Encounter Probabilities and Community Structure in Zooplankton: a Mathematical Model

Abstract

Predator–prey interactions between swimming animals of the zooplankton are studied in a mathematical model. The assumptions are: 1) the animals are points in a 1-m3 homogeneous space, 2) the animals move at random and are randomly distributed, and 3) the predator animal has an encounter radius given by its sensory system. The mathematics of encounter probabilities are developed for a 3-dimensional space. The results show two optimal strategies: 1) cruising predators which prey upon slow moving animals (herbivores), and 2) ambush (nonmoving) predators which prey upon fast cruising prey. Of the variables used (population densities, speeds of the two animal species, and encounter radius) the encounter radius has the greatest influence on the encounter probabilities. The results suggest a simple community structure and point to the importance of studies on live zooplankton.

Sit-and-wait versus active-search hunting: A behavioral ecological model of optimal search mode

“…We focus on isolating the biological properties of predator and prey that might influence the choice of either an active-search hunting strategy (forager velocity 4 0) or a sit-and-wait hunting strategy (forager velocity¼ 0) by a predator. Similar work on search mode optimization has been conducted in 3-dimensional foraging environments (Gerritsen and Strickler, 1977, see the Conclusions section for a contrast of our findings).…”

“…Although different in both scope and derivation, our model shows some similarities with previous work on foraging strategy in zooplankton in 3-dimensional space (Gerritsen and Strickler, 1977).…”

“…(a) Effect of Prey Rate of Movement on Hunting Tactic. In a search mode model similar to ours, but based on search in a 3-dimensional space, Gerritsen and Strickler (1977) find that active-searching predators are predicted to prey upon slowmoving animals, and ambush predators are predicted to prey upon fast-moving animals. Our major qualitative findings are, in this way, quite similar.…”

Trends in body size across an environmental gradient: A differential response in scavenging and non-scavenging demersal deep-sea fish

“…During this time, it uses energy from its store to fuel both its standard metabolism R and the added cost of foraging S. Assuming that food items are randomly scattered over the sea-bed at density r and can be detected if the fish passes within distance d of them, by simple geometric reasoning (see e.g. Gerritsen & Strickler (1977)), the probability of finding another meal before the energy reserves from the last meal If r declines with increasing depth, then to keep this probability constant, the term 2dvE R C S ; ð3:4Þ must increase sufficiently to compensate. From our arguments for non-scavengers we expect the denominator of (3.4) to increase with mass to a power of around 0.75 (but certainly less than one).…”

Developmental plasticity in vision and behavior may help guppies overcome increased turbidity

“…In turbid water, encounter rate with an organism's environment (e.g., habitat, conspecifics, prey) is likely decreased, since the visual range of fish in these environments is diminished (Vinyard and O'brien 1976;De Robertis et al 2003). By increasing activity in turbid water (as observed in turbid water developmental treatment fish), a fish could maintain a certain encounter rate with salient factors in its environment (Gerritsen and Strickler 1977), as has been observed in chinook salmon (Oncorhynchus tshawytscha; Gregory and Northcote 1993), perch (Perca fluviatilis; Granqvist and Mattila 2004), and Atlantic cod (Gadus morhua; Meager and Batty 2007). Thus, it may be that guppies reared in turbid water increased activity to maintain encounter rates with prey.…”