Dynamical Systems Approach to Higher-level Heritability

To explain higher-level heritability, we propose a dynamical systems approach, based on simulations of the high-dimensional replicator equation with mutation dynamics. We assume that all variants are generated from within the groups of variants through mutations. Simulating the equation with a random interaction matrix and possible variants, we report that this system tends to have many attractors, of fixed point, chaotic and quasiperiodic type. In a chaotic attractor, special gene-like variants appear to control the heritability ofthe system, in the sense that removal of the variants would easily enable the system to depart from the attractor. Those variants do not predominate in thepopulation size, but have the lowest net reproduction and mutation rates on average. Because their rate of growth is small, they are named neutral phenotypes. Additionally, combinatorial effects of these neutral variants to the entire system are reported.     

Plant litter feedback and population dynamics in an annual plant,<Emphasis Type="Italic"> Cardamine pensylvanica</Emphasis>

The presence of litter has the potential to alter the population dynamics of plants. In this paper, we explore the effects of litter on population dynamics using a simple experimental laboratory system with populations of the annual crucifer, Cardamine pensylvanica. Using a factorial experiment with four densities and three litter levels, we determined the effect of litter on biomass and plant fecundity, and the life stages responsible for these changes in yield. Although litter had significant effects on seed germination and on seedling survivorship, we show, using a population dynamics model, that these effects were not demographically significant. Rather, the potential effect of litter on population dynamics resulted almost entirely from its effect on biomass. Persistent litter suppressed plant biomass and apparently removed the direct density effect present in the absence of litter. Thus, litter changed the shape of the recruitment curve from slightly humped to asymptotic. In addition to changing the shape of the recruitment curve, litter reduced the carrying capacity of the populations. Thus, the population dynamics model indicated that not all statistically significant responses were dynamically significant. Given the potential complexity of litter effects, simple population models provide a powerful tool for understanding the potential consequences of short-term responses. Received: 8 September 1999 / Accepted: 5 April 2000     

Population Changes of Heterodera glycines and Soybean Yields Resulting from Soil Treatment with Alachlor,Fenamiphos, and Ethoprop

The population dynamics of Heterodera glycines as influenced by alachlor, fenamiphos, and ethoprop alone and in herbicide-nematicide combinations were studied in the field. Numbers of H. glycines juveniles and eggs were higher at midseason and harvest where nematicides were applied. Fenamiphos alone or in combination with alachlor provided better control of H. glycines and greater seed yields than treatments with ethoprop. Numbers of H. glycines eggs at harvest in 1980 were positively correlated with numbers of juveniles at planting in 1981 and negatively related to seed yield in 1981.     

Consumer pressure, seed versus safe-site limitation, and plant population dynamics

Plants often suffer reductions in fecundity due to insect herbivory. Whether this loss of seeds has population-level consequences is much debated and often unknown. For many plants, particularly those with long-lived seedbanks, it is frequently asserted that herbivores have minimal impacts on plant abundance because safe-site availability rather than absolute seed number determines the magnitude of future plant recruitment and hence population abundance. However, empirical tests of this assertion are generally lacking and the interplay between herbivory, spatio-temporal variability in seed- or safe-site-limited recruitment, and seedbank dynamics is likely to be complex. Here we use a stochastic simulation model to explore how changes in the spatial and temporal frequency of seed-limited recruitment, the strength of density-dependent seedling survival, and longevity of seeds in the soil influence the population response to herbivory. Model output reveals several surprising results. First, given a seedbank, herbivores can have substantial effects on mean population abundance even if recruitment is primarily safe-site-limited in either time or space. Second, increasing seedbank longevity increases the population effects of herbivory, because annual reductions in seed input due to herbivory are accumulated in the seedbank. Third, population impacts of herbivory are robust even in the face of moderately strong density-dependent seedling mortality. These results imply that the conditions under which herbivores influence plant population dynamics may be more widespread than heretofore expected. Experiments are now needed to test these predictions. Received: 3 November 1999 / Accepted: 15 February 2000