By Golasinski M., et al. (eds.)
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Extra info for Algebraic topology - old and new: M.M.Postnikov memorial conf.
Although some researchers think that an emphasis on the size of neighbors rather than their species may be a useful first approximation for describing and modeling neighborhoods (whereas other researchers think this would be "throwing out the baby with the bathwater"), even modeling size effects alone is not as straightforward as it might seem at first. The relative size of neighbors with respect to a target plant is often as important as their absolute size, because competition among plants is usually "size asymmetric," that is, larger plants have a disproportionate (for their relative size) effect on smaller plants.
However, it may be premature to reach firm conclusions: the mosaic cycles described in Chapter 4, in which there is a cyclic sequence of states within patches of vegetation, although not quantified to the level of competition matrices, appear to be driven by intransitivities. Intra- versus interspecific competition The relative magnitude of interactions within and between species is also important in the context of species coexistence. In Lotka-Volterra competition models, the coexistence of competitors is expected if intraspecific 40 A • Empirical and Statistical Background competition is stronger than interspecific competition, particularly when species are aggregated.
If trait correlations within species are the same as trait correlations between species, then the first problem can be circumvented simply by treating genotypes rather than species as the taxonomic unit. The second problem cannot be circumvented but can be accommodated by defining how the fitness of traits changes along environmental gradients. A study by Sugiyama (in press) is interesting in this context. Sugiyama investigated how varietal differences within three species of grasses 3 - Spatial Interactions among Grassland Plant Populations 41 (18 cultivars of Dactylis glomerata, 15 cultivars of Lolium perenne, 5 cultivars of Festuca arundinacea) influenced the outcome of competition against a standard cultivar of another species.
Algebraic topology - old and new: M.M.Postnikov memorial conf. by Golasinski M., et al. (eds.)