The biological control paradox is the term applied to the problem associated with many simple models: that there is an apparent tradeoff between the stability and the density of the host population such that a suppression of greater than 67% is incompatible with stability. This model-based constraint needed to be reconciled with field observations (especially from classical biological control programs) that natural enemies are able to suppress pest densities to a high degree and persist.
Two biological phenomena come to the rescue of models and avoid the biological control paradox. The first is that enemies may not be strictly monophagous. If able to switch to a different species of prey or host, then survival is possible even in the absence of the original prey species or biological control agent target. Even in the case of highly specific predator or para-sitoid species, the availability of resource subsidies such as plant pollen or nectar (see the section titled 'Conservation biological control') may allow local survival of an enemy population until the pest is again available. Linked with this dietary aspect is the metapopulation concept. A metapopulation is a series of local populations that are imperfectly connected by dispersal such that at any given time only a subset of available habitat patches are occupied by the pest and enemy. The existence of pests in a metapopulation has important consequences for the stability of biological control models, for if an efficient enemy drives the pest to extinction in one local population its survival is assured in other patches where the enemy is yet to arrive or yet to build up to numbers sufficient to cause pest extinction. Of course, the same spatiotemporal patchiness that prevents pest extinction serves also to maintain a metapopulation of the enemy.
Considerations such as these have led to a reconsideration of the early notion held by early biological control practitioners and population modelers that density-dependence-conferred stability of a pest population (at a new equilibrium density below the EIL of the crop) is essential for successful biological control. Studies of at least some biological control systems suggested that none-quilibrium models may be more realistic. One example of such a biological control system is that involving the California red scale pest and the wasp parasitoid Aphytis melinus DeBach. Studies of this parasitoid on citrus trees by Murdock and co-workers in the USA showed that it did not respond to different densities of scale hosts in a density-dependent manner; parasitism was as likely to be high in patches of scarce hosts as in patches of common hosts. Importantly, the scale insect avoided extinction by the existence of a virtual refuge in the interior of each host tree. In these locations, scale insects were less heavily parasitized because ants provided a degree of protection by disturbing parasitoids, and parasitoids preferred to forage on the outer part of the tree where the scale insects were larger and the bark a more attractive color.
The various types of general models that are considered above from a biological control perspective are explored in more detail in Prey-Predator Models.
Specific models focus on particular biological control systems and tend to be rich in environmental and biological detail of the relevant system. In contrast with the general models discussed in preceding sections, specific models overall are as concerned with predicting the outcomes of biological control as they are in developing an understanding of the nature of the system via theory. Unlike general models, which have a long history, work on specific models has been confined largely to the last 25 years.
The literature contains dozens of examples of specific biological control models that range over weed, arthropod, vertebrate, plant pathogen, mollusk targets. Agent taxa are similarly diverse including pathogens (against mollusks, arthropods, and vertebrates), parasitoids and predators (against arthropods), pathogens and herbivores (against weeds), and antagonistic microbes (against plant pathogens).
As was the case for general models, specific models may take the form of discrete-time and continuous-time models though there is a striking range of complexities apparent in models. Among the most complex are those that deal with fungal pathogens of arthropod targets. This reflects the fact that fungi are rather more sensitive to environmental conditions and may have more complex life history than applies to other taxa of agents. Accordingly, factors such as temperature and inoculum dispersal feature in models of biological control where a fungus is the agent or, less commonly, the target. Simpler models tended to be used in the case of arthropod agents for weed biological control. In these, the dynamics of the weed are the focus of the model with the impact of the agent constituting an additional mortality factor with a varying level of intensity.
An ability to predict the outcome of a specific biological control release is the 'Holy Grail' of biological control modeling. The extent to which this can be achieved, however, is limited by the importance within models of factors that cannot be predicted by theory or measured in the confines of a quarantine research station. Behavior such as dispersal, for example, will affect agent population properties such as reproduction (see Allee Effects) and its impact on the target population (e.g., via attack rate). Despite constraints such as this, however, specific models of biological control can be useful in applied aspects such as decision making and post-hoc analysis of biological programs.
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