Richard R. Vance

On Reproductive Strategies in Marine Benthic Invertebrates

Mathematical models are described relating reproductive energetic efficiency to egg size in marine benthic invertebrates with planktonic and nonplanktonic prefeeding larval development. The models are based on simplified assumptions concerning planktonic and benthic predation and the relations between egg size and method of larval nutrition and between egg size and duration of larval life. The models predictions include: (a) only the extremes of the possible range of egg size and method of nutrition (i.e., planktotrophy, lecithotrophy) are evolutionarily stable; (b) over a certain range of environmental parameters, the two developmental modes are both evolutionarily stable; (c) planktotrophy is more efficient than lecithotrophy when planktonic food is abundant and planktonic predation low, and lecithotrophy more efficient when either or both of these conditions is reversed; and (d) benthic prefeeding development results in greater efficiency when lecithotrophic development time is long and/or planktonic predation more intense than benthic predation, and planktonic prefeeding development is more efficient when these conditions are reversed. Known geographic trends in developmental patterns are discussed in light of these results, and possible explanations for these trends are offered. Ways of testing the predictions and explanations of geographical trends are suggested.

Competition and Mechanism of Coexistence in Three Sympatric of Intertidal Hermit Crabs

During monthly intervals over a 1—year period, 12,000 empty snail shells were added to a small, isolated, rocky intertidal reef in the San Juan Islands of Washington. The shells added were species normally used by the high intertidal hermit crab, Pagurus hirsutiusculus, and were placed in locations accessible to that species. The shell additions resulted in an increase in density of P. hirsutiusculus at the experimental reef, whereas no density change occurred at a nearby control reef, indicating the importance of shells as a limiting resource. To establish the generality of shell limitation, the hermit crab populations of four unmolested rocky intertidal sites (three of which are typical hermit crab habitats) were quantitatively samples to obtain species compositions and size distributions of hermit crabs, their shells, and unoccupied shells. Shell preference experiments determined the preferred shell sizes and species for each hermit crab species. Except for small size classes, empty shells were rate at the three typical areas. In addition, hermit crab size distributions followed shell size distributions, and all but small hermit crabs of three species occupied shells smaller than the preferred size. These results support the conclusion that empty shells are a limiting resource for these hermit crabs. Since shells constitute a common, necessary resource in short supply, these hermit crabs are in competition for available shells. The fourth area, chosen for its unusual shell—availability characteristics, exhibited a different pattern of shell utilization not suggesting shell limitation. Shell occupancy at the three representative intertidal sites was examined to determine the strength of the relationship between hermit crab species composition and resource availability. Though resource partitioning was demonstrated, the presence and numbers of each hermit crab species and its preferred shell types were poorly correlated. Differences in hermit crab species composition are explained by differences in the physical habitat, and collections from other areas show that the same shell species can support different hermit crab species in different but adjacent habitat types. Thus, the mechanism allowing coexistence apparently involves both resource and habitat partitioning.

Predation and Resource Partitioning in One Predator -- Two Prey Model Communities

Models of the dynamics of a predator and two competing prey are examined for conditions under which the predators presence makes competitive coexistence possible. Despite the fact that the prey in the absence of the predator exploit identical resources, predation-induced coexistence can occur; but its occurrence depends on the prey being different in at least one of several ways. Suitable differences include differences in spatial refuges from the predator, differences in appearance and/or location which induce frequency-dependent predation, and a difference in energy allocation between competitive and predatory defense. Thus these models predict, in keeping with the results of field studies on predators, that predation can play a central role in determining community species composition. However, prey species coexistence still depends on their being somehow different; i.e., Gauses Law is just as true when predators are common and important as when they are absent. Most of those prey in nature whose coexistence is known to depend on predation differ in resource use; i.e., these prey appear to partition environmental resources just as is expected of coexisting species in predator-free systems. A large proportion of cases of coexistence of similar species in nature probably results not from resource partitioning alone or from predation alone but from both mechanisms operating simultaneously.

