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Biological Control Models
Population Dynamics | Biological Control Models 403
Biological Control Models G M Gurr, Charles Sturt University, Orange, NSW, Australia ª 2008 Elsevier B.V. All rights reserved.
Introduction A Brief History Types of Models Predator Responses
The Biological Control Paradox Model Uses for Differing Biological Control Approaches Conclusion Further Reading
Introduction
researchers have turned to ecological theory and modeling to enhance success rates through better understanding of the mechanisms of biological control and to provide predictive ability.
This article presents a scientific overview of biological control models. The first section introduces the broad types of general population models before specific biological control models are explored. The penultimate section of the article considers the applied uses to which biological control models have been put and assesses broad future directions for research in this field. Biological control uses predatory, parasitic, or pathogenic agents to reduce the population of a target (usually a weed or herbivorous animal). A discrete branch of biological control targets plant diseases using antagonistic microorganisms that inhibit the disease process. The general aim of biological control is to reduce the target’s population density either indefinitely or, in the case of augmentative, inoculative, and inundative approaches (see below), for a defined period. Ideally, the new population density of the target should be such that the mortality caused by the agents maintains it below the economic injury level (EIL), that is, there is no need to use pesticidal applications or other methods to avoid economic loss in agriculture or environmental impact in the case of pests of conservation areas. In practice, however, many biological control programs fail to give consistently high levels of target population suppression. In terms of population dynamics, the target’s new equilibrium density is either too high or unstable. In cases where only partial control of the target is achieved, however, the contribution of biological control may still be valuable. Modern pest management tends to be integrated in nature such that a range of pest control methods are often brought to bear on a given pest species; none individually is completely effective but together a sufficient level of control is achieved. Despite this pragmatism, there are well-known cases of unilateral use of biological control of weed and insect targets where the level of success has been so high that practitioners naturally aim to emulate this in subsequent attempts. Though this quest has sometimes been ad hoc in nature,
A Brief History There is a long history of interplay between the development of population models and biological control. The early successes of biological control in its ‘classical’ form, such as the control of cottony-cushion scale (Icerya purchasi Mask.) in California following the introduction of the predatory vedalia beetle (Rodolia cardinalis (Muls)) from Australia in the late 1880s, provided stimulation to the development of early population dynamics theory. Since the 1930s, models have been used in attempts to develop a comprehensive theoretical foundation for biological control. The extent of use of general population models in biological control practice has, however, been limited, and this form of pest control has often been criticised for being ad hoc. Modeling attempts over the last two decades, however, have made significant advances in our understanding of the biological process and are beginning to help refine its practice.
Types of Models The term ‘model’ may be defined as a representation of some aspect of the real world that allows the investigation of that aspect’s properties and – provided the model is reliable – prediction of future behavior. Notably, though differing models of a given aspect or system may not be compatible with one another, each model may have utility in both describing the system and predicting outcomes. For example, Newtonian physics has sufficed to land humans on the Moon and navigate robotic probes to the outer planets despite the fact that Einsteinian and quantum physics are now accepted as the better models
404 Population Dynamics | Biological Control Models
without which we could not explain the universe at the smallest and largest scales. This parallel provides an important lesson for those developing and using models of biological control: though a large number of models are available and sometimes heated debate has surrounded the merits and problems of competing models, each constitutes a tool by which we may better understand or predict some aspect of biological control.
General Models A useful distinction for models relevant to biological control is general and specific. General models developed from early thinking of population growth and how predator–prey interactions help account for the fact that all populations in nature appear to be constrained. Notable among early theories and models are Malthus’ ‘struggle for existence’, Verhulst’s logistic equation, the Lotka–Volterra equations, and the Nicholson Bailey model. General models seek to provide broadly applicable rules for predator–prey, parasitoid–host, and herbivore–plant models and are strongly grounded in theory. The attendant literature is concerned with issues such as the stability of populations and magnitude of impact (suppression) of the agent or predator on the target or prey. General models may be divided into discrete-time (difference) and continuous-time (differential) models. In the context of biological control, the first of these best describes systems in which there is strong seasonality or discrete cropping phases leading the agent or target to reproduce seasonally. Within this category of models are prey-dependent and ratio-dependent models (see below). Continuous-time (differential) models are most applicable in biological control systems where the relevant organisms reproduce year round. Within this category are stage-structured models that include biological details such as the fact that most parasitoids are able to attack only one life stage of their host (most commonly the egg or larva).
