Genetic variance, coefficient of parentage, and genetic distance of six soybean populations

Plant breeders would like to predict which biparental populations will have the largest genetic variance. If the population genetic variance could be predicted using coefficient of parentage or genetic distance estimates based on molecular marker data, breeders could choose parents that produced segregating populations with a large genetic variance. Three biparental soybean {Glycine max (L.) Merr.} populations were developed by crossing parents that were closely related, based on pedigree relationships. Three additional biparental populations were developed by crossing parents that were assumed to be unrelated. The genetic variance of each population was estimated for yield, lodging, physiological maturity, and plant height. Coefficient of parentage was calculated for each pair of parents used to develop the segregating populations. Genetic distance was determined, based on the number of random amplified polymorphic markers (RAPD) that were polymorphic for each pair of parents. Genetic distance was not associated with the coefficient of parentage or the magnitude of the genetic variance. The genetic variance pooled across the three closely related populations was smaller than the genetic variance pooled across the three populations derived from crossing unrelated parents for all four traits that were evaluated. Received: 24 April 1996 / Accepted: 17 May 1996     

Cell division and the stability of cellular populations

 This paper couples a general d-dimensional (d arbitrary) model for the intracellular biochemistry of a generic cell with a probabilistic division hypothesis and examines the consequence of division for stability of cell function and structure. We show rather surprisingly that cell division is capable of giving rise to a stable population of cells with respect to function and structure even if, in the absence of cell division, the underlying biochemical dynamics are unstable. In the context of a simple example, our stability condition suggests that rapid cell proliferation plays a stabilizing role for cellular populations. Received: 15 January 1996 / Revised version: 31 July 1998     

Dispersal distance of corn pollen under fluctuating diffusion coefficient

I develop a mechanistic model for pollen dispersal by a generalization of the Brownian motion model. This model provides an explanation as to why the distribution of the dispersal distance is leptokurtic in most organisms. The pollen is assumed to move in a period between and + to the circumference of a circle of radius r that has a center at the current position. The angle of movement is chosen at random. Unlike the conventional Brownian motion model, the step length, r, fluctuates in a stochastic manner, obeying a generalized gamma distribution. The convection flow, i.e., the directional movement of pollen, is also considered. I show that this model is identical to the diffusion model where the dispersal duration weighted by the diffusion coefficient obeys a gamma distribution. Hence, the model is called the gamma model. The solution is given in an explicit form. The model is fitted to six data sets obtained from the literature by maximizing the quasi-likelihood. Another model (the inverse gamma model), which is not a mechanistic model but a phenomenological model, is also fitted to the data to evaluate the validity of the gamma model.     

Inbreeding and true seed in tetrasomic potato. II. Selfing and sib-mating in heterogeneous hybrid populations of Solanum tuberosum

 Inbreeding depression may affect the performance of consecutive generations of potatoes propagated by true potato seed (TPS). The effect of inbreeding was established using selfed and sib-mated generations of five TPS families. Correlation coefficients were calculated between the level of inbreeding and different traits. Inbreeding depression was expressed mainly by pollen viability, as measured by its stainability (r=−0.912, P<0.01), and tuber yield (r=−0.837, 0.01<P<0.05). The results also indicated that without unavoidable selection inbreeding depression is expected to be more evident. Furthermore, the TPS families responded quite differently to inbreeding depression. They did not show the same amount of depression for yield as they did for the characters concerning fertility. The high tuber-yielding families displayed a greater inbreeding depression for tuber yield than the lower-yielding families. Received: 10 November 1997 / Accepted: 3 March 1998     

A method to measure genetic distance between allogamous populations of alfalfa (Medicago sativa) using RAPD molecular markers

