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THEORETICAL POPULATION BIOLOGY, February 1999, Vol. 55, N? 1

ROHANI, Pejman; RUXTON, Graeme D.

Dispersal-induced instabilities in host-parasitoid metapopulations.

We present a general host-parasitoid metapopulation model and, using analytical techniques (supported by numerical simulations), investigate the effects of dispersal on the equilibrium stability of local populations. As has been demonstrated previously, if the intrinsic dynamics of local populations are unstable, then passive dispersal cannot stabilise. Extreme asymmetry in the dispersal fractions between the two species can, however, destabilise the metapopulation equilibrium state. Our key conclusion is that the precise effects of dispersal on stability depend critically on the underlying ecology of the interaction within each population. The presence of regulatory mechanisms, be they in the form of density-dependent host reproduction or the presence of host refugia, decreases the likelihood of observing dispersal-induced instabilities. Indeed, if the stabilising effects are sufficiently strong, then dispersal cannot be destabilising, no matter how asymmetric the dispersal fractions are. On the other hand, positive feedbacks arising from threshold effects in host reproduction or inversely density-dependent patterns of parasitism (due to, for example, long handling times or egg limitation) amplify the destabilising effects of dispersal.

(BIOLOGY, POPULATION DYNAMICS, SPECIES BEHAVIOUR).

English ? pp. 23-36.

P. Rohani, Department of Zoology, University of Cambridge, Downing Street, Cambridge, CB2 3EJ, U.K.; G. D. Ruxton, Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, U.S.A.

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DOEBELI, Michael; DE JONG, Gerdien.

Genetic variability in sensitivity to population density affects the dynamics of simple ecological models.

Many 1-dimensional discrete time ecological models contain a sensitivity parameter that does not affect the dynamic complexity of these models. We show that genetic variability in this parameter can have a strong effect on population dynamics. We incorporate ecological dynamics in two different population genetic models with one locus and two alleles. The first is the classical model of a randomly mating population in Hardy-Weinberg equilibrium, and the second is a model of differential selection in males and females. In populations in Hardy-Weinberg equilibrium, variability in the sensitivity parameter can be maintained by overdominance. In this case, the dynamics of the polymorphic population tend to be much simpler than those of monomorphic populations. In the model with different selection in males and females, polymorphisms can be maintained in various ways, e.g., by opposing directional selection in males and females. Polymorphism in the sensitivity parameter tends to simplify population dynamics in the model with different selection in males and females as well. A number of interesting dynamic effects can be observed, e.g., multiple attractors with complicated basins of attraction. Then the final state of the system after a successful invasion by mutant alleles may depend on the mutation rate and on the distribution of mutational steps. In addition, there are situations in which genetic variability destabilizes a stable population dynamic equilibrium in the monomorphic model. There is an analogy between genetic variability and variability imposed by the environment. If differences in sensitivity are caused by the environment, dynamic effects similar to those in the genetic models can be observed. In addition, source-sink structures that are known to occur in spatially structured models can be seen in the genetic model if one of the genotypes is inviable. The results suggest that combining ecological and population genetic models can lead to a number of new insights. More work is needed, e.g., with fertility models, in which fitnesses are not assigned to individuals, but to mating pairs.

(POPULATION GENETICS, ECOLOGY, GENETIC MODELS, POPULATION DYNAMICS, POLYMORPHISM).

English ? pp. 37-52.

M. Doebeli, Zoology Institute, University of Basel, Rheinsprung 9, CH-4051, Basel, Switzerland; G. De Jong, Population Genetics Group, Department of Plant Ecology and Evolutionary Biology, University of Utrecht, Padualaan 8, NL-3584 CH Utrecht, Netherlands.

doebeli@ubaclu.unibas.ch; G.deJong@boev.biol.ruu.nl.

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IHARA, Yasuo; AOKI, Kenichi.

Sexual selection by male choice in monogamous and polygynous human populations.

