Search

A dilemma in ecology is posed by the contrast between simple strategic models, which offer generality but are exceedingly difficult to test against the performance of particular real systems, and complex tactical models, which aim to account for and be tested against particular systems but which do not easily yield generality. We explore the possibility that linked sequences of individual-based models provide the means for developing a theory of population and community ecology that is both testable and general. Individual-based models are by their nature preadapted to incorporating the mechanisms that determine a system’s dynamics. In their more detailed forms they are therefore highly testable. For the same reason, they lend themselves to a process of progressive removal of particular features, which should facilitate distinguishing the “essential” mechanisms from those that account for detail rather than major dynamic features. We illustrate these ideas with a theoretical and experimental program investigating the interaction between populations of the zooplankter Daphnia and algal food supply.

This paper explores the effect of spatial processes in a heterogeneous environment on the dynamics of a host-parasitoid interaction. The environment consists of a lattice of favourable (habitat) and hostile (matrix) hexagonal cells, whose spatial distribution is measured by habitat proportion and spatial autocorrelation (inverse of fragmentation). At each time step, a fixed fraction of both populations disperses to the adjacent cells where it reproduces following the Nicholson-Bailey model. Aspects of the dynamics analysed include extinction, stability, cycle period and amplitude, and the spatial patterns emerging from the dynamics. We find that, depending primarily on the fraction of the host population that disperses in each generation and on the landscape geometry, five classes of spatio-temporal dynamics can be objectively distinguished: spatial chaos, spirals, metapopulation, mainland-island and spiral fragments. The first two are commonly found in theoretical studies of homogeneous landscapes. The other three are direct consequences of the heterogeneity and have strong similarities to dynamic patterns observed in real systems (e.g. extinction-recolonisation, source-sink, outbreaks, spreading waves). We discuss the processes that generate these patterns and allow the system to persist. The importance of these results is threefold: first, our model merges into a same theoretical framework dynamics commonly observed in the field that are usually modelled independently. Second, these dynamics and patterns are explained by dispersal rate and common landscape statistics, thus linking in a practical way population ecology to landscape ecology. Third, we show that the landscape geometry has a qualitative effect on the length of the cycles and, in particular, we demonstrate how very long periods can be produced by spatial processes.

Global conservation needs far exceed the available resources, so scarce resources must be used cost-effectively. Although many conservation priory-setting frameworks used by NGO’s or public agencies explicitly claim to emphasize efficiency or wise investment, none actually incorporates costs in a formal return-on-investment (ROI) framework. We illustrate here how an ROI framework can be applied to real world resource allocation decisions faced by conservation organizations. We present two examples: (1) allocating resources to purchase land in 21 ecoregions that make up the Temperate Forest Habitat in the US; (2) allocating resources among a variety of conservation actions (not just land purchase) in Mediterranean habitats, with rates of habitat loss factored into the analysis. An important feature of both case studies is that costs vary by orders of magnitude, depending on where or how one is doing conservation. Second, because costs and biodiversity are not well correlated, enormous savings are possible by applying an ROI analysis. Moreover, recommended priorities after including costs in the calculations often deviate substantially from priorities based solely on biodiversity measures. Hence we argue that a major effort of conservationist biologists should be to include and record the costs of conservation actions. If serious attention is not given to returns on investment, it implies that “money is no object.”

A 20-year study of suppression of California red scale, a world-wide pest of citrus, by the parasitoid Aphytis melinus has established that the interaction is dynamically stable and that the mechanisms leading to control and stability operate at a local scale: spatial processes are not important. Key features appear to be an invulnerable class in the pest and rapid development of the parasitoid compared with the pest, as well as the fact that the parasitoid is an in situ specialist on the pest. Although another parasitoid species and two predator species are also present, they play at most a negligible role in pest control. These features—long-term persistence, suppression by a single natural enemy, an invulnerable stage in the pest and rapid development in the natural enemy—appear to be common in other coccid pest systems. By contrast, in temporary crops where the pest and enemy populations are open (i.e., sustained over the long run mainly by immigration) and non-persistent locally, as is frequently found in aphid pests, we expect that multiple generalist enemies are required for control and, of course, that spatial processes are important. There are very few well-studied examples of such systems, but these support our expectations. In these cases, it also appears that neither rapid enemy development nor an invulnerable pest stage is important for successful control.

