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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. [ABSTRACT FROM AUTHOR]

Assessing the vulnerability and adaptive capacity of species, communities, and ecosystems is essential for successful conservation. Climate change, however, induces extreme uncertainty in various pathways of assessments, which hampers robust decision-making for conservation. Here, we developed a framework that allows us to quantify the level of acceptable uncertainty as a metric of ecosystem robustness, considering the uncertainty due to climate change. Under the framework, utilizing a key concept from info-gap decision theory, vulnerability is measured as the inverse of maximum acceptable uncertainty to fulfill the minimum required goal for conservation. We applied the framework to 42 natural forest ecosystems and assessed their acceptable uncertainties in terms of maintenance of species richness and forest functional type. Based on best-guess estimate of future temperature in various GCM models and RCP scenarios, and assuming that tree species survival is primarily determined by mean annual temperature, we performed simulations with increasing deviation from the best-guess temperature. Our simulations indicated that the acceptable uncertainty varied greatly among the forest plots, presumably reflecting the distribution of ecological traits and niches among species within the communities. Our framework provides acceptable uncertainty as an operational metric of ecosystem robustness under uncertainty, while incorporating both system properties and socioeconomic conditions. We argue that our framework can enhance social consensus building and decision-making in the face of the extreme uncertainty induced by global climate change. [ABSTRACT FROM AUTHOR]