There are many population statistics that describe the characteristics of populations and species (e.g., population growth rate, reproductive value, longevity, and elasticity). We developed two new population statistics: inter-stage flow matrix and reproductive-value flow matrix. The inter-stage flow and reproductive-value flow are respectively defined as a_ij u_j and a_ij v_i where a_ij is a projection matrix element, u_j is a stable stage distribution, and v_i is a normalized reproductive value. The sums of the matrix elements are equal to the population growth rate. In this study, we compared those flows between four life history/functional groups (semelparous herb, iteroparous herb, shrub, tree) using the COMPADRE plant matrix database.
We found that inter-stage flows and reproductive-value flows differ depending on population growth rate and life history/functional group. The flows for shrubs more closely resembled those of iteroparous herbs than those of trees. These flows are derived from steady state properties of the population (i.e. stable stage distributions and reproductive values). On the other hand, widely used elasticity is derived from the potential change in population growth after perturbation. Hence use of these flow matrices could provide insights into different aspects of organisms and populations.