Analysis of Clines with Variable Selection and Variable Migration

We report a likelihood-based method that estimates both dispersal and natural selection using the rate of change of the shape of a cline when selection and migration are not constant through time. We have investigated the case of local adaptation of the mosquito Culex pipiens to organophosphate insecticides in the Montpellier area in France. We have analyzed the modification of the clinal patterns at two resistance loci during the period from breeding to overwintering. We show that mosquitoes migrate extensively from breeding to overwintering sites at a rate that is markedly different from previous estimates made during the breeding season only. This migration is also strongly asymmetrical, which can be explained by different geographical distributions of breeding and overwintering sites, by variation in mosquito density along the transect, or by behavioral biases. We found that the starting time of overwintering is likely to vary between northern and southern populations and that substantial fitness costs are associated with resistance alleles at the two loci during overwintering. These results illustrate how demography and adaptive microevolution can be studied using selected markers. The method provides a framework to use population genetics and statistical models to reveal ecological and evolutionary processes.     

Clines with asymmetric migration

The consequences of asymmetric dispersion on the maintenance of an allele in a one-dimensional environmental pocket are examined. The diffusion model of migration and selection is restricted to a single diallelic locus in a monoecious population in the absence of mutation and random drift. It is further supposed that migration is homogeneous and independent of genotype, the population density is constant and uniform, and Hardy-Weinberg proportions obtain locally. If dispersion is preferentially out of an environmental pocket at the end of a very long habitat, the condition for maintaining the allele favored in the pocket becomes less stringent than for symmetric migration; dispersion preferentially into the pocket increases the severity of the condition for polymorphism. If an allele is harmful in large regions on both sides of an environmental pocket, the probability for polymorphism is decreased by asymmetric migration. The criterion for the existence of a cline is independent of the sense of the asymmetry; the cline itself is not. These phenomena are studied both analytically and numerically.—It is shown for symmetric migration and variable population density that the more densely populated parts of the habitat are more influential in determining gene frequency than the others. Thus, the higher the population density in an environmental pocket, the more easily an allele beneficial in the pocket will be maintained in the population.     

Clines with partial panmixia

In spatially distributed populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into single-locus clines maintained by migration and selection is investigated. In a diallelic, two-deme model without dominance, partial panmixia can increase or decrease both the polymorphic area in the plane of the migration rates and the equilibrium gene-frequency difference between the two demes. For multiple alleles, under the assumptions that the number of demes is large and both migration and selection are arbitrary but weak, a system of integro-partial differential equations is derived. For two alleles with conservative migration, (i) a Lyapunov functional is found, suggesting generic global convergence of the gene frequency; (ii) conditions for the stability or instability of the fixation states, and hence for a protected polymorphism, are obtained; and (iii) a variational representation of the minimal selection-migration ratio λ₀ (the principal eigenvalue of the linearized system) for protection from loss is used to prove that λ₀ is an increasing function of the panmictic rate and to deduce the effect on λ₀ of changes in selection and migration. The unidimensional step-environment with uniform population density, homogeneous, isotropic migration, and no dominance is examined in detail: An explicit characteristic equation is derived for λ₀; bounds on λ₀ are established; and λ₀ is approximated in four limiting cases. An explicit formula is also deduced for the globally asymptotically stable cline in an unbounded habitat with a symmetric environment; partial panmixia maintains some polymorphism even as the distance from the center of the cline tends to infinity.     

Genetic Drift in Clines Which Are Maintained by Migration and Natural Selection

Genetic drift will cause a migration-selection cline to wobble about its expected position. A rough linear approximation is developed, valid when local populations are large. This is used to calculate effects of genetic drift on clines in a stepping-stone model with abrupt and with gradual changes of selection coefficients at a single haploid locus. Among the quantities calculated are measures of slope, standardized variation of gene frequencies around their expected values, and correlation among neighboring populations with respect to deviations from the expected gene frequencies. These quantities appear to be primarily functions of Ns and Nm for a given pattern of selection. Computer simulation gives rough confirmation of these results. Standardized variances of gene frequencies and correlation of neighbors differ along the cline in the case of smooth changes in selection. In no case is pathological behavior of gene frequency deviations found near the boundaries of selective regions. Local behavior of gene frequences of nearby colonies is approximately predicted by a simple adaptation of the stepping-stone theory of Kimura and Weiss. Approximate measures of the lateral variation of the midpoint of a cline and the probability of non-monotonicity are also calculated and discussed.     

