Inference from Clines Stabilized by Frequency-Dependent Selection

Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between square root of s/square root of 8 sigma and square root of s/square root of 12 delta, where sigma is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations ("linkage disequilibria"), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequencies and of gametic correlations from a hybrid zone.     

A SIMULATION STUDY OF MULTILOCUS CLINES

Fisher's method of junctions is used to investigate the degree of association between selected alleles in a cline, in the limit where there is divergence between very many genes. A computer model is used to simulate one of a pair of infinite demes that exchange individuals each generation. Selection is on haploids; it is additive and is equivalent to heterozygote disadvantage. Recombination is uniform over a single chromosome. A “critical value” of selection exists at equilibrium, below which loci act independently and above which they act in association (Barton 1983). Starting with secondary contact, simulation results contrast markedly with the equilibrium solution. The “critical value” is not apparent in the simulated clines, even after many generations. Rather, loci remain associated to some extent under all degrees of selection. The simulation is consistent with the equilibrium analysis in all other respects, and therefore indicates that under weak selection the approach to equilibrium is very slow. This is borne out by further numerical calculations. The slow approach to equilibrium enables us to estimate the time since contact between two demes under idealized conditions. Extending this work toward natural hybrid zones is discussed.     

ALTITUDINAL CLINAL VARIATION IN WING SIZE AND SHAPE IN AFRICAN DROSOPHILA MELANOGASTER: ONE CLINE OR MANY?

Geographical patterns of morphological variation have been useful in addressing hypotheses about environmental adaptation. In particular, latitudinal clines in phenotypes have been studied in a number of Drosophila species. Some environmental conditions along latitudinal clines—for example, temperature—also vary along altitudinal clines, but these have been studied infrequently and it remains unclear whether these environmental factors are similar enough for convergence or parallel evolution. Most clinal studies in Drosophila have dealt exclusively with univariate phenotypes, allowing for the detection of clinal relationships, but not for estimating the directions of covariation between them. We measured variation in wing shape and size in D. melanogaster derived from populations at varying altitudes and latitudes across sub‐Saharan Africa. Geometric morphometrics allows us to compare shape changes associated with latitude and altitude, and manipulating rearing temperature allows us to quantify the extent to which thermal plasticity recapitulates clinal effects. Comparing effect vectors demonstrates that altitude, latitude, and temperature are only partly associated, and that the altitudinal shape effect may differ between Eastern and Western Africa. Our results suggest that selection responsible for these phenotypic clines may be more complex than just thermal adaptation.     

How do genetic correlations affect species range shifts in a changing environment?

Species may be able to respond to changing environments by a combination of adaptation and migration. We study how adaptation affects range shifts when it involves multiple quantitative traits evolving in response to local selection pressures and gene flow. All traits develop clines shifting in space, some of which may be in a direction opposite to univariate predictions, and the species tracks its environmental optimum with a constant lag. We provide analytical expressions for the local density and average trait values. A species can sustain faster environmental shifts, develop a wider range and greater local adaptation when spatial environmental variation is low (generating low migration load) and multitrait adaptive potential is high. These conditions are favoured when nonlinear (stabilising) selection is weak in the phenotypic direction of the change in optimum, and genetic variation is high in the phenotypic direction of the selection gradient.     

Levels of multiallelic overdominance fitness, heterozygote excess and heterozygote deficiency

Concepts and results on selection balance in multiallelic systems are described. These include a multidimensional concept of heterozygote excess and heterozygote deficiency, a hierarchy of means of assessment of heterozygote advantage, comparisons and contrasts of allelic versus gametic polymorphic states, and conditions defining stable equilibria of complementary gametic sets. The concepts are illustrated in the context of viability selection and behavioral models of kin selection and for two major categories of multilocus selection regimes.     

