Selection for Increased Mutation Rates with Fertility Differences between Matings

Previous studies of mutation modification have considered models in which selection is a result of viability differences that are sex symmetric. The results of a numerical study of a model in which selection is a result of fertility differences between mated pairs demonstrate that the type of selection to which a population is subject can have a significant impact on the evolution of various parameters of the genetic system. When the fertility of matings between individuals with different genotypes exceeds the fertility of at least some of the matings between individuals with the same genotype, selection may favor increased rates of mutation, in contrast to the results from all existing constant viability models with random mating and infinite population size. Increased mutation rates are most frequently favored when forward and back mutation occur at approximately equal rates and when the modifying locus is loosely linked to the selected locus. We present one example in which selection favors increased rates of mutation even though the selection scheme is reducible to one of differential viability between the sexes.     

Studies on assortative mating. III. The effects of incomplete penetrance in assortative mating systems

Four models of positive and negative assortative mating systems, exclusive or partial, in relation to phenotypes determined by a pair of autosomal alleles with dominance but with incomplete penetrance of the dominant allele in heterozygous state, are presented. By introducing the parameter of incomplete penetrance in the models of assortative matings, matings between individuals with identical genotypes will occur within the negative systems, as well as matings between individuals with different genotypes within the positive assortative mating systems. Thus, incomplete penetrance has the effect of retarding equilibrium on an assortative mating system, making this equilibrium equivalent to a system with a lower degree of assortative mating, where the penetrance equals 1 or 0. Another conclusion of biological interest drawn from the mathematical analysis presented in this paper is that for any value of the penetrance, the frequency of 0.5 for recessive individuals is also typical of exclusive or partial negative assortative mating systems at equilibrium.     

Age correlation between mates and average consanguinity in age-structured human populations

When population geneticists wish to determine the genetic consequences of some aspect of mating behavior, it is often necessary to compare observed levels of consanguinity to the level expected when mating is random with respect to the factor being studied. Expectations under random mating are often derived from discrete generation models that ignore age structure. Observed frequencies of consanguineous matings are due to processes that are continuous in time and are affected by variables that are functions of age structure. The extent to which this discrepancy between the models and reality might distort conclusions drawn from comparisons of observed and expected behavior has received insufficient attention. One potential source of error is the tendency for people to choose mates whose ages differ from their own by a certain amount; this tendency influences the frequency of consanguineous matings. Age correlation between mates should therefore also affect average consanguinity between mates and average inbreeding in the population. Expected levels of consanguinity might then differ depending on whether or not age structure has been taken into account. Hajnal developed a model that predicts the frequencies of consanguineous matings in age-structured populations. Hajnal's model is extended here to include relationships that are defined by lineal descent as well as by common ancestry, and to allow calculation of the frequencies of consanguineous matings in the absence of age correlation between mates. The extended model is then used to determine the effect of age correlation between mates on average consanguinity under various sets of conditions. The magnitude of this effect depends on the degree to which the increased frequency of some types of consanguineous matings is offset by the decrease in other types of matings. There is a fairly wide range of conditions under which this compensation is nearly complete and therefore under which the overall effect of age correlation is small. But the size of this effect is sensitive to many factors, especially the distribution of age differences between mates and the variances of ages at maternity and paternity. Under some conditions, age correlation between mates will have a substantial effect on average consanguinity.     

Analysis of Inbreeding Depression in Agaricus Bisporus

Inbreeding depression was observed in the commercial button mushroom, Agaricus bisporus, by examining two laboratory populations. The outbred population consisted of 20 compatible pairings, 10 homokaryons with each of the homokaryons Ag1-1 and Ag89-65. The inbred population consisted of 104 backcrosses (among which 52 were expected to be sexually compatible) obtained from the pairings of two progenitor homokaryons, Ag1-1 and Ag89-65, with 52 progeny homokaryons derived from the mating between Ag1-1 and Ag89-65. The eight fitness components examined for these two populations were successful matings as identified by the analysis of restriction fragment length polymorphisms, positive mycelial interaction in these successful matings, heterokaryon growth rate, primordium formation by the successful matings, fertile fruiting body formation, time to first break, average number of fruiting bodies per square foot, and average weight per fruiting body. The outcrossed population showed a significant advantage over the inbred population in three of eight fitness components. Two pairs of traits were significantly correlated. The multiplicative fitness ratio of the inbred to the outcrossed population was 0.18. The relevance of inbreeding depression to the evolution of fungal mating systems and to mushroom breeding is discussed.     