The theoretical possibility of coevolution of a viability-reducing female physical trait and a male mating preference for that trait by Fisherian sexual selection in monogamous and polygynous populations is demonstrated using two-locus haploid models. It is assumed that there is dichotomous variation in male resources, resource-rich males have a wider choice among females than resource-poor males, and a female has greater reproductive success when mated with a resource-rich male than a resource-poor one. Under these assumptions, we find that sexual selection operates effectively when female reproductive success is strongly dependent on male resource, the proportion of females that mate with resource-rich males is neither small nor large, the degree of polygyny is low, and resources are inherited from father to son. We suggest that some human female physical traits may have evolved by sexual selection through male choice. The evolution of skin color by sexual selection is discussed as an example.

(MATE SELECTION, POLYGYNY, MONOGAMY, GENETIC SELECTION, POPULATION DYNAMICS).

English ? pp. 77-93.

Y. Ihara and K. Aoki, Department of Biological Sciences, The University of Tokyo, Hongo, Bunkyoku, Tokyo, 113, Japan.

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THEORETICAL POPULATION BIOLOGY, April 1999, Vol. 55, N? 2

GRIFFITHS, R. C.

The time to the ancestor along sequences with recombination.

In a sample of DNA sequences where recombination can occur to the ancestors of the sample, distinct parts of the sequences may have different most recent common ancestors. This paper presents a Markov chain Monte Carlo algorithm for computing the expected time to the most recent common ancestor along the sequences, conditional on where the mutations occur on the sequences.

(POPULATION GENETICS, ANCESTORS, MUTATION, METHODOLOGY).

English ? pp. 137-144.

R. C. Griffiths, Department of Statistics, University of Oxford, U.K.

griffiths@stats.ox.ac.uk.

***

WANG, Jinliang.

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extent of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.

(POPULATION GENETICS, SUB-POPULATION, INBREEDING, POPULATION DYNAMICS, POPULATION SIZE, POPULATION COMPOSITION).

English ? pp. 176-188.

J. Wang, Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, U.K.

jinliang.wang@ed.ac.uk.

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CANTRELL, R. S.; COSNER, C.

Diffusion models for population dynamics incorporating individual behavior at boundaries: applications to refuge desin.

We construct models for dispersal of a population which incorporate the response of individuals to interfaces between habitat types. The models are based on random walks where there may be a bias in the direction an individual moves when it encounters an interface. This sort of dispersal process is called skew Brownian motion. Our models take the form of diffusion equations with matching conditions across the interface between regions for population densities and fluxes. We combine the dispersal models with linear population growth models which assume that the population growth rate differs between regions of different habitat types. We use those models to study issues of refuge design. We specifically consider how the effectiveness of buffer zones depends on their size, quality, and the population's response to the interface between the buffer zone and the refuge.

(POPULATION DYNAMICS, DEMOGRAPHIC MODELS, INTERNAL MIGRATION, POPULATION DISTRIBUTION, REFUGEES).

English ? pp. 189-207.

R. S. Cantrell and C. Cosner, Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida, 33124, U.S.A.

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TAKAHASI, Kiyosi.

Theoretical aspects of the mode of transmission in cultural inheritance.

This study investigates how evolutionary factors interact to determine the relative importance of vertical versus nonvertical mode of transmission in cultural inheritance. Simple mathematical models are provided to study the joint evolution of two cultural characters, one determining the viability and the fertility of individuals, and the other determining the vertical transmission rate of the first trait. Ordinary local stability analyses indicate that intrademic processes should lead to a greater reliance on vertical cultural transmission. On the other hand, when newly arisen variants are adaptive and favored in biased cultural transmission, interdemic processes may lead to a decrease in vertical transmission. This is because biased nonvertical transmission may effectively propagate the adaptive variants, further increasing the average growth rate of the population. These results are verified under several distinct sets of assumptions. It is also inferred that the degree and intensity of transmission bias may be the important determinants of cultural processes.

(CULTURAL CHANGE, HEREDITARY CHARACTERISTICS, REPRODUCTION, THEORETICAL MODELS).