We elucidate the mechanisms causing stability and severe resource suppression in a consumer-resource system. The consumer, the parasitoid Aphytis , rapidly controlled an experimentally induced outbreak of the resource, California red scale, an agricultural pest, and imposed a low, stable pest equilibrium. The results are well predicted by a mechanistic, independently parameterized model. The key mechanisms are widespread in nature: an invulnerable adult stage in the resource population and rapid consumer development. Stability in this biologically nondiverse agricultural system is a property of the local interaction between these two species, not of spatial processes or of the larger ecological community.

The forest insect pest Bupalus piniarius (pine looper moth) is a classic example of a natural population cycle. As is typical for populations that exhibit regular oscillations in density, there are several biological mechanisms that are hypothesized to be responsible for the cycles; but despite several decades of detailed study there has been no definite conclusion as to which mechanism is most important. We evaluated three hypotheses for which there was direct experimental evidence: (1) food quality (nutritional value of pine needles affected by defoliation); (2) parasitoids (trophic interactions with specialist parasitoids); and (3) maternal effects (maternal body size affects the performance of off- spring). We reviewed the empirical evidence for each of these hypotheses and expressed each hypothesis in the form of a mechanistic dynamic model. We used a nonlinear fore- casting approach to fit each model to three long-term population time series in Britain that exhibit some degree of regular cycling, and we used parametric bootstrap to evaluate the significance of differences between models in their goodness of fit to the data. The results differed among the three forests: at Culbin, the parasitoid and maternal effects models fit equally well; at Roseisle, the food quality and maternal effects models fit equally well; and at Tentsmuir, the parasitoid model fit best. However, the best-fit parasitism models required that the parasitism rate vary between nearly 0 and nearly 1 during a cycle, greatly exceeding the range of parasitism rates that have been observed in the field. In contrast, the required variation in the observable maternal quality variable (pupal mass) was within the range of empirical observations. Under mild constraints on the parasitism rate (though allowing a much wider range than has been measured in B. piniarius at any location), the fit of the parasitism model fell off dramatically. The maternal effects model then had uniformly strong support, outperforming the constrained parasitism model at all three sites and the food quality model at two; it performed slightly better than the food quality model at the remaining site. This represents the first system in which the maternal effects hypothesis for population cycles has been supported by both strong biological and dynamical evidence.

Dynamic energy budget models relate phenomena at many levels of ecological organization and can provide quantitative links from individual physiology to population, community, and ecosystem dynamics. A prerequisite for making these links is an empirically tested model of growth and reproduction for individual organisms in a temporally variable environment. We construct a model that is applicable to organisms with indeterminate growth. By applying a recent statistical approach attributable to S. N. Wood, we use the model to infer the size dependence of feeding rates and of energy allocation to growth vs. reproduction for Daphnia from new laboratory data on growth and egg production. The implied feeding rates are consistent with independent measurements. With one additional assumption, respiration rates can be predicted; they scale with size in a manner consistent with previous measurements of respiration allometry. These findings support the use of inverse methods to determine physiologically based functions and parameters for subsequent use in population and ecosystem models.

Coexistence of resource specialists can be maintained through various spatial mechanisms, each potentially inducing different resource dynamics. We used observational data to suggest plausible spatial coexistence mechanisms for Aphytis melinus and Encarsia perniciosi, two parasitoids of California red scale. Aphytis consistently produced more progeny from scale insects on leaves, and Encarsia produced progeny equally from scale insects on leaves and stems. To investigate the mechanism inducing this pattern, we performed field experiments to test two possible explanations. In the absence of substrate choice and at a given abundance of scale, the number of progeny produced by each species was the same on stems as on leaves. When given a choice, Encarsia had no substrate preference, while Aphytis preferred scale insects on leaves, producing results qualitatively similar to the field observations. Ecological theory suggests that this form of habitat preference may facilitate coexistence. Although this mechanism of coexistence is clearly compatible with biological control by multiple natural enemies in the red scale system, theory dealing with this type of interaction has not thoroughly examined the predictions for resource dynamics.