The Role of Shell Adequacy in Behavioral Interactions Involving Hermit Crabs

Field studies have suggested that the intertidal hermit crabs of the San Juan Islands of Washington normally occupy snail shells smaller than preferred. In this study the effects of shell size on protection from predation and on hermit crab shell fighting were studied in the laboratory. A predator (Cancer) presented with two hermit crabs (Pagurus granosimanus), identical except in size of occupied shell, preyed upon the hermit in the smaller shell first in 15 out of 16 trials. This results suggests that large shell size confers a selective advantage on the occupying crab. Shell fights involving two hermit crabs (P. hirsutiusculus) of unequal size were observed in which replicates differed only in the shell size of the larger crab. The probability of the larger crab effecting a shell exchange through fighting was shown to increase as the size of its shell decreased. However, shell size was shown to have no effect on the level of aggressiveness as measured by four criteria. The mechanism underlying the former result thus appears to involve a continual high level of general aggressiveness together with an increased tendency associated with occupancy of an inadequate shell by the dominant crab for that crab to evoke a shell exchange during an aggressive interaction.

Diel foraging patterns of the sea urchin Centrostephanus coronatus as a predator avoidance strategy

During the day, the diadematid sea urchin Centrostephanus coronatus occupies holes and crevices in shallow subtidal rocky substrata. Individuals emerge from these after sunset and forage on organisms attached to the surrounding rock surface. Each urchin travels <1 m from its shelter and returns to the same one before sunrise. The sheephead wrasse Pimelometopon pulchrum does not remove urchins from their shelters, but will attack and consume urchins placed in normal feeding locations during the daytime. The active periods of the sheephead and the urchin do not overlap; urchins begin foraging about 20 min after the diurnal sheephead retire in the evening and return to their shelters 1 to 2 h before sheephead resume feeding in the morning. We infer that the urchins daytime crevice-dwelling and nocturnal foraging habits have evolved as a response to sheephead predation. Moreover, because shelters are limited in supply, shelter fidelity may have evolved to insure refuge from sheephead.

A Mutualistic Interaction Between a Sessile Marine Clam and Its Epibionts

The jewel box clam, Chama pellucida, lives attached to shallow marine rock surfaces. The shell is normally covered by a dense growth of sessile plants and animals of diverse phyla. Removal of these epibionts seems to make detection and/or attack of Chama by the predatory starfish Pisaster giganteus more often successful in the laboratory and substantially increases Chama mor- tality through Pisaster predation in the field. Thus, Chama benefits from the presence of these attached organisms. Chama occurs commonly only in areas characterized by low mortality rate of sessile organisms. The organisms attached to Chama therefore enjoy freedom from the higher mortality rates which characterize some areas not inhabited by Chama such as sea urchin (Centrostephanus coronatus) foraging ranges. Thus, attached organisms benefit from their association with Chama. Accordingly, the interaction is mutualistic. Naturally rugose Chama shells placed in the field appear to accumulate certain epibiotic species faster than do artificially smooth shells. This result suggests that natural selection on one or both participants has favored mechanisms that facilitate their association. The interaction very likely affects the abundances of the participants. Also, by the resulting creation of the physical habitat of a Chama bed, the interaction probably affects the abundances of many other species in the community as well. Influences of mutualism in general on community composition and stability are discussed.

