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

Abstract

Summary1. 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 (a 0 ) of zero. This distribution was skewed towards positive values of a 0 , 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.

The role of transient dynamics in stochastic population growth for nine perennial plants

“…Combining several recently published databases of perennial plant models (Stott et al 2010, Crone et al 2011, Williams et al 2011, Ellis et al 2012 we identified 25 populations from nine species (Appendix) for which annual transition matrices had been constructed from annual population surveys, and for which ''white noise'' stochastic models seemed appropriate. In other words, variation among years was not due to succession after disturbance, or periodic drivers such as fire cycles.…”

“…How frequently this assumption is adequately met is unclear (Bierzychudek 1999, Williams et al 2011, as are the implications of deviances from SSD in model applications (Ezard et al 2010, Johnson et al 2010. Consequently, there has been an increasing focus on analyzing the short-term, transient dynamics that result when populations are not at SSD (e.g., Fox and Gurevitch 2000, Caswell 2007, Stott et al 2011.…”

Demography of the Clonal PalmPrestoea Acuminatain the Colombian Andes: Sustainable Household Extraction of Palm Hearts

“…Similarly, an episodic reproductive outburst after the ENSO, when drought conditions ended, could explain the observed seedling overabundance. Episodic recruitment events have been reported to produce population models where SSD is different from current observations [14,45,49]. As ENSO-related droughts are likely to become more frequent and severe due to global warming [48], the consequences of such climatic change on long-lived plant fitness and sustainable management of NTFPs should be urgently assessed.…”

“…Transient dynamics can be strong when populations are moved away from their SSD following an unusual disturbance [14,45]. The 1997-98 El Niño Southern Oscilation (ENSO) was one of the strongest ever recorded [46], causing a water shortage and high temperatures at La Planada, and a pause in flowering bud production for P. acuminata [9].…”

“…However, these models assume that the populations are in equilibrium, i.e., that model predicted stable stage distribution (SSD) does not significantly differ from observed stage distribution (OSD), which is not always the case [14]. Some recent uses of matrix models in connection with non-timber forest product (NTFP) extraction include the Brazil nut Bertholletia excelsa [15]; stems of the climbing palm Desmoncus orthacanthos [16]; palm hearts of Euterpe edulis [5]; and leaves of the understory palmlet Lepidocaryum tenue [17].…”