Although ecological theory exists to predict dynamics in communities with intraguild predation (IGP), few empirical tests have examined this theory. IGP theory, in particular, predicts that when two competitors interact via IGP, with increasing resource productivity: (1) the IG predator will increase in abundance as the IG prey declines, and (2) increasing dominance of the IG predator will cause resource density to increase. Here, we provide a first test of these predictions in a field community consisting of a scale insect and its two specialist parasitoids, Aphytis melinus (the IG predator) and Encarsia perniciosi (the IG prey). The shared resource, California red scale, is a pest of citrus, and its productivity varies across a threefold range among citrus cultivars. We examined both absolute and relative densities of parasitoids along this natural gradient of scale productivity in three citrus cultivars (orange, grapefruit and lemon). Although both parasitoid species were found in all three cultivars, their abundances reflected those predicted by IGP theory: the IG prey species dominated at low productivity and the IG predator dominated at high productivity. This relationship was caused by an increase in Aphytis density with productivity. In addition, the density of scale increased with the dominance of the IG predator. These results from a field system demonstrate the important dynamic outcomes for food webs with IGP.

1. Visual surveys for small organisms on complex substrates often yield serious underestimates of true counts. When both visual counts (relative estimates of abundance) and absolute counts can be obtained from the same sample, however, the visual counts can be calibrated such that absolute estimates can be obtained in the future from visual surveys alone. 2. A method is presented for converting quick, timed, visual counts of a sedentary insect on a shrub into absolute estimates of abundance. 3. Analogies were drawn from simple, well-known predation theories to develop a two-parameter non-linear model. Parameter estimates were obtained by both inverse prediction and direct estimation methods; the latter were found to yield more accurate predictions of absolute abundance. 4. The calibration model is mechanistic in its approach, and thus has potential for application in other systems in which all individuals are visible, but able to be missed during timed counts.

Population cycles have been remarkably resistant to explanation, in part because crucial experiments are rarely possible on appropriate spatial and temporal scales. Here we show how new approaches to nonlinear time-series analysis can distinguish between competing hypotheses for population cycles of larch budmoth in the Swiss Alps: delayed effects of budmoth density on food quality, and budmoth–parasitoid interactions. We re-examined data on budmoth density, plant quality, and parasitism rates. Our results suggest that the effect of plant quality on budmoth density is weak. By contrast, a simple model of budmoth–parasitoid interaction accounts for 90% of the variance in budmoth population growth rates. Thus, contrary to previous studies, we find that parasitoid–budmoth interaction appears to be the dominant factor driving the budmoth cycle.

A major problem in insect pest and weed management is uncertainty. Managers are faced with three main types of uncertainty: uncertainty about biological and environmental processes, and observational uncertainty. Active adaptive management (AAM) is management with a deliberate plan for learning about the managed system, so that management can be improved in the face of uncertainty. We discuss the potential benefits of applying AAM to insect pest and weed control with reference to a number of examples. We first address the possible uses for AAM in biological control, with particular reference to agent selection and release. We also propose applying AAM methods to resistance management and to spatial strategies for pest control. We conclude with an overview of AAM, a discussion of some of the potential limitations to its use in pest management, and the possibilities for increased implementation of AAM in the future.

Summary 1. This paper develops and tests in the field a model that predicts the oviposition rate and the rate of egg maturation of a synovigenic parasitic wasp during a foraging period. The parasitoid is Aphytis melinus, the highly successful biological control agent of California redscale (Aondiniella aurantii), a pest of citrus worldwide. 2. Females were sampled in the interior canopy of grapefruit trees either just before and at the end of the foraging period over 2 days and were dissected to determine the starting and ending eggload distributions. A group of females was caught before the onset of activity and kept in vials in the field in trees with honey but without access to hosts during the foraging period. Their eggload at the end of the day was used to estimate the egg maturation rate during the foraging period. 3. Two stochastic models are used to predict the eggload distribution at the end of the day. Both use the observed starting eggload distribution, the observed length of the foraging period and the estimated rate of egg maturation. The model providing the better fit uses an oviposition rate which is an increasing function of the eggload. 4. The eggload does not attain a steady state distribution during a foraging period. One-third to one-half of the population is predicted to experience egg-limitation at some time during the foraging period. Five percent of the population will experience egg-limitation a second time within a single day. 5. The common occurrence of egg-limitation over a single day and the relatively high rate of change of states between egg- and time-limitation imply that the rate of nutrient acquisition and use are likely to be subject to strong evolutionary pressures.

