The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.     

The efficiency of purifying selection in Mammals vs. Drosophila for metabolic genes

The nearly neutral theory of molecular evolution states that the efficiency of natural selection depends on the effective population size. By using a wide range of multispecies data on nucleotide polymorphism, we have tried to ascertain whether there are any differences in the level of selective constraints of metabolic process genes between Mammals and Drosophila species. The results are consistent with a higher selective constraint in Drosophila than in Mammals, according to the expected under the nearly neutral model: purifying selection seems to be more efficient in species with a larger effective population size.     

Population differences in Chinook salmon (Oncorhynchus tshawytscha) DNA methylation: Genetic drift and environmental factors

Local adaptation and phenotypic differences among populations have been reported in many species, though most studies focus on either neutral or adaptive genetic differentiation. With the discovery of DNA methylation, questions have arisen about its contribution to individual variation in and among natural populations. Previous studies have identified differences in methylation among populations of organisms, although most to date have been in plants and model animal species. Here we obtained eyed eggs from eight populations of Chinook salmon (Oncorhynchus tshawytscha) and assayed DNA methylation at 23 genes involved in development, immune function, stress response, and metabolism using a gene‐targeted PCR‐based assay for next‐generation sequencing. Evidence for population differences in methylation was found at eight out of 23 gene loci after controlling for developmental timing in each individual. However, we found no correlation between freshwater environmental parameters and methylation variation among populations at those eight genes. A weak correlation was identified between pairwise DNA methylation dissimilarity among populations and pairwise F _ST based on 15 microsatellite loci, indicating weak effects of genetic drift or geographic distance on methylation. The weak correlation was primarily driven by two genes, GTIIBS and Nkef. However, single‐gene Mantel tests comparing methylation and pairwise F _ST were not significant after Bonferroni correction. Thus, population differences in DNA methylation are more likely related to unmeasured oceanic environmental conditions, local adaptation, and/or genetic drift. DNA methylation is an additional mechanism that contributes to among population variation, with potential influences on organism phenotype, adaptive potential, and population resilience.     

The Characteristic Trajectory of a Fixing Allele: A Consequence of Fictitious Selection That Arises from Conditioning

This work is concerned with the historical progression, to fixation, of an allele in a finite population. This progression is characterized by the average frequency trajectory of alleles that achieve fixation before a given time, T. Under a diffusion analysis, the average trajectory, conditional on fixation by time T, is shown to be equivalent to the average trajectory in an unconditioned problem involving additional selection. We call this additional selection “fictitious selection”; it plays the role of a selective force in the unconditioned problem but does not exist in reality. It is a consequence of conditioning on fixation. The fictitious selection is frequency dependent and can be very large compared with any real selection that is acting. We derive an approximation for the characteristic trajectory of a fixing allele, when subject to real additive selection, from an unconditioned problem, where the total selection is a combination of real and fictitious selection. Trying to reproduce the characteristic trajectory from the action of additive selection, in an infinite population, can lead to estimates of the strength of the selection that deviate from the real selection by >1000% or have the opposite sign. Strong evolutionary forces may be invoked in problems where conditioning has been carried out, but these forces may largely be an outcome of the conditioning and hence may not have a real existence. The work presented here clarifies these issues and provides two useful tools for future analyses: the characteristic trajectory of a fixing allele and the force that primarily drives this, namely fictitious selection. These should prove useful in a number of areas of interest including coalescence with selection, experimental evolution, time series analyses of ancient DNA, game theory in finite populations, and the historical dynamics of selected alleles in wild populations.     