Predator Responses A limitation of early models was that the reproductive rate of predators was not constrained. This is clearly a biological nonsense and led to attempts to understand and incorporate into models the response of predators to changes in prey density. It is now recognized that predators (agents in the terminology of biological control) may exhibit a response at the population level termed the numerical response and a behavioral response at the individual level termed the functional response. The numerical response is intuitive in nature, being based on
(1) the aggregation of predator individuals in patches of dense prey and (2) a reproductive response reflecting greater fitness of predators when well nourished. The latter is most commonly incorporated in models of invertebrates with short generation times. The nature of the response at the individual level is less obvious. Three types of functional responses are generally accepted. The type I response consists of a linear increase in attack rate as prey density rises until the density at which attack rate matches satiation is reached. This is observed for predators such as daphnia and sedentary filter feeders, so is generally of little relevance to biological control. In contrast, the type II functional response is common in specialist insect parasitoids (which are among the most widely used biological control agents against insect targets). In this C-shaped relationship, attack rate increases at a decreasing rate with rising prey (or host) density. The type III response is S-shaped such that attack rate initially increases with rising prey density, then decreases as the asymptote is reached. This relationship is associated with generalist predators including vertebrate predators that (1) exhibit ‘switching’ from one prey to another in response to availability or (2) that aggregate in patches of dense prey. The incorporation of predator response into models has, however, led to debate over whether ‘ratio-dependent models’ that consider the ratio of prey to predators are superior to the Lotka–Volterra and Nicholson Bailey (‘prey-dependent’) models that use prey density alone. Functional responses were important in the development of population models more generally, because they led to the incorporation of model components that represent real-world variables such as the degree of hunger, time available for searching, rate of successful search, and the time it takes a predator to capture and consume a prey item (handling time). The concept of functional responses is also intellectually satisfying in relation to the notion of density-dependent regulation, that is, natural enemies kill more prey when prey are common and proportionally fewer prey when prey are scarce. Such a mechanism allows models to reflect the popularly held notion of the balance of nature whereby the numbers of a given species are kept in check but it is not forced into extinction. Despite the intuitive appeal of this concept, both modeling and empirical work suggest limitations to the density-dependence notion.
The Biological Control Paradox 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
Population Dynamics | Biological Control Models 405
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 parasitoid 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 densitydependence-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 nonequilibrium 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 of Biological Control 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.
Model Uses for Differing Biological Control Approaches A consideration of specific models requires that the general account of biological control provided in the introductory section is revisited to define the major
406 Population Dynamics | Biological Control Models Table 1 Summary of the characteristics of major biological control approaches and typical uses of population models (see text for further detail)
Classical biological control Characteristics
Low numbers of agents released Agents usually exotic Weed and arthropod targets common
Advantages
Disadvantages
Examples of modeling
Self-perpetuating Control not confined to original release location Inexpensive when it works Risk of ongoing off-target effects Poor success rate Out of farmer’s control Why many releases fail to establish or bring target under adequate control Agent release patterns and numbers Which agent to release
forms of biological control. The types of question that specific biological control models address differs to a large extent across the forms of biological control used (see Table 1).
Classical Biological Control This approach relies on the release of relatively small numbers of exotic agent individuals to a new location. Typically, release sizes are in hundreds or thousands per site. Accordingly, there is an expectation that the agents will reproduce in number, establish a self-perpetuating population (or metapopulation), and spread from the original release positions to cover all or most of the target species’ range. The major risk associated with this form of biological control is that the introduction of an exotic species into a new geographical location will damage other, nontarget species. The most infamous case of this was the 1930s introduction of the cane toad, Bufo marinus (Linneus), into Australia in an attempt to control the cane beetle. Given the magnitude of this issue, it is possibly surprising that models have not been used to any great extent to help predict the risk of nontarget impacts in classical biological control, especially since modeling has been used to predict risks associated with inundative biological control (see below). The explanation for this is likely to be that the consequences of introducing an exotic species that proves not to be target specific may be so catastrophic that decisions are made on the basis of empirical rather than theoretical or modeling work.
