Distance to stable stage distribution in plant populations and implications for near-term population projections


Correspondence author. E-mail: jwilliams@nceas.ucsb.edu


1. Matrix population models capture how variation in vital rates among life stages translates to population dynamics. Analyses of these models generally assume that populations have reached a stable stage distribution (SSD), where the proportion of individuals in each stage remains constant. However, when life stages respond differentially to environmental cues and perturbations, a population may be moved away from equilibrium. Given the multitude of stochastic processes acting in natural systems, populations may never be exactly at SSD. It is thus critical to understand how far away populations are from SSD and how distance from SSD influences near-term model projections.

2. We analysed published matrix models from 46 plant species spanning a range of life histories that reported both a current stage distribution and projection matrix. We examined the distance between observed and theoretical SSD and the associated consequences for near-term transient population dynamics for each species.

3. In the majority of studies, populations were near their expected SSD, with 80% falling within one unit of a projection distance (α0) of zero. This distribution was skewed towards positive values of α0, indicating that the majority of populations had individuals concentrated into stages with high reproductive values.

4. Half of the populations in our survey had projection distances such that transient projections of population size and growth rate were within 10% of asymptotic projections at 5 years. However, in populations where projection distance was > 2, deviations from SSD caused important (more than twofold) differences.

5. We also found that larger deviations from SSD were positively correlated with generation time and matrix size.

6.Synthesis. When some life stages within a plant population are more strongly affected by disturbances or stresses than others, the results of our literature survey suggest that equilibrium projections will tend to underestimate projections that account for the current stage distribution. Measuring the current stage distribution can help determine whether asymptotic measures of matrix model analyses are reliable, and is a crucial step to take when precise population metrics are necessary for guiding conservation and management.