Population size,habitat fragmentation,and the nature of adaptive variation in a stream fish

Whether and how habitat fragmentation and population size jointly affect adaptive genetic variation and adaptive population differentiation are largely unexplored. Owing to pronounced genetic drift, small, fragmented populations are thought to exhibit reduced adaptive genetic variation relative to large populations. Yet fragmentation is known to increase variability within and among habitats as population size decreases. Such variability might instead favour the maintenance of adaptive polymorphisms and/or generate more variability in adaptive differentiation at smaller population size. We investigated these alternative hypotheses by analysing coding-gene, single-nucleotide polymorphisms associated with different biological functions in fragmented brook trout populations of variable sizes. Putative adaptive differentiation was greater between small and large populations or among small populations than among large populations. These trends were stronger for genetic population size measures than demographic ones and were present despite pronounced drift in small populations. Our results suggest that fragmentation affects natural selection and that the changes elicited in the adaptive genetic composition and differentiation of fragmented populations vary with population size. By generating more variable evolutionary responses, the alteration of selective pressures during habitat fragmentation may affect future population persistence independently of, and perhaps long before, the effects of demographic and genetic stochasticity are manifest.     

Census vs. effective population size in chinook salmon: large- and small-scale environmental perturbation effects

Population viability has often been assessed by census of reproducing adults. Recently this method has been called into question and estimation of the effective population size (Ne) proposed as a complementary method to determine population health. We examined genetic diversity in five populations of chinook salmon (Oncorhynchus tshawytscha) from the upper Fraser River watershed (British Columbia, Canada) at 11 microsatellite loci over 20 years using DNA extracted from archived scale samples. We tested for changes in genetic diversity, calculated the ratio of the number of alleles to the range in allele size to give the statistic M, calculated Ne from the temporal change in allele frequency, used the maximum likelihood method to calculate effective population size (NeM), calculated the harmonic mean of population size, and compared these statistics to annual census estimates. Over the last two decades population size has increased in all five populations of chinook examined; however, Ne calculated for each population was low (81-691) and decreasing over the time interval measured. Values of NeM were low, but substantially higher than Ne calculated using the temporal method. The calculated values for M were generally low (M < 0.70), indicating recent population reductions for all five populations. Large-scale historic barriers to migration and development activities do not appear to account for the low values of Ne; however, available spawning area is positively correlated with Ne. Both Ne and M estimates indicate that these populations are potentially susceptible to inbreeding effects and may lack the ability to respond adaptively to stochastic events. Our findings question the practice of relying exclusively on census estimates for interpreting population health and show the importance of determining genetic diversity within populations.     

Poor condition and infection: a vicious circle in natural populations

Pathogens may be important for host population dynamics, as they can be a proximate cause of morbidity and mortality. Infection dynamics, in turn, may be dependent on the underlying condition of hosts. There is a clear potential for synergy between infection and condition: poor condition predisposes to host infections, which further reduce condition and so on. To provide empirical data that support this notion, we measured haematological indicators of infection (neutrophils and monocytes) and condition (red blood cells (RBCs) and lymphocytes) in field voles from three populations sampled monthly for 2 years. Mixed-effect models were developed to evaluate two hypotheses, (i) that individuals with low lymphocyte and/or RBC levels are more prone to show elevated haematological indicators of infection when re-sampled four weeks later, and (ii) that a decline in indicators of condition is likely to follow the development of monocytosis or neutrophilia. We found that individuals with low RBC and lymphocyte counts had increased probabilities of developing monocytosis and higher increments in neutrophils, and that high indices of infection (neutrophilia and monocytosis) were generally followed by a declining tendency in the indicators of condition (RBCs and lymphocytes). The vicious circle that these results describe suggests that while pathogens overall may be more important in wildlife dynamics than has previously been appreciated, specific pathogens are likely to play their part as elements of an interactive web rather than independent entities.     

Population size is weakly related to quantitative genetic variation and trait differentiation in a stream fish

How population size influences quantitative genetic variation and differentiation among natural, fragmented populations remains unresolved. Small, isolated populations might occupy poor quality habitats and lose genetic variation more rapidly due to genetic drift than large populations. Genetic drift might furthermore overcome selection as population size decreases. Collectively, this might result in directional changes in additive genetic variation (V_A) and trait differentiation (Q_ST) from small to large population size. Alternatively, small populations might exhibit larger variation in V_A and Q_ST if habitat fragmentation increases variability in habitat types. We explored these alternatives by investigating V_A and Q_ST using nine fragmented populations of brook trout varying 50‐fold in census size N (179–8416) and 10‐fold in effective number of breeders, N_b (18–135). Across 15 traits, no evidence was found for consistent differences in V_A and Q_ST with population size and almost no evidence for increased variability of V_A or Q_ST estimates at small population size. This suggests that (i) small populations of some species may retain adaptive potential according to commonly adopted quantitative genetic measures and (ii) populations of varying sizes experience a variety of environmental conditions in nature, however extremely large studies are likely required before any firm conclusions can be made.     

