Interstage flow matrices: Population statistic derived from matrix population models

Abstract

Abstract Many population statistics describe the characteristics of populations within and among species. These are useful for describing population dynamics, understanding how environmental factors alter demographic patterns, testing hypotheses related to the evolution of life history characteristics and informing the effective management of populations. In this study, we propose a population statistic: the interstage flow. The interstage flow is defined as the product of the element in the ith row, the jth column of the population projection matrix and the jth element of the normalized stable stage distribution. The sum of the interstage flow matrix elements is equal to the population growth rate (PGR), which is the dominant eigenvalue of the population projection matrix. The interstage flow matrix elements allow decomposition of PGR into component contributions made by transitions between developmental stages. We demonstrate the utility of interstage flow matrices using matrix population models from the COMPADRE plant matrix database. We compared interstage flows among four life history/functional groups (FGs) (semelparous herbs, iteroparous herbs, shrubs and trees) and described how PGR reflected individual transitions related to stasis, fecundity and growth. We found that the individual flows are different among FGs. Synthesis. The proposed population statistic, the interstage flow matrix, describes the contribution of individual developmental stage transitions to the PGR. The flow of individuals between developmental stages differs in distinctive ways among different life histories and FGs. The interstage flow matrix is a valuable statistic for describing these differences.