Inundative, augmentative, and inoculative biological control
Conservation biological control
Large numbers of agents released Agents often native Targets usually arthropods (some microbes) Immediacy of response, low need to plan ahead Under farmer’s control
No agents released, existing populations are enhanced Agents mostly native Targets usually arthropods
Relatively high cost Short duration of control
Release rates and timing Level of control expected under differing situations Understanding reasons for failure
Low cost Can give prolonged control Under farmer’s control Under-researched Poor immediacy of response, need to plan ahead Which aspects of agent biology most important for success (modeling little used to date)
Indeed, experimental specificity testing is a major subdiscipline in this branch of biological control. Where models have been extensively used in classical biological control is to address the historically low success rate. In the case of arthropod agents against arthropod targets, 10% of releases give complete control. Understanding reasons for this is of obvious importance and modeling-based efforts have sometimes employed high levels of biological and environmental detail. Work by Gutierrez and co-workers focused on the parasitic wasps released into Africa in classical biological control attempts to control the cassava mealybug (Phenacoccus manihoti Mat.-Ferr.). Modeling helped explain why Epidinocarsis diversicornis (Howard) failed to establish while the related species Epidinocarsis lopezi (De Santis) established and became the most important mortality factor in the pest’s population (at least during the dry season). A contrasting example, of a herbivore agent against a plant target, illustrates another way in which modeling may support decision making to enhance the success of classical biological control. In the case of knapweed (Centaurea diffusa Lam.), the biological model was far simpler than the multiple-parameter, differential equation model used in the preceding example. Here, a simple difference equation model provided an indication of the type of agent that needed to be introduced as a follow-up to the initial introduction of several insect herbivores. Since the weed was increasingly resistant to reductions in density as its numbers declined (i.e., a density-dependent response), the new population equilibrium remained above the EIL that applied to the weed’s
Population Dynamics | Biological Control Models 407
impact on forage production. Accordingly, additional agents that specialize on the fast-growing, prostrate plants typical of low-density infestations were identified as important. Related and other issues that specific models can address in classical biological control include: (1) whether a specific exotic agent will establish in a new location; (2) what number of individuals should be released per site; (3) what level of control a specific exotic agent will exert over a target; and (4) understanding why a release has failed. Augmentative, Inoculative, and Inundative Biological Control These three biological control approaches are considered together since they all are based on the release of relatively large numbers of agents in a specific time and place with the expectation of local control on a relatively shortterm basis. Augmentative biological control specifically aims to augment the action of other agents already present. Inoculative biological control typically occurs in protected agriculture where the aim is to establish a breeding population of the agent that will persist for the duration of a specific cropping phase. Inundative biological control is effectively a ‘biological pesticide’ used in response to escalating pest numbers at a specific time and place though the agent may be an arthropod or a microorganism. A problem associated with these forms of biological control is the potentially prohibitive cost of using large numbers of short-lived agents. Accordingly, a number of models have considered the level of biological control achieved at differing levels of agent release/application. In the case of work with a granulosis virus against the codling moth (Cydia pomonella Linneus), larval mortality was shown to vary with 1/10 power to the virus concentration with a consequent effect on the level of fruit damage. These biological control approaches are not, however, without risk, and modeling has also been used to address this issue. A fungal pathogen Chondrostereum purpureum was proposed as an inundative biological control agent for the perennial weed Prunus serotina Ehrh. in forests. Though the pathogen could be applied in a targeted fashion to only the pest trees by formulating it into a mycoherbicide spray, the fungus subsequently produces basidiospores that could disperse and infect nontarget plants, necessitating an analysis of risk. This involved the development of a stratified model to describe spore fluxes for differing layers and showed the significant effect of wind speed and consequent risk of dispersal of inoculum from a treated patch of forest and into commercially valuable Prunus spp. crops.