The limits to parapatric speciation: Dobzhansky-Muller incompatibilities in a continent-island model

How much gene flow is needed to inhibit speciation by the accumulation of Dobzhansky–Muller incompatibilities (DMIs) in a structured population? Here, we derive these limits in a classical migration–selection model with two haploid or diploid loci and unidirectional gene flow from a continent to an island. We discuss the dependence of the maximum gene-flow rate on ecological factors (exogeneous selection), genetic factors (epistasis, recombination), and the evolutionary history. Extensive analytical and numerical results show the following: (1) The maximum rate of gene flow is limited by exogeneous selection. In particular, maintenance of neutral DMIs is impossible with gene flow. (2) There are two distinct mechanisms that drive DMI evolution in parapatry, selection against immigrants in a heterogeneous environment and selection against hybrids due to the incompatibility. (3) Depending on the mechanism, opposite predictions result concerning the genetic architecture that maximizes the rate of gene flow a DMI can sustain. Selection against immigrants favors evolution of tightly linked DMIs of arbitrary strength, whereas selection against hybrids promotes the evolution of strong unlinked DMIs. In diploids, the fitness of the double heterozygotes is the decisive factor to predict the pattern of DMI stability.     

managedpop: a computer simulation to project allelic diversity in managed populations with overlapping generations

We present a Monte Carlo simulation, managedpop , to project the loss of allelic diversity in a population with overlapping generations supported (or invaded) by a prodigious subpopulation. Input parameters allow the user to account for complex life histories and critical management practices, such as the frequency at which supportive breeding stocks are replaced. The simulation could also be used to examine the threat of species or population level extinction via hybridization. managedpop merges theoretical formulations on the effective size of supported populations and of populations with overlapping generations using easily measured life history traits.     

Population biology of a selfish sex ratio distorting element in a booklouse (Psocodea: Liposcelis)

Arthropods harbour a variety of selfish genetic elements that manipulate reproduction to be preferentially transmitted to future generations. A major ongoing question is to understand how these elements persist in nature. In this study, we examine the population dynamics of an unusual selfish sex ratio distorter in a recently discovered species of booklouse, Liposcelis sp. (Psocodea: Liposcelididae) to gain a better understanding of some of the factors that may affect the persistence of this element. Females that carry the selfish genetic element only ever produce daughters, although they are obligately sexual. These females also only transmit the maternal half of their genome. We performed a replicated population cage experiment, varying the initial frequency of females that harbour the selfish element, and following female frequencies for 20 months. The selfish genetic element persisted in all cages, often reaching very high (and thus severely female‐biased) frequencies. Surprisingly, we also found that females that carry the selfish genetic element had much lower fitness than their nondistorter counterparts, with lower lifetime fecundity, slower development and a shorter egg‐laying period. We suggest that differential fitness plays a role in the maintenance of the selfish genetic element in this species. We believe that the genetic system in this species, paternal genome elimination, which allows maternal control of offspring sex ratio, may also be important in the persistence of the selfish genetic element, highlighting the need to consider species with diverse ecologies and genetic systems when investigating the effects of sex ratio manipulators on host populations.     

Small effective population sizes in a widespread selfing species, Lymnaea truncatula (Gastropoda: Pulmonata)

We present here a spatial and temporal population genetic survey of a common freshwater snail, also a predominantly selfing species, Lymnaea truncatula. The rate of genetic diversity loss was quantified by estimating the effective size (Ne) of the snail populations, using two different methods. A temporal survey allowed estimation of a variance effective size of the populations, and a spatial survey allowed the estimation of an inbreeding effective size, from two-locus identity disequilibria estimates. Both methods were consistent and provided low Ne values. Drift due to (i) high amounts of selfing and (ii) fluctuations in population sizes because of temporary habitats, and also selection coupled to genome-wide linkage disequilibria, could explain such reductions in Ne. The loss of genetic diversity appears to be counterbalanced only very partially by low apparent rates of gene flow.     

