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T Nagylaki

Publications and source records attributed to T Nagylaki.

At least 19 recordsLinked to original sources
PubMed2001

Patterns of multiallelic polymorphism maintained by migration and selection.

Evolution at a multiallelic locus under the joint action of migration and viability selection is investigated. Generations are discrete and nonoverlapping. The monoecious, diploid population is subdivided into finitely many panmictic colonies that exchange adult migrants independently of genotype. The forward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). Several examples of globally attracting multiallelic equilibria are presented. Migration can cause global fixation even if, without migration, there is a globally attracting multiallelic equilibrium in every colony. Migration can also cause the global fixation of an allele that, without migration, is eliminated in every colony. Without dominance, generically, the number of alleles present at equilibrium cannot exceed the number of colonies. Some general properties and examples of the Levene model are studied in detail. If in each colony there is either no dominance or, without migration, a globally attracting internal equilibrium, then there exists a globally attracting equilibrium with migration. Therefore, if an internal equilibrium exists, it is the global attractor.

Alleles↗
PubMed2000

Geographical invariance and the strong-migration limit in subdivided populations.

Invariance under population subdivision and the strong-migration limit are investigated for digenic samples in neutral models. The monoecious, diploid population is subdivided into a finite number of panmictic colonies that exchange gametes. The backward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). Results are derived for the distribution of the place and time of coalescence, for the probability of identity in the model of infinitely many alleles, and for the distribution of the number of nucleotide differences in the model of infinitely many sites without recombination.

Alleles↗
PubMed1999

The influence of spatial inhomogeneities on neutral models of geographical variation IV. Discontinuities in the population density and migration rate.

The equilibrium structure of the infinite, one-dimensional stepping-stone model with coincident discontinuities in the population density and migration rate is investigated in the diffusion approximation. The monoecious, diploid population is subdivided into an infinite linear array of equally large, panmictic colonies that exchange gametes isotropically. The population density and the migration rate have a discontinuity at the origin, but are elsewhere uniform. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus without selection; every allele mutates to new alleles at the same rate. The three dimensionless parameters in the theory are alpha=(rho(+)/rho(-))(2) (V(+)/V(-))(3/2), and beta(+/-)=4rho(+/-) 2uV(+/-), where rho(+) (rho(-)) and V(+) (V(-)) designate the population density and variance of gametic dispersion per generation to the right (left) of the discontinuity, respectively, and u denotes the mutation rate. The characteristic length on the right (left) is V(+)/(2u) (V(-)/(2u)). The probability of identity is continuous at the origin, but its partial derivatives have a discontinuity unless migration is conservative (rho(-) V(-)=rho(+) V(+)). At least for nonconservative migration, the probability of identity (including the expected homozygosity) can be nonmonotonic even if the migration rate is uniform and the population density is monotonic. Thus, there can be a nonmonotonic genetic response in a neutral model to a monotonic environment.

Animals↗
PubMed1999

Convergence of multilocus systems under weak epistasis or weak selection.

The convergence of multilocus systems under viability selection with constant fitnesses is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. It is proved that if epistasis or selection is sufficiently weak (and satisfies a certain nondegeneracy assumption whose genericity we establish), then there is always convergence to some equilibrium point. In particular, cycling cannot occur. The behavior of the mean fitness and some other aspects of the dynamics are also analyzed.

Alleles↗
PubMed1998

Fixation indices in subdivided populations.

Without restricting the evolutionary forces that may be present, the theory of fixation indices, or F-statistics, in an arbitrarily subdivided population is developed systematically in terms of allelic and genotypic frequencies. The fixation indices for each homozygous genotype are expressed in terms of the fixation indices for the heterozygous genotypes. Therefore, together with the allelic frequencies, the latter suffice to describe population structure. Possible random fluctuations in the allelic frequencies (which may be caused, e.g., by finiteness of the subpopulations) are incorporated so that the fixation indices are parameters, rather than random variables, and these parameters are expressed in terms of ratios of evolutionary expectations of heterozygosities. The interpretation of some measures of population differentiation is also discussed. In particular, F(ST) is an appropriate index of gene-frequency differentiation if and only if the genetic diversity is low.

Alleles↗
PubMed1998

The expected number of heterozygous sites in a subdivided population.

A simple, exact formula is derived for the expected number of heterozygous sites per individual at equilibrium in a subdivided population. The model of infinitely many neutral sites is posited; the linkage map is arbitrary. The monoecious, diploid population is subdivided into a finite number of panmictic colonies that exchange gametes. The backward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). With suitable weighting, the expected number of heterozygous sites is 4Neu, where Ne denotes the migration effective population number and u designates the total mutation rate per gene (or DNA sequence). For diploid migration, this formula is a good approximation if Ne >> 1.