Other issues that specific models can address for these forms of biological control include: (1) what level of control a specific agent will exert over a target, (2) optimal timing of application or release for the agent to exert maximum impact, and (3) understanding why an agent fails. Conservation Biological Control Though this form of biological control has its roots in traditional practices such as companion planting and other types of polyculture, it is only in recent decades that it has been rigorously researched. This approach aims to maximize the impact of existing natural enemies rather than accept the costs and risks of introducing and releasing exogenous agents. Reducing the pesticide-induced mortality of natural enemies and habitat manipulation to improve the local availability of resources such as food, shelter, and alternative hosts are increasingly recognized as important. However, reflecting the relative youth of this branch of biological control, there has been very little use of modeling to improve its performance. One important study by Kean and co-workers illustrates the potential value of wider use of modeling in conservation biological control. That work explored which aspects of natural enemy biology had the greatest impact on the target pest population. Modeling indicated that enemy search rate and prey conversion efficiency were the most important parameters. Maximum consumption rate and fecundity were less important while the effect of longevity depended on its interaction with other factors. Finally, the degree of spatial attraction of natural enemies to a location had an almost linear effect on pest suppression. The latter finding is of use for practitioners of conservation biological control in ephemeral habitats (e.g., annual crops), because attracting higher densities of enemies has an immediate effect on pests while other natural enemy parameters – though potentially more important – may be slower to respond and hence are likely to be more appropriate for manipulation in perennial systems such as orchards. At a finer scale, the importance of natural enemy search rate highlighted by the modeling points to the possible advantages that could be gained from conservation biological control methods that targeted this parameter of behavior. An example of this is to provide parasitoid wasp agents with nectar sources since many experimental studies have shown that this increases energy levels and flight propensity, which could, in turn, increase search rate.
Conclusion The model-derived answers to the types of questions dealt with in the preceding sections can be compared for
408 Ecological Indicators | Biological Integrity
alternative biological control approaches and for candidate agent species so that appropriate choices in methods can be made. More fundamentally, as models help refine our knowledge of the population dynamics that apply in biological control systems, our theoretical understanding of the ecology is improved. Progress in both the applied and theoretical domains offers scope to make biological control less hit-and-miss with consequent cost savings and reduced risk of environmental impact. See also: Agriculture Models; Allee Effects; Conservation Biological Control and Biopesticides in Agricultural; Growth Models; Herbivore-Predator Cycles; Insect Pest Models and Insecticide Application; Metapopulation Models; Population and Community Interactions; Predation; Prey–Predator Models; Terrestrial Arthropods.
Further Reading Barlow ND (1999) Models in biological control: A field guide. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 43–68. Cambridge: Cambridge University Press. Berryman AA (1999) The theoretical foundations of biological control. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 3–21. Cambridge: Cambridge University Press. Briggs CJ, Murdock WW, and Nisbet M (1999) Recent developments in theory for biological control of insects by parasitoids. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 22–42. Cambridge: Cambridge University Press. Gurr GM, Barlow N, Memmott J, Wratten SD, and Greathead DJ (2000) A history of methodological, theoretical and empirical approaches to biological control. In: Gurr GM and Wratten SD (eds.) Biological Control: Measures of Success, pp. 3–37. Dordrecht, The Netherlands: Kluwer. Kean J, Wratten S, Tylianakis J, and Barlow N (2003) The population consequences of natural enemy enhancement, and implications for conservation biological control. Ecology Letters 6: 604–612.
Biological Integrity J R Karr, University of Washington, Seattle, WA, USA ª 2008 Elsevier B.V. All rights reserved.
Integrity: The Natural State Moving Biological Integrity from Concept to Measurement Selecting Metrics
Properties of a Multimetric Biological Index Application of Multimetric Biological Indexes Summary Further Reading
Integrity: The Natural State
restore and maintain the chemical, physical, and biological integrity of the nation’s waters. More recently, maintenance of biological or ecological integrity became a primary goal in diverse national and international contexts (the Canada National Parks Act, the United States’ National Wildlife Refuge System Improvement Act, the Canada–United States Great Lakes Water Quality Agreement, the European Union’s Water Framework Directive, and the Earth Charter). These initiatives have established legal, philosophical, and scientific foundations for protecting our global biological heritage. For many years, agencies and institutions responsible for implementing legislation affecting water quality neglected the biological condition of waters in favor of a focus on chemical pollutants; they assumed, erroneously, that chemical measures were an adequate surrogate of biological condition. In fact, dependence on chemical evaluations chronically underreports the extent of
Biological integrity can be defined as the presence of a balanced, integrated, adaptive biological system having the full range of parts (genes, species, and assemblages) and processes (mutation, demography, biotic interactions, nutrient and energy dynamics, and metapopulation processes) expected for locations with little recent human activity. Inherent in this definition is that (1) living systems act over a variety of scales from individuals to landscapes; (2) a fully functioning living system includes items we can count (the parts) plus the processes that generate and maintain them; and (3) living systems are embedded in dynamic evolutionary and biogeographic contexts that influence and are influenced by their physical, chemical, and biological environments. The phrase biological integrity was first used in 1972 to establish the goal of the US Clean Water Act – to
Biological Control Models G M Gurr, Charles Sturt University, Orange, NSW, Australia ª 2008 Elsevier B.V. All rights reserved.