The build up of mutation-selection- drift balance in laboratory Drosophila populations

The build up of an equilibrium between mutation, selection, and drift in populations of moderate size is an important evolutionary issue, and can be critical in the conservation of endangered populations. We studied this process in two Drosophila melanogaster populations initially lacking genetic variability (C1 and C2) that were subsequently maintained during 431 or 165 generations with effective population size N(e) approximately 500 (estimated by lethal complementation analysis). Each population originated synchronously to a companion set of full-sib mutation accumulation (MA) lines, C1 and MA1 were derived from an isogenic origin and C2 and MA2 from a single MA1 line at generation 265. The results suggest that both C1 and C2 populations were close to the mutation-selection-drift balance for viability and bristle traits, and are consistent with a 2.5-fold increase of the mutation rate in C2 and MA2. Despite this increase, the average panmictic viability in C2 was only slightly below that of C1, indicating that the expressed loads due to segregating deleterious mutation were small, in agreement with the low deleterious mutation rate (0.015-0.045) previously reported for the MA1 lines. In C1, the nonlethal inbreeding depression rate for viability was 30% of that usually estimated in segregating populations. The genetic variance for bristles regenerated in C1 and C2 was moderately smaller than the average value reported for natural populations, implying that they have accumulated a substantial adaptive potential. In light of neutral and selective predictions, these results suggest that bristle additive variance was predominantly due to segregation of mutations with deleterious effects of the order of 10(-3), and is consistent with relatively weak causal stabilizing selection (V(s) approximately 30).     

Bottlenecks, drift and differentiation: the population structure and demographic history of sika deer (Cervus nippon) in the Japanese archipelago

We assessed genetic differentiation and diversity in 14 populations of sika deer (Cervus nippon) from Japan and four populations of sika deer introduced to the UK, using nine microsatellite loci. We observed extreme levels of differentiation and significant differences in diversity between populations. Our results do not support morphological subspecies designations, but are consistent with previous mitochondrial DNA analyses which suggest the existence of two genetically distinct lineages of sika deer in Japan. The source of sika introduced to the UK was identified as Kyushu. The underlying structure of Japanese populations probably derives from drift in separate glacial refugia and male dispersal limited by distance. This structure has been perturbed by bottlenecks and habitat fragmentation, resulting from human activity from the mid-nineteenth century. Most current genetic differentiation and differences in diversity among populations probably result from recent drift. Coalescent model analysis suggests sika on each of the main Japanese islands have experienced different recent population histories. Hokkaido, which has large areas of continuous habitat, has maintained high levels of gene flow. In Honshu the population is highly fragmented and is likely to have been evolving by drift alone. In Kyushu there has been a balance between gene flow and drift but all the populations have experienced high levels of drift. Habitat fragment size was not significantly associated with genetic diversity in populations but there was a significant correlation between habitat fragment size and effective population size.     

Population dynamics of the glacial relict amphipods in a subarctic lake: role of density‐dependent and density‐independent factors

Relative role of intrinsic density‐dependent factors (such as inter‐ and intraspecific competition, predation) and extrinsic density‐independent factors (environmental changes) in population dynamics is a key issue in ecology. Density‐dependent mechanisms are considered as important drivers of population dynamics in many vertebrate and insect species; however, their influence on the population dynamics of freshwater invertebrates is not clearly understood. In this study, I examined interannual variations in the abundance of the glacial relict amphipod Monoporeia affinis in a small subarctic lake based on long‐term (2002–2019) monitoring data. The results suggest that the population dynamics of amphipods in the lake is influenced by the combined effects of both intrinsic and extrinsic factors. The reproductive success of amphipod cohorts was inversely related to its initial abundance, indicating it is influenced by density‐dependent factors. M. affinis recruitment was negatively correlated with population density and near‐bottom temperature but positively correlated with food availability, which is defined as the concentration of chlorophyll a. Multiple regression with chlorophyll, temperature, and abundance of parent cohort as independent factors explained about 80% of the variation in the reproductive success of amphipods. The negative correlation between amphipod recruitment and water temperature indicates that the current climate conditions adversely affect the populations of glacial relict amphipods even in cold‐water lakes of the subarctic zone. Results of this study can be useful in environmental assessments to separate population oscillations connected with density‐dependent mechanisms from human‐mediated changes.     

