Effects of compensatory growth on population processes: a simulation study

Ecology, Dec, 1997 by Jacques Brisson, James F. Reynolds

INTRODUCTION

Competition in plants is restricted between individuals in each other's immediate vicinity. Thus, the spatial extent of the canopy or root system of a plant is often used as an index of its potential to acquire resources, such as water and nutrients (Czaran and Bartha 1992). This has given rise to two major approaches for quantifying competitive interactions between neighboring plants: (1) the "area of influence" and (2) "neighborhood" indices. Both of these are based on a circle of fixed radius centered on a plant.

Area of influence (AOI) is generally defined as the circular area around a plant where it is effectively able to acquire resources, and is based on the combined size of its crown, stem, and roots (Bella 1971). Overlap in AOI of neighboring plants is used to estimate competitive pressure. This approach is used extensively in experimental studies of intraspecific competition (Daniels et al. 1986, Tome and Burkhart 1989) and in individual-based simulation models of population dynamics (Firbank and Watkinson 1985, Leps and Kindlmann 1987, Bonan 1988, Judson 1994, Bart 1995). A "neighborhood" is generally defined as the circular area around a plant that contains all neighbors that affect its performance. Numerous indices have been proposed that are based on size, distance, and/or numbers of neighbors within a plant's neighborhood (Mack and Harper 1977, Weiner and Conte 1981, Pacala 1985).

The restriction that AOIs and neighborhoods be circular areas with plants in their center presupposes that two plants in close proximity compete strongly. There is evidence that this is not always the case. Roots of many plants preferentially grow into areas of high resource concentration (de Kroon and Hutchings 1995) or into areas with less competition to compensate for close neighbors (Harper 1985). The overlap between neighboring tree canopies is often reduced, producing asymmetry in their shape (Ng 1980, Franco 1986, Young and Hubbell 1991). In such cases, a fixed circular AOI or neighborhood will not adequately describe competitive interactions. Ross and Harper (1972) found that for Dactylis glomerata the specific position of a plant within a patch of conspecific neighbors had little influence on its overall performance, a result they attributed to its ability to expand into directions of lesser interference. Harper (1985) and Franco (1986) reported that several species of modular organisms exhibited a regulatory mechanism to avoid overlap between modules of the same or different individuals. Asymmetry in plant AOI may also indicate a compensation for the negative effect of neighborhood interactions (Hutchings 1988, Ford and Sorrensen 1992, Sorrensen-Cothern et al. 1993).

Brisson and Reynolds (1994) found spatial asymmetry in the horizontal extent of root systems in the desert shrub Larrea tridentata. The resulting lack of overlap between neighboring root systems is likely the result of growth reduction in the root zones due to resource depletion or to the effect of chemical compounds released in the soil (Mahall and Callaway 1991). We proposed a "compensatory" model of neighborhood interactions to explain such patterns: assuming that the overlap of AOI between neighbors is minimal, the growth of individuals is symmetric (circular) until neighboring root systems meet; thereafter, asymmetric growth occurs into areas free of neighbors to compensate for the "loss of resources" in the zone of interaction. Thus, if space is available in its immediate vicinity, a plant may not necessarily be negatively affected by the presence of close neighbors.

In this paper, we present a simple heuristic model of plant population dynamics that extends the concept of AOI by considering "compensatory" growth of root systems. The ability of a plant to grow roots into soil zones free of neighbors in response to competitive pressures is expressed by the value of a single parameter. Effects on population attributes resulting from competition in plants with compensatory growth are compared with populations with noncompensatory growth. Although the development of this model was influenced by our observations of the natural populations of L. tridentata, we present it as a general theoretical model to account for morphological plasticity in response to competition.

MODEL DESCRIPTION

Assumptions I

Our model simulates the development of an even-aged, monospecific population of plants distributed in a plot of Y equal-sized pixels. Armstrong (1993) discusses advantages of using pixel-based over index-based models of intraspecific competition. In particular, a pixel-based approach is well suited to simulate asymmetric growth (Armstrong 1993). The structure of the model is inspired from a model developed by van Tongeren and Prentice (1986).

The growth of a plant is represented by increases in the number of contiguous pixels it occupies. Interaction between neighboring plants is represented by competition for horizontal space; overlap of neighbors is not allowed - a pixel may belong only to one plant. The need for empirical parameters to characterize neighborhoods (e.g., mass of plant distance, size of neighborhood, dispersion, etc.) is eliminated since the negative effect of neighbors is accomplished via the direct effect of space availability, a surrogate for resource availability. The simulated plot is assumed to be homogeneous whereby each pixel contains identical resources.