The effects of habitat destruction in finite landscapes: a chain‐binomial metapopulation model

Abstract

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.

Interaction between habitat quality and an Allee-like effect in metapopulations

“…Most of these models were only able to reveal the effect of complete destruction of a certain proportion of the habitat patches (see, for example Amarasekare [1], Hill and Caswell [12], Zhou et al [22]). One notable exception is the model studied by…”

“…In this model, these events are separated into distinct phases as in [12] and [3]. First, a colonisation phase occurs during which unoccupied patches are colonised by individuals from the occupied patches.…”

“…Concave colonisation functions such as f (x) = 1 − exp(−βx), β > 0 [12] are commonly used, but non-concave functions are also relevant. The case of non-concave colonisation functions will be studied in the next section.…”

Effect of an invasive mollusc, American slipper limpet Crepidula fornicata, on habitat suitability for juvenile common sole Solea solea in the Bay of Biscay

“…A smooth long-term response of fish stocks to habitat loss can switch to sporadic drastic lower recruitment (Scheffer et al 2001). Damage to these nursery grounds and loss of their area may slow or prevent stock recovery (Hall 1998), and extinction may occur if habitat quantity and/or quality falls below a critical threshold (Hill & Caswell 2001). The consequences of the slipper limpet invasion on sole stock renewal in the Bay of Biscay, where relationship between nursery habitat capacity and recruitment has already been demonstrated (Le Pape et al 2003a), are potentially important.…”

“…Survival and growth of early fish stages are maximised in these highly productive habitats (Miller et al 1984(Miller et al , 1988 and natural shallow areas can serve as nurseries for a variety of species that are widely distributed on the continental shelf (Lenanton & Potter 1987), in particular flatfishes (Van der Veer et al 2000, Riou et al 2001. The available area and the quality of coastal nursery habitats have a considerable influence on recruitment levels (Rijnsdorp et al 1992, Gibson 1994 and damage to these habitats may slow or prevent population recoveries (Hall 1998, Hill & Caswell 2001. Thus, processes occurring locally within nursery grounds during the juvenile stage may be important for regulating the year-class strength of fishes and population size (Cowan et al 2000, Sharf 2000.…”