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.This work was supported by National Science Foundation grant BSR-9006285     

POLLEN DISCOUNTING AND THE SPREAD OF A SELFING VARIANT IN TRISTYLOUS EICHHORNIA PANICULATA: EVIDENCE FROM EXPERIMENTAL POPULATIONS

Floral traits that increase self-fertilization are expected to spread unless countered by the effects of inbreeding depression, pollen discounting (reduced outcross pollen success by individuals with increased rates of self-fertilization), or both. Few studies have attempted to measure pollen discounting because to do so requires estimating the male outcrossing success of plants that differ in selfing rate. In natural populations of tristylous Eichhornia paniculata, selfing variants of the mid-styled morph are usually absent from populations containing all three style morphs but often predominate in nontrimorphic populations. We used experimental garden populations of genetically marked plants to investigate whether the effects of population morph structure on relative gamete transmission by unmodified (M) and selfing variants (M‘) of the mid-styled morph could explain their observed distribution. Transmission through ovules and self and outcross pollen by plants of the M and M’ morphs were compared under trimorphic, dimorphic (S morph absent), and monomorphic (L and S morphs absent) population structures. Neither population structure nor floral morphology affected female reproductive success, but both had strong effects on the relative transmission of male gametes. The frequency of self-fertilization in the M' morph was consistently higher than that of the M morph under all morph structures, and the frequency of self-fertilization by both morphs increased as morph diversity of experimental populations declined. In trimorphic populations, total transmission by the M and M' morphs did not differ. The small, nonsignificant increase in selfing by the M' relative to the M morph was balanced by decreased outcross siring success, particularly on the S morph. In populations lacking the S morph, male gamete transmission by the M' morph was approximately 1.5 times greater than that by the M morph because of both increased selfing and increased success through outcross pollen donation. Therefore, gamete transmission strongly favored the M' morph only in the absence of the S morph, a result consistent with the distribution of the M' morph in nature. This study indicates that floral traits that alter the selfing rate can have large and context-dependent influences on outcross pollen donation.     

Population characteristics of Gammarus pulex (L.) from five English streams

Gammarus pulex were sampled from five English streams during April 1992. The population density, number of precopula pairs and incidence of parasitic infection were recorded, and the biomass was estimated from subsamples by relating body area to dry weight. Physical and chemical measurements were taken from each stream. The abundance and standing crop biomass differed significantly between streams, probably due to the influence of pollutants or the physical structure of the stream bed. The size of individual G. pulex also differed significantly between streams, although there was no obvious causal explanation for this. Few individuals were visibly parasitised in any of the populations. Males were significantly larger than females, both in precopula pairs and in the general populations. The sex ratio differed between populations and may explain inter-stream differences in the relationship between precopula male and female size.     

Directional and Fluctuating Asymmetry in Sexual and Asexual Otiorhynchus alpicola Populations

This study concerns the contribution of directional asymmetry (DA) and fluctuating asymmetry (FA) as a characterization of variation in six sexual (diploid) and two asexual (triploid and tetraploid) populations of the weevil Otiorhynchus alpicola. It is shown that DA in sexual populations is about 1 % of the mean length of each of the seven bilateral traits and the average contribution of DA to trait variation is even lower in asexual populations (about 0.85 in triploids and 0.65 in tetraploids forms). The average contribution of FA to the total phenotypic variance is about 23 %, 12 % and 19 % in diploid, triploid and tetraploid populations, respectively. Since FA is generally regarded as a measure of developmental stability, our data indicate that triploid forms of O. alpicola are developmentally more stable than diploid and tetraploid forms. The relationship between the level of ploidy and FA is discussed.     

Genetic analysis of populations of threatened snake species using RAPD markers

Snakes are a particularly threatened vertebrate taxon, with distributions of many species and populations becoming increasingly fragmented. At present, little is known about the degree of genetic differentiation that exists between isolated populations even though such information may be critical to their survival and conservation. As an example of how recently developed RAPD genetic markers can be used in conservation genetics, we present preliminary results from a study which used these DNA-based markers to assess population divergence in two threatened Canadian snakes, the black rat snake ( Elaphe o. obsoleta ) and the eastern massasauga rattlesnake ( Sistrurus c. catenatus ). We present information on the levels of variation and reliability of amplification for fragments generated from five primers. We then use a recently developed analytical technique to estimate levels of nucleotide diversity within populations and sequence divergence between populations. Our results show that intrapopulation levels of divergence as estimated by the methods of Clark & Lanigan ( Molecular Biology and Evolution 1993, 10 , 1096–1111) approximate those found for mtDNA in vertebrates and that diversity between snake populations is small and non-significant when tested using randomization procedures. Thus, our study provides an example of how RAPDs can be applied to conservation genetic studies of vertebrates and suggest that the snake populations we examined have only recently become isolated and maybe considered genetically equivalent from a conservation perspective, although this conclusion needs to be confirmed with other DNA-based markers.     

Intraspecific evolution ofMicroseris pygmaea (Asteraceae,Lactuceae) analyzed by cosegregation of phenotypic characters (QTLs) and molecular markers (RAPDs)

The Chilean annual,Microseris pygmaea, has differentiated in distinct coastal and inland series of populations after long-distance dispersal from western North America. Two plants from the most diverse biotypes were crossed, a large F₂ was raised and analysed for segregation of 30 phenotypic characters. Segregation of molecular markers (47 RAPDs, 1 RFLP, 2 isozymes) was determined in a subpopulation of 45 plants which include all extremes for the phenotypic characters. 32 marker/character cosegregations were significant at the 1% level in t-tests between dominant and homozygous recessive marker genotypes. Considering linkage among markers and pleiotropy of certain marker loci, the number of independent quantitative trait loci (QTLs) is reduced to about 18. Interactions among 2 or 3 QTLs affecting one character have been characterized. The phenotypic differentiation ofM. pygmaea during its evolution from a single founder individual begins to be understood at the level of single-gene mutants.     

Genetic diversity in a seed production population vs. natural populations of Sitka Spruce

Isozyme analysis was applied to estimate the level of variation and the genetic structure of a seed-production population (i.e., seed orchard) and 10 range-wide natural populations of Sitka spruce (Picea sitchensis (Bong.) Carr.). Gene diversity and heterozygosity estimates were comparatively high in both the seed orchard and the natural populations studied. The seed orchard population showed a significantly higher number of alleles per locus and percentage of polymorphic loci. Though not significant, mean heterozygosity of the seed orchard was higher than that observed for all natural populations. Genetic distance analysis indicated that the seed-orchard population was genetically similar to three natural populations from which the parent trees were selected. Parent trees sampling breadth has been identified as the major cause for the observed increased level. The impact of recurrent selection and seed orchard biology and management on maintaining the genetic diversity is discussed.     

Effective population size,genetic diversity,and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.     

Numerical solution of structured population models

Numerical methods are presented for a general age-structured population model with demographic rates depending on age and the total population size. The accuracy of these methods is established by solving problems for which alternate solution techniques are available and are used for comparison. The methods reliably solve test problems with a variety of dynamic behavior. Simulations of a blowfly population exhibit cyclic fluctuations, whereas a simulated squirrel population reaches a stable age distribution and stable equilibrium population size. Life-history attributes are easily studied from the computed solutions, and are discussed for these examples. Recovery of a stressed population back to equilibrium is examined by computing the transition in age structure, and the transient behavior of other properties of the population such as the per capita growth rate, the average age, and the generation length.