Читать книгу Ecology - Michael Begon - Страница 115

sensitivities and elasticities

In contrast to the retrospective LTRE analysis of the data contained in population projection matrices or IPMs, it is also possible to carry out prospective sensitivity or elasticity analyses (Caswell, 2001). Without going into the algebraic details, the general principle is one of ‘perturbing’ the values of elements, or combinations of elements, in the matrix, and then noting the effects of those perturbations on aggregate properties such as R. The sensitivity of each element (i.e. each transition, birth or survival, in the overall life cycle) is the amount by which R would change for a given absolute change in the value of the matrix element, with the value of all the other elements held constant. Thus, sensitivities are highest for those processes that have the greatest power to influence R. However, whereas survival elements (gs and ps) are constrained to lie between 0 and 1, fecundities are not, and R therefore tends to be more sensitive to absolute changes in survival than to absolute changes of the same magnitude in fecundity. Moreover, R can be sensitive to an element in the matrix even if that element takes the value 0 (because sensitivities measure what would happen if there was an absolute change in its value). These shortcomings are overcome, though, by using the elasticity of each element to determine its contribution to R, since this measures the proportional change in R resulting from a proportional change in that element. Conveniently, too, with the matrix formulation, the elasticities sum to 1, so that the meaning of an elasticity of 0.5, say, is clear: the element concerned accounts for half the variation in R.