Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants

Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is 1/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from 1/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.     

Genetic variance of mating frequency in the honeybee (Apis mellifera L.)

Summary. The genetic variance of queen mating frequency was studied in honeybees (Apis mellifera carnica). Worker offspring (N = 966) of 28 naturally mated half sister-queens (r = 0.25) from seven unrelated breeding lines were genotyped at four DNA microsatellites. The mating frequencies of the queens were derived from the offspring genotypes. The number of observed matings per queen ranged from 10 to 28 with an average of 17.32 ± 1.10 (number of estimated matings: 24.94 ± 2.51; number of effective matings: 20.09 ± 1.73). Half-sib analyses of the breeding lines were used to estimate heritability. Heritability was h² = 0.449 ± 0.135 for the estimated number of matings and h² = 0.262 ± 0.103 for the number of effective males, which are both significantly different from zero. We conclude that a high genetic variance for polyandry in honeybees can be favored by balanced selection between individual queen and colony level.Received 16 October 2003; revised 4 May 2004; accepted 4 May 2004.     

Sex ratio conflicts, mating frequency, and queen fitness in the ant Formica truncorum

We examined the effect of facultative sex allocation by workerson queen fitness in a Furnish population of the ant Formicatruncorum. Workers rear female-biased broods in colonies headedby a singly mated queen and male-biased broods in colonies headedby a multiply mated queen. As a result, multiply mated queenshave a 37% fitness advantage over singly mated queens. Neitherreproductive output nor worker population of colonies variedwith queen mating frequency. We suggest that singly mated queenspersist in the population because fitness benefits to multiplymated queens via sex allocation are balanced by costs of additionalmatings. Alternatively, singly mated queens may persist simplybecause some queens lack opportunities to mate multiply or becausemale control sometimes prevents additional matings by queens.     

INFERENCE OF SPERM COMPETITION FROM BROODS OF FIELD-CAUGHT DROSOPHILA

In field studies of multiple mating and sperm competition there typically is no experimental control over the number of times that a female mates, the interval between matings, or the genetic identity of multiple fathers contributing to a brood. Irrespective of this complexity, high-resolution molecular markers can be used to assign paternity with considerable confidence. This study employed two highly heterozygous microsatellite loci to assess multiple paternity and sperm displacement in a sample of broods taken from a natural population of Drosophila melanogaster. The large number of alleles present at each of the loci makes it difficult to derive explicit maximum-likelihood estimates for multiple paternity and sperm displacement from brood samples. Monte Carlo simulations were used to estimate maximum-likelihood parameters for the distribution of female remating frequency and the proportion of offspring sired by the second or subsequent mating males. Estimates were made based on genotypes scored at two distinct marker loci because they were found to give statistically homogeneous results. Fitting a Poisson distribution of number of matings, the mean number of males mated by a female was 1.82. The sperm displacement parameter estimated from doubly mated females were 0.79 and 0.86 for the two loci (0.83 for the joint estimate). The overall probability that a multiply mated female will be misclassified as singly mated was only 0.006, which indicates that microsatellites can provide excellent resolution for identifying multiple mating. In addition, microsatellites can be used to generate relatively precise estimates of sperm precedence in brood-structured samples from a natural population.     

Life span of queens in the antFormica exsecta

Summary The antFormica exsecta commonly has two types of colonies: either polygynous and polydomous or monogynous and monodomous. The longevity of queens was studied in monogynous colonies in southern Finland by indirect methods using genetic markers; these data were also used to estimate the number of matings and queen replacement. The average genetic relatedness among worker nest mates was 0.72. Taking inbreeding into account (the inbreeding coefficient wasF=0.16), this value agrees with the assumption that 40% of the queens mated with one male and 60% with two males. The distribution of genotypes within colonies remained stable in successive years, indicating that queen replacement did not occur or was extremely rare. This means that the life span of nests reflects directly the life span of the queens. Eleven of the 16 nests found in 1979 were still alive ten years later. This corresponds to an annual mortality of 3.7% and a mean life span of 27 years. A total of 57 colonies were mapped in the population over a period of ten years. Averaging over the years, the annual mortality was estimated to be 4.9%. This represents a mean life span of 20 years if mortality was independent of age.     

Diploid males in the bumble beeBombus terrestris

The frequency of colonies that produce diploid males after brother-sister (50%) and nephew-niece (37.5%) matings proves that inB. terrestris the sex is determined by a single multi-allelic sex locus. The diploid males which develop normally into adults make up 50% of the diploid brood. In the laboratory the growth rate of colonies with diploid males is influenced only slightly. Of 41 colony founding queens caught out of a natural population, all produced a colony without any diploid males. Therefore, the number of sex alleles in this population is estimated to be at least 24. This means that in commercial rearing systems for bumble bees, involving several generations, the occurrence of diploid males can largely be prevented by a good scheme for crossings.     

