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description= 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 ...;
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duced to two when focusing on special cases the gain though is considerable in that our view of the kinds of resource consumer interactions that can occur fig 1 appendix s1 is now considerably enlarged along with this enlargement comes a whole new set of ecological and evolutionary questions that can be addressed in a quantitatively rigorous framework using methodologies such as evolutionarily stable strategy theory that have proved their worth when used in conjunction with lotka volterra type formulations of population interactions cressman garay 2003 among these questions are how might we expect the dynamics of the feeding deficit stress variables v i to reflect the life history dichotomy of miners vs gatherers this is an issue that relates to time constants associated with rates of feeding deficit stress accumulation and accommodation as well as time to death under complete starvation and how life histories evolve to deal with variable interresource encounter periods for gatherers moreover for many species metabolic rates may adaptively decrease when food intake rates do not meet normal metabolic needs i e periods where v i increases because φ i α i so that d α i dv 0 is an adaptive strategy as is the case of animals that go into hibernation during seasonal resource dearths although the formulation through the inclusion of the feeding deficit stress variables v i deals with the problem that population processes need to include inertial effects including the well studied maternal effect inchausti ginzburg 1998 the approach ultimately needs to be generalised to take into account two forms of heterogeneity that apply to all paradigms and not just btw the first form is spatial heterogeneity and requires elaboration of how particular population processes vary over space and how animals move to mitigate gradients in these processes that naturally arise such as moving to places where feeding rates can be higher or where they are less likely to succumb to being extracted by predators the second form is individual variation due to both genetic and random processes in which two individuals in the same place are subject to different rates of food acquisitions different rates of parasitism and different risks of being consumed by other species this results in a phenomenon known as buffering revilla wiegand 2008 one of the strengths of btw is that it provides a unified framework in which the approach to modelling populations to first order is independent of the trophic level another strength of btw is that it deals with scavengers just as easily as it does with croppers or parasites thus it has application to a much wider array of food web systems than current methods generally have including systems of importance to disease management or conservation biology a case in point is evaluating how many dead trees are needed to sustain the white backed woodpecker that relies on insect larvae that use dead trees as a food source during winter gjerde et al 2005 the btw presented here is an outgrowth of the metaphysiological approach to modelling trophic interactions getz 1991 1993 this approach by taking a biomass flow rather than a birth death migration viewpoint of growth formulates growth in terms of extraction and senescent processes rather than directly in terms of the state variables themselves this allows the formulation of equations to be unified across trophic levels as evidenced by the general model box 1 in addition the structure of the equations is rather transparent and hence easily implemented for particular systems as illustrated in our derivation of the nine variable anthrax btw model in appendix s4 in terms of food web theory itself by extending populations to account separately for both live and dead biomass new topological relationships emerge and the strength of these relationships as mediated by scavengers parasites disease and senescence processes can now be included this topological refinement will affect such characterising measures as l the number of feeding relationships in webs which has been used in a number of food web studies e g williams martinez 2000 romanuk et al 2009 as lazzaro et al 2009 recently pointed out the structure and dynamics of prey populations are shaped by the foraging behaviours of their predators yet there is still little documentation on how distinct predator foraging types control biodiversity food web architecture and ecosystem functioning this statement was made in the context of foraging strategies per se e g visual vs filter feeders rather than in the context of biomass type viz live vs dead the statement applies equally well to the btw formulation which places live and dead material on an explicit co footing similar considerations arise in the context of adaptive foraging in food webs with flexible topology křivan schmitz 2003 particularly in the context of adaptive scavenging the btw formulation provides a paradigm for exploring these various questions more thoroughly and systematically than before furthermore once we move beyond homogeneous to spatially structured webs the need for a miner gatherer dichotomy takes on additional force when the ecological aspects of movement nathan et al 2008 are introduced supplementary material 1 nihms262544 supplement 1 pdf 407 9kb pdf acknowledgements i thank steve bellan paul cross lev ginzburg matt plucinski mary power norman owen smith and wendy turner for comments and especially peter baxter for extensive comments and various references this research was supported by nih grant gm083863 and the stellenbosch institute for advanced study in south africa footnotes supporting information additional supporting information may be found in the online version of this article appendix s1 consumer categories appendix s2 differential equation for deficit stress variable appendix s3 cropping and scavenging appendix s4 anthrax in enp model appendix s5 anthrax in enp parameters as a service to our authors and 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