Clines in polygenic traits

This article outlines theoretical models of clines in additive polygenic traits, which are maintained by stabilizing selection towards a spatially varying optimum. Clines in the trait mean can be accurately predicted, given knowledge of the genetic variance. However, predicting the variance is difficult, because it depends on genetic details. Changes in genetic variance arise from changes in allele frequency, and in linkage disequilibria. Allele frequency changes dominate when selection is weak relative to recombination, and when there are a moderate number of loci. With a continuum of alleles, gene flow inflates the genetic variance in the same way as a source of mutations of small effect. The variance can be approximated by assuming a Gaussian distribution of allelic effects; with a sufficiently steep cline, this is accurate even when mutation and selection alone are better described by the 'House of Cards' approximation. With just two alleles at each locus, the phenotype changes in a similar way: the mean remains close to the optimum, while the variance changes more slowly, and over a wider region. However, there may be substantial cryptic divergence at the underlying loci. With strong selection and many loci, linkage disequilibria are the main cause of changes in genetic variance. Even for strong selection, the infinitesimal model can be closely approximated by assuming a Gaussian distribution of breeding values. Linkage disequilibria can generate a substantial increase in genetic variance, which is concentrated at sharp gradients in trait means.     

Inversion Clines in Populations of DROSOPHILA MELANOGASTER

Twenty different natural populations of Drosophila melanogaster were sampled to determine the frequencies of inversions. Based on their frequencies and geographical distributions, the inversions could be classified as follows: (1) Common cosmopolitan inversions that are present in many populations in frequencies exceeding five percent and that may exhibit frequency clines over large geographical regions; (2) Rare cosmopolitan inversions that occur throughout the species range but usually at frequencies below five percent and that may be absent in many populations; (3) Recurrent endemic inversions that are found in several adjacent populations in frequencies usually not exceeding one or two percent; and (4) Unique endemic inversions that are found only among the progeny of a single individual and that may represent one aspect of the syndrome termed "hybrid dysgenesis". Four common cosmopolitan inversions that exhibit highly significant clines in populations in the eastern United States are In(2L)t, In(2R)NS, In(3L)P and In(3R)P.     

Clines with partial panmixia in an unbounded unidimensional habitat

In geographically structured populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines maintained by migration and selection in an unbounded unidimensional habitat is investigated. Migration and selection are both weak. The former is homogenous and isotropic; the latter has no dominance. The population density is uniform. A simple, explicit formula is derived for the maximum value β₀ of the scaled panmictic rate β for which a cline exists. The former depends only on the asymptotic values of the scaled selection coefficient. If the two alleles have the same average selection coefficient, there exists a unique, globally asymptotically stable cline for every β≥0. Otherwise, if β≥β₀, the allele with the greater average selection coefficient is ultimately fixed. If β<β₀, there exists a unique, globally asymptotically stable cline, and some polymorphism is retained even infinitely far from its center. The gene frequencies at infinity are determined by a continuous-time, two-deme migration-selection model. An explicit expression is deduced for the monotone cline in a step-environment. These results differ fundamentally from those for the classical cline without panmixia.     

Conditions for the Existence of Clines

A very general partial differential equation in space and time satisfied by the gene frequency in a monoecious population distributed continuously over an arbitrary habitat is derived. The treatment is restricted to a single diallelic locus in the absence of mutation and random drift, and it is supposed that time is continuous, births and deaths occur at random, and migration is independent of genotype. With the further assumptions that migration is isotropic and homogeneous, the population density is constant and uniform (as permitted by the population regulation mechanism included in the formulation), and Hardy-Weinberg proportions obtain locally, this partial differential equation reduces to the simplest multidimensional generalization of the classical Fisher-Haldane cline model. The efficacy of migration and selection in maintaining genetic variability at equilibrium in this model is investigated by deducing conditions for the existence of clines under various circumstances. The effects of the degree of dominance, a neutral belt between the regions where a particular allele is advantageous and deleterious, finiteness of the habitat, and habitat dimensionality are evaluated. Provided at least one of the alleles is favored only in a finite region, excluding the special case in which its total effective selective coefficient is zero, if conditions for supporting a cline are too unfavorable because migration is too strong, selection is too weak, or both, a cline cannot exist at all. Thus, unless there is overdominance, the population must be monomorphic. It is possible for a cline which can barely exist under the prevailing ecological circumstances to show a large amount of variation in gene frequency.     

Clines in the presence of asymmetric migration

If a population, which consists of individuals having genetic variation at one locus, with two alleles A and a, evolves under the influence of migration and selection, gradients in the distribution of alleles may arise. We consider the effect of asymmetry in the migration and spatial dependence of the selection process, upon the emergence and stability of such gradients.     

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.     

