Interpretation of Elasticity Matrices as an Aid to the Management of Plant Populations for Conservation

Abstract

Population projection (Lefkovitch) matrices are now a standard method for quantifying and analyzing the demography and population dynamics of plants. Elasticity analysis of such a matrix indicates the relative effect on the population growth rate (λ) of small changes to matrix elements representing different transitions in the life cycle. In a comparison of elasticity matrices for 84 species of plants we show that the relative importance of recruitment from seed (measured by composite elasticity F), stasis (measured by composite elasticity L), and growth (measured by composite elasticity G) varies systematically between the groups semelparous herbs, iteroparous herbs of open habitats, forest herbs, shrubs, and trees. We discuss how this result might be used to construct rules of thumb useful in plant conservation. By looking in detail at how λ covaries with the composite elasticities F, L, and G among 16 populations of the semelparous herb Cirsium vulgare and among 15 populations of the rare iteroparous herb Pedicularis furbishiae, we show that a naive interpretation of elasticities can give a misleading prescription for management. Instead, we show that elasticity analysis supports management prescriptions based upon the successional status of a species or upon its response to disturbance.

Variation in life-cycle between three rare and endangered floodplain violets in two regions: implications for population viability and conservation

“…In contrast, the contribution of different stages and vital rates varied strongly between regions in V. stagnina. In growing populations, the contributions of growth and fecundity increased, which has also been confirmed for Gentiana pneumonanthe (Oostermeijer et al 1996), and for Cirsium vulgare and Pedicularis furbishiae (Silvertown et al 1996). Elasticities of vital rates varied between years and populations in Agrimonia eupatoria and Geum rivale (Kiviniemi 2002) and Primula vulgaris (Valverde & Silvertown 1998), whereas they were relatively constant in three species of Pinguicula (Svensson et al 1993).…”

“…Elasticities of vital rates varied between years and populations in Agrimonia eupatoria and Geum rivale (Kiviniemi 2002) and Primula vulgaris (Valverde & Silvertown 1998), whereas they were relatively constant in three species of Pinguicula (Svensson et al 1993). The fact that matrix transitions are not independent of each other and that elasticity varies with population growth rate (Oostermeijer et al 1996;Silvertown et al 1996;Caswell 2001) makes it difficult to identify unique stages or vital rates as sensitive phases or processes for conservation or management. Additionally, since elasticity is calculated as sensitivity multiplied by the quotient of the transition value (a ij ) and λ (de Kroon et al 1986;Caswell 2001), common transitions will often also have a high elasticity, whereas rare transitions may be better targets for conservation or recovery plans.…”

“…We chose elasticity instead of sensitivity (response of λ to absolute changes in transitions), since elasticity sums to unity across each matrix, which makes comparisons of elasticity among species easier. Additionally, life-cycle elasticities, summarised for vital rates representing growth, stasis plus regression and fecundity can be compared with the elasticities spectrum of other species from the literature (Silvertown et al 1996).…”

Effect of Density Reduction on Uinta Ground Squirrels: Analysis of Life Table Response Experiments

“…One of the most promising uses of prospective methods is in formulating conservation or management plans (e.g., Crouse et al 1987, Doak et al 1994, Heppel et al 1994, Silvertown et al 1995, Mills et al 1998, de Kroon et al 2000. For example, Crouse et al (1987) used elasticities to demonstrate that growth rates of populations of loggerhead sea turtles (Caretta caretta) were relatively insensitive to changes in fertility.…”

Nesting Behavior, Provisioning Rates, and Parental Roles of Ferruginous Hawks in New Mexico

“…Furthermore, while a proportional change in adult fecundity does not affect λ to the same degree as an equivalent change in adult survival, λ is still quite sensitive to variation in fecundity. This raises the point that although a factor may have high elasticity or sensitivity, the mathematics of the matrix model does not address the political, financial, or logistical constraints that may be imposed on our ability to manage that specific factor (Nichols et al 1980, Silvertown et al 1996, Citta and Mills 1999, Reed et al 2002. In certain instances, management actions focused on factors other than the one with the highest elasticity or sensitivity may produce the largest influence on population change (Nichols and Hines 2002).…”