Ecology is a leading discipline in the synthesis of diverse knowledge. Ecologists have had considerable experience in bringing together diverse, multinational data sets, disciplines, and cultural perspectives to address a wide range of issues in basic and applied science. Now is the time to build on this foundation and invest in ecological synthesis through new national or international programs. While synthesis takes place through many mechanisms, including individual efforts, working groups, and research networks, centers are extraordinarily effective institutional settings for advancing synthesis projects.

Population cycles have long fascinated ecologists. Even in the most-studied populations, however, scientists continue to dispute the relative importance of various potential causes of the cycles. Over the past three decades, theoretical ecologists have cataloged a large number of mechanisms that are capable of generating cycles in population models. At the same time, statisticians have developed new techniques both for characterizing time series and for fitting population models to time-series data. Both disciplines are now sufficiently advanced that great gains in understanding can be made by synthesizing these complementary, and heretofore mostly independent, quantitative approaches. In this paper we demonstrate how to apply this synthesis to the problem of population cycles, using both long-term population time series and the often-rich observational and experimental data on the ecology of the species in question. We quantify hypotheses by writing mathematical models that embody the interactions and forces that might cause cycles. Some hypotheses can be rejected out of hand, as being unable to generate even qualitatively appropriate dynamics. We finish quantifying the remaining hypotheses by estimating parameters, both from independent experiments and from fitting the models to the time-series data using modern statistical techniques. Finally, we compare simulated time series generated by the models to the observed time series, using a variety of statistical descriptors, which we refer to collectively as “probes.” The model most similar to the data, as measured by these probes, is considered to be the most likely candidate to represent the mechanism underlying the population cycles. We illustrate this approach by analyzing one of Nicholson’s blowfly populations, in which we know the “true” governing mechanism. Our analysis, which uses only a subset of the information available about the population, uncovers the correct answer, suggesting that this synthetic approach might be successfully applied to field populations as well.

Continuous-time, age structured, host–parasitoid models exhibit three types of cyclic dynamics: Lotka–Volterra-like consumer-resource cycles, discrete generation cycles, and “delayed feedback cycles” that occur if the gain to the parasitoid population (defined by the number of new female parasitoid offspring produced per host attacked) increases with the age of the host attacked. The delayed feedback comes about in the following way: an increase in the instantaneous density of searching female parasitoids increases the mortality rate on younger hosts, which reduces the density of future older and more productive hosts, and hence reduces the future per head recruitment rate of searching female parasitoids. Delayed feedback cycles have previously been found in studies that assume a step-function for the gain function. Here, we formulate a general host–parasitoid model with an arbitrary gain function, and show that stable, delayed feedback cycles are a general phenomenon, occurring with a wide range of gain functions, and strongest when the gain is an accelerating function of host age. We show by examples that locally stable, delayed feedback cycles commonly occur with parameter values that also yield a single, locally stable equilibrium, and hence their occurrence depends on initial conditions. A simplified model reveals that the mechanism responsible for the delayed feedback cycles in our host–parasitoid models is similar to that producing cycles and initial-condition-dependent dynamics in a single species model with age-dependent cannibalism.

Dynamic energy budget (DEB) models describing the allocation of assimilate to the competing processes of growth, reproduction and maintenance in individual organisms have been applied to a variety of species with some success. There are two contrasting model formulations based on dynamic allocation rules that have been widely used (net production and net assimilation formulations). However, the predictions of these two classes of DEB models are not easily distinguished on the basis of simple growth and fecundity data. It is shown that different assumptions incorporated in the rules determining allocation to growth and reproduction in two classes of commonly applied DEB models predict qualitatively distinct patterns for an easily measured variable, cumulative reproduction by the time an individual reaches an arbitrary size. A comparison with experimental data from Daphnia pulex reveals that, in their simplest form, neither model predicts the observed qualitative pattern of reproduction, despite the fact that both formulations capture basic growth features. An examination of more elaborate versions of the two models, in which the allocation rules are modified to account for brief periods of starvation experienced in the laboratory cultures, reveals that a version of the net production model can predict the qualitative pattern seen for cumulative eggs as a function of mass in D. pulex. The analysis leads to new predictions which can be easily tested with further laboratory experiments.