Allelic Variation in a Willow Warbler Genomic Region Is Associated with Climate Clines

Local adaptation is an important process contributing to population differentiation which can occur in continuous or isolated populations connected by various amounts of gene flow. The willow warbler (Phylloscopus trochilus) is one of the most common songbirds in Fennoscandia. It has a continuous breeding distribution where it is found in all forested habitats from sea level to the tree line and therefore constitutes an ideal species for the study of locally adapted genes associated with environmental gradients. Previous studies in this species identified a genetic marker (AFLP-WW1) that showed a steep north-south cline in central Sweden with one allele associated with coastal lowland habitats and the other with mountainous habitats. It was further demonstrated that this marker is embedded in a highly differentiated chromosome region that spans several megabases. In the present study, we sampled 2,355 individuals at 128 sites across all of Fennoscandia to study the geographic and climatic variables associated with the allele frequency distributions of WW1. Our results demonstrate that 1) allele frequency patterns significantly differ between mountain and lowland populations, 2) these allele differences coincide with extreme temperature conditions and the short growing season in the mountains, and milder conditions in coastal areas, and 3) the northern-allele or “altitude variant” of WW1 occurs in willow warblers that occupy mountainous habitat regardless of subspecies. Finally these results suggest that climate may exert selection on the genomic region associated with these alleles and would allow us to develop testable predictions for the distribution of the genetic marker based on climate change scenarios.     

Clines in clock genes: fine-tuning circadian rhythms to the environment

The dissection of the circadian clock into its molecular components represents the most striking and well-studied example of a gene regulatory network underlying a complex behavioural trait. By contrast, the evolutionary analysis of the clock has developed more slowly. Here we review studies that have surveyed intraspecific clock gene variation over large geographical areas and have discovered latitudinal clines in gene frequencies. Such spatial patterns traditionally suggest that natural selection shapes genetic variation, but it is equally possible that population history, or a mixture of demography and selection, could contribute to the clines. We discuss how population genetics, together with functional assays, can illuminate these possible cases of natural selection in Drosophila clock genes.     

Clines and adaptive evolution in the methuselah gene region in Drosophila melanogaster

In an effort to characterize further the patterns of selection and adaptive evolution at the methuselah locus in Drosophila species, we extended an analysis of geographical variation to include single nucleotide polymorphisms (SNPs) in adjacent genes on either side of the mth locus, and examined the molecular variation in a neighbouring methuselah paralogue (mth2). An analysis of 13 SNPs spanning a region of nearly 19 kilobases surrounding the mth locus demonstrated that a clinal pattern associated with the most common mth haplotype does not extend to adjacent gene loci, providing compelling evidence that the clinal pattern results from selection on as yet unidentified sites associated with the functional mth locus. mth2 exhibited a significant pattern of adaptive divergence among D. melanogaster, D. simulans and D. yakuba similar to that seen at mth. However, Ka : Ks ratios indicate a difference in levels of functional constraint at the two methuselah, loci with mth2 exhibiting a five- to six-fold reduction in levels of amino acid divergence relative to mth.     

Clines, clusters, and the effect of study design on the inference of human population structure

Previously, we observed that without using prior information about individual sampling locations, a clustering algorithm applied to multilocus genotypes from worldwide human populations produced genetic clusters largely coincident with major geographic regions. It has been argued, however, that the degree of clustering is diminished by use of samples with greater uniformity in geographic distribution, and that the clusters we identified were a consequence of uneven sampling along genetic clines. Expanding our earlier dataset from 377 to 993 markers, we systematically examine the influence of several study design variables—sample size, number of loci, number of clusters, assumptions about correlations in allele frequencies across populations, and the geographic dispersion of the sample—on the “clusteredness” of individuals. With all other variables held constant, geographic dispersion is seen to have comparatively little effect on the degree of clustering. Examination of the relationship between genetic and geographic distance supports a view in which the clusters arise not as an artifact of the sampling scheme, but from small discontinuous jumps in genetic distance for most population pairs on opposite sides of geographic barriers, in comparison with genetic distance for pairs on the same side. Thus, analysis of the 993-locus dataset corroborates our earlier results: if enough markers are used with a sufficiently large worldwide sample, individuals can be partitioned into genetic clusters that match major geographic subdivisions of the globe, with some individuals from intermediate geographic locations having mixed membership in the clusters that correspond to neighboring regions.     

Aerobiological Clines: The Role of Topography As a Barrier for Establishing Dispersal Corridors

