of the X²-statistics for single comparisons. For only two categories the asymptotic distributions of these test statistics result from DUNNETT'S many-one tests and TUKEY'S range test (cf. MILLER, 1981). The percentage points for comparisons with control are computed from the limit distribution of the test statistic under the overall hypothesis H₀. To some extent the applicability of these bounds is investigated by simulation. The bounds can also be used to improve Holm's sequentially rejective Bonferroni test procedure (cf. HOLM, 1979). The percentage points for all pair comparisons are obtained by large simulations. Especially for 3×3-tables the limit distribution of the test statistic under H₀ is derived also for samples of unequal size. Also these bounds can improve the corresponding Bonferroni-Holm procedure. Finally from SKIDÁK's probability inequality for normal random vectors (cf. SKIDÁK, 1967) a similar inequality is derived for dependent X²-variables applicable to simultaneous X²-tests.     

Inclusive Fitness from Multitype Branching Processes

I use multitype branching processes to study genetic models for the evolution of social behaviour, i.e. behaviours that, when acted out, affect the success of the actor’s neighbours. Here, I suppose an individual bearing a mutant copy of a gene influences the reproductive success of a neighbour by altering its own competitive ability. Approximations based on assumptions about the rareness of the mutant allele and the strength of selection allow me to formulate statements concerning the probability of mutant extinction in terms of inclusive fitness. Inclusive fitness is an idea well known to biologists and can be thought of as a sum of an individual’s fitness and the fitness of each of its relatives, weighted by some measure of genetic relatedness. Previous work has led to some confusion surrounding the definition of the inclusive-fitness effect of a mutant allele when individuals carrying that allele experience demographic conditions that fluctuate randomly. In this paper, I emphasise the link between inclusive fitness and the probability of mutant extinction. I recover standard results for populations of constant size, and I show that inclusive fitness can be used to determine the short-term fate of mutants in the face of stochastic demographic fluctuations. Overall, then, I provide a connection between certain inclusive-fitness-based approaches routinely applied in theoretical studies of social evolution.     

Pooling hair samples to increase DNA yield for PCR

Hairs are useful non-invasive sources of DNA, but the DNA yield can be very small, thus promoting genotyping errors. Using multiple hairs can counter this problem, but may introduce multiple contributors to a sample if collected remotely. With microsatellite genotyping, samples representing multiple animals are obvious if three or more alleles are detected at any locus: these samples can then be removed from any analyses. However, some multiple-individual samples may have only one or two alleles at each of the loci examined. We investigated the probability of failing to identify mixed pooled samples by simulating pooled samples (10 000 replicates) from microsatellite data from the northern and southern hairy-nosed wombats (NHNW, Lasiorhinus krefftii; SHNW, L. latifrons), species with low and high genetic diversity respectively. The majority (81.7%) of the 40 000 simulated samples had three or four alleles, so were readily identified as mixed. In the remaining 1-or-2-allele SHNW samples, forensic science software (DNAMIX) correctly identified mixed versus single-individual samples for all cases when the probability of locus failure was low (P _(LF) = 0.1), and 99% of samples when locus failure was high (P _(LF) = 0.5). For NHNW however, the probability of failing to identify a mixed sample was too high for population size estimation (0.05), even when the probability of locus failure was low. In cases such as this, pooled samples may be adequate for less demanding tasks, such as estimation of allele proportions. However, for animal populations with at least average levels of genetic variation, pooling of samples could safely be utilised for most applications. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.     

Females benefit from multiple mating but not multiple mates in the burying beetle Nicrophorus vespilloides

Male reproductive success generally increases with number of mates but this need not be true for females. If females are the limiting sex, as few as one mate can be optimal. Despite the theoretical differences driving multiple mating in the sexes, multiple mating is the norm rather than the exception. Empirical investigations are therefore required to determine why females mate with multiple males. Both nonadaptive (correlated responses to selection on males, given the mean mating rates have to be the same) and adaptive (direct or indirect fitness benefits) can drive the evolution of multiple mating in females. Females of the burying beetle Nicorphorus vespilloides often mate repeatedly with the same male, but this appears to be a correlated response to selection on males rather than reflecting direct benefits to females for multiple mating. However, an unexamined alternative to this nonadaptive explanation is that females benefit by mating with multiple different males and therefore are selected for general promiscuity. Here we examine if mating polyandrously provides fitness benefits by examing the effects of number of mates (1, 2 or 3), mating system (monogamous, polyandrous) and their interaction. The only significant influence was mating more than once. This did not depend on type of mating. We suggest that unlike most other species examined, in N. vespilloides mating with the same male repeatedly or with several different males reflects an indiscriminate willingness to mate as a result of correlated selection on males for high rates of mating.     