 Alfalfa (Medicago sativa L.) is a forage legume of world-wide importance whose both allogamous and autotetraploid nature maximizes the genetic diversity within natural and cultivated populations. This genetic diversity makes difficult the discrimination between two related populations. We analyzed this genetic diversity by screening DNA from individual plants of eight cultivated and natural populations of M. sativa and M.  falcata using the RAPD method. A high level of genetic variation was found within and between populations. Using five primers, 64 intense bands were scored as present or absent across all populations. Most of the loci were revealed to be highly polymorphic whereas very few population-specific polymorphisms were identified. From these observations, we adopted a method based on the Roger’s genetic distance between populations using the observed frequency of bands to discriminate populations pairwise. Except for one case, the between-population distances were all significantly different from zero. We have also determined the minimal number of bands and individuals required to test for the significance of between-population distances. Received: 7 July 1997 / Accepted: 28 October 1997     

The diffusive spread of alleles in heterogeneous populations

The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c = 2 square root of (rD), that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations.     

Stochastic epidemics in dynamic populations: quasi-stationarity and extinction

Empirical evidence shows that childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct (and is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals are born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for τ, the mean-parameter in the exponential distribution of the time to extinction for the finite population. The expression is used to study how τ depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours. Received: 14 February 2000 / Revised version: 5 June 2000 / Published online: 24 November 2000     

Ecologically heterogeneous populations of the invasive ant Wasmannia auropunctata within its native and introduced ranges

Abstract 1. The biology of most invasive species in their native geographical areas remains largely unknown. Such studies are, however, crucial in shedding light on the ecological and evolutionary processes underlying biological invasions. 2. The present study focuses on the little fire ant Wasmannia auropunctata, a species native to Central and South America that has been widely introduced and which has become invasive throughout the tropics. We characterise and compare several ecological traits of native populations in French Guiana with those in one of its introduced ranges, New Caledonia. 3. We found ecologically heterogeneous populations of W. auropunctata coexisting in the species’ native geographical area. First, we found populations restricted to naturally perturbed areas (particularly floodplains) within the primary forest, and absent from the surrounding forest areas. These populations were characterised by low nest and worker densities. Second, we found dominant populations in recent anthropogenic areas (e.g. secondary forest or forest edge along road) characterised by high nest and worker densities, and associated with low ant species richness. The local dominance of W. auropunctata in such areas can be due to the displacement of other species (cause) or the filling‐up of empty habitats unsuitable to other ants (effect). With respect to their demographic features and ant species richness, the populations of native anthropogenic habitats were to a large extent similar to the invasive populations introduced into remote areas. 4. The results point to the need for greater research efforts to better understand the ecological and demographic features of invasive species within their native ranges.     

Estimation of linkage in trisomic inheritance

 Based on F₂ families derived from selfed F₁ trisomic plants we have developed a genetic model to estimate linkage relationships between pairs of loci located on the extra chromosome. Genotypic frequencies of each class expected in a trisomic F₂ family have been calculated and the maximum-likelihood equations for recombination-fraction estimation have been derived for a variety of genetic situations. Morton’s test of homogeneity was used to compare recombination fractions estimated between loci exhibiting trisomic segregation to those obtained in families where the same loci showed Mendelian segregation. This method has been applied to an analysis of morphological, isozyme and RAPD data from faba bean (Vicia faba L.). Received: 11 October 1996 / Accepted: 21 March 1997     

Regional structuring of genetic variation in short-lived rock pool populations of Branchipodopsis wolfi (Crustacea: Anostraca)

The genetic structure of three metapopulations of the southern African anostracan Branchipodopsis wolfi was compared by analysing allozyme variation at four loci (PGM, GPI, APK, AAT). In total, 17 local populations from three sites (metapopulations) were analysed from rock pools in south-eastern Botswana ranging from 0.2 to 21 m² in surface area. In three populations we found significant deviations from Hardy-Weinberg (H-W) equilibrium at one or more loci due to heterozygote deficiencies. Genetic variability at one site was significantly lower than at the other sites, which may be linked to a greater incidence of extinction and recolonisation, as the basins at this site are shallower and have shorter hydrocycles. Across all local populations, a significant level of population differentiation was revealed. More than 90% of this variation was explained by differentiation among sites (metapopulations), although this differentiation did not correlate with geographic distance, or with environmental variables. Genetic differentiation among populations within metapopulations was low, but significant at all sites. At only one of the sites was a significantly positive association measured between genetic and geographic distance among local populations. Our data suggest that persistent stochastic events and limited effective long-range dispersal appear to dominate genetic differentiation among populations of B. wolfi inhabiting desert rock pools. The lack of association between geographic distance and genetic or ecological differences between rock pool sites is indicative of historical stochastic events. Low heterozygosity, the significant deviations from H-W equilibrium, and the large inter- but low intra-site differentiation are suggestive of the importance of short-range dispersal. Gene flow between metapopulations of B. wolfi appears to be seriously constrained by distances of 2 km or even less. Received: 28 June 1999 / Accepted: 10 January 2000     

