Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a "fitness function" and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.     

Random Amplified Polymorphic DNA Diversity among Surface and Subterranean Populations of Asellus aquaticus (Crustacea: Isopoda)

The ecological and evolutionary processes leading to isolation and adaptation of cave animals compared to their surface ancestors are not yet unequivocally understood. In this study the genetic relations of four cave and three surface population of the freshwater crustacean Asellus aquaticus in the Karst region of SW Slovenia and NE Italy were assessed using RAPDs as genetic markers. The results suggest that specialized populations from two caves invaded their subterranean habitat independently, and that their morphological similarity is a result of convergent evolution. Another, less specialized cave population seems to originate from a later colonization of a cave system already inhabited by a more specialized population, but the two populations do not interbreed. This series of temporally and spatially independent invasions has generated a diversity hotspot of non-interbreeding populations of a ubiquitous freshwatercrustacean, which is uniform over most of its range. Genetic variability estimated by the percentage of polymorphic RAPD fragments was similar (86–91%) in most cave and surface populations. Substantially lower values (as low as 49%) were found in two cave populations affected by heavy pollution. Two a priori groupings of populations, traditional subspecies and hydrologically connected groups, were rejected as not significant by means of nested analysis of molecular variance (AMOVA). On the other hand, groupings revealed by UPGMA clustering displayed a significant component of among-group variance. An analysis of gene flow between populations using estimated migration rates confirmed these findings.     

Extranuclear differentiation and gene flow in the finite island model

Use of sequence information from extranuclear genomes to examine deme structure in natural populations has been hampered by lack of clear linkage between sequence relatedness and rates of mutation and migration among demes. Here, we approach this problem in two complementary ways. First, we develop a model of extranuclear genomes in a population divided into a finite number of demes. Sex-dependent migration, neutral mutation, unequal genetic contribution of separate sexes and random genetic drift in each deme are incorporated for generality. From this model, we derive the relationship between gene identity probabilities (between and within demes) and migration rate, mutation rate and effective deme size. Second, we show how within- and between-deme identity probabilities may be calculated from restriction maps of mitochondrial (mt) DNA. These results, when coupled with our results on gene flow and genetic differentiation, allow estimation of relative interdeme gene flow when deme sizes are constant and genetic variants are selectively neutral. We illustrate use of our results by reanalyzing published data on mtDNA in mouse populations from around the world and show that their geographic differentiation is consistent with an island model of deme structure.     

Inbreeding coefficients and coalescence times.

This paper describes the relationship between probabilities of identity by descent and the distribution of coalescence times. By using the relationship between coalescence times and identity probabilities, it is possible to extend existing results for inbreeding coefficients in regular systems of mating to find the distribution of coalescence times and the mean coalescence times. It is also possible to express Sewall Wright's FST as the ratio of average coalescence times of different pairs of genes. That simplifies the analysis of models of subdivided populations because the average coalescence time can be found by computing separately the time it takes for two genes to enter a single subpopulation and time it takes for two genes in the same subpopulation to coalesce. The first time depends only on the migration matrix and the second time depends only on the total number of individuals in the population. This approach is used to find FST in the finite island model and in one- and two-dimensional stepping-stone models. It is also used to find the rate of approach of FST to its equilibrium value. These results are discussed in terms of different measures of genetic distance. It is proposed that, for the purposes of describing the amount of gene flow among local populations, the effective migration rate between pairs of local populations, M, which is the migration rate that would be estimated for those two populations if they were actually in an island model, provides a simple and useful measure of genetic similarity that can be defined for either allozyme or DNA sequence data.     