ESTIMATING THE FORM OF NATURAL SELECTION ON A QUANTITATIVE TRAIT

The fitness function f relates fitness of individuals to the quantitative trait under natural selection. The function is useful in predicting fitness differences among individuals and in revealing whether an optimum is present within the range of phenotypes in the population. It may also be thought of as describing the ecological environment in terms of the trait. Quadratic regression will approximate the fitness function from data (e.g., Lande and Arnold, 1983), but the method does not reliably indicate features of f such as the presence of modes (stabilizing selection) or dips (disruptive selection). I employ an alternative procedure requiring no a priori model for the function. The method is useful in two ways: it provides a nonparametric estimate of f, of interest by itself, and it can be used to suggest an appropriate parametric model. I also discuss measures of selection intensity based on the fitness function. Analysis of six data sets yields a variety of forms of f and provides new insights for some familiar cases. Low amounts of variation and a low density of data points near the tails of many phenotype distributions emerge as limitations to gaining information on fitness functions. An experimental approach in which the distribution of a quantitative trait is broadened through manipulation would minimize these problems.     

Modularity and the units of evolution

Summary While many developmental processes (e. g., gene networks or signaling pathways) are astonishingly conserved during evolution, they may be employed differently in different metazoan taxa or may be used multiply in different contexts of development. This suggests that these processes belong to building blocks or modules, viz., highly integrated parts of the organism, which develop and/or function relatively independent from other parts. Such modules may be relatively easy to dissociate from other modules and, therefore, could also serve as units of evolution. However, in order to further explore the implications of modularity for evolution, the vague notion of “modularity” as well as its relation to concepts like “unit of evolution” need to be more precisely specified. Here, a module is characterized as a certain type of dynamic pattern of couplings among the constituents of a process. It may or may not form a spatially contiguous unit. A unit of selection is defined as a unit of those constituents of a reproducing process/system, which exists in different variants and acts as a non-decomposable unit of fitness and variant reproduction during a particular selection process. The more general notion of a unit of evolution is characterized as a nondecomposable unit of constituents with reciprocal fitness dependence, be it due to fitness epistasis or due to the lack of independent variability. Because such fitness dependence may only be observed for some combinations of variants, several constituents may act as a unit of evolution only with a certain probability (coevolution probability). It is argued, that under certain conditions modules are likely to act as units of evolution with high coevolution probabilities, because there is likely to be a close tie between the pattern of couplings of the constituents of a reproducing system and their interdependent fitness contributions. Moreover and contrary to the traditional dichotomy of genes versus organisms as units of selection, modules tend to be more important in delimiting actual units of selection than either organisms or genes, because they are less easily disrupted by recombination than organisms, while having less contextsensitive fitness values than genes. Finally, it is suggested that the evolution of modularity is self-reinforcing, because the flexibility of intermodular connections facilitates the recombination among modules and their multiple employment in new contexts.     

Generalized Maximum Range Tests for Pairwise Comparisons of Several Populations

A multiple comparison procedure (MCP) is proposed for the comparison of all pairs of several independent samples. This MCP is essentially the closed procedure with union-intersection tests based on given single tests Q_ij for the minimal hypotheses H_ij. In such cases where the α-levels of the nominal tests associated with the MCP can be exhausted, this MCP has a uniformly higher all pair power than any refined Bonferroni test using the same Q_ij. Two different general algorithms are described in section 3. A probability inequality for ranges of i.i.d. random variables which is useful for some algorithms is proved in section 4. Section 5 contains the application to independent normally distributed estimates and section 6 the comparisons of polynomial distributions by multivariate ranges. Further applications are possible. Tables of the 0.05-bounds for the tests of section 5 and 6 are enclosed.     

Adaptive Topography in Fertility-Viability Selection Models: The Haplodiploid Case

A linear combination of partial changes of mean fitnesses from one generation to the next one is shown to be approximately equal to the additive genetic variance in fitness after enough generations and away from equilibrium in random mating haplodiploid populations under arbitrary weak frequency-dependent selection on sex-differentiated viability of individuals and sex-differentiated fertility of matings controlled at a single multiallelic locus. The result can be applied to X-linked locus models in diploid populations. The result is used to deduce approximate adaptive topographies far frequency-independent selection models in the cases of nonsex-differentiated fertilities and multiplicative sex-differentiated fertilities and for kin selection models in family-structured populations under the assumptions of single insemination and multiple insemination of females. Multiple insemination creates frequency-dependent selection regimes.     

