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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.

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.

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.

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.

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

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.

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.

In the preceding paper (McCauley et al. 1990) we developed a new model for the growth and fecundity of Daphnia based on a quantitative review of short-term physiological rates and energy allocation for D. pulex. In this paper, we formulate a fully dynamic version of this model and test its predictions against experimentally observed growth and fecundity schedules obtained independently under a variety of different experimental protocols. Preliminary testing falsifies two simplifying hypotheses made in our original development and we propose modifications of these hypotheses. With the aid of these modifications our model yields predictions that are in good agreement with a large body of data on the growth and fecundity schedules of individual D. pulex. Although our model contains 18 parameters, the values of the great majority are independently determined from short-term physiological measurements, leaving only two as freely adjustable @'fitting parameters.@' The target dataset, which contains four complete growth curves (@?80 observations) and 32 growth or fecundity characterizations, thus provides a stringent test of the model, and our success in matching our predictions to it provides strong evidence that measurements of short-term physiological rates can be used successfully as predictors of long-term growth and fecundity.

Patterns of growth, development, and reproduction have been observed in many Daphnia species, and there have been some attempts to explain them using models that take into account rates of intake, assimilation, maintenance, and energy allocation rules. We show, however, that existing models cannot capture some essential features of individual growth, especially under conditions of low food supply that are typical of field conditions. These features include: (1) a sigmoid growth curve, and (2) the time to starvation or the performance of individuals during periods of low food availability. We propose and test a new hypothesis based on the idea that allometric relationship for physiological rates are stage dependent. We show that ingestion rates increase much faster with juvenile body size than with adult body size for several Daphnia species. Existing data suggest that allometric relationships for respiration are not stage dependent, and we derive a maintenance function that takes into account overheads associated with growth and basal metabolic rates. The new allometric relationships for ingestion and maintenance, along with an accurate description of the onset of maturity and partitioning of energy between growth and reproduction, can account for the sigmoid growth pattern displayed by Daphnia. Existing models cannot explain Daphnia's performance when food availability is low, and this led us to examine how Daphnia stores energy and uses reserves. Our review synthesizes disparate observations on the structure and dynamics of reserves, and forms the basis for a new model of Daphnia pulex.

In a population convergence experiment, the initial densities of adults of the predatory backswimming bug Notonecta hoflmanni were set above and below a putative equilibrium density in stock tanks. The experiment was done at two constant rates of food supply (wingless Drosophila) for the larger instars (in natural pools Notonecta feed mainly on terrestrial arthropods that fall on the water surface). It was predicted that the densities of the resulting populations would converge on an equilibrium set by the rate of food supply for the larger instars. The tanks also contained zooplankton (mainly Daphnia), which were the main food supply of the smaller instars of Notonecta. The resulting over- wintering populations converged towards the appropriate equilibrium densities, via density- dependent and food-dependent fecundity and then cannibalism. However, the populations overshot their equilibria, producing overconvergence. In natural populations such over- convergence might tend to produce 2-yr cycles in abundance. Overconvergence resulted from the insensitivity of the survivorship of the original adults (at least over the short term) to differences in food supply between treatments, allowing them to continue to affect (via cannibalism and reproduction) the eventual density of the new overwintering popu- lation. Because Notonecta population density was determined by the externally supplied, locally uncoupled food supply, even though the early instars depended for food largely upon dynamic populations of zooplankton, the dynamics of the Notonecta population were simpler than a description of the food web might suggest.

Red scale populations in eight grapefruit trees in a grove in southern Cali- fornia were sampled over 18 mo. We established that the interior of the trees was an area of partial refuge from parasitism by the major control agent, the parasitoid Aphytis melinus, and also by Encarsia, which was the second major parasitoid in the system. The refuge (interior) population contained >75% of the scale and >90% of the adult scale in the average tree. Parasitism by Aphytis in the exterior (twigs) was 27 times as high as in the refuge for second-instar scale, and 6 times as high for third instars. The differences in instantaneous parasitism rates were greater. Parasitism by Encarsia in the exterior was about twice that in the refuge. A field experiment showed that Aphytis could search in the interior and that it parasitized scales that had been placed there on lemons. Low parasitism rates in the interior may have been caused by the parasitoids' response to the bark substrate. The refuge population may account for the observed stability of the Aphytis-red scale interaction in some citrus groves.

