Lattice population dynamics for plants with dispersing seeds and Vegetative propagation

The population dynamics of plants in a lattice structured habitat are studied theoretically. Plants are assumed to propagate both by producing seeds that scatter over the population and by vegetative reproduction by extending runners, rhizomes, or roots, to neighboring vacant sites. In addtion, the seed production rate may be dependent on the local density in the neighborhood, indicating beneficial or harmful crowding effects. Two sets of population dynamical equation(s) are derived: one based onmean-field approximation and the other based onpair approximation (tracing both global and local densities simultaneously). We examine the accuracy of these approximate dynamics by comparing them with direct computer simulation of the stochastic lattice model. Pair approximation is much more accurate than mean-field approximation. Mean-field approximation overestimates the parameter range for persistence if crowding effects on seed production are harmful or weakly beneficial, but underestimates it if crowding effects are highly beneficial. Dynamics may show bistability (both population persistence and extinction) if the effect of crowding is strongly beneficial. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximised by a mixture of seed production and vegetative reproduction, rather than by pure seed production or by pure vegetative reproduction. This result is correctly predicted by pair approximation but not by mean-field approximation.     

Competition and evolutionary stability of plants in a spatially structured habitat

We modelled the population dynamics of two types of plants with limited dispersal living in a lattice structured habitat. Each site of the square lattice model was either occupied by an individual or vacant. Each individual reproduced to its neighbors. We derived a criterion for the invasion of a rare type into a population composed of a resident type based on a pair-approximation method, in which the dynamics of both average densities and the nearest neighbor correlations were considered. Based on this invasibility criterion, we showed that, when there is a tradeoff between birth and death rates, the evolutionarily stable type is the one that has the highest ratio of birth rate to mortality. If these types are different species, they form segregated spatial patterns in the lattice model in which intraspecific competitive interactions occur more frequently than interspecific interactions. However, stable coexistence is not possible in the lattice model contrary to results from completely mixed population models. This clearly shows that the casual conclusion, based on traditional well mixed population models, that different species can coexist if intraspecific competition is stronger than interspecific competition, does not hold for spatially structured population models.     

Modelling and analyzing density-dependent population processes: Comparison between wild and laboratory strains of the bean weevil,Callosobruchus chinensis (L.)

Three models were constructed for analyzing the population characteristics ofC. chinensis on stored beans; model A describing the whole reproductive process with a single equation, model B describing the three age-specific processes (oviposition, egg survival and larval survival) with separate equations, and model C which describes all these processes not for the whole habitat but for the individual beans comprizing it. The logit equation was employed here as a common basis to describe the density-response relationship involved. All three models showed very good fit to the experimental data obtained for both laboratory and wild strains of the weevil. The parameter values characterizing the population dynamics were, however, widely different between the two strains; the laboratory one which had been reared for some 500 generations showed significantly higher reproductive capacity, less sensitive and gentler response to crowding in both adult and egg stages, and more uniform egg distribution among individual beans, as compared with the wild strain newly introduced. Sensitivity analyses using these models suggested that these changes in population characteristics have been attained by the process of domestication or adaptation to stable laboratory conditions through a long period of time. This process seemed in effect to have optimized the population's performances in the laboratory environment. Evolutionary significance of such optimization was discussed with reference to the selection pressure which may have acted upon individuals.