Diploidy↗
PubMed1997

Multinomial-sampling models for random genetic drift.

Three different derivations of models with multinomial sampling of genotypes in a finite population are presented. The three derivations correspond to the operation of random drift through population regulation, conditioning on the total number of progeny, and culling, respectively. Generations are discrete and nonoverlapping; the diploid population mates at random. Each derivation applies to a single multiallelic locus in a monoecious or dioecious population; in the latter case, the locus may be autosomal or X-linked. Mutation and viability selection are arbitrary; there are no fertility differences. In a monoecious population, the model yields the Wright-Fisher model (i.e., multinomial sampling of genes) if and only if the viabilities are multiplicative. In a dioecious population, the analogous reduction does not occur even for pure random drift. Thus, multinomial sampling of genotypes generally does not lead to multinomial sampling of genes. Although the Wright-Fisher model probably lacks a sound biological basis and may be inaccurate for small populations, it is usually (perhaps always) a good approximation for genotypic multinomial sampling in large populations.

Genetics, Population↗
PubMed1996

The diffusion model for migration and selection in a dioecious population.

The diffusion approximation is derived for migration and selection at a multiallelic locus in a dioecious population subdivided into a lattice of panmictic colonies. Generations are discrete and nonoverlapping; autosomal and X-linked loci are analyzed. The relation between juvenile and adult subpopulation numbers is very general and includes both soft and hard selection; the zygotic sex ratio is the same in every colony. All the results hold for both adult and juvenile migration. If ploidy-weighted average selection, drift, and diffusion coefficients are used, then the ploidy-weighted average allelic frequencies satisfy the corresponding partial differential equation for a monoecious population. The boundary conditions and the unidimensional transition conditions for coincident discontinuities in the carrying capacity and migration rate extend identically. The previous unidimensional formulation and analysis of symmetric, nearest-neighbor migration of a monoecious population across a geographical barrier is generalized to symmetric migration of arbitrary finite range, and the transition conditions are shown to hold for a dioecious population. Thus, the entire theory of clines and of the wave of advance of favorable alleles is applicable to dioecious populations.

Animals↗
PubMed1995

The inbreeding effective population number in dioecious populations.

The inbreeding effective population number in a dioecious population with discrete, nonoverlapping generations is investigated for both autosomal and X-linked loci. The recursion relations for the probabilities of genic identity, and the effective population numbers are analyzed and compared in two cases: (i) the offspring identified by sex in the calculation of the probability of common parentage and (ii) the offspring not so identified. Case i gives the correct evolution of the probabilities of identity, but case ii has been more widely studied and applied. A general symmetric framework that reduces the number of parameters is developed and used to examine a wide variety of models of panmixia and monogamy. Cases i and ii agree in many, but not all, models.

Animals↗
PubMed1994

Geographical variation in a quantitative character.

A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.

Biological Evolution↗
PubMed1993

The evolution of multilocus systems under weak selection.

The evolution of multilocus systems under weak selection is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multi-allelic loci, the linkage map, dominance, and epistasis are arbitrary. The genotypic fitnesses may depend on the gametic frequencies and time. The results hold for s << cmin, where s and cmin denote the selection intensity and the smallest two-locus recombination frequency, respectively. After an evolutionarily short time of t1 approximately (ln s)/ln(1 - cmin) generations, all the multilocus linkage disequilibria are of the order of s [i.e., O(s) as s-->0], and then the population evolves approximately as if it were in linkage equilibrium, the error in the gametic frequencies being O(s). Suppose the explicit time dependence (if any) of the genotypic fitnesses is O(s2). Then after a time t2 approximately 2t1, the linkage disequilibria are nearly constant, their rate of change being O(s2). Furthermore, with an error of O(s2), each linkage disequilibrium is proportional to the corresponding epistatic deviation for the interaction of additive effects on fitness. If the genotypic fitnesses change no faster than at the rate O(s3), then the single-generation change in the mean fitness is delta W = W-1Vg+O(s3), where Vg designates the genic (or additive genetic) variance in fitness. The mean of a character with genotypic values whose single-generation change does not exceed O(s2) evolves at the rate delta Z = W-1Cg+O(s2), where Cg represents the genic covariance of the character and fitness (i.e., the covariance of the average effect on the character and the average excess for fitness of every allele that affects the character). Thus, after a short time t2, the absolute error in the fundamental and secondary theorems of natural selection is small, though the relative error may be large.

Alleles↗
PubMed1992

Rate of evolution of a quantitative character.

