Analyses of spatial patterns and population processes of clonal plants

The nonrandom spatial structure of terrestrial plants is formed by ecological interactions and reproduction with a limited dispersal range, and in turn this may strongly affect population dynamics and population genetics. The traditional method of modelling in population ecology is either to neglect spatial pattern (e.g. in transition matrix models) or to do straightforward computer simulation. We review here three analytical mothods to deal with plant populations in a lattice-structured habitat, which propagate both by seeds that scatter over the whole habitat and by vegetative reproduction (producing runners, rhizomes, etc.) to neighboring vacant sites. [1]Dynamics of global and local densities: Dynamical equations of population density considering nearest-neighbor correlation (spatial clumping) are developed as the joint dynamics of global average density and local density (comparable to mean crowding) based onpair approximation. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximized by engaging both means of reproduction. This result is accurately predicted by the pair approximation method, but not by mean-field approximation (neglect of spatial structure). [2]Cluster size distributions: Using global and local densities obtained by pair approximation, we predicted cluster size distribution, i.e. the number of clusters of occupied sites of various sizes. [3]Clonal identity probability decreasing with distance: Multi-locus measurement of allozymes or other neutral molecular markers tells us whether or not a given pair of individuals belong to the same clone. From the pattern of clonal identity probability decreasing with the distance between ramets, we can estimate the relative importance of two modes of reproduction: vegetative propagation and sexual seed production.     

A simple evolutionary model of dormancy and dispersal in heterogeneous patches with special reference to phytophagous lady beetles: I. Stable environments

Summary A simple evolutionary model of dormancy and dispersal is presented with special reference to phytophagous lady beetles. In order to investigate spatially heterogeneous environments, we assume the simplest patch structure, that is, there are only two patches, main and sub. Environments are also assumed to be temporally constant. The main patch is superior to the sub patch, but density effect at the main patch is higher than at the sub patch. Optimal dormancy and dispersal are obtained at the same time by the method of evolutionarily stable strategy (ESS). In the univoltine life cycle, dormancy strategy vanishes because dormant individuals do not reproduce at all but suffer from a certain mortality rate during winter hibernation. In the bivoltine life cycle, the dormancy and dispersal rates constitute a trade-off: the rates change together with a negative correlation when the mortality rate during dispersal or during winter hibernation changes. When suitability of the main patch gradually deteriorates, the optimal strategy changes as follows: neither dormancy nor dispersal is adopted at the most suitable condition, the dispersal rate is increased without dormancy in the intermediate condition, and then the dormancy rate is increased with a constant dispersal rate. We discuss the field observation data of lady beetles in the light of results of our model.