Cline is a largely known and studied concept in ecology, but is not part of the aerobiological vocabulary. Some attempts have been undertaken in the past to put in evidence aerobiological clines, but their true significance, especially in relation to dispersal, remains unknown. One of the ideal situations to visualise clines is a dispersal corridor. Looking at the geomorphological and phytogeographical localization of Montreal island, the Hudson River corridor (with its continuation through Lake George, Champlain canal & Lake and Richelieu River), seems to be a natural corridor linking the Oak–Chestnut Forest region (which present a tongue on the Hudson river up to Albany, New York, USA) to the Hemlock – White Pine – Northern Hardwoods region of the St-Lawrence lowlands (Quebec, Canada), through the Adirondacks and the Green Mountains. Pollen and spores were collected in the early summer of 2001 (June 13 to July 17) in a mountain (Five Mile Mountain, 685 m.a.s.l) situated on the west ridge of Lake George. Sampling was repeated for a total of 5 sites, through the western slope (out of the corridor) and eastern slope (Lake George side, into the corridor). In this preliminary analysis, the differences in concentration into and out of the corridor of 5 pollen types (Poaceae, Pinus, Juglans, Carya and Ambrosia) and 6 spore types (Alternaria, Cladosporium, Epicoccum, Ganoderma, Ustilago and Ascospores) in addition to Myxomycetes spores and microscopic algae were investigated. Preliminary results indicate that:(1) there are some significant differences in pollen and spores concentrations out and into the corridor (western and eastern slopes); (2) along the transect, the differences were lower between sampling sites located at the same slope than between sites at different slopes; (3) high concentrations of pollen grains of flowering species several kilometres southward were found on the eastern slope. This could confirm the role of the corridor as an aerobiological conveyor belt or cline from South to North.     

Clines: character number and the multivariate analysis of simple patterns of geographic variation

The stability of a clinal pattern geographic variation in relation to character number was investigated by the random selection of real characters. The characters used were selected from a set of 18 significant characters, drawn from four different character systems, and had a low within-group correlation. Principal component/coordinate analysis was used to elucidate the main pattern of geographic variation and the first principal coordinate was plotted against a geographical transect to illustrate this pattern. The existence of 'clinal' or 'monotically clinal' variation was assessed by the rank correlation between geographic position and coordinate score and the congruence between patterns of geographic variation was assessed by the correlation between the first principal coordinates of the appropriate analyses.
Two procedural models were used: A, the congruence between completely independent character sets based on 1–9 characters, and B, congruence between the 'total' analysis and those analyses based on 1–16 characters. The frequency of the types of pattern of geographic variation shown by these Model B analyses was also determined. Congruence is asymptotic in relation to character number and is described by various mathematical models, depending upon parameter and procedure. A broad pattern of clinal variation occurred in all analyses based on six or more characters and appears to be a stable feature of the racial affinities that is unlikely to be influenced by character choice. The details of the clinal pattern cannot be shown to be stable and may be influenced by the choice of character. This study had several findings in common with a previous study of categorical variation, e.g. the approximately hyperbolic relationship between character number and congruence in Model B, which may prove to be generally true in comparable situations.     

A Population Study of Spergula arvensis: I. Two Clines and their Significance

Two seed-coat forms (the presence or absence of papillae) andtwo hairiness forms (medium or densely hairy) of Spergula arvensisare differently distributed through the British Isles, theirrelative frequencies being correlated with latitude and altitude.The proportions of the non-papillate and densely hairy formsincrease with increasing distance from Kent to the north-north-westand also with increasing altitude. A possible explanation is that the diverse forms indicate selectivedifferences. Experiments have been carried out to test thishypothesis and the evidence supports it. The non-papillate formproduces a lower proportion of fertile capsules than the papillateform when grown at a high temperature and low humidity. Alsothe non-papillate seeds germinate more readily than the papillateseeds at low temperatures, whereas at higher temperatures thereverse is true. It is suggested that hybrid vigour, fluctuating selection intensities,and migration may all play a part in maintaining the observeddistribution of the various forms.     

Clines revisited: The timing of pupping in the harbour seal (Phoca vitulina)

The regional variation in the pupping season of the harbour seal ( Phoca vitulina ) was reviewed using the birth periods reported for 65 colony sites distributed over a range from 30.4 to 78.5 North latitude. The birth timing of P. v. vitulina was not related to latitude, but birthing in P. v. concolor along eastern North America exhibited a latitudinal cline. The timing of birth in P. v. richardsi varied in three distinct patterns: (1) a significant unidirectional latitudinal cline extending between Baja California and the west coast of Washington; (2) a cluster comprised of Puget Sound, Washington and Vancouver Island, British Columbia colonies in which birthing occurred an average of 65 days later than on the Washington coast; and (3) a cluster from northern British Columbia and Alaska which did not demonstrate a latitudinal cline. Insufficient data were available for the analysis of P. v. mellonae or P. v. stejnegeri .
We found great regional variation in the timing of birth among all colonies, with mean birth dates occurring as early as 15 March and as late as 3 September. Little variation existed north of 50. To the south of 50, however, most of the variation could be attributed to correlation with latitude or to affiliation with the Puget Sound, Washington-Vancouver Island, British Columbia geographic area.
Clinal variation in pupping could result from: (1) geographic variations in a selective factor with perhaps gene exchange between contiguous populations playing a role in smoothing the variation; or (2) for populations between Mexico and the west coast of Washington, regional variation in a non-selective environmental variable, such as photoperiod.