Using elasticity analysis of demographic models to link toxicant effects on individuals to the population level: an example

Abstract

Summary 1.A simple two-stage population model was applied to data from a previously published life-table response experiment (LTRE), which examined the toxicity of 4-n-nonylphenol to life-history traits of the polychaete Capitella sp. I. Population growth rates (λ) and the relative sensitivities (= elasticities) of λ to changes in each of the individual life-history traits were calculated. 2. In the present study, the life-history parameters measured in laboratory-reared individuals were manipulated to simulate potential effects of competition and predation on fecundity, time to reproductive maturity and juvenile survival to explore how such factors might influence the sensitivity of population growth rate to toxicant-caused changes in individual life-history traits. 3. Dramatic changes in elasticity patterns among simulations indicate that population growth rates may respond very differently to toxicant exposure depending on the extent to which other demographically limiting factors (e.g. competitors and/or predators) are operating on the population. 4. Effectively predicting the population-level consequences arising from toxicant effects measured on individuals can be improved by exploring the elasticity pattern of λ for the population over a range of realistic ecological situations.

Toxicant Impacts on Density-Limited Populations: A Critical Review of Theory, Practice, and Results

“…In other words, density dependence will act to buffer the effects of toxicant exposure on population dynamics, consistent with a less-than-additive model. Hansen et al (1999) simulated potential influences of competition and predation on population-level response of the polychaete Capitella capitata (Type I) to 4-n-nonylphenol. By considering scenarios in which fecundity was reduced, time to maturity was extended, and/or juvenile survival was reduced by realistic amounts, the authors explored how the sensitivity of population growth rate to toxicant-caused changes in individual life-history traits was influenced.…”

“…Although the relationship between PGR and the individual life-history traits contributing to it is predictable, e.g., by the EulerLotka equation, the sensitivity of PGR to changes in the different traits is not obvious. It appears that the sensitivity of PGR to changes in the traits contributing to it depends on (1) the starting value of PGR, (2) the absolute values of the traits (i.e., the life-history type of the organism), and (3) the relative responsiveness of the different traits to toxicant exposure (Calow et al 1997, Hansen et al 1999Forbes et al 2001).…”

“…Whereas theoretical calculations based on life-history models (see case for S a given above) indicate that virtually all types of interactions between toxicants and density dependence are possible, intuitive arguments (Calow et al 1997) and simulation studies (Grant 1998, Hansen et al 1999 have suggested that compensatory interactions, and hence buffering of toxicant effects on the dynamics of density-limited populations are likely. Results of experimental studies are mixed: Winner et al's (1977) results and Klü ttgen and Ratte's (1994) results suggest additive effects on r, Marshall's (1978) results suggest less-than-additive effects on r, and Chandini's (1988) results suggest more-than-additive effects on r. Linke-Gamenick et al's (1999) results suggest that the type of interaction that occurs may vary with increasing toxicant concentration, with effects on shifting from less than additive at low toxicant concentrations to more than additive at higher toxicant concentrations.…”

Modeling effects of toxin exposure in fish on long-term population size, with an application to selenium toxicity in bluegill (Lepomis macrochirus)

“…The most common population-level measure of toxicity is its effect on the popula-tion growth rate (PGR), which can be expressed as the continuous growth rate r per unit time, or by the discrete multiplicative rate, λ, where λ = e r (Hansen et al, 1999;Stark and Danken, 1999;Forbes et al, 2000;Kuhn et al, 2000;Stark and Vargas, 2003;Stark, 2005). Forbes and Calow (1999) concluded that the PGR is a better response variable than individual-level endpoints, such as condition factor or fecundity, since r explicitly integrates individual-level responses to contaminants at the population level.…”

“…Forbes and Calow (1999) concluded that the PGR is a better response variable than individual-level endpoints, such as condition factor or fecundity, since r explicitly integrates individual-level responses to contaminants at the population level. Hansen et al (1999) performed sensitivity analyses of the PGR with respect to changes in life-history traits of the polycheate Capitella. Similarly, Forbes et al (2000) analyzed the elasticity of the PGR with respect to life cycle variables in a semelparous benthic macroinvertebrate, an iteroparous fish, a daphnid, and an algal species.…”