Seed size,number and strategies in annual plants: a comparative functional analysis and synthesis

Background and AimsPlants depend fundamentally on establishment from seed. However, protocols in trait-based ecology currently estimate seed size but not seed number. This can be rectified. For annuals, seed number should simply be a positive function of vegetative biomass and a negative function of seed size.MethodsUsing published values of comparative seed number as the ‘gold standard’ and a large functional database, comparative seed yield and number per plant and per m² were predicted by multiple regression. Subsequently, ecological variation in each was explored for English and Spanish habitats, newly calculated C-S-R strategies and changed abundance in the British flora.Key ResultsAs predicted, comparative seed mass yield per plant was consistently a positive function of plant size and competitive ability, and largely independent of seed size. Regressions estimating comparative seed number included, additionally, seed size as a negative function. Relationships differed numerically between regions, habitats and C-S-R strategies. Moreover, some species differed in life history over their geographical range. Comparative seed yield per m² was positively correlated with FAO crop yield, and increasing British annuals produced numerous seeds. Nevertheless, predicted values must be viewed as comparative rather than absolute: they varied according to the ‘gold standard’ predictor used. Moreover, regressions estimating comparative seed yield per m² achieved low precision.ConclusionsFor the first time, estimates of comparative seed yield and number for >800 annuals and their predictor equations have been produced and the ecological importance of these regenerative traits has been illustrated. ‘Regenerative trait-based ecology’ remains in its infancy, with work needed on determinate vs. indeterminate flowering (‘bet-hedging’), C-S-R methodologies, phylogeny, comparative seed yield per m² and changing life history. Nevertheless, this has been a positive start and readers are invited to use estimates for >800 annuals, in the Supplementary data, to help advance ‘regenerative trait-based ecology’ to the next level.     

Gene flow and melanism in garter snakes revisited: a comparison of molecular markers and island vs. coalescent models

Within populations, the stochastic effect of genetic drift and deterministic effect of natural selection are potentially weakened or altered by gene flow among populations. The influence of gene flow on Lake Erie populations of the common garter snake has been of particular interest because of a discontinuous colour pattern polymorphism (striped vs. melanistic) that is a target of natural selection. We reassessed the relative contributions of gene flow and genetic drift using genetic data and population size estimates. We compared all combinations of two marker systems and two analytical approaches to the estimation of gene flow rates: allozymes (data previously published), microsatellite DNA (new data), the island model ( F _ST-based approach), and a coalescence-based approach. For the coalescence approach, mutation rates and sampling effects were also investigated. While the two markers produced similar results, gene flow based on F _ST was considerably higher (Nm > 4) than that from the coalescence-based method (Nm < 1). Estimates of gene flow are likely to be inflated by lack of migration-drift equilibrium and changing population size. Potentially low rates of gene flow (Nm < 1), small population size at some sites, and positive correlations of number of microsatellite DNA alleles and island size and between M , mean ratio of number of alleles to range in allele size, and island size suggest that in addition to selection, random genetic drift may influence colour pattern frequencies. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 389–399.     

The roles of cytoplasmic poly(A)-binding proteins in regulating gene expression: a developmental perspective.

Poly(A)-binding proteins (PABPs) are central to the regulation of messenger RNA (mRNA) translation and stability; however, the roles and contributions of different PABP family members in controlling gene expression are not yet fully understood. In this paper, the current state of knowledge of the different cytoplasmic PABP proteins and their function in animal cells will be summarised, with particular reference to their roles in development. Possible regulatory mechanisms and potential new roles for these proteins in the control of specific mRNAs are also highlighted.