Effects of Grazing by the Sea Urchin, Centrostephanus Coronatus, on Prey Community Composition

Individuals of Centrostephanus coronatus, a diadematid sea urchin, restrict their graz- ing to relatively confined areas on subtidal rock surfaces. To determine the effects of Centrostephanus grazing on the composition and diversity of the attached biota within these areas, I removed sea urchins from an experimental site and photographically monitored subsequent events in marked quad- rats at monthly intervals for 27 mo. Grazed and ungrazed control sites were similarly monitored. These observations were supplemented by dietary data obtained from grazed control site urchins at the end of the experiment, permitting assessment of food preferences through the use of electivity indices. Taxonomic composition in the exclusion site changed dramatically following urchin removal, nearly converging to that of the ungrazed control site. Algae, sponges, tunicates, and erect bryozoa replaced encrusting coralline algae and encrusting bryozoa as the dominants. The urchins diet in- cludes all of these taxa, and the most preferred ones increase most upon urchin removal. Taxonomic diversity increased in the exclusion site as a result of replacement of a small number of taxa which can withstand urchin grazing by a larger number of competitively superior ones which cannot. Thus the effect of Centrostephanus on the community is to decrease diversity where it actually grazes, but to increase diversity in the community as a whole by creating local environmental patches favorable to otherwise rare taxa.

THE EFFECT OF DISPERSAL ON POPULATION STABILITY IN ONE-SPECIES, DISCRETE-SPACE POPULATION GROWTH MODELS

Here I propose a general formulation of population growth with dispersal in one-species systems. The species range is viewed as a collection of spatially separate habitats, and population growth with dispersal is described as a discrete parameter process. I examine the effect of dispersal on system stability using a series of special cases of this general formulation. A system is considered relatively stable if, for a fixed pattern of external perturbation, it exhibits a low degree of variability. Measures of variability are proposed that quantify this idea. Dispersal increases the degree of stability of many of the systems examined. This effect arises if juveniles disperse as a fixed feature of the life history and population density does not severely reduce birth rate. It also arises if adults disperse facultatively in response to overcrowding. Habitat selection augments dispersals stabilizing tendency. Explicit inclusion of habitat locations complicates the mathematics but does not alter this qualitative dispersal effect. Dispersal does not always increase population stability. If population density strongly suppresses birth rate, obligate juvenile dispersal can actually reduce stability. In this case, more juveniles are produced by sparse than by dense populations, and dispersal causes growing populations to lose more potential recruits than they gain. Adult dispersal strongly stimulated by population growth rate can also reduce population stability for the same reason. In discrete time, dispersal can actually destroy asymptotic stability. The conclusion that dispersal can sometimes stabilize and sometimes destabilize populations also emerges from more thoroughly studied continuous-space diffusion models. The discrete-space systems studied here are generally mathematically simpler than diffusion equations, and this approach may expedite the task of combining dispersal with other population phenomena into more inclusive models.

THE STABLE COEXISTENCE OF TWO COMPETITORS FOR ONE RESOURCE

A mechanistic model of interspecies competition expresses population growth in terms of resource consumption rate, consumption in terms of resource encounter rate, and encounters in terms of resource searching rate and resource abundance, which themselves depend on population sizes. Standard isocline analysis reveals that it is possible, under a variety of conditions on the component functions, for one resource to support two competing species at globally stable equilibrium population sizes. Under this formulation, stable coexistence requires a suitable form of interference competition. The possibilities include greater intraspecific than interspecific interference in resource searching rates or resource encounter rates and a pattern of internal energy allocation that ensures that the less aggressive interference competitor is the more efficient resource consumer. Hypothetical examples are phrased in terms of actively foraging animals, terrestrial plants, and suspension-feeding marine benthic invertebrates. The mechanistic nature of the model helps resolve long-standing semantic difficulties concerning limiting resources that arise from the Lotka-Volterra model, and it encourages both future theoretical extensions and empirical testing.

A nonautonomous model of population growth.

With x = population size, the nonautonomous equation x = xf(t,x) provides a very general description of population growth in which any of the many factors that influence the growth rate may vary through time. If there is some fixed length of time (usually long) such that during any interval of this length the population experiences environmental variability representative of the variation that occurs in all time, then definite conclusions about the populations long-term behavior apply. Specifically, conditions that produce population persistence can be distinguished from conditions that cause extinction, and the difference between any pair of solutions eventually converges to zero. These attributes resemble corresponding features of the related autonomous population growth model x = xf(x).