Claudia Neuhauser

Spatial Dynamics in Model Plant Communities: What Do We Really Know?

A variety of models have shown that spatial dynamics and small‐scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch models. Studies using all three frameworks agree that spatial dynamics need not enhance coexistence nor slow down dynamics; their effects depend on the underlying competitive interactions in the community. When similar species would coexist in a nonspatial habitat, endogenous spatial structure inhibits coexistence and slows dynamics. When a dominant species disperses poorly and the weaker species has higher fecundity or better dispersal, competition‐colonization trade‐offs enhance coexistence. Even when species have equal dispersal and per‐generation fecundity, spatial successional niches where the weaker and faster‐growing species can rapidly exploit ephemeral local resources can enhance coexistence. When interspecific competition is strong, spatial dynamics reduce founder control at large scales and short dispersal becomes advantageous. We describe a series of empirical tests to detect and distinguish among the suggested scenarios.

COMMUNITY GENETICS: EXPANDING THE SYNTHESIS OF ECOLOGY AND GENETICS

Community genetics synthesizes community ecology and population genetics and yields fresh insights into the interplay between evolutionary and ecological processes. A community genetics framework proves especially valuable when strong selection on traits results from or impinges on interspecific interactions, an increasingly common phenomenon as more communities are subject to direct management or anthropogenic disturbances. We draw illustrations of this perspective from our ongoing studies of three representative communities, two managed and one natural, that have recently undergone large perturba- tions. The studied communities are: (1) insect pests of crop plants genetically engineered to produce insecticidal toxins; (2) insect-pollinated plants in habitats severely fragmented by agriculture and urbanization; and (3) a pathogen and its crop host now grown extensively outside their native ranges. We demonstrate the value of integrating genetic and ecological processes to gain a full understanding of community dynamics, particularly in nonequilib- rium systems that are subject to strong selection.

Ergodic theorems for the multitype contact process

SummaryThis paper studies a process involving competition of two types of particles (1 and 2) for the empty space (0). Each site of the latticeZd is therefore in one of three possible states: 0, 1, or 2. Particles of each type die with rate 1, while an empty site becomes occupied by a particle of typei with rate λi (proportion of neighbors of typei). The set of neighbors of a sitex is of the form {y:‖x−y‖≦J}, for a positive integerJ and a norm ‖·‖. Assuming there are only 0s and 1s present at the beginning, the process reduces to the contact process, with the critical rate of survival of 1s being λc. The basic problem we address is the existence of equilibria in which both types of particles coexist. Without loss of generality, one can restrict to the case λ2 ≧ λ1 > λcand in this case we show:(1)If λ2 > λ1, and the initial state is translation invariant and contains infinitely many 2s, then the 1s go away and the process approaches the invariant measure of the contact process with only 2s and 0s present,(2)If λ2 = λ1, andd≦2, then clustering occurs: starting from a translation invariant initial measure with no mass on all 0s, the process converges weakly to a convex combination of the two invariant measures obtained with only one type of particles present, and(3)If λ2 = λ1, andd≧3, then there is a one-parameter family of invariant measures including both types.

Patch Aging and the S-Allee Effect: Breeding System Effects on the Demographic Response of Plants to Habitat Fragmentation

We used empirical and modeling approaches to examine effects of plant breeding systems on demographic responses to habitat fragmentation. Empirically, we investigated effects of local flowering plant density on pollination and of population size on mate availability in a common, self‐incompatible purple coneflower, Echinacea angustifolia, growing in fragmented prairie habitat. Pollination and recruitment increased with weighted local density around individual flowering plants. This positive density dependence is an Allee effect. In addition, mean mate compatibility between pairs of plants increased with population size. Based on this empirical study, we developed an individual‐based, spatially explicit demographic model that incorporates autosomal loci and an S locus. We simulated habitat fragmentation in populations identical except for their breeding system, self‐incompatible (SI) or self‐compatible (SC). Both populations suffered reduced reproduction in small patches because of scarcity of plants within pollination distance (potential mates) and inbreeding depression. But SI species experienced an additional, genetic contribution to the Allee effect (S‐Allee effect) caused by allele loss at the S locus, which reduces mate availability, thereby decreasing reproduction. The strength of the S‐Allee effect increases through time (i.e., patches age) because random genetic drift reduces S‐allele richness. We investigate how patch aging influences extinction and discuss how the S‐Allee effect influences communities in fragmented habitat.

Toward a mechanistic understanding of how natural bacterial communities respond to changes in temperature in aquatic ecosystems

We examine how heterotrophic bacterioplankton communities respond to temperature by mathematically defining two thermally adapted species and showing how changes in environmental temperature affect competitive outcome in a two-resource environment. We did this by adding temperature dependence to both the respiration and uptake terms of a two species, two-resource model rooted in Droop kinetics. We used published literature values and results of our own work with experimental microcosms to parameterize the model and to quantitatively and qualitatively define relationships between temperature and bacterioplankton physiology. Using a graphical resource competition framework, we show how physiological adaptation to temperature can allow organisms to be more, or less, competitive for limiting resources across a thermal gradient (2–34 °C). Our results suggest that the effect of temperature on bacterial community composition, and therefore bacterially mediated biogeochemical processes, depends on the available resource pool in a given system. In addition, our results suggest that the often unclear relationship between temperature and bacterial metabolism, as reported in the literature, can be understood by allowing for changes in the relative contribution of thermally adapted populations to community metabolism.

