Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold

The dynamics of a specific consumer-resource model for Daphnia magna is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.

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Consumer-Resource Dynamics and Emergent Density Dependence

Fish Ecology, Evolution, and Exploitation ◽

10.23943/princeton/9780691192956.003.0010 ◽

2019 ◽

pp. 163-182

Author(s):

Ken H. Andersen

Keyword(s):

Density Dependence ◽

Population Size ◽

Fisheries Management ◽

Late Life ◽

Static Model ◽

Size Spectrum ◽

Resource Model ◽

Single Population ◽

Resource Dynamics ◽

Consumer Resource

This chapter focuses on a generalization of a classic consumer-resource model with a single population embedded in a community. It develops this physiologically structured consumer-resource model by extending the static model in Chapter 4. The chapter then studies how density dependence emerges in the model, and how it changes the population size spectrum. Finally, the chapter explores how some of the standard fisheries impact assessments from Chapter 5 are changed when density dependence is in the form of competition or cannibalism. Specifically, it shows how the appearance of late-life density dependence rocks one of the cornerstones of contemporary fisheries management: that we should fish only the largest fish. In some cases, it turns out that yield is instead maximized by fishing juveniles.

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Inquiline predator increases nutrient-cycling efficiency of Nepenthes rafflesiana pitchers

Biology Letters ◽

10.1098/rsbl.2019.0691 ◽

2019 ◽

Vol 15 (12) ◽

pp. 20190691

Author(s):

Weng Ngai Lam ◽

Ying Yi Chou ◽

Felicia Wei Shan Leong ◽

Hugh Tiang Wah Tan

Keyword(s):

Experimental Data ◽

Nutrient Cycling ◽

Ecosystem Functioning ◽

Trophic Levels ◽

Resource Model ◽

Pitcher Plants ◽

Predator Prey ◽

Invertebrate Prey ◽

Cycling Efficiency ◽

Consumer Resource

The modified-leaf pitchers of Nepenthes rafflesiana pitcher plants are aquatic, allochthonous ecosystems that are inhabited by specialist inquilines and sustained by the input of invertebrate prey. Detritivorous inquilines are known to increase the nutrient-cycling efficiency (NCE) of pitchers but it is unclear whether predatory inquilines that prey on these detritivores decrease the NCE of pitchers by reducing detritivore populations or increase the NCE of pitchers by processing nutrients that may otherwise be locked up in detritivore biomass. Nepenthosyrphus is a small and poorly studied genus of hoverflies and the larvae of one such species is a facultatively detritivorous predator that inhabits the pitchers of N. rafflesiana . We fitted a consumer–resource model to experimental data collected from this system. Simulations showed that systems containing the predator at equilibrium almost always had higher NCEs than those containing only prey (detritivore) species. We showed using a combination of simulated predator/prey exclusions that the processing of the resource through multiple pathways and trophic levels in this system is more efficient than that accomplished through fewer pathways and trophic levels. Our results thus support the vertical diversity hypothesis, which predicts that greater diversity across trophic levels results in greater ecosystem functioning.

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