A test of heterogeneous mixing as a mechanism for ecological persistence in a disturbed environment

Abstract

Persistence is a central issue in population ecology with important implications for population management. Most theoretical studies have focused on continually interacting populations, even though many systems are subject to ecological disturbances which confound analysis of persistence. In this paper, we use a combination of a simple parasite-hyperparasite model with disturbances and field data to investigate the factors contributing to the observed persistence of the parasite population. The field data are taken from a two-year experiment (including five growing seasons) investigating the use of the mycoparasite Sporidesmium scleroti orum as a persistent biological control agent of Sclerotinia minor, an economically important fungal parasite of lettuce. We show that the standard assumption of homogeneous mixing fails to predict the observed persistence of the parasite population. We demonstrate that allowing for heterogeneous mixing prevents the fade-out predicted in the homogeneous mixing case. The implications of the results for broad classes of host-parasite systems are discussed.

Biological control in a disturbed environment

“…When fitting the models with a heterogeneous mixing response to the S. minor-S. sclerotivorum data, we have obtained estimates for the mixing parameters, m < 1 and n > 1 (tables 1 and 2; see also Gubbins & Gilligan 1997a, their table 1). In this appendix, we prove the results on the influence these values for mixing parameters have on the stability of the population dynamics, as discussed in § 8 b.…”

“…Fitting was by empirical weighted least squares with the reciprocal of the variance for each compartment using FACSIMILE (1995). The goodness of fit was tested by examination of the residual plots and the consistency and convergence of the parameter estimates for small differences in initial estimates (Gubbins & Gilligan 1996, 1997a. The consistency of the parameter estimates across the three data sets was also examined since, other things being equal, differences in X 0 would not be expected to affect parameters in the model.…”

“…Following earlier work (Gubbins & Gilligan 1997a), the influence of the delta function pulses and seasonal forcing were separately tested for the twoand three-species models with the basic and heterogeneous mixing responses. For brevity, results are shown only for the three-species model with the heterogeneous mixing response (figure 6).…”

“…The mean data from this trial are used to test the model. The first model is developed from the classical predator-prey model used by Gubbins & Gilligan (1997a) to allow aspects of the dynamics of both the parasite and hyperparasite to be examined. The hyperparasite can only reproduce on infected parasites ; infected parasites die more rapidly than uninfected ones, while only uninfected parasites are able to infect a host and reproduce (Adams & Ayers 1982).…”

Patterns of Zooplankton Functional Response in Communities with Vertical Heterogeneity: a Model Study

“…to incorporate implicitly effects of spatial aggregation and clustering of species. The modified mean-field approach was successively applied in different fields of theoretical ecology [13,27]. Another way to incorporate implicitly the space is the use of 'the scale transition approach' based on the moment approximation method [5,8].This technique allows to extrapolate results obtained with small-scale experiments to scales of natural habitats.…”