Convergence of two-locus gamete frequencies in random mating age-structured populations

We study two models describing infinite random mating age-structured populations. Under model I, the number of matings at any time is proportional to the number of mature females at that time, and the fecundity of a mating is assumed to be a product of factors that depend upon the ages of the mates, but not upon sex. Under model II, individuals can mate only with others of the same age group, and the number of matings of individuals of an age group is, at any time, proportional to the number of females of that age group. If model II holds, or the special case of model I in which the fecundity of all matings is the same, it is possible to show that, in the long run, allele frequencies converge and the gametic disequilibrium approaches zero at a geometric rate. A heuristic argument and a numerical example suggest that these things are also more generally true for model I. A good approximation to the time that it takes to reduce the gametic disequilibrium by a fraction equal to the recombination rate turns out to be the measure of the generation interval in Leslie's theory of population growth.     

WinPop 2.5: software for representing population genetics phenomena

The curriculum for genetics courses is shifting from a classical to a more molecular genetics focus, increasing the importance of subjects such as population genetics. Population genetics is a computational and statistical field that requires a good understanding of the nature of stochastic events. It is a difficult field for biology students with a limited mathematical background and there is a need for visualisation tools to facilitate understanding by the use of practical examples. WinPop provides students and researchers with a visual tool to allow the simulation and representation of population genetics phenomena. WinPop is a user-friendly software meant for use in population genetics courses and basic research. WinPop 2.5 contains six different modules that represent and simulate population genetics models. Genotype and allele frequencies are calculated under the different models: panmixia, genetic drift, assortative matings, selection, gene flow and mutation. The program's interface presents information in Cartesian graphics and isosceles triangular coordinate systems, allowing the user to save graphical and textual data output from the simulations. WinPop is developed in Visual Basic 6.0 and uses Windows 95 and higher. WinPop 2.5 can be downloaded from http://www.genedrift.org/winpop.php.     

Female mating success and risk of pre-reproductive death in a protandrous grasshopper

Numerous studies have assessed the adaptive value of protandry for males in several insect species, considering that male emergence is determined by female availability. However, the possible advantage of the time of emergence for females on their mating success in protandrous insect species has only been explored theoretically. By studying the grasshopper Sphenarium purpurascens we evaluated the hypothesis that late emergence could be adaptive for females. If female maturation occurs when the population density is higher and the sex ratio (males/females) is biased to males, their probability of mating increases. Thus, in this study we estimated (1) the opportunity for mating in females as a function of their sexual maturation time, population density, and sex ratio at the moment they reached sexual maturity. In addition, (2) an analysis incorporating female body size and the total number of female matings was performed. Both analyses support the occurrence of protandry in the studied population. Under the first approach, females with intermediate maturation time had a higher probability of being mated than earlier and late matured females. Thus, it suggests that stabilising selection is acting on female maturation time and this may affect selection on male maturation time. Furthermore, the proportion of mated females increased when the sex ratio was biased to males, and stabilising selection on maturation time was detected also. However, the number of matings of a female depended on her body size. Females with larger body size had more matings than smaller ones at the beginning of the reproductive season. Because selection acts differently on maturation time in males and females of S. purpurascens this result is consistent with a condition for the maintenance of protandry in the population. The present results are discussed in the light of the models for the evolution of protandry.     