An analytical model for the estimation of chromosome substitution effects in the offspring of individuals heterozygous at a segregating marker locus

Summary Use of marker genes for quantitative traits has been suggested as a supplement to selection for livestock species. Linkage relationships can be estimated by using data from offspring of a heterozygous parent, if offspring can be positively assigned segregation of one or the other of the marker alleles. In field data, some data on offspring can be characterized and used to estimate the difference in chromosome substitution effects, but other matings result in uncertain transfer of the marker alleles. In this study, an alternative estimation procedure is proposed that would allow incorporation of data on all offspring of a heterozygous parent, even those where chromosome segregation is ambiguous. If the frequency of the marker alleles is known in the population of mates of a heterozygous individual, the mean and variance of the heterozygous offspring can be used in a generalized leastsquares model to estimate the chromosome substitution effect. When gene frequencies are not known, maximum likelihood estimates can be obtained from the data for use in a conditional estimate. Monte Carlo simulations of data following the assumed genetic model were analyzed as proposed, and parameter estimates were characterized. Estimates of chromosome substitution effects were reasonable approximations of input values. Distributions of t-statistics testing the null hypothesis of no difference between marked chromosome segments were unbiased, with only slightly larger variance than expected. Addition of data from heterozygous offspring improved the efficiency of detection of chromosome substitution effects by more than four times when marker gene frequencies were low.     

Estimation of the neutral mutation rate in a finite population from DNA sequence data

The sampling theory for the infinite site model taking into account the phylogenetic relationship between the alleles is developed for those cases in which two or three alleles are observed in the sample. From this theory a maximum likelihood estimate of θ = 4Nμ can be obtained. Unlike the maximum likelihood estimate of θ based on the infinite allele model or the number of segregating sites, this estimate of θ is a function of the frequencies of the alleles. This method is used to estimate θ for mitochondrial DNA in Drosophila melanogaster and D. virilis from data obtained by Shah and Langley (1979. Nature (London)281, 696–699) using restriction endonucleases.     

Deviations from Hardy-Weinberg Proportions: Sampling Variances and Use in Estimation of Inbreeding Coefficients

An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients (f) obtained from these deviations.—If f is small, the best estimate of f in large samples is shown to be 2Σ _i(T_ii/N_i)/(k - 1), where T_ii is an unbiased measure of the excess of the ith homozygote and N_i the number of the ith allele in the sample [frequency = N_i/(2N)]. No extra information is obtained from the T_ij, where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the T_ij, ignoring the T_ii. Also (1) the variance of the estimate of f equals 1/(N(k - 1)) when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n, the variance is increased by a proportion (n - 1)/4 but is not increased by a half-sib relationship.—If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.     

Estimating the total number of alleles using a sample coverage method.

Previously reported methods for estimating the number of different alleles at a single locus in a population have not described a useful general result. Using the number of alleles observed in a sample gives an underestimate for the true number of alleles. The similar problem of estimating the number of species in a population was first investigated in 1943. In this article we use the sample coverage method proposed by Chao and Lee in 1992 to estimate the number of alleles in a population when there are unequal allele frequencies. Simulation studies under the recurrent mutation model show that, for reasonable sample sizes, a significantly better estimate of the true number can be obtained than that using only the observed alleles. Results under the stepwise mutation model and infinite-allele model are presented. Possible applications include improving the characterization of the prior distribution for the allele frequencies, adjusting the estimates of genetic diversity, and estimating the range of microsatellite alleles.     

Reproductive parameters vary with social and ecological factors in the polygynous ant Formica exsecta

Due to their haplo‐diploid sex determination system and the resulting conflict over optimal sex allocation between queens and workers, social Hymenoptera have become important model species to study variation in sex allocation. While many studies indeed reported sex allocation to be affected by social factors such as colony kin structure or queen number, others, however, found that sex allocation was impacted by ecological factors such as food availability. In this paper, we present one of the rare studies that simultaneously investigated the effects of social and ecological factors on social insect nest reproductive parameters (sex and reproductive allocation, nest productivity) across several years. We found that the sex ratio was extremely male biased in a polygynous (multiple queens per nest) population of the ant Formica exsecta. Nest‐level sex allocation followed the pattern predicted by the queen‐replenishment hypothesis, which holds that gynes (new queens) should only be produced and recruited in nests with low queen number (i.e. reduced local resource competition) to ensure nest survival. Accordingly, queen number (social factor) was the main determinant on whether a nest produced gynes or males. However, ecological factors had a large impact on nest productivity and therefore on a nest's resource pool, which determines the degree of local resource competition among co‐breeding queens and at what threshold in queen number nests should switch from male to gyne production. Additionally, our genetic data revealed that gynes are recruited back to their parental nests after mating. However, our genetic data are also consistent with some adult queens dispersing on foot from nests where they were produced to nests that never produced queens. As worker production is reduced in gyne‐producing nests, queen migration might be offset by workers moving in the other direction, leading to a nest network characterized by reproductive division of labour. Altogether our study shows that both, social and ecological factors can influence long‐term nest reproductive strategies in insect societies.     