Parallel speciation in Astyanax cave fish (Teleostei) in Northern Mexico

We investigated differentiation processes in the Neotropical fish Astyanax that represents a model system for examining adaptation to caves, including regressive evolution. In particular, we analyzed microsatellite and mitochondrial data of seven cave and seven surface populations from Mexico to test whether the evolution of the cave fish represents a case of parallel evolution. Our data revealed that Astyanax invaded northern Mexico across the Trans-Mexican Volcanic Belt at least three times and that populations of all three invasions adapted to subterranean habitats. Significant differentiation was found between the cave and surface populations. We did not observe gene flow between the strongly eye and pigment reduced old cave populations (Sabinos, Tinaja, Pachon) and the surface fish, even when syntopically occurring like in Yerbaniz cave. Little gene flow, if any, was found between cave populations, which are variable in eye and pigmentation (Micos, Chica, Caballo Moro caves), and surface fish. This suggests that the variability is due to their more recent origin rather than to hybridization. Finally, admixture of the young Chica cave fish population with nuclear markers from older cave fish demonstrates that gene flow between populations that independently colonized caves occurs. Thus, all criteria of parallel speciation are fulfilled. Moreover, the microsatellite data provide evidence that two co-occurring groups with small sunken eyes and externally visible eyes, respectively, differentiated within the partly lightened Caballo Moro karst window cave and might represent an example for incipient sympatric speciation.     

Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.     

Regressive evolution: ontogeny and genetics of cavefish eye rudimentation

Two hypotheses exist to explain ontogenetic eye reduction in Astyanax cave fish: first, after lens induction by the primordial eye cup, the lens plays the role of a central regulator of eye and retina regression or, second, the retina itself is an independent unit of eye development. A comparative study of five blind cave fish populations and their surface sister form was performed to investigate the differences of ontogenetic eye regression between the cave populations during different stages of development. The study revealed that, in addition to the initial formation of smaller primordia, eye regression is also caused during later ontogeny by different relative growth and specific histological characteristics. Whereas the cave fish lens never properly differentiates, the regressive process of the retina is transitorily interrupted by ongoing differentiation. In the newly-discovered Molino cave population, even visual cells with well-organized outer segments develop, which are secondarily reduced at a later ontogenetic stage. This result shows that the retina and lens are independent developmental units within the eye ball. Presumably, the genetic systems responsible for both show independent inheritance, which is also corroborated by hybrids of F ₂-crosses between the cave and surface fish, in which lens and retina development do not correlate. During ontogeny, the eye size differs between the cave populations. In Pachón cave fish, the relatively large eye size correlates with an ancient introgression from a surface population, which may have delayed eye regression.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 92 , 287–296.     

The effect of life-history and mode of inheritance on neutral genetic variability

Formulae for the effective population sizes of autosomal, X-linked, Y-linked and maternally transmitted loci in age-structured populations are developed. The approximations used here predict both asymptotic rates of increase in probabilities of identity, and equilibrium levels of neutral nucleotide site diversity under the infinite-sites model. The applications of the results to the interpretation of data on DNA sequence variation in Drosophila, plant, and human populations are discussed. It is concluded that sex differences in demographic parameters such as adult mortality rates generally have small effects on the relative effective population sizes of loci with different modes of inheritance, whereas differences between the sexes in variance in reproductive success can have major effects, either increasing or reducing the effective population size for X-linked loci relative to autosomal or Y-linked loci. These effects need to be accounted for when trying to understand data on patterns of sequence variation for genes with different transmission modes.     

Der Micos-Fisch,Höhlenfisch in statu nascendi oder Bastard ?

The Micos Population–cave fish in statu nascendi or hybrid? Observations on the evolution of cavernicoles The Micos-Cave in the Sierra de la Colmena in the State of San Luis Potosi, Mexico, contains a cavernicolous population of Astyanax mexicanus, whose members are for the most part blind, but, in contrast to other cave dwelling populations of the same species, appear almost normal in their pigmentation. Besides these, there are also large eyed and pigmented specimens to be found in this cave. Any transitional stages between the blind and the normal visioned fish are lacking. Offspring of the blind cavernicoles that are raised under light conditions develop a superficially lying eye which is markedly smaller than normal, attaining its size proportional to the light-intensity of the experimental conditions. The size and structure of the eye-remnants of the blind fish as well as the eyes of their offspring are considerably more variable than in the river specimens. Crossings of the blind Micos fish with the river fish Astyanax and also with a blind and unpigmented troglobiont of the same species - Sabinos fish - result in both cases in a more or less intermediate F¹-hybrid. A strict inbreeding within the Micos fish, selecting specimens with especially large eyes, produced animals whose eyes are comparable to those of the river fish after only three offspring generations. Electrophoresis studies on the allozyme variability at various loci prove that the Micos fish is genetically only slightly different compared to the river fish. On the other hand in some allele frequencies there is an alternative variation between the two. The Micos fish also differs from the typical troglobionts which are monomorphic at almost all loci examined and also possess alleles that are not found in the river form. Based on the genetic constitution, the Micos fish and the river fish found in the cave do not form a panmictic population. It is also doubtful that the Micos fish is the progeny of a hybrid swarm which previously resulted from a cross between a real troglobiont and the newly arrived river fish, because the Micos fish is in every characteristic genetically very similar to the river fish, whereas no clear traces of troglobiont relationship are found. Thus the Micos fish actually appears to be a cave form in statu nascendi against which the river fish that find their way in from time to time cannot compete.     