Half-sib mating structures

All ways in which all matings in a population can be between half-sibs under a generalization of regular systems of inbreeding are characterized for both finite and infinite populations. A model of random half-sib mating is developed and analyzed, and the asymptotic configuration of populations subject to it is described. The classical model of half-sib mating which ensues from the standard definition of regular systems of inbreeding is only one of many ways a population can propagate by half-sib mating, and a wide range of genetic identity is possible dependent on which half-sib mating structure governs a population.     

Acuity of selective mechanisms operating on ABO, Rh, and MN blood groups

Selection in ABO, Rh, and MN blood groups was studied in 216 matings and their children in an endogamous population. Incompatibility status with respect to these three systems was considered simultaneously. There is no effect of incompatibility on number of pregnancies. Analysis of variance between groups confirms that prenatal loss is associated with incompatibility, and it is greater when the matings are incompatible for any two systems. There is no significant intergenerational change in ABO and Rh polymorphisms. Segregation analysis for the ABO system suggests that there is no significant difference in the proportion of A, B, and O children, based on the compatibility of the parents, while analysis for Rh-D system showed a segregation distortion which is not related to the known antigenic specificities (mother-child incompatibility).     

FUNCTIONAL INCOMPATIBILITY BETWEEN THE FERTILIZATION SYSTEMS OF TWO ALLOPATRIC POPULATIONS OF CALLOSOBRUCHUS MACULATUS (COLEOPTERA: BRUCHIDAE)

Abstract Recent studies indicate that postcopulatory sexual selection may represent an important component of the speciation process by initiating reproductive isolation via the evolutionary divergence of fertilization systems. Using two geographically isolated populations of the polyandrous beetle Callosobruchus maculatus, we investigated divergence in fertilization systems by determining the extent of postcopulatory functional incompatibility. Through reciprocal, cross‐population matings we were able to separately estimate the effects of male and female population origin and their interaction on the extent of last‐male sperm precedence, female receptivity to further copulation and female oviposition. Our results indicate partial incompatibility between the fertilization systems of the two populations at all three functional levels. Males derived from the same population as females outcompete rival, allopatric males with respect to sperm preemption, sperm protection, and ability to stimulate female oviposition. This pattern is reciprocated in both populations indicating that postcopulatory, prezygotic events represent important mechanisms by which between‐population gene flow is reduced. We suggest the partial gametic isolation observed is a by‐product of the coevolution of male and female fertilization systems by a process of cryptic female choice. Our results are consistent with a mechanism akin to conventional mate choice models although they do not allow us to reject antagonistic sexual coevolution as the mechanism of cryptic female choice.     

Seed production from the mixed mating system of Chesapeake Bay (USA) eelgrass (Zostera marina; Zosteraceae)

In monoecious plants, gametes can be exchanged in three ways: among unrelated genets (outbreeding), with close relatives (inbreeding), or within individuals (geitonogamous selfing). These different mating systems may have consequences for population demography and fitness. The experiment presented herein used artificial crosses to examine the mating system of Chesapeake Bay, Virginia, USA eelgrass (Zostera marina L; Zosteraceae), a bisexual submerged aquatic plant that can outbreed, inbreed, and self. Genetic data indicate severe heterozygosity deficiencies and patchy genotype distribution in these beds, suggesting that plants therein reproduce primarily by vegetative propagation, autogamy, or geitonogamy. To clarify eelgrass reproductive strategies, flowers from three genetically and geographically distinct beds were hand-pollinated in outbred, inbred, and selfed matings. Fertilization success and seed production, life history stages which contribute greatly to the numeric maintenance of populations, were monitored. We found no evidence that inbreeding had negative consequences for seed production. On the contrary, selfed matings produced seeds significantly more frequently than outcrossed matings and produced significantly larger numbers of seeds than either inbred or outbred matings. These results contrast with patterns for eelgrass in other regions but might be expected for similar populations in which pollen limitation or a short reproductive season renders selfing advantageous.     