Nonrandom larval dispersal can steepen marine clines

Sharp and stable clinal variation is enigmatic when found in species with high gene flow. Classical population genetic models treat gene flow as a random homogenizing force countering local adaptation across habitat discontinuities. Under this view, dispersal over large spatial scales will lower the effectiveness of adaptation by natural selection at finer spatial scales. Thus, random gene flow will create a shallow phenotypic cline across an ecotone in response to a steep selection gradient. In sedentary marine species that disperse primarily as larvae, nonrandom dispersal patterns are expected due to coastal hydrodynamics. Surprisingly sharp phenotypic and genotypic clines have been documented in marine species with high gene flow. We are interested in the extent to which nonrandom dispersal could accentuate such clines. We model a linear species range in which populations have stable and uniform densities along a selection gradient; in contrast to random dispersal, convergent advection of larvae can amplify phenotypic differentiation if coupled with a semipermeable dispersal barrier in the convergence zone. The migration load caused by directional dispersal pushes the phenotypic mean away from the local trait optimum in downstream populations, that is, near the convergence zone. A dispersal barrier is possible as a result of colliding currents if the water and larvae are mostly displaced offshore, away from suitable settlement habitat. Disjunctions in a quantitative trait were enlarged in the convergence zone by faster current flows or a more complete dispersal barrier. With advection of larvae per generation one-third as far as the average dispersal distance by diffusion, convergence on a dispersal barrier with 40% permeability generated a trait disjunction across the convergence zone of two phenotypic standard deviations. Without directional dispersal, similar clines also developed across a habitat gap, where population density was low, or across dispersal barriers with less than 1% permeability. These findings suggest that the types of hydrographic phenomena often associated with marine transition zones can strongly affect the balance between gene flow and selection and generate surprisingly steep clines given the large-scale gene flow expected from larvae.     

Coevolutionary clines across selection mosaics

Abstract. Much of the dynamics of coevolution may be driven by the interplay between geographic variation in reciprocal selection (selection mosaics) and the homogenizing action of gene flow. We develop a genetic model of geographically structured coevolution in which gene flow links coevolving communities that may differ in both the direction and magnitude of reciprocal selection. The results show that geographically structured coevolution may lead to allele-frequency clines within both interacting species when fitnesses are spatially uniform or spatially heterogeneous. Furthermore, the results show that the behavior and shape of clines differ dramatically among different types of coevolutionary interaction. Antagonistic interactions produce dynamic clines that change shape rapidly through time, producing shifting patterns of local adaptation and maladaptation. Unlike antagonistic interactions, mutualisms generate stable equilibrium patterns that lead to fixed spatial patterns of adaptation. Interactions that vary between mutualism and antagonism produce both equilibrium and dynamic clines. Furthermore, the results demonstrate that these interactions may allow mutualisms to persist throughout the geographic range of an interaction, despite pockets of locally antagonistic selection. In all cases, the coevolved spatial patterns of allele frequencies are sensitive to the relative contributions of gene flow, selection, and overall habitat size, indicating that the appropriate scale for studies of geographically structured coevolution depends on the relative contributions of each of these factors.     

