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environment in pest-management programs ( Turelli and Hoffmann 1991, Turelli
et  al. 1992, Kiszewski and Spielman 1998, Tsitrone et  al. 1999, Hoy 2000, Dobson
2003, Le Rouzic and Capy 2006, Alphey et  al. 2007, Marshall 2009, Alphey et  al.
2011, Diaz et al. 2011, Hancock et al. 2011, Matthews et al. 2011 ). We do not know,
however, which model types are most likely to be predictive of the actual outcome
of field releases because few models have been validated with empirical data.
Predicting field results from mathematical models can be difficult; for exam-
ple, three models were developed to predict the success of a biological control
program involving applications of fungi for control of grasshoppers and locusts
( Wood and Thomas 1999 ). All three models fit the empirical data; one predicted
sustained control at low levels after a single pathogen application, but the other
two predicted that repeated pathogen applications would be necessary. Analysis
of these divergent expectations demonstrated that two assumptions made by
ecologists and modelers were suspect: Wood and Thomas (1999) concluded that
quantitatively similar models need not give even qualitatively similar predic-
tions (contrary to expectations and the sensitivity analysis of model predictions
to parameter variation is not always sufficient to ensure the accuracy of the
predictions.
Population models may lack key ingredients, such as partial reproductive iso-
lation. For example, Caprio and Hoy (1995) developed a stochastic simulation
model that varied the degree of mating bias between pesticide-resistant and
-susceptible strains of natural enemies, diploidy state (diplo- or haplo-diploid),
degree of dominance of the resistance allele, and degree to which mating biases
extended to the hybrid progeny. The results were counterintuitive, but demon-
strated that models offer insights into the complexities of population genetics
and dynamics that might be overlooked. A common assumption made in many
models is that all genotypes of a species mate at random, but this assumption
may mask important interactions such as mating bias or partial reproductive
incompatibilities. The efficacy of GMA releases could be jeopardized if mating
biases exist between released and wild populations.
Empirical data generally are lacking to compare the relative usefulness of dif-
ferent model types in predicting population dynamics. Theoretical ecologists
usually assume homogeneous and continuous populations. Metapopulation
models, by contrast, assume that populations exist in patches varying in area,
degree of isolation, and quality. Metapopulation biology increasingly is being
recognized as relevant to our understanding of population ecology, genetics,
and evolution ( Hanski 1998 ). Recent data, and a variety of metapopulation mod-
els, indicate that spatial structure affects populations as much as birth and death
rates, competition, and predation ( Caprio and Hoy 1994 ).
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