Understanding patterns and processes in models of trophic cascades

Michael R Heath,Douglas C Speirs,John H Steele,Kevin Lafferty

doi:10.1111/ele.12200

Michael R Heath, Douglas C Speirs + Show 2 more

Open Access

https://doi.org/10.1111/ele.12200

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Abstract

Climate fluctuations and human exploitation are causing global changes in nutrient enrichment of terrestrial and aquatic ecosystems and declining abundances of apex predators. The resulting trophic cascades have had profound effects on food webs, leading to significant economic and societal consequences. However, the strength of cascades–that is the extent to which a disturbance is diminished as it propagates through a food web–varies widely between ecosystems, and there is no formal theory as to why this should be so. Some food chain models reproduce cascade effects seen in nature, but to what extent is this dependent on their formulation? We show that inclusion of processes represented mathematically as density-dependent regulation of either consumer uptake or mortality rates is necessary for the generation of realistic ‘top-down’ cascades in simple food chain models. Realistically modelled ‘bottom-up’ cascades, caused by changing nutrient input, are also dependent on the inclusion of density dependence, but especially on mortality regulation as a caricature of, e.g. disease and parasite dynamics or intraguild predation. We show that our conclusions, based on simple food chains, transfer to a more complex marine food web model in which cascades are induced by varying river nutrient inputs or fish harvesting rates.

Highlights

Worldwide impacts of the losses of top predator fauna from terrestrial and aquatic ecosystems, largely as a result of human activity, have penetrated deep into food webs, affecting vegetation cover, biogeochemistry, disease, erosion and hydrological cycles (Estes et al 2011)
The steady-state solutions for the three-level food chain model based on a linear prey-dependency with regulation at the bottom and top levels showed that with mortality regulation, increasing the density dependence parameter k suppressed the response of the top-level component (x2) to a doubling of the top-down forcing factor (d)
We examined top-down and bottom-up cascade effects in a marine food web model of intermediate complexity (Allen & Fulton 2010; Steele et al 2013), which represents the fluxes of nutrient through the North Sea ecosystem from dissolved inorganic to birds and mammals, and regeneration through excretion and mineralisation of detritus (Heath 2012; see Appendix S2 in Supporting Information)

Summary

INTRODUCTION

Worldwide impacts of the losses of top predator fauna from terrestrial and aquatic ecosystems, largely as a result of human activity, have penetrated deep into food webs, affecting vegetation cover, biogeochemistry, disease, erosion and hydrological cycles (Estes et al 2011). Regulation in such a model is effected by a combination of nutrient supply at the smallest end of the size spectrum, the recruitment process within each trait, and within-trait predation subject to the constraint of a given prey size selection interval The latter process is analogous to the density-dependent mortality terms, representing intra-guild predation, in food chain models. The steady-state solutions for the three-level food chain model based on a linear prey-dependency with regulation at the bottom and top levels (eqn 16–21; Tables S3–S4) showed that with mortality regulation, increasing the density dependence parameter k suppressed the response of the top-level component (x2) to a doubling of the top-down forcing factor (d). With top-level uptake regulation the Type-II food chain had a more complicated response to top-down and bottom-up forcing producing either amplification or attenuation, depending on the value of the density-dependent parameter υ and the rate of nutrient input

Plants

DISCUSSION