Interstage flow matrices: population statistic derived from matrix population models

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 i th row, the j th column of the population projection matrix, and the j th element of the normalized stable stage distribution. The sum of the interstage flow matrix elements is equal to the population growth rate, which is the dominant eigenvalue of the population projection matrix. The interstage flow matrix elements allow decomposition of population growth rate 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 (semelparous herbs, iteroparous herbs, shrubs, and trees) and described how population growth rate reflected individual transitions related to stasis, fecundity, and growth. We found that the individual flows are different among functional groups. Synthesis: The proposed population statistic, the interstage flow matrix, describes the contribution of individual developmental stage transitions to the population growth rate. The flow of individuals between developmental stages differs in distinctive ways among different life histories and functional groups. The interstage flow matrix is a valuable statistic for describing these differences.