Primary-Productivity Gradients and Short-Term Population Dynamics in Open Systems

Abstract

We present three models representing the trophic and behavioral dynamics of a simple food chain (primary producers, grazers, and predators) at temporal scales shorter than the scale of consumer reproduction, and at the spatial scales typically employed in field experiments. These models incorporate flexible behavioral responses of organisms to their predators and resources in spatially heterogeneous environments that are open to immigration and emigration. The basic models include passive immigration at all trophic levels, producer growth rates and losses to grazer consumption, grazer emigration rate as a behavioral response to producer and predator densities, grazer losses to predator consumption, and predator emigration as a function of grazer density. We model this system as: (1) a set of ordinary differential equations (“well‐mixed model”); (2) a set of partial differential equations describing a population of discrete grazers foraging on discrete patches of primary producers (“discrete‐grazer model”); and (3) a set of simulation rules describing the movement and foraging of individual grazers and the growth of primary producers on discrete patches in explicit space (“individual‐based model”). The ordinary differential‐equation models produced similar results to individual‐based models with well‐mixed producers, and the discrete‐grazer and individual‐based models produced similar results when grazers possessed a long‐term memory of patch reward rates. The well‐mixed and discrete‐grazer models thus represent specific, limiting cases of the general individual‐based model. Multiple equilibria and sustained oscillations are possible but are less likely in the discrete‐grazer and individual‐based models than in the well‐mixed model, because localized foraging of discrete grazers leads to the rapid development of spatial heterogeneity in producer biomass and, hence, to a decrease in overall primary production. All models predict that stable equilibrium densities of all trophic levels increase with enrichment, provided grazers increase their emigration rates as predator density increases. If increasing predator density leads to decreasing grazer‐emigration rates, predator and grazer densities increase, but producer biomass may increase or decrease with enrichment. These results contrast with predictions from models that assume ideal free distributions of grazers and/or predators with respect to their resources. Our models also predict that densities at all trophic levels will increase with increasing producer immigration, and that producer density will decline with increasing grazer immigration and increase with increasing predator immigration. Our qualitative findings on enrichment are used to interpret an experiment dealing with the short‐term dynamics of a stream community open to grazers and predators.

Cascading predator control interacts with productivity to determine the trophic level of biomass accumulation in a benthic food web

“…The results of this study demonstrate that the biomass of organisms occupying lower trophic levels depends both on the number of trophic levels and the production of the system, which are in line with the predictions from prey-dependent models of both long-term (EEH) (Oksanen et al 1981;Oksanen and Oksanen 2000) and short-term population dynamics (Nisbet et al 1997). Consumer-controlled compartments of the algal community, i.e., the number of algal recruits, increased with algal production when three trophic levels were present in the food web, while gastropod grazer biomass increased with algal production only when the food web was reduced to two trophic levels with the removal of the larger predators.…”

“…The positive effect of the combination of production and predator presence on the density of macroalgal recruits follows robust mathematical theory incorporating short-term population dynamics. This theory predicts that for a variety of assumptions and models, producer abundances increase due to both increased resource availability and predator immigration rates and decrease from increased grazer immigration rates (Nisbet et al 1997). Prey-dependent models of short-term population dynamics also predict a general increase in grazer abundances with increased producer production (Nisbet et al 1997), but this relationship only degenerates in the presence of predators in models where predators actively disperse depending on resource availability (e.g., Wootton and Power 1993).…”

“…This theory predicts that for a variety of assumptions and models, producer abundances increase due to both increased resource availability and predator immigration rates and decrease from increased grazer immigration rates (Nisbet et al 1997). Prey-dependent models of short-term population dynamics also predict a general increase in grazer abundances with increased producer production (Nisbet et al 1997), but this relationship only degenerates in the presence of predators in models where predators actively disperse depending on resource availability (e.g., Wootton and Power 1993). At the scale of our experiment, all main predators moved freely between the treatments and showed aggregation in habitat patches with vegetation, clearly demonstrating that predators did not distribute passively.…”

“…Accordingly, field studies support a positive relationship between primary production and trophic cascades in some systems (e.g., Sinclair et al 2000;Elmhagen and Rushton 2007;Moksnes et al 2008;Eriksson et al 2009;Sieben et al 2011), whereas a recent set of meta-analyses suggests that, in general, it is the traits of consumer species, and not productivity, that determine the prevalence of trophic cascades in predator removal experiments (Borer et al 2005(Borer et al , 2006. However, models that incorporate short-term population dynamics and allow for dispersal suggest that the an alternating positive relationship between trophic levels and primary productivity should also appear in environments where consumers immigrate and emigrate actively between patches depending on resource availability (Wootton and Power 1993;Oksanen et al 1995;Nisbet et al 1997). A key condition for trophic cascades in these models is that top-predators must employ active dispersal and distribute freely, while passive dispersal generates a positive relationship between primary productivity and all trophic levels (Nisbet et al 1997).…”

“…However, models that incorporate short-term population dynamics and allow for dispersal suggest that the an alternating positive relationship between trophic levels and primary productivity should also appear in environments where consumers immigrate and emigrate actively between patches depending on resource availability (Wootton and Power 1993;Oksanen et al 1995;Nisbet et al 1997). A key condition for trophic cascades in these models is that top-predators must employ active dispersal and distribute freely, while passive dispersal generates a positive relationship between primary productivity and all trophic levels (Nisbet et al 1997).…”