Boom or bust? A comparative analysis of transient population dynamics in plants

Abstract

Summary1. Population dynamics often defy predictions based on empirical models, and explanations for noisy dynamics have ranged from deterministic chaos to environmental stochasticity. Transient (short-term) dynamics following disturbance or perturbation have recently gained empirical attention from researchers as further possible effectors of complicated dynamics. 2. Previously published methods of transient analysis have tended to require knowledge of initial population structure. However, this has been overcome by the recent development of the parametric Kreiss bound (which describes how large a population must become before reaching its maximum possible transient amplification following a disturbance) and the extension of this and other transient indices to simultaneously describe both amplified and attenuated transient dynamics. 3. We apply the Kreiss bound and other transient indices to a data base of matrix models from 108 plant species, in an attempt to detect ecological and mathematical patterns in the transient dynamical properties of plant populations. 4. We describe how life history influences the transient dynamics of plant populations: species at opposite ends of the scale of ecological succession have the highest potential for transient amplification and attenuation, whereas species with intermediate life history complexity have the lowest potential. 5. We find ecological relationships between transients and asymptotic dynamics: faster-growing populations tend to have greater potential magnitudes of transient amplification and attenuation, which could suggest that short-and long-term dynamics are similarly influenced by demographic parameters or vital rates. 6. We describe a strong dependence of transient amplification and attenuation on matrix dimension: perhaps signifying a potentially worrying artefact of basic model parameterization. 7. Synthesis. Transient indices describe how big or how small plant populations can get, en route to long-term stable rates of increase or decline. The patterns we found in the potential for transient dynamics, across many species of plants, suggest a combination of ecological and modelling strategy influences. This better understanding of transients should guide the formulation of management and conservation strategies for all plant populations that suffer disturbances away from stable equilibria.

Fast–slow continuum and reproductive strategies structure plant life-history variation worldwide

“…We also tested the robustness of the results to spurious correlations using randomization tests. Finally, to test the usefulness of the suggested framework for plant species classification, we derived the damping ratio [the rate at which populations recover from disturbance (22,31)] and the rate of change of the population (22) [r = log(λ)] via two-way ANOVAs with PCA 1 and 2 scores as explanatory variables. …”

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

“…Amplification measures the potential for a population to increase relative to its asymptotic dynamics, and attenuation measures the potential for a population to decrease. Transient responses at different time steps have been found to be strongly correlated (Stott et al 2010;Ellis 2013), so we analyzed only amplification and attenuation at t ¼ 1 (i.e., reactivity and first step attenuation, calculated analytically as the maximal and minimal column sums of the population mean matrix). These analyses resulted in one measure of amplification and attenuation for each population.…”

“…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. To date, these methods have focused on the effect of a single initial disturbance, or departure from SSD, on a constant, deterministic matrix (e.g., Neubert and Caswell 1997, Caswell 2007, Townley et al 2007, Townley and Hodgson 2008, Stott et al 2010. Because these methods consider only deterministic environments, the approach is somewhat inconsistent with much of the literature emphasizing the role of stochasticity in matrix population models.…”

Matrix Dimensions Bias Demographic Inferences: Implications for Comparative Plant Demography

“…Studies using large numbers of projection matrices have allowed for linkage between specific demographic processes and stages along ecological succession gradients (Silvertown et al 1992); for the establishment of methodologies to study the responses of populations to ecotones (Angert 2006), herbivory (Maron and Crone 2006), or habitat fragmentation (Bruna et al 2009); and for comparing demographic dynamics of native and invasive plant species (Ramula et al 2008), phylogenetic relationships of life-history strategies (Burns et al 2010), or relationships between short-term (transient) and long-term (asymptotic) population dynamics (Stott et al 2010). The number of demographic studies based on projection matrices is growing rapidly (fig.…”

“…1). The dimension of projection matrices influences the apparent demographic processes of a specific class, such as per capita fecundities (de Matos and Silva Matos 1998), as well as other parameters derived from the matrix, such as population growth rates (Lamar and McGraw 2005;Ramula and Lehtilä 2005); transient dynamics (Tenhumberg et al 2009;Stott et al 2010); elasticities of matrix elements Enright et al 1995) and vital rates (Zuidema 2000;Salguero-Gó mez and Casper 2010); elasticities of demographic pathways (Salguero-Gó mez and Casper 2010), as analyzed by loop analysis (van Groenendael et al 1994); and demographic relationships based on phylogeny (Burns et al 2010;Stott et al 2010). This is a nontrivial issue because matrix dimension varies a great deal, from two (Sohn and Policansky 1977) to 24 (Meagher 1982).…”