Reduction of slow-fast discrete models coupling migration and demography

This work deals with a general class of two-time scales discrete nonlinear dynamical systems which are susceptible of being studied by means of a reduced system that is obtained using the so-called aggregation of variables method. This reduction process is applied to several models of population dynamics driven by demographic and migratory processes which take place at two different time scales: slow and fast. An analysis of these models exchanging the role of the slow and fast dynamics is provided: when a Leslie type demography is faster than migrations, a multi-attractor scenario appears for the reduced dynamics; on the other hand, when the migratory process is faster than demography, the reduction process gives rise to new interpretations of well known discrete models, including some Allee effect scenarios.     

The time of detection of recessive visible genes with non-random mating.

Expressions for the probability and average time of detection of a recessive visible gene in populations where there is partial selfing or partial full-sib mating are presented. A small increase in the proportion of inbred matings greatly reduces the average time until detection and increases the proportion detected. Unless the proportion of inbred matings or the population size is very small, the time and proportion detected are approximately independent of the population size.     

With selection for fecundity the mean fitness does not necessarily increase

A population with two alleles at one locus is considered. It is assumed that there is random mating of adults and that matings in which a particular pair of genotypes is involved may have a different mean number of offspring, or fecundity, than other types of matings. There is assumed to be no other selection. It is shown that the genotypic frequencies that maximize the mean fecundity of the population are not necessarily the same as the stable equilibrium frequencies. Thus, examples can be found for which the mean fecundity decreases from one generation to the next, and one such example is presented. An example in which there is no stable equilibrium, and the mean fecundity oscillates, is also given.     

Are extra‐pair males different from cuckolded males? A case study and a meta‐analytic examination

Traditional models for female extra‐pair matings assume that females benefit indirectly from extra‐pair mating behaviour. Under these so‐called adaptive models, extra‐pair males are hypothesized to have more compatible genotypes, larger body size, exaggerated ornaments or to be older than cuckolded males. Alternatively, (‘nonadaptive’) models that consider female extra‐pair matings to be a by‐product posit that female extra‐pair mating can be maintained even if there is no benefit to females. This could happen if, for example, males gained fitness benefits from extra‐pair mating, while female and male extra‐pair mating behaviours were genetically correlated. Extra‐pair males are also expected to be older and larger if this improves their ability to convince or coerce females to mate. We investigated whether a female's extra‐pair mates differed from her cuckolded mate in both genetic and phenotypic traits by analysing data from an insular house sparrow population. We found that extra‐pair males were older than cuckolded males, consistent with both models. However, in contrast to the expectations from from adaptive models, extra‐pair and cuckolded males were of similar genetic relatedness, and hence expected compatibility, with the female, and had comparable body size and secondary sexual traits. We also updated previous meta‐analyses examining differences between extra‐pair and cuckolded males. The meta‐analytic results matched results from our house sparrow case study. Although we cannot completely exclude indirect benefits for females, nonadaptive models may better explain female extra‐pair matings. These neglected alternative models deserve more research attention, and this should improve our understanding of the evolution of mating systems.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.     

Estimation of the Number of Sex Alleles and Queen Matings from Diploid Male Frequencies in a Population of APIS MELLIFERA

The distribution of diploid males in a population of Apis mellifera was obtained by direct examination of the sexual phenotypes of the larvae. Using these data, estimates are derived for the number of sex alleles and the number of matings undergone by the queen. The number of sex alleles is estimated to be 18.9. The estimate is larger than previous ones, which have ranged between 10 and 12. However, the increase in the number of sex alleles can be explained by the large effective population number for our data. The best estimator of the number of matings by a queen is a maximum likelihood type that assumes a prior distribution on the number of matings. For the data presented here, this estimate is 17.3. This estimate is compared to others in the literature obtained by different approaches.     