California red scale, an insect that is a worldwide pest of citrus, is controlled in many areas by parasitoids of the genus Aphytis. In southern California, Aphytis lingnanensis provided inadequate control of red scale in inland valleys. Aphytis melinus was introduced, competitively displaced A. lingnanensis within a few red scale generations, and caused satisfactory biological control. Aphytis melinus can obtain female offspring from smaller-sized scale than A. lingnanensis, and we present a stage-structured parasitoid-host model in which the two parasitoid species are the same except for A. melinus's size-dependent advantage in sex allocation. This model can account for the competitive displacement of A. lingnanensis in such a short time and the improvement in biological control. Aphytis melinus can also obtain an additional female egg from larger red scale, and this increases its advantage in competition, the speed of displacement, and the degree of host suppression. We examine the effects of other mod...

It has been argued that ecological theory has not been useful to the practice of biological control. The purpose of this article is to show how recent theoretical advances may reverse this situation. We first discuss four issues that have arisen in the development of theory for biological control. (1) Recent work has clarified and resolved earlier disagreements concerning the effect of aggregation of the parasitoid to local host density on the stability of parasitoid-host models; this work emphasizes that such aggregation increases the ability of the parasitoid to reduce pest density. (2) There has been disagreement over the conditions under which stability, in the mathematical sense and on a local spatial scale, is an appropriate goal for classical biological control of insect pests, and whether a metapopulation may sometimes provide a more appropriate framework. We also comment on (3) relative size of refuges, which has been proposed as a unifying concept, and (4) density dependence and ratio dependence. We then discuss recent models using a stage-structured approach, particularly those that compare potential biological control agents or agents that have been differentially successful in practice. We argue that this approach has already produced valuable insights into the factors operating in several field situations. It demonstrates the importance of identifying which pest stages are most injurious to the crop, since the natural enemy that wins in competition may not be the most effective at suppressing the crucial pest stage(s): in general, the winning parasitoid reduces the density of the host stage attacked by its competitor below the level at which the latter can maintain a positive growth rate when at low density. A useful criterion is that pest equilibrium density is suppressed most by the parasitoid species that needs the fewest host individuals to allow a female parasitoid to replace herself in the next generation. Caveats are that this may apply only under equilibrium conditions and that the pest stage most suppressed is the one we wish to control. We discuss the connection between successful biological control and evolutionary considerations.

Red scale, an insect pest of citrus, is under control by the parasitoid Aphytis melinus in many areas, and in our study area the interaction appears dynamically stable. The bark on the interior branches and trunk of trees provides a partial refuge for red scale, which are rarely attacked there by the parasitoid. In a grapefruit grove, we carried out a two-way experiment in which we manipulated the refuge population (present or removed) and either left trees connected with the rest of the grove or isolated individual trees with cages to test for metapopulation effects. The experiment ran for 17 mo, encompassing three generations of scale. Scale density in the exterior of refuge-removed trees decreased by about 60%. However, neither removal of the refuge population nor isolation of individual trees increased the temporal variability of the scale population in the exterior or led to drift in population density. Indeed, removal of the refuge population caused a decrease in temporal variability. We conclude th...

This paper considers the relationship between the demographic mechanisms of population control and the energetics of the individuals who comprise the population. We examine the equilibrium properties of a class of structured population models in which individuals compete for some environmental resource (such as food) and demonstrate that population demography is independent of the nature of the feedback loop which establishes the equilibrium state. We thus derive general insights into the influence exerted by individual energetic and allocation strategies on population average demographic characteristics. We show that models of individual energetics which produce apparently very similar predictions at the individual level can result in very different behaviour at the population level. In addition, we observe that different models of individual mortality can imply marked differences in population demography and that the common assumption of constant mortality can be responsible for potentially unrealistic model behaviour. Our results emphasise the substantial data requirements for parameterising and testing individual-based models.

In this paper, we investigate whether a stage-structured population model can explain major features of dynamics of the herbivores Daphnia galeata and Bosmina longirostris reared under controlled laboratory conditions. Model parameters are determined from independent individual-based information gleaned from the literature on feeding, growth, reproduction, and survivorship of these herbivores. We tested predictions of our model against published observations on the dynamics of laboratory populations. The feeding protocols used in these experiments present a highly dynamic food environment that rigorously challenges the ability of stage-structured models to predict the dynamics of populations as they approach equilibrium. For both herbivore species, the models correctly predict feasible equilibria and some features of their dynamics (e.g., periodicity, cycle amplitude, demography, and fecundity) for experiments in which the species were raised in isolation and food transfers were relatively frequent (at least one transfer per instar). With frequent food transfers, the model also correctly predicts coexistence of the herbivores during competition experiments and suggests a novel mechanism for coexistence. The model fails to predict correctly single-species dynamics and the outcome of competition in experiments where food transfers were infrequent and utilization of internal reserves by individuals in the populations must have been high.