English ? pp. 208-225.

K. Takahasi, Department of Biological Sciences, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0133, Japan.

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THEORETICAL POPULATION BIOLOGY, June 1999, Vol. 55, N? 3

STONE, Lewi; HART, Deborah.

Effects of immigration on the dynamics of simple population models.

Many simple population models exhibit the period doubling route to chaos as a single parameter, commonly the growth rate, is increased. Here we examine the effect of an immigration process on such models and explain why in the case of one-dimensional ("single-humped") maps, immigration often tends to suppress chaos and stabilise equilibrium behaviour or cyclical oscillations of long period. The conditions for which an increase of immigration "simplifies" population dynamics are examined.

(IMMIGRATION, DEMOGRAPHIC MODELS, POPULATION DYNAMICS, SIMULATION).

English ? pp. 227-234.

L. Stone, Department of Zoology, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel; D. Hart, Northeast Fisheries Science Center, National Oceanic and Atmospheric Administration, 166 Water Street, Woods Hole, MA 02543, U.S.A.

lewi@lanina.tau.ac.il.

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KLEIN, Etienne K.; AUSTERLITZ, Fr?d?ric; LAR?DO, Catherine.

Some statistical improvements for estimating population size and mutation rate from segregating sites in DNA sequences.

In population genetics, under a neutral Wright-Fisher model, the scaling parameter =4N? represents twice the average number of new mutants per generation. The effective population size is N and ? is the mutation rate per sequence per generation. Watterson proposed a consistent estimator of this parameter based on the number of segregating sites in a sample of nucleotide sequences. We study the distribution of the Watterson estimator. Enlarging the size of the sample, we asymptotically set a Central Limit Theorem for the Watterson estimator. This exhibits asymptotic normality with a slow rate of convergence. We then prove the asymptotic efficiency of this estimator. In the second part, we illustrate the slow rate of convergence found in the Central Limit Theorem. To this end, by studying the confidence intervals, we show that the asymptotic Gaussian distribution is not a good approximation for the Watterson estimator.

(POPULATION GENETICS, GENETIC MODELS, MUTATION, METHODOLOGY).

English ? pp. 235-247.

E. K. Klein, F. Austerlitz, Laboratoire ?volution et Syst?matique, URA 2154, Universit? Paris XI, B?timent 362, F-91405 Orsay Cedex, France; C. Lar?do, Laboratoire de Biom?trie, Institut National de Recherche Agronomique, F-78350 Jouy-en-Josas, France.

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WIUF, Carsten; HEIN, Jotun.

Recombination as a point process along sequences.

Histories of sequences in the coalescent model with recombination can be simulated using an algorithm that takes as input a sample of extant sequences. The algorithm traces the history of the sequences going back in time, encountering recombinations and coalescence (duplications) until the ancestral material is located on one sequence for homologous positions in the present sequences. Here an alternative algorithm is formulated not as going back in time and operating on sequences, but by moving spatially along the sequences, updating the history of the sequences as recombination points are encountered. This algorithm focuses on spatial aspects of the coalescent with recombination rather than on temporal aspects as is the case of familiar algorithms. Mathematical results related to spatial aspects of the coalescent with recombination are derived.

(POPULATION GENETICS, GENETIC MODELS, SIMULATION, GEOGRAPHICAL DISTRIBUTION).

English ? pp. 248-259.

C. Wiuf and J. Hein, Institute of Biological Sciences, University of Aarhus, DK-8010, Aarhus, Denmark.

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CAMPBELL, R. B.

The coalescent time in the presence of background fertility selection.

Selection ultimately entails differential reproductive success over several generations. This can be measured as a correlation of the number of progeny an individual has with the number of progeny its parent had. This correlation could have a genetic or a cultural basis. The effect of such a correlation is to multiply the single generation sampling variance (Vp) in the diffusion approximation for fixation time by (1-b)+b?(1+r)/(1-r), where b?rn is the correlation between the number of progeny of an individual and its ancestor n generations ago (e.g., b is the heritability and br is the resultant parent-offspring progeny number correlation if the progeny number is genetically determined). This results in a reduction of the fixation or coalescent time by division by this factor. Sex differences in this correlation have been observed, and this provides an explanation for the difference of coalescent times of y-chromosomes and mitochondria.