The coupling hypothesis: why genome scans may fail to map local adaptation genes

Genomic scans of multiple populations often reveal marker loci with greatly increased differentiation between populations. Often this differentiation coincides in space with contrasts in ecological factors, forming a genetic-environment association (GEA). GEAs imply a role for local adaptation, and so it is tempting to conclude that the strongly differentiated markers are themselves under ecologically based divergent selection, or are closely linked to loci under such selection. Here, we highlight an alternative and neglected explanation: intrinsic (i.e. environment-independent) pre- or post-zygotic genetic incompatibilities rather than local adaptation can be responsible for increased differentiation. Intrinsic genetic incompatibilities create endogenous barriers to gene flow, also known as tension zones, whose location can shift over time. However, tension zones have a tendency to become trapped by, and therefore to coincide with, exogenous barriers due to ecological selection. This coupling of endogenous and exogenous barriers can occur easily in spatially subdivided populations, even if the loci involved are unlinked. The result is that local adaptation explains where genetic breaks are positioned, but not necessarily their existence, which can be best explained by endogenous incompatibilities. More precisely, we show that (i) the coupling of endogenous and exogenous barriers can easily occur even when ecological selection is weak; (ii) when environmental heterogeneity is fine-grained, GEAs can emerge at incompatibility loci, but only locally, in places where habitats and gene pools are sufficiently intermingled to maintain linkage disequilibria between genetic incompatibilities, local-adaptation genes and neutral loci. Furthermore, the association between the locally adapted and intrinsically incompatible alleles (i.e. the sign of linkage disequilibrium between endogenous and exogenous loci) is arbitrary and can form in either direction. Reviewing results from the literature, we find that many predictions of our model are supported, including endogenous genetic barriers that coincide with environmental boundaries, local GEA in mosaic hybrid zones, and inverted or modified GEAs at distant locations. We argue that endogenous genetic barriers are often more likely than local adaptation to explain the majority of Fst-outlying loci observed in genome scan approaches - even when these are correlated to environmental variables.     

Evolutionary responses of tree phenology to the combined effects of assortative mating,gene flow and divergent selection

The timing of bud burst (TBB) in temperate trees is a key adaptive trait, the expression of which is triggered by temperature gradients across the landscape. TBB is strongly correlated with flowering time and is therefore probably mediated by assortative mating. We derived theoretical predictions and realized numerical simulations of evolutionary changes in TBB in response to divergent selection and gene flow in a metapopulation. We showed that the combination of the environmental gradient of TBB and assortative mating creates contrasting genetic clines, depending on the direction of divergent selection. If divergent selection acts in the same direction as the environmental gradient (cogradient settings), genetic clines are established and inflated by assortative mating. Conversely, under divergent selection of the same strength but acting in the opposite direction (countergradient selection), genetic clines are slightly constrained. We explored the consequences of these dynamics for population maladaptation, by monitoring pollen swamping. Depending on the direction of divergent selection with respect to the environmental gradient, pollen filtering owing to assortative mating either facilitates or impedes adaptation in peripheral populations.     

Broad Concordance in the Spatial Distribution of Adaptive and Neutral Genetic Variation across an Elevational Gradient in Deer Mice

When species are continuously distributed across environmental gradients, the relative strength of selection and gene flow shape spatial patterns of genetic variation, potentially leading to variable levels of differentiation across loci. Determining whether adaptive genetic variation tends to be structured differently than neutral variation along environmental gradients is an open and important question in evolutionary genetics. We performed exome-wide population genomic analysis on deer mice sampled along an elevational gradient of nearly 4,000 m of vertical relief. Using a combination of selection scans, genotype−environment associations, and geographic cline analyses, we found that a large proportion of the exome has experienced a history of altitude-related selection. Elevational clines for nearly 30% of these putatively adaptive loci were shifted significantly up- or downslope of clines for loci that did not bear similar signatures of selection. Many of these selection targets can be plausibly linked to known phenotypic differences between highland and lowland deer mice, although the vast majority of these candidates have not been reported in other studies of highland taxa. Together, these results suggest new hypotheses about the genetic basis of physiological adaptation to high altitude, and the spatial distribution of adaptive genetic variation along environmental gradients.     

Patterns of divergence across the geographic and genomic landscape of a butterfly hybrid zone associated with a climatic gradient