Genetics and hybridization in surface and cave Astyanax (Teleostei): a comparison of regressive and constructive traits

Change in ecological conditions, as seen in surface and cave populations of Astyanax (Teleostei), has caused the divergent evolution of a large number of traits like eyes, coloration, taste, lateral line, and different kinds of behaviour like schooling, sleep or feeding posture. Because of the interfertility of surface and cave forms these fish are an exceptional object to study the morphological and genetic basis of the evolution of such complex regressive and constructive traits. Classical crossing analyses and genomic studies are contributing to growing understanding. Both kinds of traits mostly rely on multiple genetic bases and the phenotypic manifestation in the various crosses is similar. The gene effect underlying the phenotypic manifestation may exhibit an exponential increase at differing amounts in the various traits and crosses. Missing or presence of such genetic interaction helps determine whether the variability of eyes or pigmentation exhibited by Astyanax cave fish populations like Micos, is due to a more recent origin or to secondary hybridization with the surface fish. Neither crossing analysis nor QTL mapping revealed that eye reduction is pleiotropically antagonistically related to the increase of taste buds or lateral line sense. Independent inheritance of traits suggests that Astyanax cave fish are subjected to mosaic evolution.     

Disequilibrium among several linked neutral genes in finite population. II. Variances and covariances of disequilibria

A method is derived for computing the variances and covariances of linkage disequilibria between neutral genes in finite populations, which is based on a linear transformation of results given previously for the mean values of disequilibria. The formulae obtained are limited to moments of sixth order or less, such as the variance of the three-locus disequilibrium. It is shown that there is no covariance between any pair of disequilibria in populations starting equilibrium. The pattern of change with time in variance of the three-locus disequilibrium from populations initially in equilibrium is similar to that for two loci, except that the highest values are achieved rather earlier and are smaller.     

Standing genetic variation as a potential mechanism of novel cave phenotype evolution in the freshwater isopod,Asellus aquaticus

Novel phenotypes can come about through a variety of mechanisms including standing genetic variation from a founding population. Cave animals are an excellent system in which to study the evolution of novel phenotypes such as loss of pigmentation and eyes. Asellus aquaticus is a freshwater isopod crustacean found in Europe and has both a surface and a cave ecomorph which vary in multiple phenotypic traits. An orange eye phenotype was previously revealed by F₂ crosses and backcrosses to the cave parent within two examined Slovenian cave populations. Complete loss of pigmentation, both in eye and body, is epistatic to the orange eye phenotype and therefore the orange eye phenotype is hidden within the cave populations. Our goal was to investigate the origin of the orange eye alleles within the Slovenian cave populations by examining A. aquaticus individuals from Slovenian and Romanian surface populations and Asellus aquaticus infernus individuals from a Romanian cave population. We found orange eye individuals present in lab raised surface populations of A. aquaticus from both Slovenia and Romania. Using a mapping approach with crosses between individuals of two surface populations, we found that the region known to be responsible for the orange eye phenotype within the two previously examined Slovenian cave populations was also responsible within both the Slovenian and the Romanian surface populations. Complementation crosses between orange eye Slovenian and orange eye Romanian surface individuals suggest that the same gene is responsible for the orange eye phenotype in both surface populations. Additionally, we observed a low frequency phenotype of eye loss in crosses generated between the two surface populations and also in the Romanian surface population. Finally, in a cave population from Romania, A. aquaticus infernus, we found that the same region is also responsible for the orange eye phenotype as the Slovenian cave populations and the Slovenian and Romanian surface populations. Therefore, we present evidence that variation present in the cave populations could originate from standing variation present in the surface populations and/or transgressive hybridization of different surface phylogenetic lineages rather than de novo mutations.     