(POPULATION GENETICS, GENETIC SELECTION, DIFFERENTIAL FERTILITY).

English ? pp. 260-269.

R. B. Campbell, Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa, 50614-0506, U.S.A.

campbell@math.uni.edu.

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ROUSSET, Fran?ois.

Genetic differentiation in populations with different classes of individuals.

I formulate and analyse a model of population structure with different classes of individuals. These different classes may be age classes, other demographic classes, or different types of habitats homogeneously distributed over a geographical area. The value of population differentiation under an island model of dispersal and the increase of differentiation with geographical distance in one- and two-dimensional "isolation by distance" models are then obtained for a generalization of the FST measure of population structure, as a function of "effective" mutation, migration, and population size parameters. The relevant effective subpopulation size is related to the "mutation effective population size" of a single isolated subpopulation and, in models of age-structured populations, to the inbreeding effective population size.

(POPULATION GENETICS, POPULATION COMPOSITION, GEOGRAPHICAL DISTRIBUTION, INBREEDING, MUTATION, POPULATION SIZE).

English ? pp. 297-308.

F. Rousset, Laboratoire G?n?tique et Environnement, Institut des Sciences de l'?volution, Universit? de Montpellier II, F-34095 Montpellier, France.

rousset@isem.univ-montp2.fr.

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THEORETICAL POPULATION BIOLOGY, August 1999, Vol. 56, N? 1

BRUNET, Robert C.; STRUCHINER, Claudio J.

A non-parametric method for the reconstruction of age- and time-dependent incidence from the prevalence data of irreversible diseases with differential mortality.

A method is proposed for reconstructing the time and age dependence of incidence rates from successive age-prevalence cross sections taken from the sentinel surveys of irreversible diseases when there is an important difference in mortality between the infected and susceptible subpopulations. The prevalence information at different time-age points is used to generate a surface; the time-age variations along the life line profiles of this surface and the difference in mortality rates are used to reconstruct the time and age dependence of the incidence rate. Past attempts were based on specified parametric forms for the incidence or on the hypothesis of time-invariant forms for the age-prevalence cross sections. The proposed method makes no such assumptions and is thus capable of coping with rapidly evolving prevalence situations. In the simulations carried out, it is found to be resilient to important random noise components added to a prescribed incidence rate input. The method is also tested on a real data set of successive HIV age-prevalence cross sections from Burundi coupled to differential mortality data on HIV+ and HIV- individuals. The often-made assumption that the incidence rate can be written as the product of a calendar time component and an age component is also examined. In this case, a pooling procedure is proposed to estimate the time and the age profiles of the incidence rate using the reconstructed incidence rates at all time-age points.

(DISEASE INCIDENCE, DISEASE PREVALENCE, MORBIDITY, DIFFERENTIAL MORTALITY, METHODOLOGY, AIDS, BURUNDI).

English ? pp. 76-90.

R. C. Brunet, D?partement de Math?matiques et de Statistique, Universit? de Montr?al, Montr?al, Qu?bec H3C 3J7, Canada; C. J. Struchiner, Escola Nacional de Sa?de P?blica, Funda??o Oswaldo Cruz, 21041, Rio de Janeiro, RJ, Brazil.

brunet@dms.umontreal.ca; stru@malaria.procc.fiocruz.br.

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KOOI, B. W.; KOOIJMAN, S. A. L. M.

Discrete event versus continuous approach to reproduction in structured population dynamics.

The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life stages are assumed, the egg and the adult stage where the adults do not grow. These assumptions hold true, for instance, for rotifers. From the model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.

(POPULATION DYNAMICS, REPRODUCTION, DEMOGRAPHIC MODELS, METHODOLOGY).

