Musical chairs mortality functions: density-dependent deaths caused by competition for unguarded refuges.

Structural refuges within which prey can escape from predators can be an important limiting resource for the prey. In a manner that resembles the childhood game of musical chairs, many prey species rapidly retreat to shared, unguarded refuges whenever a predator threatens, and only when refuges are relatively abundant do all prey individuals actually escape. The key feature of this process is that the per capita prey mortality rate depends on the ratio of prey individuals to refuges. We introduce a new class of mortality functions with this feature and then demonstrate statistically that they describe field mortality data from a well-studied coral reef fish species, the Caribbean bridled goby Coryphopterus glaucofraenum, substantially better than do several mortality functions of more conventional form.

The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model.

A global method of nullcline endpoint analysis is employed to determine the outcome of competition for sunlight between two hypothetical plant species with clonal growth form that differ solely in the height at which they place their leaves above the ground. This difference in vertical leaf placement, or canopy partitioning, produces species differences in sunlight energy capture and stem metabolic maintenance costs. The competitive interaction between these two species is analyzed by considering a special case of a canopy partitioning model (RR Vance and AL Nevai, J. Theor. Biol. 2007, 245:210-219; AL Nevai and RR Vance, J. Math. Biol. 2007, 55:105-145). Nullcline endpoint analysis is used to partition parameter space into regions within which either competitive exclusion or competitive coexistence occurs. The principal conclusion is that two clonal plant species which compete for sunlight and place their leaves at different heights above the ground but differ in no other way can, under suitable parameter values, experience stable coexistence even though they occupy an environment which varies neither over horizontal space nor through time.

SPATIAL DENSITY DEPENDENCE SCALES UP BUT DOES NOT PRODUCE TEMPORAL DENSITY DEPENDENCE IN A REEF FISH.

Field experiments provide rigorous tests of ecological hypotheses but are typically of short duration and use small spatial replicates. We assessed empirically whether the results of experiments testing for density dependence applied at larger spatial domains and explained temporal population dynamics. We studied a small coral reef fish, the goldspot goby (Gnatholepis thompsoni), in the Bahamas. We assessed the effects of interactions with conspecifics and with an ecologically similar species, the bridled goby (Coryphopterus glaucofraenum). Two density manipulations on small reef patches revealed that goldspot goby mortality over one month increased as conspecifics became crowded. On five large natural reefs, we correlated the initial year-class density of both species (annual larval settlement) with the subsequent decline of goldspot goby year-classes for five years. Mortality was correlated with conspecific density among reefs for all years, but not among years for all reefs. Thus, spatial density dependence in mortality scaled up qualitatively from small patches to entire reefs but was not associated with temporal density dependence. Our results support the conclusion that field experiments may be extrapolated to larger spatial domains with care, but that using small spatial comparisons to predict temporal responses is difficult without knowing the underlying biological mechanisms.

Plant interspecies competition for sunlight: a mathematical model of canopy partitioning.

We examine the influence of canopy partitioning on the outcome of competition between two plant species that interact only by mutually shading each other. This analysis is based on a Kolmogorov-type canopy partitioning model for plant species with clonal growth form and fixed vertical leaf profiles (Vance and Nevai in J. Theor. Biol., 2007, to appear). We show that canopy partitioning is necessary for the stable coexistence of the two competing plant species. We also use implicit methods to show that, under certain conditions, the species' nullclines can intersect at most once. We use nullcline endpoint analysis to show that when the nullclines do intersect, and in such a way that they cross, then the resulting equilibrium point is always stable. We also construct surfaces that divide parameter space into regions within which the various outcomes of competition occur, and then study parameter dependence in the locations of these surfaces. The analysis presented here and in a companion paper (Nevai and Vance, The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model, in review) together shows that canopy partitioning is both necessary and, under appropriate parameter values, sufficient for the stable coexistence of two hypothetical plant species whose structure and growth are described by our model.

Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning.

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by self-shading. This first of three related papers formulates a prototype single species Canopy Structure Model from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissues. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a Canopy Partitioning Model, to two competing species.

Assessing the magnitude of intra- and interspecific competition in two coral reef fishes.

Many field experiments have tested for effects of competition in nature, but relatively few have used designs allowing simultaneous assessment of the influence of intra- and interspecific competition. Using a response surface design and a press manipulation of densities, we tested effects of competition within and between two species of coral reef fishes (Coryphopterus glaucofraneum and Gnatholepis thompsoni). By tracking individually tagged fishes, we showed that the per-capita effect of intraspecific competitors on individual growth was at least twice as great as the effect of interspecific competitors. Growth rate was better predicted by measures of density that incorporated body size, rather than numerical density, suggesting interference competition. Individuals of both species interacted aggressively with conspecifics at least twice as often as with heterospecifics. Individuals of both species also covered more area while foraging and spent less time in shelter when crowded than when at lower densities. In combination, these behaviours suggest that increased metabolic costs at high density contribute to competitive effects on growth. These competitive interactions occurred among adult fishes, so reduced growth may translate to reduced fecundity as well as reduced survival, and so contribute to population regulation.

Growth of estuarine fish is associated with the combined concentration of sediment contaminants and shows no adaptation or acclimation to past conditions.

We tested whether the growth rates of small benthic fish (Gillichthys mirabilis) in three southern California estuaries corresponded with the local concentrations of contaminants. Fish originating from each estuary were transplanted to cages in each estuary in two reciprocal transplant experiments. The growth rates of caged fish, and the size-distribution of natural populations, showed the same pattern of difference among estuaries. Twelve metals and organic contaminants occurred in bulk sediments at concentrations close to their individual ERL values, and a simple index of their combined concentration (the mean ERL quotient) was inversely correlated to the growth of caged fish. Metals in the water column occurred at lower concentrations, relative to toxicity thresholds, than those in sediments and were unrelated to fish growth. Fish used in the field caging experiments, and other fish held in the laboratory under constant conditions, showed no difference in growth according to their estuary of origin. Fish originating from different estuaries also showed no consistent differences in their tissue burden of organic contaminants. Our results thus suggested no genetic adaptation or physiological acclimation to the past contaminant regime, but revealed a possible association between fish growth rates and the combined concentration of multiple sediment contaminants.