The robustness of neutral models of geographical variation

The approximation of diploid migration by gametic dispersion is studied. The monoecious, diploid population is subdivided into panmictic colonies that exchange migrants. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to a new allele at the same rate u. Diploid-migration models without self-fertilization and with selfing at the “random” rate (equal to the reciprocal of the deme size in each deme) are investigated; in the gametic-dispersion models, selfing occurs at the random rate. It is shown for the unbounded stepping-stone model in one and two dimensions, the circular stepping-stone model, and the island model that the probabilitities of identity in state at equilibrium for diploid migration are close to those for gametic dispersion if the mutation rate is small or the deme size is large. Explicit error bounds are presented in all the above cases. It is also proved that if the number of demes is finite and the migration matrix is arbitrary but time independent and ergodic, then in the strong-migration approximation the equilibrium and the ultimate rate and pattern of convergence of both diploid-dispersion models are close to the corresponding gametic-dispersion formulae. For the strong-migration approximation at equilibrium, migration must dominate both mutation and random drift; for the convergence results, it suffices that migration dominate random drift. All the results apply to a dioecious population if the migration pattern and mutation rate are sex independent.     

Comprehensive passage (COMPASS) model: a model of downstream migration and survival of juvenile salmonids through a hydropower system

Migratory fish populations are impacted worldwide by river impoundments. Efforts to restore populations will benefit from a clear understanding of survival and migration process over a wide-range of river conditions. We developed a model that estimates travel time and survival of migrating juvenile salmonids (Oncorhynchus spp.) through the impounded Snake and Columbia rivers in the northwestern United States. The model allows users to examine the effects of river management scenarios, such as manipulations of river flow and spill, on salmonid survival. It has four major components: dam passage and survival, reservoir survival, fish travel time, and hydrological processes. The probability that fish pass through specific routes at a dam and route-specific survival probabilities were based on hydroacoustic, radio telemetry, PIT tag, and acoustic tag data. We related reservoir mortality rate (per day and per km) to river flow, water temperature, and percentage of fish passing through spillways and then fit the relationships to PIT-tag survival data. We related fish migration rate to water velocity, percentage of fish passing through spillways, and date in the season. We applied the model to two threatened “Evolutionarily Significant Units” (as defined under the US Endangered Species Act): Snake River spring/summer Chinook salmon (O. tshawytscha Walbaum) and Snake River steelhead (O. mykiss Walbaum). A sensitivity analysis demonstrated that for both species survival through the hydropower system was responsive to water temperature, river flow, and spill proportion. The two species, however, exhibited different patterns in their response. Such information is crucial for managers to effectively restore migratory fish populations in regulated rivers. Guest editors: R. L. Welcomme & G. Marmulla Hydropower, Flood Control and Water Abstraction: Implications for Fish and Fisheries     

Methods to estimate effective population size using pedigree data: Examples in dog,sheep, cattle and horse

Background

Effective population sizes of 140 populations (including 60 dog breeds, 40 sheep breeds, 20 cattle breeds and 20 horse breeds) were computed using pedigree information and six different computation methods. Simple demographical information (number of breeding males and females), variance of progeny size, or evolution of identity by descent probabilities based on coancestry or inbreeding were used as well as identity by descent rate between two successive generations or individual identity by descent rate.

Results

Depending on breed and method, effective population sizes ranged from 15 to 133 056, computation method and interaction between computation method and species showing a significant effect on effective population size (P < 0.0001). On average, methods based on number of breeding males and females and variance of progeny size produced larger values (4425 and 356, respectively), than those based on identity by descent probabilities (average values between 93 and 203). Since breeding practices and genetic substructure within dog breeds increased inbreeding, methods taking into account the evolution of inbreeding produced lower effective population sizes than those taking into account evolution of coancestry. The correlation level between the simplest method (number of breeding males and females, requiring no genealogical information) and the most sophisticated one ranged from 0.44 to 0.60 according to species.

