Comparing plant life histories using elasticity analysis: the importance of life span and the number of life-cycle stages

Abstract

Recent studies have used transition matrix elasticity analysis to investigate the relative role of survival (L), growth (G) and fecundity (F) in determining the estimated rate of population increase for perennial plants. The relative importance of these three variables has then been used as a framework for comparing patterns of plant life history in a triangular parameter space. Here we analyse the ways in which the number of life-cycle stages chosen to describe a species (transition matrix dimensionality) might influence the interpretation of such comparisons. Because transition matrix elements describing survival (“stasis”) and growth are not independent, the number of stages used to describe a species influences their relative contribution to the population growth rate. Reduction in the number of stages increases the apparent importance of stasis relative to growth, since each becomes broader and fewer individuals make the transition to the next stage per unit time period. Analysis of a test matrix for a hypothetical tree species divided into 4–32 life-cycle stages confirms this. If the number of stages were defined in relation to species longevity so that mean residence time in each stage were approximately constant, then the elasticity of G would reflect the importance of relative growth rate to λ. An alternative, and simpler, approach to ensure comparability of results between species may be to use the same number of stages regardless of species longevity. Published studies for both herbaceous and woody species have tended to use relatively few stages to describe life cycles (herbs: n=45, $\bar x = 6.16 \pm 4.63$; woody plants: n=21, $\bar x = 8.38 \pm 3.57$) and so approximate this approach. By using the same number of stages regardless of longevities, the position of species along the G-L side of the triangular parameter space largely reflects differences in longevity. The extent of variation in elasticity for L, G and F within and between species may also be related to factors such as successional status and habitat. For example, the shade-tolerant woody species, Araucaria cunninghamii, shows greater importance for stasis (L), while the gap-phase congener species, Araucaria hunsteinii, shows higher values for G (although values are likely to vary with the stage of stand development).