Introduction A Brief History Types of Models Predator Responses
The Biological Control Paradox Model Uses for Differing Biological Control Approaches Conclusion Further Reading
Introduction
researchers have turned to ecological theory and modeling to enhance success rates through better understanding of the mechanisms of biological control and to provide predictive ability.
This article presents a scientific overview of biological control models. The first section introduces the broad types of general population models before specific biological control models are explored. The penultimate section of the article considers the applied uses to which biological control models have been put and assesses broad future directions for research in this field. Biological control uses predatory, parasitic, or pathogenic agents to reduce the population of a target (usually a weed or herbivorous animal). A discrete branch of biological control targets plant diseases using antagonistic microorganisms that inhibit the disease process. The general aim of biological control is to reduce the target’s population density either indefinitely or, in the case of augmentative, inoculative, and inundative approaches (see below), for a defined period. Ideally, the new population density of the target should be such that the mortality caused by the agents maintains it below the economic injury level (EIL), that is, there is no need to use pesticidal applications or other methods to avoid economic loss in agriculture or environmental impact in the case of pests of conservation areas. In practice, however, many biological control programs fail to give consistently high levels of target population suppression. In terms of population dynamics, the target’s new equilibrium density is either too high or unstable. In cases where only partial control of the target is achieved, however, the contribution of biological control may still be valuable. Modern pest management tends to be integrated in nature such that a range of pest control methods are often brought to bear on a given pest species; none individually is completely effective but together a sufficient level of control is achieved. Despite this pragmatism, there are well-known cases of unilateral use of biological control of weed and insect targets where the level of success has been so high that practitioners naturally aim to emulate this in subsequent attempts. Though this quest has sometimes been ad hoc in nature,
A Brief History There is a long history of interplay between the development of population models and biological control. The early successes of biological control in its ‘classical’ form, such as the control of cottony-cushion scale (Icerya purchasi Mask.) in California following the introduction of the predatory vedalia beetle (Rodolia cardinalis (Muls)) from Australia in the late 1880s, provided stimulation to the development of early population dynamics theory. Since the 1930s, models have been used in attempts to develop a comprehensive theoretical foundation for biological control. The extent of use of general population models in biological control practice has, however, been limited, and this form of pest control has often been criticised for being ad hoc. Modeling attempts over the last two decades, however, have made significant advances in our understanding of the biological process and are beginning to help refine its practice.
Types of Models The term ‘model’ may be defined as a representation of some aspect of the real world that allows the investigation of that aspect’s properties and – provided the model is reliable – prediction of future behavior. Notably, though differing models of a given aspect or system may not be compatible with one another, each model may have utility in both describing the system and predicting outcomes. For example, Newtonian physics has sufficed to land humans on the Moon and navigate robotic probes to the outer planets despite the fact that Einsteinian and quantum physics are now accepted as the better models
404 Population Dynamics | Biological Control Models
without which we could not explain the universe at the smallest and largest scales. This parallel provides an important lesson for those developing and using models of biological control: though a large number of models are available and sometimes heated debate has surrounded the merits and problems of competing models, each constitutes a tool by which we may better understand or predict some aspect of biological control.
General Models A useful distinction for models relevant to biological control is general and specific. General models developed from early thinking of population growth and how predator–prey interactions help account for the fact that all populations in nature appear to be constrained. Notable among early theories and models are Malthus’ ‘struggle for existence’, Verhulst’s logistic equation, the Lotka–Volterra equations, and the Nicholson Bailey model. General models seek to provide broadly applicable rules for predator–prey, parasitoid–host, and herbivore–plant models and are strongly grounded in theory. The attendant literature is concerned with issues such as the stability of populations and magnitude of impact (suppression) of the agent or predator on the target or prey. General models may be divided into discrete-time (difference) and continuous-time (differential) models. In the context of biological control, the first of these best describes systems in which there is strong seasonality or discrete cropping phases leading the agent or target to reproduce seasonally. Within this category of models are prey-dependent and ratio-dependent models (see below). Continuous-time (differential) models are most applicable in biological control systems where the relevant organisms reproduce year round. Within this category are stage-structured models that include biological details such as the fact that most parasitoids are able to attack only one life stage of their host (most commonly the egg or larva).