Hybrid zones are a valuable tool for studying the process of speciation and for identifying the genomic regions undergoing divergence and the ecological (extrinsic) and nonecological (intrinsic) factors involved. Here, we explored the genomic and geographic landscape of divergence in a hybrid zone between Papilio glaucus and Papilio canadensis. Using a genome scan of 28,417 ddRAD SNPs, we identified genomic regions under possible selection and examined their distribution in the context of previously identified candidate genes for ecological adaptations. We showed that differentiation was genomewide, including multiple candidate genes for ecological adaptations, particularly those involved in seasonal adaptation and host plant detoxification. The Z chromosome and four autosomes showed a disproportionate amount of differentiation, suggesting genes on these chromosomes play a potential role in reproductive isolation. Cline analyses of significantly differentiated genomic SNPs, and of species‐diagnostic genetic markers, showed a high degree of geographic coincidence (81%) and concordance (80%) and were associated with the geographic distribution of a climate‐mediated developmental threshold (length of the growing season). A relatively large proportion (1.3%) of the outliers for divergent selection were not associated with candidate genes for ecological adaptations and may reflect the presence of previously unrecognized intrinsic barriers between these species. These results suggest that exogenous (climate‐mediated) and endogenous (unknown) clines may have become coupled and act together to reinforce reproductive isolation. This approach of assessing divergence across both the genomic and geographic landscape can provide insight about the interplay between the genetic architecture of reproductive isolation and endogenous and exogenous selection.     

A fine-scale spatial analysis of the mosaic hybrid zone between Gryllus firmus and Gryllus pennsylvanicus

Abstract.— The pattern of character variation within a hybrid zone, the hybrid zone structure, has been used to infer the processes that maintain hybrid zones. Unfortunately it is difficult to infer process from structure alone because many different processes can produce the same pattern of character variation. Mosaic hybrid zones may be maintained by exogenous selection in a heterogeneous environment and/or endogenous selection against hybrid individuals; habitat preference, premating isolating barriers and/or fertility selection can also contribute. The spatial scale at which a hybrid zone is sampled affects its apparent structure; a hybrid zone may appear clinal at one scale and mosaic at another. Here, we sample the mosaic hybrid zone between two field crickets, Gryllus firmus and G. pennsylvanicus , at a scale that spans the boundaries between individual soil-habitat patches. From our analysis, we find that at fine scales, the mosaic hybrid zone resolves into a set of steep clines across patch boundaries. Both morphological and molecular traits exhibit sharp and generally concordant clines. However, clines for mitochondrial DNA and one anonymous nuclear marker are clearly displaced as a result of current hybridization or past introgression (the "ghost of hybridization past"). Thus, scale is important for the structure of this and probably other hybrid zones. The extremely sharp, concordant clines across patch boundaries indicate that the cricket hybrid zone is undoubtedly structured by selection. However, the detailed mechanisms responsible for the maintenance of the hybrid zone–whether endogenous selection against hybrids, exogenous selection by the environment, and/or behavioral preferences for mates or habitats– remain to be elucidated. Determining these mechanisms will depend on closer inspection of the organisms themselves and their interactions, as is the case for all hybrid zones.     

The structure of clines with fitness-dependent dispersal

Spatial models commonly assume that dispersal does not depend on environmental conditions or phenotype. For example, these assumptions underpin explanations for clines on the basis of a trade-off between dispersal and local adaptation. We reexamine clines when an individual's decisions over whether and where to disperse depend on its fitness. We compare fitness-dependent dispersal with cases where dispersal responds to juvenile survivorship only. Clines are steeper the more responsive dispersal is to environmental conditions for all dispersal behaviors that we consider. Clines eventually become stepped as the responsiveness of dispersal to environmental conditions is increased for half of the dispersal behaviors we consider, but smooth clines are maintained for the remaining cases. Smooth clines are maintained by the biased movement of individuals out of the hybrid zone when individuals move directionally in response to gradients in juvenile survivorship, which is a different mechanism to that maintaining smooth clines in classic cline theory.     

