We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described successional dynamics by species turnover rates, recurrence times, and the entropy of the transition matrix. We used perturbation analysis to quantify the response of diversity to successional rates and species removals. The equilibrium community was dominated by an encrusting sponge (Hymedesmia) and a bryozoan (Crisia eburnea). The equilibrium structure explained 98% of the variance in observed species frequencies. Dominant species have low probabilities of disturbance and high rates of colonization and persistence. On average, species turn over every 3.4 years. Recurrence times varied among species (7-268 years); rare species had the longest recurrence times. The community converged to equilibrium quickly (9.5 years), as measured by Dobrushin's coefficient of ergodicity. The largest changes in evenness would result from removal of the dominant sponge Hymedesmia. Subdominant species appear to increase evenness by slowing the dominance of Hymedesmia. Comparison of the subtidal community with intertidal and coral reef communities revealed that disturbance rates are an order of magnitude higher in coral reef than in rocky intertidal and subtidal communities. Colonization rates and turnover times, however, are lowest and longest The dynamics of an ecological community are often described by changes in species composition over time. We use the term "succession" to refer to these changes. Succession is no longer viewed as a deterministic development toward a unique stable climax community (Connell and Slatyer 1977). Instead, it is widely recognized that disturbance, dispersal, colonization, and species interactions produce patterns and variability on a range of temporal and spatial scales.Markov chains were introduced as models of succession by Waggoner and Stephens (1970) and Horn (1975). These models imagine the landscape as a large (usually infinite) set of patches or points in space. The state of a point is given by the list of species that occupy it. In one class of models, this list may include multiple coexisting populations; such models are called patch-occupancy models (e.g., Caswell andCohen 1991a, 1991b). In another class of models, points are occupied by single individuals rather than populations. Such models have been applied to forests (Waggoner and Stephens 1970;Horn 1975;Runkle 1981;Masaki et al. 1992), plant communities (Isagi and Nakagoshi 1990; Aaviksoo 1995), insect assemblages (Usher 1979), coral reefs (Tanner et al. 1994(Tanner et al. , 1996, and rocky intertidal communities (Wootton 2001b(Wootton , 2001c.Successional dynamics are modeled by defining the pro...

Habitat fragmentation is a potentially critical factor in determining population persistence. In this paper, we explore the effect of fragmentation when the fragmentation follows a fractal pattern. The habitat is divided into patches, each of which is suitable or unsuitable. Suitable patches are either occupied or unoccupied, and change state depending on rates of colonization and local extinction. We compare the behaviour of two models: a spatially implicit patch‐occupancy (PO) model and a spatially explicit cellular automaton (CA) model. The PO model has two fixed points: extinction, and a stable equilibrium with a fixed proportion of occupied patches. Global extinction results when habitat destruction reduces the proportion of suitable patches below a critical threshold. The PO model successfully recreates the extinction patterns found in other models. We translated the PO model into a stochastic cellular automaton. Fractal arrangements of suitable and unsuitable patches were used to simulate habitat fragmentation. We found that: (i) a population on a fractal landscape can tolerate more habitat destruction than predicted by the patch‐occupancy model, and (ii) the extinction threshold decreases as the fractal dimension of the landscape decreases. These effects cannot be seen in spatially implicit models. Landscape struc‐ture plays a vital role in mediating the effects of habitat fragmentation on persistence.

Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.

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.

Hill, M. F. and Caswell, H. 2001. The effects of habitat destruction in finite landscapes: a chain-binomial metapopulation model. -Oikos 93: 321 -331.We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasiequilibrium distribution of occupied patches, the expected extinction time (t), and the probability of persistence (l( (x)) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given value of N, the model shows that: (1) t and l( (x) are highly sensitive to changes in S and (2) there is a threshold value of S at which t declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxia, and its specialist parasitoid Cotesia melitaearum. We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia. The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes.

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Summary 1.Understanding the role endogenous vs. exogenous forces play in determining the dynamics and abundance of natural populations has important implications for their conservation. 2. Changes in environmental conditions often have different effects on closely related species. For instance, recent studies show that a physical shift in ocean conditions in the mid-1970s in the California current have reduced coho salmon ( Oncorhynchus kisutsch ) populations, but not chinook salmon ( O. tshawytscha ).3. An important question is whether this pattern is due to differences in the ability of coho and chinook salmon to respond to changing ocean conditions or to differences in their life-history traits. 4. We analysed a series of population models to test whether observed abundance patterns of coho and chinook salmon could be explained by one of the major differences in their life history, the spawning age distribution; in the California current, female coho salmon are considered to be obligate semelparous, spawning at age 3, while chinook salmon are considered indeterminate semelparous, with populations spawning over a range of ages. 5.Results from a deterministic model indicate that the sensitivity of the population growth rate to changes in ocean survival depends little on the spawning age structure, especially when the growth rate is small ( λ ≈ 1). 6. Analysis of linear and non-linear stochastic models indicate that the probability of persistence increases with the width of the spawning age distribution, as the fraction of adults spawning at age 3 decreases from 100% to 95%. Further increases in the spawning age distribution have negligible affects on persistence. 7. Because coho salmon are not absolutely obligate semelparous (e.g. as many as 25% of males can spawn precociously at age 2 and their effect on annual reproduction is unknown), this range of sensitivity does not provide a firm basis for assuming that the observed abundance patterns of coho and chinook is due to differences in their spawning age distribution. 8. While other life-history differences could play a role, we recommend that ongoing field studies focus on the different effects changing ocean conditions have on the survival of individual salmon species.

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