Predator Responses A limitation of early models was that the reproductive rate of predators was not constrained. This is clearly a biological nonsense and led to attempts to understand and incorporate into models the response of predators to changes in prey density. It is now recognized that predators (agents in the terminology of biological control) may exhibit a response at the population level termed the numerical response and a behavioral response at the individual level termed the functional response. The numerical response is intuitive in nature, being based on
(1) the aggregation of predator individuals in patches of dense prey and (2) a reproductive response reflecting greater fitness of predators when well nourished. The latter is most commonly incorporated in models of invertebrates with short generation times. The nature of the response at the individual level is less obvious. Three types of functional responses are generally accepted. The type I response consists of a linear increase in attack rate as prey density rises until the density at which attack rate matches satiation is reached. This is observed for predators such as daphnia and sedentary filter feeders, so is generally of little relevance to biological control. In contrast, the type II functional response is common in specialist insect parasitoids (which are among the most widely used biological control agents against insect targets). In this C-shaped relationship, attack rate increases at a decreasing rate with rising prey (or host) density. The type III response is S-shaped such that attack rate initially increases with rising prey density, then decreases as the asymptote is reached. This relationship is associated with generalist predators including vertebrate predators that (1) exhibit ‘switching’ from one prey to another in response to availability or (2) that aggregate in patches of dense prey. The incorporation of predator response into models has, however, led to debate over whether ‘ratio-dependent models’ that consider the ratio of prey to predators are superior to the Lotka–Volterra and Nicholson Bailey (‘prey-dependent’) models that use prey density alone. Functional responses were important in the development of population models more generally, because they led to the incorporation of model components that represent real-world variables such as the degree of hunger, time available for searching, rate of successful search, and the time it takes a predator to capture and consume a prey item (handling time). The concept of functional responses is also intellectually satisfying in relation to the notion of density-dependent regulation, that is, natural enemies kill more prey when prey are common and proportionally fewer prey when prey are scarce. Such a mechanism allows models to reflect the popularly held notion of the balance of nature whereby the numbers of a given species are kept in check but it is not forced into extinction. Despite the intuitive appeal of this concept, both modeling and empirical work suggest limitations to the density-dependence notion.
The Biological Control Paradox 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
Population Dynamics | Biological Control Models 405
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 parasitoid 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 densitydependence-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 nonequilibrium 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 of Biological Control 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.
Model Uses for Differing Biological Control Approaches A consideration of specific models requires that the general account of biological control provided in the introductory section is revisited to define the major
406 Population Dynamics | Biological Control Models Table 1 Summary of the characteristics of major biological control approaches and typical uses of population models (see text for further detail)
Classical biological control Characteristics
Low numbers of agents released Agents usually exotic Weed and arthropod targets common
Advantages
Disadvantages
Examples of modeling
Self-perpetuating Control not confined to original release location Inexpensive when it works Risk of ongoing off-target effects Poor success rate Out of farmer’s control Why many releases fail to establish or bring target under adequate control Agent release patterns and numbers Which agent to release
forms of biological control. The types of question that specific biological control models address differs to a large extent across the forms of biological control used (see Table 1).
Classical Biological Control This approach relies on the release of relatively small numbers of exotic agent individuals to a new location. Typically, release sizes are in hundreds or thousands per site. Accordingly, there is an expectation that the agents will reproduce in number, establish a self-perpetuating population (or metapopulation), and spread from the original release positions to cover all or most of the target species’ range. The major risk associated with this form of biological control is that the introduction of an exotic species into a new geographical location will damage other, nontarget species. The most infamous case of this was the 1930s introduction of the cane toad, Bufo marinus (Linneus), into Australia in an attempt to control the cane beetle. Given the magnitude of this issue, it is possibly surprising that models have not been used to any great extent to help predict the risk of nontarget impacts in classical biological control, especially since modeling has been used to predict risks associated with inundative biological control (see below). The explanation for this is likely to be that the consequences of introducing an exotic species that proves not to be target specific may be so catastrophic that decisions are made on the basis of empirical rather than theoretical or modeling work.