A gene's eye view of epistasis,selection and speciation

In this mini‐review, I discuss the effects of gene interaction or epistasis from a `gene's eye view.' By a `gene's eye view' of epistasis, I mean that I will consider a single, bi‐allelic locus, A , whose effects on fitness result only from its interactions with alleles of another, unknown locus, X . I will show how changes in the frequencies of alleles at the background locus affect the relationship of alleles at the A ‐locus to fitness. Changing the genetic background changes the fundamental characteristics of the A ‐locus, such as the magnitude and sign of allelic effects on fitness, and, consequently, it changes the strength and pattern of selection. I consider each of the four kinds of pair–wise interactions between two loci and show that some kinds of epistasis are more sensitive than others to population genetic subdivision. Lastly, I show that some kinds of epistasis are more likely than others to affect the process of speciation and contribute to or be responsible for general genetic features of interspecific hybrids, such as Haldane's rule.     

Sampling Considerations for Disease Surveillance in Wildlife Populations

Abstract Disease surveillance in wildlife populations involves detecting the presence of a disease, characterizing its prevalence and spread, and subsequent monitoring. A probability sample of animals selected from the population and corresponding estimators of disease prevalence and detection provide estimates with quantifiable statistical properties, but this approach is rarely used. Although wildlife scientists often assume probability sampling and random disease distributions to calculate sample sizes, convenience samples (i.e., samples of readily available animals) are typically used, and disease distributions are rarely random. We demonstrate how landscape-based simulation can be used to explore properties of estimators from convenience samples in relation to probability samples. We used simulation methods to model what is known about the habitat preferences of the wildlife population, the disease distribution, and the potential biases of the convenience-sample approach. Using chronic wasting disease in free-ranging deer (Odocoileus virginianus) as a simple illustration, we show that using probability sample designs with appropriate estimators provides unbiased surveillance parameter estimates but that the selection bias and coverage errors associated with convenience samples can lead to biased and misleading results. We also suggest practical alternatives to convenience samples that mix probability and convenience sampling. For example, a sample of land areas can be selected using a probability design that oversamples areas with larger animal populations, followed by harvesting of individual animals within sampled areas using a convenience sampling method.     

The influence of potential stressors on oviposition site selection and subsequent growth,survival and emergence of the non‐biting midge (Chironomus tepperi)

Theory predicts that animals should prefer habitats where their fitness is maximized but some mistakenly select habitats where their fitness is compromised, that is, ecological traps. Understanding why this happens requires knowledge of the habitat selection cues animals use, the habitats they prefer and why, and the fitness costs of habitat selection decisions. We conducted experiments with a freshwater insect, the non‐biting midge Chironomus tepperi to ask: (a) whether females respond to potential oviposition cues, (b) to explore whether oviposition is adaptive in relation to metal pollution and conductivity, and (c) whether individuals raised in poor quality sites are more likely to breed in similarly poor locations. We found the following: (a) females responded to some cues, especially conductivity and conspecifics, (b) females preferred sites with higher concentrations of bioavailable metals but suffered no consequences to egg/larval survival, (c) females showed some avoidance of high conductivities, but they still laid eggs resulting in reduced egg hatching, larval survival, and adult emergence, and (d) preferences were independent of natal environment. Our results show that C. tepperi is susceptible to ecological traps, depending on life stage and the relative differences in conductivities among potential oviposition sites. Our results highlight that (a) the fitness outcomes of habitat selection need to be assessed across the life cycle and (b) the relative differences in preference/suitability of habitats need to be considered in ecological trap research. This information can help determine why habitat preferences and their fitness consequences differ among species, which is critical for determining which species are susceptible to ecological traps.     

The song of the old mother: Reproductive senescence in female drosophila

Among animals with multiple reproductive episodes, changes in adult condition over time can have profound effects on lifetime reproductive fitness and offspring performance. The changes in condition associated with senescence can be particularly acute for females who support reproductive processes from oogenesis through fertilization. The pomace fly Drosophila melanogaster is a well-established model system for exploring the physiology of reproduction and senescence. In this review, we describe how increasing maternal age in Drosophila affects reproductive fitness and offspring performance as well as the genetic foundation of these effects. Describing the processes underlying female reproductive senescence helps us understand diverse phenomena including population demographics, condition-dependent selection, sexual conflict, and transgenerational effects of maternal condition on offspring fitness. Understanding the genetic basis of reproductive senescence clarifies the nature of life-history trade-offs as well as potential ways to augment and/or limit female fertility in a variety of organisms.     