A common measure of the temporal variability of a population is the standard deviation of the logarithms of successive estimated population sizes, ln(Dt). This measure overestimates true temporal variability (the standard deviation of the logarithms of true population density, ln[Δt]) because it is contaminated by spatial variance (variability among samples taken on the same date). The random error in Dt causes an overestimation of temporal variance, both directly and also indirectly, by causing ln(Dt) to underestimate ln(Δt). Both problems are more severe if spatial variance is large or the sample size, on a date, is small. We develop an alternative estimator, which uses an estimate of spatial variance to correct for both problems. To evaluate it, we sampled from simulated populations with a wide range of clumping. The results show that the standard estimate can be badly biased. The new estimator is much better and is quite accurate over a broad range of conditions. Our results suggest a reanalysis of so...

California red scale is suppressed to very low densities by the parasitoid Aphytis melinus. The system also appears stable. We report on an experimental test of the hypothesis that stability is caused by a refuge for scale. In a grapefruit grove in southern California in 1984-1985, the bark in the interior part of the tree provided a partial refuge from parasitism. Scale were -100 times denser there than in the exterior of trees. In a field experiment, we removed Argentine ants from some blocks of trees to test whether (1) ants caused the refuge by interfering with Aphytis and (2) the expected reduction in scale density in the refuge would lead to an unstable interaction in the exterior. We also tested for density- dependent parasitism, host mutilation, and predation by analyzing data from samples and from scale placed in the field. The temporal variability of the scale was at the low end of the range recorded in field populations. The experiment provided some evidence in support of the refuge hypothesis. The population in the refuge fluctuated much less than that in the exterior. Ant exclusion led to increased parasitism and lower scale density in the interior, and to increased fluc- tuations in abundance in the refuge and exterior. However, these changes were relatively small and perhaps temporary, suggesting that (1) ants are not the main cause of the refuge and that (2) we did not reduce the refuge density enough to determine whether the system would go unstable in the absence of the refuge population. Parasitism, host mutilation, and predation rates on scale showed no temporal density dependence, either direct or delayed, though detection of such patterns is difficult. Possible alternative stabilizing mechanisms include size-dependent interactions between red scale and Aphytis.

Population regulation is a fundamental process related to most phenomena in ecology, including evolutionary ecology. I review the conceptual basis for defining reg- ulation as bounded fluctuations in abundance, in contrast to the unbounded fluctuations of random-walk populations. Regulation arises as a result of potentially stabilizing density- dependent processes, even when brought about by "non-equilibrium" mechanisms. Al- though the phenomenon is unambiguous in theory, detecting regulation by finding evidence for density dependence in a series of population estimates faces unsolved statistical prob- lems. So, while there is growing evidence for widespread regulation, severe detection prob- lems remain. I illustrate these with data from bird populations. Whether regulation is typically achieved by local stabilizing mechanisms or via metapopulation dynamics remains to be determined. I summarize recent studies on a particularly well-regulated system - red scale (Aonidiella aurantii) and its controlling parasitoid, Aphytis melinus. We tested and failed to find evidence for eight hypotheses that might account for the system's stability, including spatial heterogeneity in attack rates, a refuge, and metapopulation dynamics. We also failed to find evidence for density-dependent parasitism, but such density dependence might be still size-structured~rthu host.eipen

In a set of three new papers, Grenfell and collaborators lay bare measles dynamics in England and Wales over 50 years. They use a simple mechanistic model and current statistical techniques to analyse records of measles infections in every town and city, and show that measles dynamics, including the spatial spread of the disease, is astonishingly clockwork like, and the underlying processes are remarkably simple.

