Spatio‐temporal variation in Markov chain models of subtidal community succession

Abstract

In this paper we ask whether succession in a rocky subtidal community varies in space and time, and if so how much affect that variation has on predictions of community dynamics and structure. We describe succession by Markov chain models based on observed frequencies of species replacements. We use loglinear analysis to detect and quantify spatio-temporal variation in the transition matrices describing succession. The analysis shows that space and time, but not their interaction, have highly significant effects on transition probabilities. To explore the ecological importance of the spatiotemporal variability detected in this analysis, we compare the equilibria and the transient dynamics among three Markov chain models: a time-averaged model that includes the effects of space on succession, a spatially averaged model that include the effects of time, and a constant matrix that averages over the effects of space and time. All three models predicted similar equilibrium composition and similar rates of convergence to equilibrium, as measured by the damping ratio or the subdominant Lyapunov exponent. The predicted equilibria from all three models were very similar to the observed community structure. Thus, although spatial and temporal variation is statistically significant, at least in this system this variation does not prevent homogeneous models from predicting community structure.

Markov models of territory occupancy: implications for the management and conservation of competing species

“…Real and Mañosa 1997;Steenhof et al 1997;Pedrini and Sergio 2002;WhitWeld et al 2004;López-López et al 2007a, b), with territory occupancy and turnover often being the only reliable data available to plan conservation strategies in large sectors of their range. Insights from relatively simple models like this one are likely to be more helpful for managers than uncertain predictions based on untested complex models (Hanski 1999). Such predictions, with their inevitable uncertainties are not as useful as comparisons of alternative scenarios with appropriate sensitivity analyses (see Hanski 1999 and references therein).…”

“…Insights from relatively simple models like this one are likely to be more helpful for managers than uncertain predictions based on untested complex models (Hanski 1999). Such predictions, with their inevitable uncertainties are not as useful as comparisons of alternative scenarios with appropriate sensitivity analyses (see Hanski 1999 and references therein). Thus, our aim here was not to accurately predict population trajectories for these species (we acknowledge that in the long-term environmental changes will modify the observed transition probabilities, and that our estimates are not perfectly accurate), but to test the value of a simple tool to evaluate the potential contribution of alternative management decisions, based on the kind of information that is usually available for decision-makers.…”

Markov Chain Analysis of Succession in a Rocky Subtidal Community

“…This is not true because the estimation procedure and the comparison of structure use different, statistically independent parts of the data set. See Hill et al (2002) for details.…”

“…Time-varying models can be analyzed as nonhomogeneous Markov chains (e.g., Hill et al 2002). Models with dependence on local state frequencies are nonlinear stochastic cellular automata (e.g., Caswell and Etter 1999).…”

“…Here, we use such a chain to analyze succession in a rocky subtidal community. A detailed statistical analysis of the model that examined the effects of spatial and temporal variation showed that although statistically significant, the effects are so small as to be biologically trivial, regardless of whether asymptotic or transient properties of the community are examined (Hill et al 2002). We will explore the effects of nonlinearity elsewhere.…”