(Joint work with Joshua Ross, King's College Cambridge)
Abstract: Many animals live naturally in communities, with migration linking these communities across a broader scale. Furthermore, an ever-increasing number of species are forced to live in fragmented landscapes due to the destruction of their habitat, generally caused by anthropogenic disturbance. These metapopulations are consequently drawing much attention in both the theoretical and applied ecology literature.
Habitat fragmentation caused by habitat loss, in combination with other factors such as climate change, is placing many species at high risk of extinction, and ecologists and conservation biologists must attempt to limit this risk. With less funding than is required to protect all species, triage becomes necessary, and hence the need to efficiently evaluate extinction risk in order to determine a priority for allocating funding. Additionally, in order to use the resources available most efficiently, it is necessary to determine the optimal investment that minimises the threat of extinction.
We present here two 'rules of thumb' for metapopulation management, which are established using a simple metapopulation model. The first rule [R1] identifies an explicit formula for the persistence time of the population, and thus enables the population manager to form a priority species ranking by identifying those species most at risk of extinction. The second rule [R2] identifies an optimal management strategy that gives direction on how to alter the colonisation rate c (creation or improvement of habitat corridors) and local extinction rate e (restoring habitat quality or expanding habitat) in order to maximise the persistence time under a budgetary constraint.
We employ a stochastic version of the Levins (1969) metapopulation model. In order to use our rules of thumb it is necessary that this simple model first be calibrated to a spatially-realistic model. Thus we propose an explicit method for calibration for a general spatially-realistic model.
Rule [R1] is based on exact and approximate formulae for the expected time to extinction starting from a given initial number of occupied patches. Rule [R2] defines an optimal management strategy in terms of a total budget B and costs K_{c} and K_{e} for respective (per unit) changes in c and e:
Invest in reducing e to its allowable minimum, unless B < K_{e} e - K_{c} c, in which case invest in increasing c.
We conclude by testing our rules on computer-generated patch networks from a spatially-realistic metapopulation model and a model for malleefowl (Leipoa ocellata) in the Bakara region of South Australia. These result suggest that our rules of thumb, derived from the stochastic Levins model, are robust. This, as well as optimal methods based on approximations for other spatially-realistic models, will be explored fully elsewhere.
Acknowledgement: This work is supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
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Last modified: 15th July 2009