捕食者-猎物关系的理论和应用研究

捕食者和猎物相互关系的研究,长期以来一直是动物生态学研究的中心课题之一。这种研究可区分为3种类型:第一是理论研究,即组建各种数学模型以便模拟捕食者和猎物间的相互关系;第二是实验种群研究,通常是在实验室内选用原生动物和节肢动物实验种群对捕食一猎物间的动态关系进行观察,并将观察结果与理论模型进行比较;第三是在田间对自然种群中的捕食者-猎物关系进行研究,并利用从理论研究和实验种群研究中所总结出来的各种基本原理对观察资料进行分析。在应用生态学领域中,常常靠引进新的更加有效的天敌来控制各种害虫。这些实际工作有些已获得成功,也有不少未取得预期效果,不管成功与否,它们都可被看作是对捕食者-猎物关系所进行的田间实验.     

Behavioral choices based on patch selection: a model using aggregation methods

The aim of this work is to study the influence of patch selection on the dynamics of a system describing the interactions between two populations, generically called 'population N' and 'population P'. Our model may be applied to prey-predator systems as well as to certain host-parasite or parasitoid systems. A situation in which population P affects the spatial distribution of population N is considered. We deal with a heterogeneous environment composed of two spatial patches: population P lives only in patch 1, while individuals belonging to population N migrate between patch 1 and patch 2, which may be a refuge. Therefore they are divided into two patch sub-populations and can migrate according to different migration laws. We make the assumption that the patch change is fast, whereas the growth and interaction processes are slower. We take advantage of the two time scales to perform aggregation methods in order to obtain a global model describing the time evolution of the total populations, at a slow time scale. At first, a migration law which is independent on population P density is considered. In this case the global model is equivalent to the local one, and under certain conditions, population P always gets extinct. Then, the same model, but in which individuals belonging to population N leave patch 1 proportionally to population P density, is studied. This particular behavioral choice leads to a dynamically richer global system, which favors stability and population coexistence. Finally, we study a third example corresponding to the addition of an aggregative behavior of population N on patch 1. This leads to a more complicated situation in which, according to initial conditions, the global system is described by two different aggregated models. Under certain conditions on parameters a stable limit cycle occurs, leading to periodic variations of the total population densities, as well as of the local densities on the spatial patches.     

The transition to social inbred mating systems in spiders: role of inbreeding tolerance in a subsocial predecessor

The social spiders are unusual among cooperatively breeding animals in being highly inbred. In contrast, most other social organisms are outbred owing to inbreeding avoidance mechanisms. The social spiders appear to originate from solitary subsocial ancestors, implying a transition from outbreeding to inbreeding mating systems. Such a transition may be constrained by inbreeding avoidance tactics or fitness loss due to inbreeding depression. We examined whether the mating system of a subsocial spider, in a genus with three social congeners, is likely to facilitate or hinder the transition to inbreeding social systems. Populations of subsocial Stegodyphus lineatus are substructured and spiders occur in patches, which may consist of kin groups. We investigated whether male mating dispersal prevents matings within kin groups in natural populations. Approximately half of the marked males that were recovered made short moves (< 5m) and mated within their natal patch. This potential for inbreeding was counterbalanced by a relatively high proportion of immigrant males. In mating experiments, we tested whether inbreeding actually results in lower offspring fitness. Two levels of inbreeding were tested: full sibling versus non-sib matings and matings of individuals within and between naturally occurring patches of spiders. Neither full siblings nor patch mates were discriminated against as mates. Sibling matings had no effect on direct fitness traits such as fecundity, hatching success, time to hatching and survival of the offspring, but negatively affected offspring growth rates and adult body size of both males and females. Neither direct nor indirect fitness measures differed significantly between within patch and between-patch pairs. We tested the relatedness between patch mates and nonpatch mates using DNA fingerprinting (TE-AFLP). Kinship explained 30% of the genetic variation among patches, confirming that patches are often composed of kin. Overall, we found limited male dispersal, lack of kin discrimination, and tolerance to low levels of inbreeding. These results suggest a history of inbreeding which may reduce the frequency of deleterious recessive alleles in the population and promote the evolution of inbreeding tolerance. It is likely that the lack of inbreeding avoidance in subsocial predecessors has facilitated the transition to regular inbreeding social systems.