Marker-assisted selection with spatial analysis of unreplicated field trials

 Many studies have shown that molecular markers can improve the efficiency of the selection of quantitative traits in plant breeding provided that large population sizes are used. As a way to limit experimental costs it appears that the use of unreplicated trials may be more valuable than the use of replicated plots in one trial. In this particular context of unreplicated large trials, spatial heterogeneity within the field may reduce the efficiency of the selection. The problem of controlling spatial heterogeneity was seldom considered in the case of marker-assisted selection (MAS). Here, we propose an integrated method to predict genetic values considering simultaneously marker information and possible spatial heterogeneity. This method was applied to a population of 300 F₃ lines of maize evaluated in 11 unreplicated trials for grain yield. We show that when spatial field heterogeneity is considered through appropriate statistical models the accuracy of genetic value predictions is improved and the same genetic gain can be achieved with a reduced number of trials. Received: 7 January 1998 / Accepted: 20 July 1998     

Effect of patch size and plant density of Paterson"s curse (Echium plantagineum) on the oviposition of a specialist weevil, Mogulones larvatus

This study examines the oviposition response of a specialist weevil (Mogulones larvatus) to patches of its host, the noxious weed Paterson"s curse/salvation Jane (Echium plantagineum). We simultaneously examined the effect of patch size and plant density (and their interaction), on the recorded oviposition patterns. Our results show that oviposition first occurred on the largest patches with the highest number of plants. However, there was no significant effect of patch size or number of plants per patch at the end of the experiment. At this time the level of attack per plant was negatively correlated with plant density. This negative effect of density on the level of oviposition was not mediated by a reduction in plant size at higher densities. The pattern observed may indicate a risk-spreading strategy by females. Received: 15 July 1999 / Accepted: 14 April 2000     

Predominance of one T-cell antigen receptor BV haplotype in African populations

 The human T-cell antigen receptor (TCR) is the counter-receptor for the HLA/peptide complex displayed on the surface of antigen-presenting cells. It confers antigen specificity on T lymphocytes and therefore plays a central role in pathogen recognition and host response. The most frequently used form of the TCR is a heterodimer composed of variable α and β chains. We investigated allele frequencies for four variable-region gene segments of the β chain (2S1, 3S1, 8S3, and 15S1) in 146 Caucasians and 165 Africans. The results reveal significant unexpected differences between the two populations for allele frequencies, phenotypes, genotypes, and haplotypes. Among Caucasians, there are 43 phenotypes, whereas there are 31 among the Africans studied. There are 17 haplotypes in the Caucasian sample but only 10 in Africans. This loss of diversity is largely due to the high frequency of one haplotype in the African sample which represents 65% of the informative chromosomes. At least one copy of this haplotype is present in 90% of informative individuals. As a result, 29% of Africans are homozygous for the common haplotype. Less genetic diversity at TCRBV is unexpected, since Africans usually show greater genetic diversity than other ethnic groups. For example, there are approximately twice as many HLA haplotypes in Africans compared to Caucasians. Homozygosity is also unexpected because it reduces the number of TCR variants available to recognize HLA pathogen-derived peptide complexes. Received: 23 September 1999 / Revised: 2 November 1999     

Inheritance of resistance to southern corn rust in tropical-by-corn-belt maize populations