BIOLOGICAL AGING — CRITERIA FOR MODELING AND A NEW MECHANISTIC MODEL

To stimulate interaction and collaboration across scientific fields, we introduce a minimum set of biological criteria that theoretical models of aging should satisfy. We review results of several recent experiments that examined changes in age-specific mortality rates caused by genetic and environmental manipulation. The empirical data from these experiments is then used to test mathematical models of aging from several different disciplines, including molecular biology, reliability theory, physics, and evolutionary biology/population genetics. We find that none of the current models are consistent with all of the published experimental findings. To provide an example of how our criteria might be applied in practice, we develop a new conceptual model of aging that is consistent with our observations.

Founder control and coexistence in a simple model of asymmetric competition for light.

Size asymmetry in plant light acquisition complicates predictions of competitive outcomes in light-limited communities. We present a mathematically tractable model of asymmetric competition for light and discuss its implications for predicting outcomes of competition during establishment in two-, three-, and many-species communities. In contrast to the resource-reduction model of symmetric competition for a single resource, the model we present predicts that outcomes of asymmetric competition for light will sometimes depend on the timing of establishment and the consequent hierarchy among species in canopy position. Competitive outcomes in the model depend on the minimum light requirements (L(c)) and self-shading of species lower in the canopy compared to the light available (L(out)(*)) beneath species higher in the canopy. Succession progresses towards species with decreasing values for L(c), but arrested successions occur when initial dominants have relatively high values for L(c) but low values for L(out)(*), leading to founder control. A theoretically limitless number of species may coexist in competition for light when dominance is founder controlled. These model predictions have implications for an array of applied ecological questions, including methods to control invasive species in light-limited restored ecosystems.

A long range sexual reproduction process

We describe a long range growth model with sexual reproduction on [var epsilon] in which particles die at rate 1 and pairs of adjacent particles produce offspring at rate [lambda]. The offspring is sent to a site chosen at random from the neighborhood of the parent particles. If the site is already occupied, the birth is suppressed, that is, we allow at most one particle per site. The size of the neighborhood increases as [var epsilon] tends to 0. We investigate the behavior for small [var epsilon]. In the limit as [var epsilon] --> 0, the particle density evolves according to an integro-differential equation which has traveling wave solutions whose wave speed is a nondecreasing function of [lambda]. We compare the system for small [var epsilon] with the limiting system and discuss phase transition. We show that the behavior of the particle system for sufficiently small [var epsilon] is similar to the behavior of the limiting system. That is, if [lambda] is sufficiently small so that the wave speed of the traveling wave of the limiting equation is negative, then, for small enough [var epsilon], the pointmass at the all-empty configuration is the only stable equilibrium. If [lambda] is large enough, so that the wave speed of the traveling wave of the limiting equation is positive, them, for small enough [var epsilon], the system has a positive probability of survival, that is, in addition to the pointmass at the all-empty configuration, there is a nontrivial equilibrium. Not predicted by the limiting system, there is a range of values of [lambda] for which the all-empty configuration is the only stable equilibrium but for which the particle system exhibits metastable bahavior.

Natural Enemies and the Evolution of Resistance to Transgenic Insecticidal Crops by Pest Insects: The Role of Egg Mortality

Abstract We explore the influence of egg mortality dynamics on the rate at which target pests evolve resistance to high-dose transgenic insecticidal crops. We develop a two-patch deterministic population genetic model in which pests can develop in either toxic or nontoxic (refuge) fields, and their eggs are subject to varying levels and forms of egg mortality. The three standard forms of egg mortality are studied: density independence (DI), positive density dependence (PDD), and inverse density dependence (IDD). Resistance is modeled as a single locus with a fully recessive allele that confers complete resistance with no fitness cost. Insect movement and oviposition is modeled as follows: males move panmictically before mating and females may either stay in their natal patch to oviposit or move after mating before oviposition. While our simulations show that both the magnitude and form of egg mortality can influence the rate of resistance evolution, important caveats apply. Higher levels of DI egg mortality can lead to substantial delays in resistance evolution, but this effect is dependent on the presence of intraspecific competition among larvae. The rate of resistance evolution is affected by the form of density dependence (DI versus PDD versus IDD), but these effects are dependent on at least some females ovipositing in their natal field. If this condition is met, the rate of resistance evolution is fastest when eggs are subject to PDD mortality and slowest when eggs are subject to IDD egg mortality. DI egg mortality produces intermediate rates of resistance evolution.

A spatially explicit model for competition among specialists and generalists in a heterogeneous environment

Competition is a major force in structuring ecological communities. The strength of competition can be measured using the concept of a niche. A niche comprises the set of requirements of an organism in terms of habitat, environment and functional role. The more niches overlap, the stronger competition is. The niche breadth is a measure of specialization: the smaller the niche space of an organism, the more specialized the organism is. It follows that, everything else being equal, generalists tend to be more competitive than specialists. In this paper, we compare the outcome of competition among generalists and specialists in a spatial versus a nonspatial habitat in a heterogeneous environment. Generalists can utilize the entire habitat, whereas specialists are restricted to their preferred habitat type. We find that although competitiveness decreases with specialization, specialists are more competitive in a spatial than in a nonspatial habitat as patchiness increases.