English ? pp. 91-105.

B. W. Kooi and S. A. L. M. Kooijman, Biological Laboratory, Free University, De Boelelaan, 1087, 1081 HV, Amsterdam, The Netherlands.

kooi@bio.vu.nl.

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PASCUAL, Mercedes; LEVIN, Simon A.

Spatial scaling in a benthic population model with density-dependent disturbance.

This work investigates approaches to simplifying individual-based models in which the rate of disturbance depends on local densities. To this purpose, an individual-based model for a benthic population is developed that is both spatial and stochastic. With this model, three possible ways of approximating the dynamics of mean numbers are examined: a mean-field approximation that ignores space completely, a second-order approximation that represents spatial variation in terms of variances and covariances, and a patch-based approximation that retains information about the age structure of the patch population. Results show that space is important and that a temporal model relying on mean disturbance rates provides a poor approximation to the dynamics of mean numbers. It is possible, however, to represent relevant spatial variation with second-order moments, particularly when recruitment rates are low and/or when disturbances are large and weak. Even better approximations are obtained by retaining patch age information.

(POPULATION DYNAMICS, DEMOGRAPHIC MODELS, GEOGRAPHICAL DISTRIBUTION, POPULATION DENSITY, METHODOLOGY).

English ? pp. 106-122.

M. Pascual, Center of Marine Biotechnology, University of Maryland Biotechnology Institute, Baltimore, Maryland, 21202, U.S.A.; S. A. Levin, Department of Ecology and Evolutionary Biology, Princeton University, Eno Hall, Princeton, New Jersey, 08540, U.S.A.

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THEORETICAL POPULATION BIOLOGY, October 1999, Vol. 56, N? 2

WIUF, Carsten; DONNELLY, Peter.

Conditional genealogies and the age of a neutral mutant.

This paper is concerned with the structure of the genealogy of a sample in which it is observed that some subset of chromosomes carries a particular mutation, assumed to have arisen uniquely in the history of the population. A rigorous theoretical study of this conditional genealogy is given using coalescent methods. Particular results include the mean, variance, and density of the age of the mutation conditional on its frequency in the sample. Most of the development relates to populations of constant size, but we discuss the extension to populations which have grown exponentially to their present size.

(POPULATION GENETICS, MUTATION, GENEALOGY, AGE).

English ? pp. 183-201.

C. Wiuf and P. Donnelly, Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, U.K.

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NEUHAUSER, Claudia.

The ancestral graph and gene genealogy under frequency-dependent selection.

Minority-advantage frequency-dependent selection has been proposed as the cause for the high level of observed polymorphism in some self/nonself-recognition systems. We present a mathematically rigorous derivation of the ancestral graph for a sample of genes that evolved according to a haploid infinite-alleles model of minority-advantage frequency-dependent selection. In the case of sufficiently weak selection, the gene genealogy can be extracted from the ancestral graph. We demonstrate that the gene genealogy under this model is identical to that obtained for a diploid model with heterozygote advantage. The case of strong selection is exemplified by a one-locus haploid self-incompatibility system; in this context, we investigate the number of alleles that can be maintained in a spatial versus a non-spatial habitat. Finally, we compare gametophytic self-incompatibility to the haploid self-incompatibility model.

(POPULATION GENETICS, GENETIC SELECTION, ANCESTORS, GENEALOGY, GENETIC MODELS).

English ? pp. 203-214.

C. Neuhauser, School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota, 55455, U.S.A.

nhauser@math.umn.

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THEORETICAL POPULATION BIOLOGY, December 1999, Vol. 56, N? 3

GYLLENBERG, M.; HEMMINKI, J.; TAMMARU, T.

Allee effects can both conserve and create spatial heterogeneity in population densities.

