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. 2011 Feb;14(2):113-24.
doi: 10.1111/j.1461-0248.2010.01566.x. Epub 2010 Dec 27.

Biomass transformation webs provide a unified approach to consumer-resource modelling

Wayne M Getz  1
Affiliations

Biomass transformation webs provide a unified approach to consumer-resource modelling

Wayne M Getz. Ecol Lett. 2011 Feb.

Abstract

An approach to modelling food web biomass flows among live and dead compartments within and among species is formulated using metaphysiological principles that characterise population growth in terms of basal metabolism, feeding, senescence and exploitation. This leads to a unified approach to modelling interactions among plants, herbivores, carnivores, scavengers, parasites and their resources. Also, dichotomising sessile miners from mobile gatherers of resources, with relevance to feeding and starvation time scales, suggests a new classification scheme involving 10 primary categories of consumer types. These types, in various combinations, rigorously distinguish scavenger from parasite, herbivory from phytophagy and detritivore from decomposer. Application of the approach to particular consumer-resource interactions is demonstrated, culminating in the construction of an anthrax-centred food web model, with parameters applicable to Etosha National Park, Namibia, where deaths of elephants and zebra from the bacterial pathogen, Bacillus anthracis, provide significant subsidies to jackals, vultures and other scavengers.

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Figures

Figure 1
Figure 1
Consumer categories (see Appendix S1 and Table S1 for more details).
Figure 2
Figure 2
A biomass flow diagram of a general resource–consumer system modelled by eqn 6 in which the consumer, but not the resource population, may be subject to cannibalism. For simplicity, the diversion functions θ12 and θ22 are not illustrated.
Figure 3
Figure 3
Specific cases of the biomass flow diagram illustrated in Fig. 2 (same legend applies), with flow and influence structures detailed in Table 2, for (a) a cropper, with the link that corresponds to the influence of harassment specifically labelled; (b) a parasite, with the overlapping death compartments indicated; (c) scavengers that feed only on dead resources and (d)scavengers that feed both on dead resources and cannibalistically on their own dead biomass.
Figure 4
Figure 4
A simplified anthrax-centred biomass transformation web in Etosha National Park, Namibia. See Appendix S4 for equations modelling this system.
Figure 5
Figure 5
The zebra/elephant biomass abundance x1(t) (Scale 1 = 18 000 metric tons) and anthrax spore abundance x2(t) (Scale 1 = 200 unspecified units) solutions to eqn 12 are plotted over a 30-year period for the parameter values given in Table S2 (Appendix S5), except as noted: (a) a2 = 0.5 and μ22 = 0.0001, (b) a2 = 0.5 and μ22 = 0, (c) a2 = 0.8 and μ22 = 0, and (d) a2 = 1.2 and μ22 = 0.
Figure 6
Figure 6
Jackal biomass abundance x4(t) (Scale 1 = 20 metric tons) solutions to eqn 12 are plotted over a 25-year period for the parameter values given in Table S2 (Appendix S5), except as labelled in (a) for the four illustrated cases. The same applies to (b), except here the deficit stress variable v4 (Scale 1 = 10−1) is also plotted for the labelled case.
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