Queen–worker conflict over male production and the sex ratio in a facultatively polyandrous bumblebee, Bombus hypnorum: the consequences of nest usurpation

Evolutionary conflicts among social hymenopteran nestmates are theoretically likely to arise over the production of males and the sex ratio. Analysis of these conflicts has become an important focus of research into the role of kin selection in shaping social traits of hymenopteran colonies. We employ microsatellite analysis of nestmates of one social hymenopteran, the primitively eusocial and monogynous bumblebee Bombus hypnorum, to evaluate these conflicts. In our 14 study colonies, B. hypnorum queens mated between one and six times (arithmetic mean 2.5). One male generally predominated, fathering most of the offspring, thus the effective number of matings was substantially lower (1-3.13; harmonic mean 1.26). In addition, microsatellite analysis allowed the detection of alien workers, those who could not have been the offspring of the queen, in approximately half the colonies. Alien workers within the same colony were probably sisters. Polyandry and alien workers resulted in high variation among colonies in their sociogenetic organization. Genetic data were consistent with the view that all males (n = 233 examined) were produced by a colony's queen. Male parentage was therefore independent of the sociogenetic organization of the colony, suggesting that the queen, and not the workers, was in control of the laying of male-destined eggs. The population-wide sex ratio (fresh weight investment ratio) was weakly female biased. No evidence for colony-level adaptive sex ratio biasing could be detected.     

Sociogenetic organization of the ants Myrmica ruginodis and Myrmica lobicornis: Number,relatedness and longevity of reproducing individuals

The number and relationships of reproducing individuals create the observed genetic heterogeneity within a social insect colony. These are referred to as sociogenetic organization and were studied in the red ants M. ruginodis and M. lobicornis. Direct observations of the queen numbers were obtained by excavating colonies. The effective number of reproducing individuals was estimated from genetic relatedness based on genotype frequency data. Sociogenetic organization of colonies of both species is simple. The number of queens is low, single mating of queens is the rule and queen to queen variation in worker production is minor. The important variables of sociogenetic organization are the number and relatedness of coexisting queens in polygynous colonies. Queen nestmates are related on average by 0.405 in polygynous colonies of M. ruginodis, showing that colonies recruit their own daughters as new reproductives. The distribution of queen number in M. ruginodis indicates that the study population contains both microgyna and macrogyna types of the species. The large proportion of colonies where the resident queen(s) is not the mother of the workers shows that the average life span of a queen is short and colonies are serially polygynous.     

Colony sex ratios vary with queen number but not relatedness asymmetry in the ant Formica exsecta

Split-sex-ratio theory assumes that conflict over whether to produce predominately males or female reproductives (gynes) is won by the workers in haplodiploid insect societies and the outcome is determined by colony kin structure. Tests of the theory have the potential to provide support for kin-selection theory and evidence of social conflict. We use natural variation in kinship among polygynous (multiple-queen) colonies of the ant Formica exsecta to study the associations between sex ratios and the relatedness of workers to female versus male brood (relatedness asymmetry). The population showed split sex ratios with about 89% of the colonies producing only males, resulting in an extremely male-biased investment ratio in the population. We make two important points with our data. First, we show that queen number may affect sex ratio independently of relatedness asymmetry. Colonies producing only males had greater genetic effective queen number but did not have greater relatedness asymmetry from the perspective of the adult workers that rear the brood. This lack of a difference in relatedness asymmetry between colonies producing females and those producing only males was associated with a generally low relatedness between workers and brood. Second, studies that suggest support for the relatedness-asymmetry hypothesis based on indirect measures of relatedness asymmetry (e.g. queen number estimated from relatedness data taken from the brood only) should be considered with caution. We propose a new hypothesis that explains split sex ratios in polygynous social insects based on the value of producing replacement queens.     

