Some examples of Applications to Ecological Issues

In recent years, metapopulation models have been connected to management always more in the ecological literature:

a)    Glanville fritillary butterfly, Melitæa cinxia, Hanski and its research group, in several papers

b)    European nuthatch, Sitta europea, ter Braak et al., 1998

c)    American pika, Ochotona princeps, Moilanen et al., 1998

d)    Southern Emu–wren, Stipiturus malachurus intermedius, Westphal et al., 2003

e)    Gypsy moth, Lymantria dispar , Bogich & Shea, 2008

f)     Common toad, Bufo bufo, Gilioli et al., 2008

g)    Malleefowl, Leipoa ocellata, Nicol & Chadès, 2011

h)    Acorn weevils, Curculio, Govindan et al., 2012

i)      Pine processionary moth, Traumatocampa pityocampa, Gilioli et al., 2013.

This short list, very far to be complete, contains papers where metapopulations models, like the IFM in a), b) and c), are mainly used to gain insight about the metapopulation dynamics at the timescale at which managers operate. This is the main exploitation of (spatially explicit) metapopulation models.  A less explored use is for management strategies evaluation, that is for a quantitative evaluation of the expected consequences of different management practices. This kind of evaluation is very important, as the outcomes of conservation management actions are not always as expected. Models are key components on management programs, as they provide a means of predicting outcomes of alternative management actions (Nichols, 2012). Metapopulation models should be embedded in a decision-making framework to give managers the capability of ranking alternative decisions (Westphal et al., 2003). This means that a decision problem should be clearly stated, by defining

This means that the objectives of the management should be explicitly and clearly stated in terms of metapopulation model variables (Possingham et al., 2001; Gilioli et al., 2013).

This has been done, for instance, by applying stochastic dynamic programming, like in d), e) and g). However, stochastic dynamic programming is computationally complex and its applicability limited to small metapopulations (Nicol and Chadès, 2011).

In f) and i) a different approach has been developed, to evaluate a finite number of metapopulation management strategies. It aims at evaluating the extent to which each strategy makes the metapopulation dynamics either close to or far from some situation of reference:

The use of stochastic metapopulation models allows the comparison of probability distributions of future observations under the effect of each strategy, provided that strategies are expressed in terms of the model elements, as in Figure 1.8. In f) and i), that probability distributions come from an Incidence Function Model.

The distance between the predicted metapopulations dynamics and the reference situation of total extinction is measured by the Kullback-Leibler divergence, also known as Kullback-Leibler information measure (Kullback and Leibler, 1951; see also Dacunha-Castelle and Duflo, 1986).

In the following sections the results obtained in f) for amphibian conservation and in i) for pest control will be summarized, by omitting any further mathematics.