No abstract

Malus sieversii (Lebed.) M. Roem. is a wild progenitor species of the domesticated apple. It is found across a mountainous region of central Asia and has been the focus of several collection expeditions by the USDA-ARS-National Plant Germplasm System. This study used microsatellite variation at seven loci to estimate diversity and differentiation within M. sieversii using several complimentary approaches. Multilocus genotypes were amplified from 949 individuals representing seedling trees from 88 half-sib families from eight M. sieversii populations collected in Kazakhstan. Apportioning of genetic variation was estimated at both the family and site level. Analyses using a hierarchical model to estimate F st showed that differentiation among individual families is more than three times greater than differentiation among sites. In addition, average gene diversity and allelic richness varied significantly among sites. A rendering of a genetic network among all sites showed that differentiation is largely congruent with geographical location. In addition, nonhierarchical Bayesian assignment methods were used to infer genetic clusters across the collection area. We detected four genetic clusters in the data set. The quality of these assignments was evaluated over multiple Markov Chain Monte Carlo runs using both posterior likelihood and stability of the assignments. The spatial pattern of genetic assignments among the eight collection sites shows two broadly distributed and two narrowly distributed clusters. These data indicate that the southwestern collection sites are more admixed and more diverse than the northern sites.

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.

Rangeland ecologists have elucidated 2 apparently distinct processes underlying rangeland dynamics. In some cases, disturbed or recovering rangelands move through a gradual, continuous series of changes which has been termed succession. In other illsfances, rangeland dynamics are typlfied by sudden, discontinuous changes in the vegetation, and this has been called state-and-transition. Catastrophe theory is a mathematical framework designed for the study of discontinuous phenomena, but it also generates models that permit continuous dynamics. Based on available literature, it appears that rangeland ecosystems conform to the mathematics of catastrophe theory. Rangelands exhibit the 5 essential symptoms of catastrophe systems: modality (distinct conditions or states of existence), inaccessibility (conditions which are very unstable), sudden changes (relatively rapid movement between states), hysteresis (processes associated with degradation or recovery are not readily reversible by simply inverting the sequence of events), and divergence (relatively small changes in initial conditions can result in dramatically different outcomes with time). Catastrophe theory has been successfully used to model rangeland grasshopper population dynamics, and it appears that many of the same control variables affecting insects (e.g., temperature and precipitation) may also underlie vegetative community dynamics. Application of catastrophe theory to empirical data sets will require relatively long-term but low-intensity research efforts.

Methods for collecting genetic diversity from in situ populations are important tools for plant conservation. Many quantitative collection strategies for sampling populations without a priori information regarding the ecology, reproductive biology, or population genetic structure of the taxa have been proposed, but their different assumptions regarding the collection scale and the basis for diversity often make them difficult to compare. Understanding the limitations of the different strategies enables collectors to make more informed choices when implementing conservation and restoration projects or collecting for germplasm improvement. We compare two genetically based strategies under a common set of assumptions and extend the probabilistic arguments of the strategies to accommodate rare alleles, multiple loci, and multiple populations. The recommendations of many models are based on a single locus, but larger numbers of individuals must be collected to assure with a high probability (>0.95) the acquisition of alleles at multiple independent loci within a population. Sampling from multiple populations linked by gene flow may offset this increase. Additionally, the likelihood of capturing rare alleles remains high when sampling for multiple loci or across multiple populations. Comparison of the models provides germplasm collectors with a basis to evaluate risks of over‐ and undersampling to capture genetic diversity within a species.