Inundative, augmentative, and inoculative biological control
Conservation biological control
Large numbers of agents released Agents often native Targets usually arthropods (some microbes) Immediacy of response, low need to plan ahead Under farmer’s control
No agents released, existing populations are enhanced Agents mostly native Targets usually arthropods
Relatively high cost Short duration of control
Release rates and timing Level of control expected under differing situations Understanding reasons for failure
Low cost Can give prolonged control Under farmer’s control Under-researched Poor immediacy of response, need to plan ahead Which aspects of agent biology most important for success (modeling little used to date)
Indeed, experimental specificity testing is a major subdiscipline in this branch of biological control. Where models have been extensively used in classical biological control is to address the historically low success rate. In the case of arthropod agents against arthropod targets, 10% of releases give complete control. Understanding reasons for this is of obvious importance and modeling-based efforts have sometimes employed high levels of biological and environmental detail. Work by Gutierrez and co-workers focused on the parasitic wasps released into Africa in classical biological control attempts to control the cassava mealybug (Phenacoccus manihoti Mat.-Ferr.). Modeling helped explain why Epidinocarsis diversicornis (Howard) failed to establish while the related species Epidinocarsis lopezi (De Santis) established and became the most important mortality factor in the pest’s population (at least during the dry season). A contrasting example, of a herbivore agent against a plant target, illustrates another way in which modeling may support decision making to enhance the success of classical biological control. In the case of knapweed (Centaurea diffusa Lam.), the biological model was far simpler than the multiple-parameter, differential equation model used in the preceding example. Here, a simple difference equation model provided an indication of the type of agent that needed to be introduced as a follow-up to the initial introduction of several insect herbivores. Since the weed was increasingly resistant to reductions in density as its numbers declined (i.e., a density-dependent response), the new population equilibrium remained above the EIL that applied to the weed’s
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impact on forage production. Accordingly, additional agents that specialize on the fast-growing, prostrate plants typical of low-density infestations were identified as important. Related and other issues that specific models can address in classical biological control include: (1) whether a specific exotic agent will establish in a new location; (2) what number of individuals should be released per site; (3) what level of control a specific exotic agent will exert over a target; and (4) understanding why a release has failed. Augmentative, Inoculative, and Inundative Biological Control These three biological control approaches are considered together since they all are based on the release of relatively large numbers of agents in a specific time and place with the expectation of local control on a relatively shortterm basis. Augmentative biological control specifically aims to augment the action of other agents already present. Inoculative biological control typically occurs in protected agriculture where the aim is to establish a breeding population of the agent that will persist for the duration of a specific cropping phase. Inundative biological control is effectively a ‘biological pesticide’ used in response to escalating pest numbers at a specific time and place though the agent may be an arthropod or a microorganism. A problem associated with these forms of biological control is the potentially prohibitive cost of using large numbers of short-lived agents. Accordingly, a number of models have considered the level of biological control achieved at differing levels of agent release/application. In the case of work with a granulosis virus against the codling moth (Cydia pomonella Linneus), larval mortality was shown to vary with 1/10 power to the virus concentration with a consequent effect on the level of fruit damage. These biological control approaches are not, however, without risk, and modeling has also been used to address this issue. A fungal pathogen Chondrostereum purpureum was proposed as an inundative biological control agent for the perennial weed Prunus serotina Ehrh. in forests. Though the pathogen could be applied in a targeted fashion to only the pest trees by formulating it into a mycoherbicide spray, the fungus subsequently produces basidiospores that could disperse and infect nontarget plants, necessitating an analysis of risk. This involved the development of a stratified model to describe spore fluxes for differing layers and showed the significant effect of wind speed and consequent risk of dispersal of inoculum from a treated patch of forest and into commercially valuable Prunus spp. crops.
