Direct Perturbation Analysis for Better Conservation

Abstract

Only demographic studies can link in a quantitative way observed trends in population growth rate to parts of the life cycle. Population growth rate has been used for some time to assess the overall status of populations in conservation management. More recently there has been an increasing interest in elaborating methods that can assess the relative importance of different life-cycle phases for observed population growth trends (Silvertown et al. 1993, 1996; Caswell 1996a; Royama 1996). This kind of information is essential to identifying critical life-cycle stages and concentrating management efforts on them. One tool that has become widely used to extract information from demographic data is population projection matrices (Caswell 1978, 1989a; van Groenendael et al. 1988; Silvertown et al. 1993, 1996; Schemske et al. 1994). Silvertown et al. (1996) discuss elasticity matrices as a way to identify such critical life-cycle stages and as an aid to constructing rules of thumb useful in plant conservation. They warn against a naive interpretation of elasticities and argue that the state of the populationits rate of increase-must be taken into account. We want to focus attention on some additional problems with the use of elasticity values for identifying key phases of the life cycle and to propose an alternative method that reduces these problems. The rate of increase of a population (X) depends on ageor stage-specific vital rates such as survival, growth, and reproduction. Sensitivity analysis explores this dependence by calculating the effects on X of infinitely small absolute changes to matrix element aij, which represents particular transitions in the life cycle (Caswell 1978, 1989a). Hence, the sensitivity sii of a matrix element aii is