 The inheritance of resistance to southern rust (caused by Puccinia polysora Underw.) was investigated in two F_2:3 populations derived from crossing two temperate-adapted, 100% tropical maize (Zea mays L.) inbred lines (1416-1 and 1497-2) to a susceptible Corn Belt Dent hybrid, B73Ht×Mo17Ht. The inbred lines possess high levels of resistance to southern rust and may be unique sources of resistance genes. Heritability for resistance was estimated as 30% and 50% in the two populations from regression of F_2:3 family mean scores on F₂ parent scores, and as 65% and 75% from variances among F_2:3 families on a single-plot basis. RFLP loci on three chromosomal regions previously known to possess genes for resistance to either southern rust or common rust (P. sorghi Schw.) were used to localize genes affecting resistance to southern rust in selected genotypes of both populations, and to estimate their genetic effects. A single locus on 10S, bnl3.04, was associated with 82–83% of the variation among field resistance scores of selected F_2:3 families in the two populations. Loci on chromosomes 3 (umc26) and 4 (umc31) were significantly associated with resistance in the 1497-2 population, each accounting for 13–15% of the phenotypic variation for F_2:3 field scores. Multiple-marker locus models, including loci from chromosomes 3, 4, and 10 and their epistatic interactions, accounted for 96–99% of the variation in F_2:3 field scores. Similar results were obtained for resistance measured by counting pustules on juvenile plants in the greenhouse. An attempt was made to determine if the major gene for resistance from 1416-1 was allelic to Rpp9, which is also located on 10S. Testcross families from the cross (1416-1×B37Rpp9)×B14AHt were evaluated for resistance to southern rust in Mexico. Neither source of resistance was completely effective in this environment, preventing determination of allelism of the two genes; however, both sources of resistance had better partial resistance to southern rust than did B14AHt. Received: 6 May 1997/Accepted: 19 September 1997     

Parasitic systems and the structure of parasite populations

 The analysis of population systems is carried out on the basis of the spatial and functional classification of populations developed by V.N. Beklemishev. The population system is a functional part of a particular community. Steady interrelationships between population systems of different species within the community (referred to as ”community links”) appear to be a prerequisite for the formation of a complex of population systems. A prominent example of this is the parasitic system. The parasitic system is the population system of a parasite with all the connected populations of its hosts. The complexity of a parasitic system depends on: (1) peculiarities of the life cycle of the parasite, since its population system is the organizing component of the parasitic system and (2) subdivision of the environment for the parasites. The first trait is discussed from the standpoint of the phase structure of populations, which is clearly seen in parasites. The second one comprises the organization of the parasites’ environment according to the scale of variability (interspecies, interpopulation or intrapopulation) of hosts. These make it possible to recognize spatial and functional parts in the framework of the parasitic system. A critical review of the terminology is presented together with a list of the pertaining vocabulary. Received: 15 January 1998 / Accepted: 15 October 1998     

Mapping of the entomocidal fragment of Spodoptera -specific Bacillus thuringiensis toxin CryIC

 Insecticidal CryI protoxins of Bacillus thuringiensis are activated by proteolysis in the midgut of insects. A conservation of proteolytic cleavage sites in the CryI proteins facilitates the expression of active toxins in transgenic plants to obtain protection from various insects. However, the engineering of CryIC toxins has, thus far, failed to yield applicable resistance to armyworms of Spodoptera species representing common insect pests worldwide. To improve the production of recombinant CryIC toxins, we established a CryIC consensus sequence by comparative analysis of three cryIC genes and tested the stability and protease sensitivity of truncated CryIC toxins in Escherichia coli and in vitro. In contrast to previous data, the boundaries of trypsin-resistant CryIC core toxin were mapped to amino acid residues I28 and R627. Proteolysis of the truncated CryIC proteins showed that Spodoptera midgut proteases may further shorten the C-terminus of CryIC toxin to residue A615. However, C-terminal truncation of CryIC to residue L614, and a mutation causing amino acid replacement I610T, abolished the insecticidal activity of CryIC toxin to S. littoralis larvae, as well as its resistance to trypsin and Spodoptera midgut proteases. Because no CryIC toxin carrying a proteolytically processed N-terminus could be stably expressed in bacteria, our data indicate that, in contrast to other CryI poteins, an entomocidal fragment located between amino acid positions 1 and 627 is required for stable production of recombinant CryIC toxins. Received: 15 April 1996/Accepted: 10 July 1996     