A Distribution-Free Two-Sample Equivalence Test Allowing for Tied Observations

A new testing procedure is derived which enables to assess the equivalence of two arbitrary noncontinuous distribution functions from which unrelated samples are taken as the data to be analyzed. The equivalence region is defined to consist of all pairs (F,G) of distribution functions such that for independent X ∼ F, Y ∼ G the conditional probability of {X > Y} given {X ≠ Y} lies in some short interval around 1/2. The test rejects the null hypothesis of nonequivalence if and only if the standardized distance between the U-statistics estimator of P[X > Y ∣ X ≠ Y] and the center of the equivalence interval (1/2 — ε₁, 1/2 + ε₂) does not exceed a critical upper bound which has to be computed as the α-quantile of a χ²-distribution with one degree of freedom and a random noncentrality parameter proportional to the squared length of that interval. The test is shown to maintain the asymptotic significance level under very weak regularity conditions. Results of an extensive simulation study suggest that its level properties are very satisfactory in small samples as well. The power turns out to be inversely related to the rate P[X = Y] of ties between observations from different samples.     

On Asymptotically Distribution-Free Confidence Bounds for P (X1≥X2) Based on Samples not Necessarily Independent

If X₁, X₂, denote the random variables of measurement under two treatments then the probability P (X₁ ≥ X₂) is a quantity of great practical interest, especially if we consider both to be measured for the same unity. In this case the random variables cannot be assumed to be independent any longer. The following paper describes a procedure to compute approximate confidence bounds for P (X₁ ≥ X₂) where correlations between X₁, X₂ are admitted as well as between replications of the X_j. There is some relation to the FRIEDMAN-statistic with or without repeated measurements and as a special case to the sign-test. Application may be extended to ordinal data.     

Autosomal suppression and fitness costs of an old driving X chromosome in Drosophila testacea

Driving X chromosomes (X^Ds) bias their own transmission through males by killing Y‐bearing gametes. These chromosomes can in theory spread rapidly in populations and cause extinction, but many are found as balanced polymorphisms or as “cryptic” X^Ds shut down by drive suppressors. The relative likelihood of these outcomes and the evolutionary pathways through which they come about are not well understood. An X^D was recently discovered in the mycophagous fly, Drosophila testacea, presenting the opportunity to compare this X^D with the well‐studied X^D of its sister species, Drosophila neotestacea. Comparing features of independently evolved X^Ds in young sister species is a promising avenue towards understanding how X^Ds and their counteracting forces change over time. In contrast to the X^D of D. neotestacea, we find that the X^D of D. testacea is old, with its origin predating the radiation of three species: D. testacea, D. neotestacea and their shared sister species, Drosophila orientacea. Motivated by the suggestion that older X^Ds should be more deleterious to carriers, we assessed the effect of the X^D on both male and female fertility. Unlike what is known from D. neotestacea, we found a strong fitness cost in females homozygous for the X^D in D. testacea: a large proportion of homozygous females failed to produce offspring after being housed with males for several days. Our male fertility experiments show that although X^D male fertility is lower under sperm‐depleting conditions, X^D males have comparable fertility to males carrying a standard X chromosome under a free‐mating regime, which may better approximate conditions in wild populations of D. testacea. Lastly, we demonstrate the presence of autosomal suppression of X chromosome drive. Our results provide support for a model of X^D evolution where the dynamics of young X^Ds are governed by fitness consequences in males, whereas in older X^D systems, both suppression and fitness consequences in females likely supersede male fitness costs.     

Quantification and decomposition of environment‐selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait‐absolute fitness relationship remains constant. We apply and extend a regression‐based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment‐selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait‐fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.     

KIN-MEDIATED MORPHOGENESIS IN FACULTATIVELY CANNIBALISTIC TADPOLES

Inclusive fitness theory predicts that organisms can increase their fitness by helping or not harming relatives, and many animals modify their behavior toward kin in a manner consistent with this prediction. Morphogenesis also may be sensitive to kinship environment, particularly in species where certain individuals facultatively develop structures that can be used against conspecifics as weaponry. We tested this hypothesis by examining whether and how consanguinity affected the probability that a structurally distinctive carnivore phenotype, which is opportunistically cannibalistic, would be produced in plains spadefoot toad tadpoles (Spea bombifrons) and southern spadefoot toad tadpoles (S. multiplicata). For tadpoles of S. multiplicata, individuals were significantly more likely to express the carnivore phenotype in mixed sibship groups than in pure sibship groups. For tadpoles of S. bombifrons, individuals were significantly more likely to express the carnivore phenotype when reared alone than in pure sibship groups. Both outcomes were independent of food availability or sibship specific differences in size or growth rate, and waterborne chemical signals from nonkin were sufficient to trigger expression of the carnivore phenotype. Our results suggest that morphogenesis may be responsive to kinship environment in any species or population that occurs as multiple, environmentally induced forms (polyphenism) that differ in their ability to help or to harm others.