Adaptation to a steep environmental gradient and an associated barrier to gene exchange in Littorina saxatilis

Steep environmental gradients offer important opportunities to study the interaction between natural selection and gene flow. Allele frequency clines are expected to form at loci under selection, but unlinked neutral alleles may pass easily across these clines unless a generalized barrier evolves. Here we consider the distribution of forms of the intertidal gastropod Littorina saxatilis, analyzing shell shape and amplified fragment length polymorphism (AFLP) loci on two rocky shores in Britain. On the basis of previous work, the AFLP loci were divided into differentiated and undifferentiated groups. On both shores, we have shown a sharp cline in allele frequencies between the two morphs for differentiated AFLP loci. This is coincident with a habitat transition on the shore where the two habitats (cliff and boulder field) are immediately contiguous. The allele frequency clines coincide with a cline in shell morphology. In the middle of the cline, linkage disequilibrium for the differentiated loci rises in accordance with expectation. The clines are extremely narrow relative to dispersal, probably as a result of both strong selection and habitat choice. An increase in F(ST) for undifferentiated AFLPs between morphs, relative to within-morph comparisons, is consistent with there being a general barrier to gene flow across the contact zone. These features are consistent either with an episode of allopatric divergence followed by secondary contact or with primary, nonallopatric divergence. Further data will be needed to distinguish between these alternatives.     

Searching for the bull's eye: agents and targets of selection vary among geographically disparate cyanogenesis clines in white clover (Trifolium repens L.)

The recurrent evolution of adaptive clines within a species can be used to elucidate the selective factors and genetic responses that underlie adaptation. White clover is polymorphic for cyanogenesis (HCN release with tissue damage), and climate-associated cyanogenesis clines have evolved throughout the native and introduced species range. This polymorphism arises through two independently segregating Mendelian polymorphisms for the presence/absence of two required components: cyanogenic glucosides and their hydrolyzing enzyme linamarase. Cyanogenesis is commonly thought to function in herbivore defense; however, the individual cyanogenic components may also serve other physiological functions. To test whether cyanogenesis clines have evolved in response to the same selective pressures acting on the same genetic targets, we examined cyanogenesis cline shape and its environmental correlates in three world regions: southern New Zealand, the central United States and the US Pacific Northwest. For some regional comparisons, cline shapes are remarkably similar despite large differences in the spatial scales over which clines occur (40–1600 km). However, we also find evidence for major differences in both the agents and targets of selection among the sampled clines. Variation in cyanogenesis frequency is best predicted using a combination of minimum winter temperature and aridity variables. Together, our results provide evidence that recurrent adaptive clines do not necessarily reflect shared adaptive processes.     

Altitudinal and climatic adaptation is mediated by flowering traits and FRI, FLC, and PHYC genes in Arabidopsis

Extensive natural variation has been described for the timing of flowering initiation in many annual plants, including the model wild species Arabidopsis (Arabidopsis thaliana), which is presumed to be involved in adaptation to different climates. However, the environmental factors that might shape this genetic variation, as well as the molecular bases of climatic adaptation by modifications of flowering time, remain mostly unknown. To approach both goals, we characterized the flowering behavior in relation to vernalization of 182 Arabidopsis wild genotypes collected in a native region spanning a broad climatic range. Phenotype-environment association analyses identified strong altitudinal clines (0-2600 m) in seven out of nine flowering-related traits. Altitudinal clines were dissected in terms of minimum winter temperature and precipitation, indicating that these are the main climatic factors that might act as selective pressures on flowering traits. In addition, we used an association analysis approach with four candidate genes, FRIGIDA (FRI), FLOWERING LOCUS C (FLC), PHYTOCHROME C (PHYC), and CRYPTOCHROME2, to decipher the genetic bases of this variation. Eleven different loss-of-function FRI alleles of low frequency accounted for up to 16% of the variation for most traits. Furthermore, an FLC allelic series of six novel putative loss- and change-of-function alleles, with low to moderate frequency, revealed that a broader FLC functional diversification might contribute to flowering variation. Finally, environment-genotype association analyses showed that the spatial patterns of FRI, FLC, and PHYC polymorphisms are significantly associated with winter temperatures and spring and winter precipitations, respectively. These results support that allelic variation in these genes is involved in climatic adaptation.     