Most species live in species-rich food webs; yet, for a century, most mathematical models for population dynamics have included only one or two species1,2,3. We ask whether such models are relevant to the real world. Two-species population models of an interacting consumer and resource collapse to one-species dynamics when recruitment to the resource population is unrelated to resource abundance, thereby weakening the coupling between consumer and resource4,5,6. We predict that, in nature, generalist consumers that feed on many species should similarly show one-species dynamics. We test this prediction using cyclic populations, in which it is easier to infer underlying mechanisms7, and which are widespread in nature8. Here we show that one-species cycles can be distinguished from consumer–resource cycles by their periods. We then analyse a large number of time series from cyclic populations in nature and show that almost all cycling, generalist consumers examined have periods that are consistent with one-species dynamics. Thus generalist consumers indeed behave as if they were one-species populations, and a one-species model is a valid representation for generalist population dynamics in many-species food webs.

Several special cases of a general model in which two parasitoid species attack different developmental stages of a single host species are presented. The inclusion of different mathematical forms of a maturation weighting function allows us to investigate the effect of several aspects of variation in immature stage durations on the outcome of competitition between the parasitoids. The two parasitoid species cannot coexist if the host developmental stages are fixed in duration. The outcome of competition depends in part on the relative duration of the two stages attacked by the parasitoid species. However, coexistence is possible if there is sufficient variation in the time that different host individuals remain in each stage. Distributed host developmental delays promote coexistence because they cause the host population to be composed of a mixture of host types with different relative egg versus larval stage durations. Each host type is thus largely available to only one of the parasitoid species.

The rapid global loss of natural habitats and biodiversity, and limited resources, place a premium on maximizing the expected benefits of conservation actions. The scarcity of information on the fine-grained distribution of species of conservation concern, on risks of loss, and on costs of conservation actions, especially in developing countries, makes efficient conservation difficult. The distribution of ecosystem types (unique ecological communities) is typically better known than species and arguably better represents the entirety of biodiversity than do well-known taxa, so we use conserving the diversity of ecosystem types as our conservation goal. We define conservation benefit to include risk of conversion, spatial effects that reward clumping of habitat, and diminishing returns to investment in any one ecosystem type. Using Argentine grasslands as an example, we compare three strategies: protecting the cheapest land (“minimize cost”), maximizing conservation benefit regardless of cost (“maximize benefit”), and maximizing conservation benefit per dollar (“return on investment”). We first show that the widely endorsed goal of saving some percentage (typically 10%) of a country or habitat type, although it may inspire conservation, is a poor operational goal. It either leads to the accumulation of areas with low conservation benefit or requires infeasibly large sums of money, and it distracts from the real problem: maximizing conservation benefit given limited resources. Second, given realistic budgets, return on investment is superior to the other conservation strategies. Surprisingly, however, over a wide range of budgets, minimizing cost provides more conservation benefit than does the maximize-benefit strategy.

This chapter contains sections titled: Introduction Background to global conservation priority schemes Methods in relation to goals Thresholds for identifying priority regions Scoring systems for identifying priority regions General issues relating to existing approaches Return on investment

It is well known that the model equilibrium in the Nicholson-Bailey framework for parasitoid-host interactions can be stabilized if there is variation in the risk of parasitism among individual hosts. We show that the shape of the distribution of risk among hosts is crucial in determining stability. Stability for all values of the reproduction rate R of the host requires the distribution to be skewed, with a modal risk of zero. As a consequence, a distribution of risk with nonzero mode but otherwise sufficiently high variability will not stabilize the host-parasitoid equilibrium for certain values of R. We also develop a new, simple, and general criterion for stability, according to which the host-parasitoid equilibrium is stable if and only if the adult host equilibrium density increases as host reproductive rate R increases. This reinforces previous results that skewed risk of the type needed for stability reduces parasitoid efficiency and hence the parasitoid's ability to suppress the host. Finally, we identify appropriate measures that can be made in the field to relate skew in risk of parasitism to stability.

We analyze a metapopulation model of the interactions between Lotka-Volterra-type prey and predators that occur in two environmentally distinguishable patches and are linked by migration. Environmental differences between the patches tend to stabilize the otherwise neutrally stable model by causing the per capita immigration rate on a patch to be temporally density-dependent, partly as a consequence of out-of-phase fluctuations in density. However, the environmental differences can also lead to indirect effects on the temporal dependence of per capita prey death rate on prey density in each patch and on temporal dependence of per capita predator birthrate on predator density in each patch. Spatially density-dependent movement by the prey can be either uniformly destabilizing or initially stabilizing and then destabilizing as the degree of density dependence increases, depending on the overall rate of prey movement. Aggregation by the predator to the patch with more prey modifies one or more of the three processes listed above. Typically, weak aggregation is stabilizing, and strong aggregation is destabilizing. Aggregation can also render unstable an initially stable model. We conclude that metapopulation and single-population models are not good analogues of each other and that predator aggregation affects the two types of models via different mechanisms.