The rate of change of the mean of a quantitative character is evaluated exactly and also under the hypothesis of linear biparental regression. Generations are discrete and nonoverlapping; the monoecious population mates at random. The genotypic and environmental contributions to the character are additive and stochastically independent. The character is influenced by arbitrarily many multiallelic loci and has constant genotypic values; dominance, epistasis, and the linkage map are also arbitrary. The population is initially in linkage equilibrium, and there is no position effect. If the biparental regression is linear, then the regression coefficient is simply Vgam/V, and hence the single-generation change in the mean is deltaZ = (Vgam/V)S, where Vgam and V denote the gametic and total variances in the character and S designates the selection differential. The corresponding exact result is DeltaZ = (C/W) + (B/W2), where C, W and B represent the gametic covariance of the character and fitness, the mean fitness, and a correction term, respectively. If selection is weak, then DeltaZ approximately C/W. Furthermore, deltaZ = C/W if either there is no environmental contribution and the gametic effects are additive or the character is fitness itself. In the latter case, C is the gametic variance in fitness. Thus, even in linkage equilibrium, weakness of selection generally does not suffice to validate the linear-regression result. This conclusion holds even for additive loci.

Journal Article↗
PubMed1991

Error bounds for the fundamental and secondary theorems of natural selection.

Error bounds are derived for the approximation delta Z approximately C/W, where delta Z, C, and W denote the rate of change of the mean of a character under selection, the genic (or additive genetic) covariance of the character and fitness (i.e., the covariance of the average effect on the character and the average excess for fitness of every allele that affects the character), and the mean fitness, respectively. Generations are discrete and nonoverlapping; the monoecious population mates at random. The character is determined by arbitrarily many multiallelic loci without epistasis; the linkage map is also arbitrary. The genotypic values of the character are constant. Rounds on the absolute error in the above approximation are deduced for an arbitrary character, and these are converted to bounds on the relative error when the character is fitness itself. In that case, C is the genic variance in fitness, and the relative error cannot exceed one half the greatest genotypic selection coefficient.

Alleles↗
PubMed1990

Gene conversion, linkage, and the evolution of repeated genes dispersed among multiple chromosomes.

The evolution of the probabilities of genetic identity within and between the loci of a multigene family dispersed among multiple chromosomes is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, but the same for every chromosome; the dependence of the probabilities of identity on the location on each chromosome is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. Under the assumption of loose linkage (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), explicit approximations are obtained for the equilibrium values of the probabilities of identity and of the linkage of disequilibria. The probabilities of identity are of order one [i.e., O(1)] and do not depend on location; the linkage disequilibria are of O(epsilon) and, within each chromosome, depend on location through the crossover rates. It is demonstrated also that the ultimate rate and pattern of convergence to equilibrium are close to that of a much simpler, location-independent model. If intrachromosomal conversion is absent, the above results hold even without the assumption of loose linkage. In all cases, the relative errors are of O(epsilon). Even if the conversion rate between genes on nonhomologous chromosomes is considerably less than between genes on the same chromosome or homologous chromosomes, the probabilities of identity between the former genes are still almost as high as those between the latter, and the rate of convergence is still not much less than with equal conversion rates. If the crossover rates are much less than 1/2, then most of the linkage disequilibrium is due to intrachromosomal conversion. If linkage is loose, the reduction of the linkage disequilibria to O(epsilon) requires only O(-ln epsilon) generations.

Alleles↗
PubMed1989

Diffusion approximations of the two-locus Wright-Fisher model.

Diffusion approximations are established for the multiallelic, two-locus Wright-Fisher model for mutation, selection, and random genetic drift in a finite, panmictic, monoecious, diploid population. All four combinations of weak or strong selection and tight or loose linkage are treated, though the proof in the case of strong selection and loose linkage is incomplete. Under certain conditions, explicit formulas are obtained for the stationary distributions of the two diffusions with loose linkage.

Genetic Linkage↗
PubMed1989

Rate of evolution of a character without epistasis.

IT IS SHOWN THAT THE RATE OF CHANGE OF THE MEAN OF A CHARACTER UNDER SELECTION IS [FORMULA: see text] where C, W, DeltaZ, and B denote the genic (additive genetic) covariance of the character and fitness (i.e., the covariance of the average effect on the character and the average excess for fitness of every allele that affects the character), the mean fitness, the average of the changes in the genotypic values of the character over the next generation, and a correction term, respectively. Generations are discrete and nonoverlapping; the monoecious population mates at random. The character is determined by arbitrarily many multiallelic loci without epistasis; the linkage map is also arbitrary. If there is no dominance, then B = 0; if, in addition, the genotypic values of the character are constant, then Delta Z = C/ W. Even if dominance is present, for weak selection and slowly varying genotypic values, Delta Z approximately C/ W. If the character is fitness itself, then C is the genic variance in fitness.

Journal Article↗
PubMed1989

The maintenance of genetic variability in two-locus models of stabilizing selection.

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.

Chromosome Mapping↗