Divergent character clines across a recent secondary contact zone in a Hispaniolan lizard

Studies of genetic contact zones provide valuable information regarding the processes of population divergence, adaptation and speciation. In this paper, I examine transitions in morphology, mitochondrial DNA (mtDNA) and nuclear DNA (nDNA) haplotypes across a recent secondary contact zone in a Hispaniolan lizard Ameiva chrysolaema . Maximum likelihood cline fitting analyses suggest non-coincidence of cline centers and that the mtDNA cline is significantly displaced to the west of the remaining clines. nDNA and morphological clines are coincident and tend to be associated with the prevailing environmental gradient. The lack of cytonuclear disequilibrium near the center of the contact zone and the non-coincidence of character clines suggest that this zone does not conform to a tension zone model of hybridization; thus, gene flow across the zone does not seem to be impeded. The extremely narrow width of the dorsal scale size cline and the close association of this cline with the steepness of the environmental (precipitation) gradient suggest that this character may be under environmental selection. Taken together, this contact zone appears to be structured by a combination of mtDNA introgression, possibly associated with eastward movement of the zone, and environmental selection on some characters.     

The exact values of the probability of fixation of underdominant chromosomal rearrangements.

A numerical analysis of the probability of fixation of a chromosomal mutation with partial sterility of the heterozygote in a single population is performed. Three different genetic models are considered: the first model entails constant selection against the heterozygote and is the model almost universally used in previous works; in the other two models selection against the heterozygote depends on its frequency. The exact values of the fixation probability are found by iterating transition matrices with genotype specification. Differences in results among models are small. The exact values found in the first model are compared to estimates obtained from approximations. Solutions based on diffusion models give good approximations when selection against the heterozygote is low, especially if the population is very small. For the higher values of the selection coefficient against the heterozygote, the estimates are rather imprecise, especially when the populations are not very small.     

Clinal colour variation within a panmictic population of tree squirrels,Tamiasciurus douglasii (Rodentia: Sciuridae), across an ecological gradient

Local adaptation occurs when a population in a heterogeneous environment experiences divergent ecological selection but only if selection is stronger than the homogenizing effects of gene flow. The forest environments of Oregon vary along a physical and biotic gradient from a wet, closed‐canopy forest near the coast to a drier open‐canopy forest eastward across the Cascade Mountains. The present study explores patterns of local adaptation in Douglas squirrels (Tamiasciurus douglasii) in relation to these transitions in forest structure and ecology. We test for the presence of morphological clines in relation to gene flow and, more specifically, whether any such character clines correspond with environmental clines. We sampled animals at six locations (10 specimens each) and evaluated environmental parameters across a 240‐km west‐to‐east transect. Population structure analysis of 18 microsatellite loci indicates a single, panmictic squirrel population across the entire transect. Coalescent‐based estimates show bidirectional gene flow at similar west–east intensities between squirrels in coastal and interior forests. Of the four skull traits examined, none shows a significant clinal transition. By contrast, ventral fur colour shows a strong clinal transition, from deep‐orange in coastal forest to whitish–yellow in the interior forest. This pattern of phenotypic divergence coincides with the gradient in tree‐canopy cover. Ventral fur colour of T. douglasii exemplifies a gradation of continuous phenotypic variation maintained despite ongoing gene flow in a panmictic population. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 536–546.     

The spatial scale of local adaptation in a stochastic environment

The distribution of phenotypes in space will be a compromise between adaptive plasticity and local adaptation increasing the fit of phenotypes to local conditions and gene flow reducing that fit. Theoretical models on the evolution of quantitative characters on spatially explicit landscapes have only considered scenarios where optimum trait values change as deterministic functions of space. Here, these models are extended to include stochastic spatially autocorrelated aspects to the environment, and consequently the optimal phenotype. Under these conditions, the regression of phenotype on the environmental variable becomes steeper as the spatial scale on which populations are sampled becomes larger. Under certain deterministic models – such as linear clines – the regression is constant. The way in which the regression changes with spatial scale is informative about the degree of phenotypic plasticity, the relative scale of effective gene flow and the environmental dependency of selection. Connections to temporal models are discussed.