Species-area relationships (SARs) are fundamental to the study of key and high-profile issues in conservation biology and are particularly widely used in establishing the broad patterns of biodiversity that underpin approaches to determining priority areas for biological conservation. Classically, the SAR has been argued in general to conform to a power-law relationship, and this form has been widely assumed in most applications in the field of conservation biology. Here, using nonlinear regressions within an information theoretical model selection framework, we included uncertainty regarding both model selection and parameter estimation in SAR modeling and conducted a global-scale analysis of the form of SARs for vascular plants and major vertebrate groups across 792 terrestrial ecoregions representing almost 97% of Earth's inhabited land. The results revealed a high level of uncertainty in model selection across biomes and taxa, and that the power-law model is clearly the most appropriate in only a minority of cases. Incorporating this uncertainty into a hotspots analysis using multimodel SARs led to the identification of a dramatically different set of global richness hotspots than when the power-law SAR was assumed. Our findings suggest that the results of analyses that assume a power-law model may be at severe odds with real ecological patterns, raising significant concerns for conservation priority-setting schemes and biogeographical studies.

We construct a model of an aquatic plant-herbivore system which takes explicit account of the cycling of the element limiting plant growth. The work is motivated by experiments on the population dynamics of the waterflea Daphnia where the Daphnia population is regulated by the availability of algal food, but the algae are phosphorus limited. The model is used to investigate the possibility that the system may be stabilised by a mechanism in which the Daphnia constitute a temporary phosphorus “sink”. We conclude that this is unlikely if the system is closed to external input of the nutrients limiting plant growth.

In many consumer-resource systems the consumer population has synchronized reproduction at regular intervals (e.g., years) but consumes the resource and dies continuously, while the resource population grows continuously or has overlapping generations that are short relative to the time between consumer reproductive events. Such systems require "semi-discrete" models that have both discrete and continuous components. This paper defines and analyzes a canonical, semi-discrete model for a widespread class of consumer-resource interactions in which the consumer is a discrete breeder and the resource reproduction can be described continuously. The model is the analog of the Nicholson-Bailey and Lotka-Volterra models for discrete and continuous systems, respectively. It thereby develops the basis for understanding more realistic, and hence more complex, semi-discrete models. The model can display stable equilibria, consumer-resource cycles, and single-species-like overcompensation cycles. Cycles are induced by high maximum fecundity in the consumer. If the resource grows rapidly and the consumer has high maximum fecundity, the model reduces to a single-species discrete-time model of the consumer, which can exhibit overcompensation cycles. By contrast, such cycles in discrete consumer-resource models typically occur only in the resource once the consumer is extinct. Also unlike a common class of discrete models that do not display consumer-resource cycles with periods below four years, semi-discrete models can exhibit consumer-resource cycles with periods as short as two years.

1. Laboratory experiments and field studies were conducted to explain the coexistence of an endoparasitoid, Encarsia perniciosi Tower, and an ectoparasitoid, Aphytis melinus DeBach, both of which were introduced into California to control the California red scale, Aonidiella aurantii (Mask.). 2. Encarsia parasitized all scale stages but it preferred first and second instar scales. This is in contrast to Aphytis melinus, in which previous studies have shown that it parasitizes second and third instar females and second instar males but prefers third instar female scales. Encarsia developed most rapidly when it parasitized an early second instar and slowest when it parasitized the mature female scale. However, on early second instar scales it was about 80% as fecund as a wasp that emerged from a mature female scale. 3. Second instar scales parasitized by Encarsia were accepted by Aphytis as readily as unparasitized scales. 4. Encarsia did not distinguish between unparasitized hosts and those previously parasitized by Aphytis. 5. Encarsia always outcompeted by Aphytis when both species parasitize the same host. 6. Encarsia prefers scale on stems whereas Aphytis prefers those on leaves and fruits. This, too, may be a result of interspecific competition with Aphytis. 7. The partitioning of the scale resource by the two species explains why they coexist in coastal southern California but it does not explain why Encarsia disappeared from citrus groves in the inland valleys coincident with the introduction of Aphytis melinus into southern California.