The persistence of cultivar alleles in wild populations of sunflowers five generations after hybridization

 The development of transgenic plants has heightened concern about the possible escape of genetically engineered material into the wild. Hybridization between crops and their wild relatives provides a mechanism by which this could occur. While hybridization has been documented between several crops and wild or weedy relatives, little is known about the persistence of cultivar genes in wild populations in the generations following hybridization. Wild and weedy sunflowers occur sympatrically with cultivated sunflowers throughout much of the cultivation range, and hybridization is known to occur. We surveyed two cultivar-specific RAPD markers in 2700 progeny in a naturally occurring population of wild Helianthus annuus over five generations following a single generation of hybridization with the cultivar. Moderate levels of gene flow were detected in the first generation (42% hybrids at the crop margin) and cultivar allele frequencies did not significantly decline over four subsequent generations. These results indicate that gene flow from cultivated into wild populations of sunflowers can result in the long-term establishment of cultivar alleles in wild populations. Furthermore, we conclude that neutral or favorable transgenes have the potential to escape and persist in wild sunflower populations. Received: 1 November 1996/Accepted: 17 January 1997     

Growth of newly established alien populations: comparison of North American gypsy moth colonies with invasion theory

A common characteristic observed in many biological invasions is the existence of a lag between the time of arrival by the alien population and the time when established populations are noticed. Considerable advances have been made in modeling the expansion of invading species, and there is often remarkable congruence between the behavior of these models with spread of actual populations. While these models have been used to characterize expansion of very newly founded colonies, there have been few attempts to compare the behavior predicted from theory with spread in actual newly founded populations, largely due to the difficulty of sampling sparse populations. Models predict that time lags in the radial expansion of newly invaded populations may be due to time requirements for the population to grow from founding to detectable levels. Models also indicate that these time lags can be predicted based upon population parameters such as the intrinsic rate of population growth and diffusion coefficient. In this paper, we compared the behavior of these models with historical data on gypsy moth, Lymantria dispar, establishment and spread to show similarities between model predictions and observed population spread, both of which exhibited temporal lags of expansion. However, actual populations exhibited certain behaviors that were not predicted, and this could be due, in part, to the existence of Allee effects and stochasticity. Further work that incorporates these effects is needed to more fully understand the growth of incipient colonies of invading species. Ultimately, this information can be of critical importance in the selection of effective strategies for their detection and eradication.     

Genetic distance of inbred lines and prediction of maize single-cross performance using RAPD markers

 To evaluate the genetic diversity of 18 maize inbred lines, and to determine the correlation between genetic distance and single-cross hybrid performance, we have used random amplified polymorphic DNA (RAPD), a PCR-based technique. Eight of these lines came from a Thai synthetic population (BR-105), and the others derived from a Brazilian composite population (BR-106). Thirty two different primers were used giving a total of 325 reproducible amplification products, 262 of them being polymorphic. Genetic divergence was determinated using Jaccard’s similarity coefficient, and a final dendrogram was constructed using an unweighted pair-group method with arithmetical averages (UPGMA). Cluster analysis divided the samples into three distinct groups (GI, GII and GIII) that were confirmed by principal-coordinate analysis. The genetic distances (GD) were correlated with important agronomic traits for single-cross hybrids and heterosis. No correlation was found when group division was not considered, but significant correlations were detected between GI×GII and GI×GIII GDs with their respective single-cross hybrid grain-yield values. Three groups were identified; that is, the BR-106 population was divided in two different groups and the BR-105 population remained mostly as one group. The results indicated that RAPD can be used as a tool for determining the extent of genetic diversity among tropical maize inbred lines, for allocating genotypes into different groups, and also to aid in the choice of the superior crosses to be made among maize inbred lines, so reducing the number of crosses required under field evaluation. Received: 24 May 1996 / Accepted: 22 November 1996