Other issues that specific models can address for these forms of biological control include: (1) what level of control a specific agent will exert over a target, (2) optimal timing of application or release for the agent to exert maximum impact, and (3) understanding why an agent fails. Conservation Biological Control Though this form of biological control has its roots in traditional practices such as companion planting and other types of polyculture, it is only in recent decades that it has been rigorously researched. This approach aims to maximize the impact of existing natural enemies rather than accept the costs and risks of introducing and releasing exogenous agents. Reducing the pesticide-induced mortality of natural enemies and habitat manipulation to improve the local availability of resources such as food, shelter, and alternative hosts are increasingly recognized as important. However, reflecting the relative youth of this branch of biological control, there has been very little use of modeling to improve its performance. One important study by Kean and co-workers illustrates the potential value of wider use of modeling in conservation biological control. That work explored which aspects of natural enemy biology had the greatest impact on the target pest population. Modeling indicated that enemy search rate and prey conversion efficiency were the most important parameters. Maximum consumption rate and fecundity were less important while the effect of longevity depended on its interaction with other factors. Finally, the degree of spatial attraction of natural enemies to a location had an almost linear effect on pest suppression. The latter finding is of use for practitioners of conservation biological control in ephemeral habitats (e.g., annual crops), because attracting higher densities of enemies has an immediate effect on pests while other natural enemy parameters – though potentially more important – may be slower to respond and hence are likely to be more appropriate for manipulation in perennial systems such as orchards. At a finer scale, the importance of natural enemy search rate highlighted by the modeling points to the possible advantages that could be gained from conservation biological control methods that targeted this parameter of behavior. An example of this is to provide parasitoid wasp agents with nectar sources since many experimental studies have shown that this increases energy levels and flight propensity, which could, in turn, increase search rate.
Conclusion The model-derived answers to the types of questions dealt with in the preceding sections can be compared for
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alternative biological control approaches and for candidate agent species so that appropriate choices in methods can be made. More fundamentally, as models help refine our knowledge of the population dynamics that apply in biological control systems, our theoretical understanding of the ecology is improved. Progress in both the applied and theoretical domains offers scope to make biological control less hit-and-miss with consequent cost savings and reduced risk of environmental impact. See also: Agriculture Models; Allee Effects; Conservation Biological Control and Biopesticides in Agricultural; Growth Models; Herbivore-Predator Cycles; Insect Pest Models and Insecticide Application; Metapopulation Models; Population and Community Interactions; Predation; Prey–Predator Models; Terrestrial Arthropods.
Further Reading Barlow ND (1999) Models in biological control: A field guide. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 43–68. Cambridge: Cambridge University Press. Berryman AA (1999) The theoretical foundations of biological control. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 3–21. Cambridge: Cambridge University Press. Briggs CJ, Murdock WW, and Nisbet M (1999) Recent developments in theory for biological control of insects by parasitoids. In: Hawkins BA and Cornell HV (eds.) Theoretical Approaches to Biological Control, pp. 22–42. Cambridge: Cambridge University Press. Gurr GM, Barlow N, Memmott J, Wratten SD, and Greathead DJ (2000) A history of methodological, theoretical and empirical approaches to biological control. In: Gurr GM and Wratten SD (eds.) Biological Control: Measures of Success, pp. 3–37. Dordrecht, The Netherlands: Kluwer. Kean J, Wratten S, Tylianakis J, and Barlow N (2003) The population consequences of natural enemy enhancement, and implications for conservation biological control. Ecology Letters 6: 604–612.
Biological Integrity J R Karr, University of Washington, Seattle, WA, USA ª 2008 Elsevier B.V. All rights reserved.
Integrity: The Natural State Moving Biological Integrity from Concept to Measurement Selecting Metrics
Properties of a Multimetric Biological Index Application of Multimetric Biological Indexes Summary Further Reading
Integrity: The Natural State
restore and maintain the chemical, physical, and biological integrity of the nation’s waters. More recently, maintenance of biological or ecological integrity became a primary goal in diverse national and international contexts (the Canada National Parks Act, the United States’ National Wildlife Refuge System Improvement Act, the Canada–United States Great Lakes Water Quality Agreement, the European Union’s Water Framework Directive, and the Earth Charter). These initiatives have established legal, philosophical, and scientific foundations for protecting our global biological heritage. For many years, agencies and institutions responsible for implementing legislation affecting water quality neglected the biological condition of waters in favor of a focus on chemical pollutants; they assumed, erroneously, that chemical measures were an adequate surrogate of biological condition. In fact, dependence on chemical evaluations chronically underreports the extent of
Biological integrity can be defined as the presence of a balanced, integrated, adaptive biological system having the full range of parts (genes, species, and assemblages) and processes (mutation, demography, biotic interactions, nutrient and energy dynamics, and metapopulation processes) expected for locations with little recent human activity. Inherent in this definition is that (1) living systems act over a variety of scales from individuals to landscapes; (2) a fully functioning living system includes items we can count (the parts) plus the processes that generate and maintain them; and (3) living systems are embedded in dynamic evolutionary and biogeographic contexts that influence and are influenced by their physical, chemical, and biological environments. The phrase biological integrity was first used in 1972 to establish the goal of the US Clean Water Act – to