Conclusions

When choosing a method to compute effective population size, particular attention should be paid to the species and the specific genetic structure of the population studied.     

Genetic variability and divergence between populations and species of Nesticus cave spiders

Genetic variability and divergence at 21 enzyme loci were studied in and between Italian populations of the cave spiders Nesticus eremita (13 populations), N. menozzii and N. sbordonii (one population each). The three species differ with respect to the degree of specialization to cave life, dispersion ability, isolation of populations, abundancy, extent of the distribution area, and range from the troglophilic and widespread N. eremita to the troglobitic N. sbordonii, endemic to a single cave in the Central Appennines.Heterozygosity ranges from 0.05 to 0.15 in N. eremita populations and appears to be largely controlled by the occurrence and the extent of gene flow among populations. The relatively low polymorphism levels of N. menozzii (H=0.081) and N. sbordonii (H=0.106) are also associated with reduced gene flow and small population sizes.Genetic distances between N. eremita populations vary considerably and are strictly related to the geographical distances involved, again indicating a major role of gene flow in determining the patterns of genetic differentiation between populations. This view is strongly supported by the results of a principal component analysis applied to the gene-frequency data. Estimates of genetic divergence between species suggest that the major cladogenetic events leading to complete separation of these three Nesticus species occurred in the Middle-late Pliocene.     

Parallel evolution leads to reduced shoaling behavior in two cave dwelling populations of Atlantic mollies (<Emphasis Type="Italic">Poecilia mexicana</Emphasis>, Poeciliidae,Teleostei)

Shoaling behavior protects fishes from avian and piscine predation, but at the same time costs of group living arise due to several mechanisms including increased food competition. Most cave fishes live in an environment in which avian and piscine predators are lacking, and cave environments are often characterized by low food availability, leading to increased food competition. Altogether, this should favor the reduction of shoaling in cave fishes. We compared shoaling behavior (i.e. the tendency to associate with a stimulus shoal) among surface dwelling populations of the Atlantic molly, Poecilia mexicana, and two cave forms of that species. The first cave population of P. mexicana originated from the Cueva del Azufre and was previously recognized as the only cave form of a poeciliid fish. The second cave population examined came from a cave that was discovered only recently (Cueva Luna Azufre). In both cave forms shoaling behavior was reduced compared with surface dwelling mollies.     

Reaction to Alarm Substance in Cave Populations of Astyanax fasciatus (Characidae,Pisces)1

The effect of species-specific skin-extract containing alarm substance has been studied in two epigean and three hypogean populations of the Mexican-tetra Astyanax fasciatus. In all populations tested the feeding rate at the water surface decreased significantly after introducing the alarm substance and the fish avoided this surface area. Additionally epigean fish and some individuals from the Chica cave showed zigzag movements, rapid swimming and hiding. The fish did not respond to a skinextract of a species without alarm substance.     

THE EFFECT OF DELAYED POPULATION GROWTH ON THE GENETIC DIFFERENTIATION OF LOCAL POPULATIONS SUBJECT TO FREQUENT EXTINCTIONS AND RECOLONIZATIONS

I investigated the effects of delayed population growth on the genetic differentiation among populations subjected to local extinction and recolonization, for two different migration functions; (1) a constant migration rate, and (2) a constant number of migrants. A delayed period of population growth reduces the size of the newly founded populations for one or several generations. Whether this increases differentiation among local populations depends on the actual pattern of migration. With a constant migration rate, fewer migrants move into small populations than into large, thus providing ample opportunity for drift to act within a population. A prolonged period of population growth thus makes the conditions for enhanced differentiation between local populations less restrictive and also inflates the actual levels of differentiation. The effect depends on the relative magnitudes of k_e, the effective number of colonizers and k, the actual number of colonizers. When there is a constant number of migrants into a population per generation, migration into small populations is increased. This increase of migration in small populations counteracts the effects of genetic drift due to small population size. It increases the rate by which populations approach equilibrium, as small populations are swamped by migrants from larger populations closer to genetic equilibrium, and overall levels of differentiation are thus reduced. I also discuss situations for which the results of this paper are relevant.     

The Dynamics of a Fish Stock Exploited in Two Fishing Zones

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities.