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Mass-Balance Analyses of Boreal Forest Population Cycles: Merging Demographic and Ecosystem Approaches

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Mass-Balance Analyses of Boreal Forest Population Cycles: Merging Demographic and Ecosystem Approaches Ecosystems (2002) 5: 138–158 DOI: 10.1007/s10021-001-0061-9 ECOSYSTEMS © 2002 Springer-Verlag Mass-Balance Analyses of Boreal Forest Population Cycles: Merging Demographic and Ecosystem Approaches Jennifer L. Ruesink,1* Karen E. Hodges,2** and Charles J. Krebs2 1Department of Zoology, University of Washington, Box 351800, Seattle, Washington 98195, USA; and 2Department of Zoology, 6270 University Boulevard, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada ABSTRACT Using Ecopath, a trophic mass-balance modeling the causes and consequences of the snowshoe framework, we developed six models of a Cana- hare cycle. The snowshoe hare decline and low dian boreal forest food web centered around phases were coincident with times when per cap- snowshoe hares, which have conspicuous 10- ita production was relatively low and predation year population cycles. Detailed models of four pressure high. At these times, ecotrophic efficien- phases of the cycle were parameterized with cies (EE) suggest there was little production that long-term population data for 12 vertebrate taxa. remained unconsumed by predators. The impor- We also developed five other models that, instead tance of both production and consumption im- of observed data, used parameter values derived plies that bottom–up and top–down factors inter- from standard assumptions. Specifically, in the acted to cause the cycle. EEs of other herbivores basic model, production was assumed to equal (ground squirrels, red squirrels, small mammals, adult mortality, feeding rates were assumed to be small birds, grouse) were generally low, suggest- allometric, and biomass was assumed to be con- ing weak top–down effects. Predation rates on stant. In the actual production, functional re- these “alternative” prey, except ground squirrels, sponse, and biomass change models, each of these were highest when predators were abundant, not assumed values from the basic model was re- when hares were rare; consequently, any top– placed individually by field data. Finally, constant down effects reflected predator biomass and were biomass models included actual production by all not a function of diet composition or functional species and functional responses of mammalian responses. Finally, several predators (lynx, coy- predators and revealed the proportion of herbi- otes, great-horned owls) showed clear bot- vore production used by species at higher trophic tom–up regulation, reproducing only when prey levels. By comparing these models, we show that exceeded threshold densities. Taken altogether, detailed information on densities and demo- these results demonstrate that ecosystem models graphics was crucial to constructing models that parameterized by population data can describe captured dynamic aspects of the food web. These the dynamics of nonequilibrial systems, but only detailed models reinforced an emerging picture of when detailed information is available for the species modeled. Received 30 November 2000; Accepted 6 September 2001. Key words: snowshoe hare; boreal forest; lynx; **Current address: Wildlife Biology Program, School of Forestry, University of Montana, Missoula, Montana 59812, USA arctic ground squirrel; red squirrel; Ecopath; mass- *Corresponding author: e-mail: [email protected] balance models; food web. 138 Ecosystem Models of Population Cycles 139 INTRODUCTION concepts of utilization efficiency or the ecotrophic coefficient (Kozlovsky 1968). Unconsumed produc- Because of their opposing foci on energy flow and tion becomes detritus, for instance via disease, in- population abundances, respectively, ecosystem jury, starvation-induced mortality, or uneaten kills. and population approaches have traditionally been Biomass accumulation and emigration (⌬B greater viewed as alternative strategies for understanding than 0) raise the value of EE calculated in Ecopath. ecological systems (O’Neill and others 1986). Al- The aquatic ecosystems commonly modeled in Eco- though linking the two represents a challenge path are generally assumed to be at equilibrium (⌬B (Hairston and Hairston 1993; Jones and Lawton equals 0) for a given period, during which the 1995), it may provide insight into the structure and transfer of biomass among portions of the food web function of complex multispecies assemblages. As a is assumed not to alter standing stocks. Production basic currency of life, energy can be transferred and consumption rates are generally also modeled among organisms or dissipated but is never created as invariant. Production (P/B) is often based on de novo. Available energy and the efficiency of adult mortality, because production must match transfer thus set bounds to the interaction webs that mortality if a closed population is equilibrial (Allen can persist. Conversely, the rates at which energy 1971). Consumption (Q/B) is often based on allo- can be consumed and transferred into new produc- metric relationships between body size and meta- tion are affected by population parameters, includ- bolic rate (Peters 1983). ing life histories and the body sizes of taxa (Peters Common assumptions about steady-state values 1983; Nagy 1987; Yodzis and Innes 1992). of biomass, production, and consumption do not In this paper, we develop ecosystem models hold for the boreal forest food web. We know a based on population-level data to analyze a dra- priori that there are dramatic changes in standing matic ecological phenomenon: the 10-year popula- biomass because of the pronounced cyclicity. Fur- tion cycle of snowshoe hares (Lepus americanus) and thermore, research on this food web has demon- their predators that occurs across Canada and strated cyclic changes in productivity (reproduction Alaska (Keith 1990; Krebs and others 1995; Sten- and growth) and consumption (numeric and func- seth and others 1999; Hodges 2000). Extensive pop- tional responses of predators) (Keith 1990; ulation-level data from the Kluane boreal forest O’Donoghue and Krebs 1992; Krebs and others ecosystem (Krebs and others 2001b) allow us to 1995; Rohner 1996; Slough and Mowat 1996; parameterize energy-flow models using various as- O’Donoghue and others 1997, 1998b; Stefan 1998; sumptions about production, consumption, and Karels and others 2000). Appropriate parameteriza- steady states. We use these parameterizations, tion of Ecopath models for the boreal forest food along with calculated values of ecological efficien- web may therefore require considerably more com- cies, to gain insight into causes of vertebrate food plex models than are acceptable for systems that are web dynamics. As an added benefit, we explore the closer to equilibrium. When EE is greater than 1, important issue of how much and what kind of data models are unbalanced because there is not enough are needed to parameterize an ecosystem model production to account for all of the known fates of without making major biological blunders. a species’ biomass. However, because of our focus We use a mass–balance modeling system, Eco- on modeling nonequilibrial dynamics, we never at- path, that has been used primarily to describe fish- tempt to “balance” the biomass flows in our models, centered aquatic food webs (Christensen and Pauly instead relying on inequalities to compare parame- 1992, 1993). The Ecopath master equation is: terization methods and ecological processes govern- ing different phases of the cycle. P Q ⅐ ͩ rͪ ⅐ ϭ ͸ͫ͑ ͒ ⅐ ͩ cͪ ⅐ ͑ ͒ͬ ϩ ⌬ The use of energy-flow models to understand Br EEr Bc drc Br Br all c Bc community dynamics has met with considerable (1) skepticism because there is no strict correlation be- tween energy flow and trophic impact (Paine 1980; where B is biomass, P is net production, Q is con- Polis 1994). Here, however, we do not focus on the sumption (ingestion), with subscripts referring to magnitude of transfers, but on the efficiencies, resource (r) and consumer (c) taxa. The proportion which have direct relevance for understanding top– ⌬ ϭ of r in the diet of c is drc. At equilibrium, Br 0. A down and bottom–up effects in this cyclic system. taxon’s ecotrophic efficiency (EE) is the ratio of Ecotrophic efficiencies indicate the strength of top– how much of that taxon is consumed by higher down interactions, especially if EE primarily reflects trophic level species relative to the taxon’s net pro- consumption. Specifically, for EE approximately duction. Ecotrophic efficiency thus parallels earlier equal to 1 in a steady-state system, all production is 140 J. L. Ruesink and others Table 1. Six Parameterizations for Ecopath Models of the Kluane Boreal Forest Ecosystem ⌬B ϭ 0 ⌬B ϭ empirical P/B ϭ adult mortality P/B ϭ empirical P/B ϭ adult mortality P/B ϭ empirical Q/B ϭ allometric Basic Actual production Biomass change Q/B ϭ empirical Functional response Constant biomass Detailed used by consumers, indicating that consumers can trophic dynamics in the boreal forest food web, affect the standing stock of the resource. Alterna- specifically to assess the top–down versus bot- tively, if EE is much less than 1, consumers simply tom–up nature of the dynamics during the snow- skim off a bit of excess production without exerting shoe hare cycle. Model development and interpre- a top–down effect. The rate at which a resource is tation are potentially affected by parameterization consumed relative to its production rate alters the at two levels: How are parameter values calculated? strength of the interaction between species (Rue- And within each method of parameterization, how sink 1998). Additionally, trophic structure
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