In order to determine conditions which allow the Allee effect (caused by biparental reproduction) to conserve and create spatial heterogeneity in population densities, we studied a deterministic model of a symmetric two-patch metapopulation. We proved that under certain conditions there exist stable equilibria with unequal population densities in the two patches, a situation which can be interpreted as conserved heterogeneity. Furthermore, the Allee effect can lead to instability of the equilibrium with equal population densities if some degree of competition is assumed to occur between the subpopulations (non-local competition). This indicates the potential of the Allee effect to create spatial heterogeneity. Neither of these effects appear under biologically realistic parameter values in a model where uniparental reproduction is assumed. We proved that both the between-patch migration intensity and the degree of non-local competition are decisive in determining boundaries between these types of behaviour of the spatial system with Allee effect. Therefore, we propose that the Allee effect, migration intensity, and non-local competition should be considered jointly in studies focusing on problems like pattern formation in space and invasions of spreading species.

(POPULATION DENSITY, DEMOGRAPHIC MODELS, THEORETICAL MODELS, GEOGRAPHICAL DISTRIBUTION).

English ? pp. 231-242.

M. Gyllenberg, Department of Mathematics, T. Tammaru, Section of Ecology, Department of Biology, University of Turku, 20114 Turku, Finland; J. Hemminki, Institute of Zoology and Botany, Riia 181, 51014 Tartu, Estonia.

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BAHLO, Melanie.

The expected number of alleles in a gene conversion model with mutation.

Gene conversions and mutations affect the number of different alleles in a population as it evolves. Here these effects are studied for a sample of r individuals represented by one chromosome, each with n loci. The long-term evolution of the sample is modelled with the coalescent. Gene conversions can only occur within a chromosome between a pair of loci. Recombination is not included in the model. Mutations occur according to the infinitely many alleles model. A new expression for the expected number of alleles is derived using the backward time approach. It is then possible to simulate the expectation for various sample paths. The new estimator is computationally inexpensive and has a lower variance than the conventional, forward time, approximation by simulation.

(POPULATION GENETICS, MUTANT GENE, POPULATION DYNAMICS, GENETIC MODELS, SIMULATION).

English ? pp. 265-277.

M. Bahlo, Genetics and Bioinformatics Group, Parkville 3050, Victoria, Australia.

bahlo@wehi.edu.au.

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HUZIMURA, Ryoitiro; MATSUYAMA, Toyoki.

A mathematical model with a modified logistic approach for singly peaked population processes.

When a small number of individuals of a single species are confined in a closed space with a limited amount of indispensable resources, breeding may start initially under suitable conditions, and after peaking, the population should go extinct as the resources are exhausted. Starting with the logistic equation and assuming that the carrying capacity of the environment is a function of the amount of resources, a mathematical model describing such a pattern of population change is obtained. An application of this model to a typical set of population records, that of deer herds by V. B. Scheffer (1951, Sci. Monthly 73, 356-362) and E. C. O'Roke and F. N. Hamerstrom (1948, J. Wildlife Management 12, 78-86), yields estimates of the initial amount of indispensable food and its availability or nutritional efficiency which were previously unspecified.

(MATHEMATICAL MODELS, POPULATION DYNAMICS, FOOD, REPRODUCTION, POPULATION GROWTH).

English ? pp. 301-306.

R. Huzimura, Department of Economics, Osaka Gakuin University, 2-36-1 Kishibe-minami, Suita-shi, Osaka, 564-8511, Japan; T. Matsuyama, Department of Physics, Nara University of Education, Takabatake-cho, Nara, 630-8528, Japan.

matsuyat@nara-edu.ac.jp.

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AYATI, Bruce P.; DUPONT, Todd F.; NAGYLAKI, Thomas.

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. 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.

(POPULATION GENETICS, DEMOGRAPHIC MODELS, POPULATION DENSITY, MIGRATION, THEORETICAL MODELS).

English ? pp. 337-347.

B. P. Ayati, Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street S.E., Minneapolis, Minnesota 55455, U.S.A.; T. F. Dupont, Departments of Computer Science and Mathematics, The University of Chicago, 1101-1114 East 58th Street, Chicago, Illinois 60637, U.S.A.; T. Nagylaki, Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, Illinois 60637, U.S.A.

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