The Evolution of Extreme Polyandry in Social Insects: Insights from Army Ants

The unique nomadic life-history pattern of army ants (army ant adaptive syndrome), including obligate colony fission and strongly male-biased sex-ratios, makes army ants prone to heavily reduced effective population sizes (N _e). Excessive multiple mating by queens (polyandry) has been suggested to compensate these negative effects by increasing genetic variance in colonies and populations. However, the combined effects and evolutionary consequences of polyandry and army ant life history on genetic colony and population structure have only been studied in a few selected species. Here we provide new genetic data on paternity frequencies, colony structure and paternity skew for the five Neotropical army ants Eciton mexicanum, E. vagans, Labidus coecus, L. praedator and Nomamyrmex esenbeckii; and compare those data among a total of nine army ant species (including literature data). The number of effective matings per queen ranged from about 6 up to 25 in our tested species, and we show that such extreme polyandry is in two ways highly adaptive. First, given the detected low intracolonial relatedness and population differentiation extreme polyandry may counteract inbreeding and low N _e. Second, as indicated by a negative correlation of paternity frequency and paternity skew, queens maximize intracolonial genotypic variance by increasingly equalizing paternity shares with higher numbers of sires. Thus, extreme polyandry is not only an integral part of the army ant syndrome, but generally adaptive in social insects by improving genetic variance, even at the high end spectrum of mating frequencies.     

The Evolution of Multiple Mating Behavior by Honey Bee Queens (APIS MELLIFERA L.)

A model is presented showing that natural selection operating at the individual level can adequately explain the evolution of multiple mating behavior by honey bee queens. Group selection need not be invoked. The fitness of a given female genotype is a function of the number of sex alleles in the population, the number of matings by an individual female and the specific parameters that determine the relationship of brood viability to individual fitness. Even though the exact relationship is not known, it is almost certainly not linear. A nonlinear relationship between worker brood viability and fitness and a significant genetic load associated with the sex-determination system in honey bees are the essential components of this model.     

Determining colony densities in wild honeybee populations (<Emphasis Type="Italic">Apis mellifera</Emphasis>) with linked microsatellite DNA markers

Estimating the population size of social bee colonies in the wild is often difficult because nests are highly cryptic. Because of the honeybee (Apis mellifera) mating behaviour, which is characterized by multiple mating of queens at drone congregation areas (DCA), it is possible to use genotypes of drones caught at these areas to infer the number of colonies in a given region. However, DCAs are difficult to locate and we assess the effectiveness of an alternative sampling technique to determine colony density based on inferring male genotypes from queen offspring. We compare these methods in the same population of wild honeybees, Apis mellifera scutellata. A set of linked microsatellite loci is used to decrease the frequency of recombination among marker loci and therefore increase the precision of the estimates. Estimates of population size obtained through sampling of queen offspring is significantly larger than that obtained by sampling drones at DCAs. This difference may be due to the more extensive flying range of queens compared with drones on mating flights. We estimate that the population size sampled through queen offspring is about double that sampled through drones.     

Gene Duplication within the Family Salmonidae: Disomic Inheritance of Two Loci Reported to Be Tetrasomic in Rainbow Trout

We describe our studies of the genetics of allelic variation for NADP-dependent isocitrate dehydrogenase (IDH) in rainbow trout (Salmo gairdneri). Five populations of rainbow trout were studied to determine the phenotypic distribution of IDH; 453 progeny from a number of controlled matings were examined to determine the nature of inheritance of these alleles. The variation was found to be the result of four alleles producing protein subunits of differing electrophoretic mobilities. Progeny from crosses clearly demonstrated the presence of two disomic loci controlling the variation, rather than one tetrasomic locus as had been previously reported. These findings support our contention that the hypothesis of a tetraploid event in salmonid evolution should not be uncritically accepted.     

Are mistakes inevitable? Sex allocation specialization by workers can reduce the genetic information needed to assess queen mating frequency

Insect workers can increase their inclusive fitness by biasing colony sex allocation towards males when their mother queen is mated to multiple males and females when she is singly mated. Workers need heritable variation in odour diversity to assess queen mating frequency. Here we present a simple one-locus two-allele model, which shows that the sex ratio specialization itself will often select against rare alleles that would provide additional information for the assessment of queen mating frequency. However, under certain rather restricted conditions, such as when sex ratios are highly female biased, and when worker reproduction is rare, sex ratio specialization can select for rare alleles. This suggests that sex allocation biasing by workers will usually reduce the very information that workers need to assess queen mating frequency. Our model is an example where an explicit treatment of underlying genetics and mechanisms of behaviour, such as information use, is necessary to fully understand the evolution of an adaptive behavioural strategy.     

Multiallelic restriction fragment polymorphisms in genetic counseling: population genetic considerations

The use of selectively neutral, multiallelic molecular markers to trace the transmission of tightly linked genes is examined theoretically for all genetic counseling situations in which the diagnosis of deleterious progeny is desired. Formulae are computed in terms of the gametic frequency distribution in the population, for the expected fraction of matings (alpha i) which allow exact diagnosis on the basis of the marker alleles transmitted, assuming an arbitrary number (n) of alleles segregating at the marker locus and possibly nonrandom associations between the loci. In each case, it is shown that the diagnostic value of a multiallelic marker increases as n increases, with approximately 1-1/n matings informative, on average.