Growth of the backswimmer Notonecta hoffmani is better on a diet of Daphnia pulex than on a diet of Ceriodaphnia reticulata. Offered a choice of these two zooplankton species, Notonecta selects Daphnia or large individuals of either species. To test whether this preference affects prey species and size-classes differently, we measured population changes when the predator and one prey species or the other were placed together in plastic tubs for 7-8 wk. Roughly half of the replicated laboratory populations of Daphnia pulex that were exposed to predation by a constant number and age-class of Notonecta were driven extinct within 8 wk. The remainder of these populations maintained densities similar to those of control populations without predators. Populations surviving at each sampling period partially compensated for mortality caused by predators by small increases in individual fecundity, which maintained their population birth rates at the same level as those of control populations. Fecundity was inversely related to the density of adult Daphnia and to the total biomass of Daphnia. In populations exposed to predation, the other compensatory mechanism was a decrease in the mortality of young from factors (probably starvation) other than predation. Predation reduced the average size of individuals in Daphnia populations and consequently markedly reduced the average biomass. This presumably increased the food per capita available to juveniles and small adults in predation treatments over the level available to their coun- terparts in controls, and hence both reduced mortality from starvation and increased size-related fecundity. Populations exposed to predation appeared to have stable dynamics for varying periods. However, as the experiment progressed, apparently random events in some populations caused the predation rate to exceed Daphnia's ability to compensate, and in each successive intersampling period a few populations were driven extinct. Extinction was probabilistic. Thus both a deterministic and a stochastic framework are required to explain the dynamics of these laboratory populations. Only two of 18 Ceriodaphnia populations were driven extinct. Notonecta instar II had the largest effect on the density of this species and also caused its temporal variability to increase. We have less information on the dynamics of this zooplankter than on D. pulex.

The presence of a physical refuge (an area where mortality due to parasitism is very low) has been demonstrated for California red scale, a pest of citrus. Density of red scale is very high, and parasitism by the principal parasitoid wasp, Aphytis melinus DeBach, is low on the trunk and woody branches of citrus trees as compared with the exterior twigs and leaves. One possible explanation for the low rate of parasitism is that scale in the refuge are less frequently parasitized due to their smaller size. Laboratory experiments show that Aphytis selects larger hosts, and the size distribution of parasitized scale in samples from a citrus grove shows a bias towards larger host individuals in the field. However, size—selectivity can account for only °10% of the observed difference in parasitism rate and thus cannot be the primary explanation for the presence of the refuge.

We investigated size—selective predation upon Daphnia pulex and D. magna by the mosquitofish (Gambusia). The independent variables were the relative size of predator and prey, prey density, and predator satiation. Gambusia actively chose to attack small prey (which we showed to be more profitable). Gambusia's preference increased monotonically, or decreased, or peaked at an intermediate prey size, depending upon fish size, prey size, and fish satiation level. These results contrast with the hypothesis the "gape—limited predators" select the largest prey available, and "size—limited predators" select small or intermediate—sized prey. Optimal diet theory predicts that a predator should drop less profitable prey items from the diet at higher prey densities. In contrast, Gambusia maintained a mixed diet and its preferences did not change in response to changes in either the absolute or the relative abundance of prey. Moreover, the ingestion rate would have been higher if less profitable (larger) prey types had been ignored. Gambusia did sharply alter its size—selective feeding behavior in response to its own satiation level, and we expect that this factor is correlated with prey density in the field. Well—fed fish concentrated their attacks, to a greater degree than starved fish, on small, more profitable prey. They also ingested less biomass per unit time. This last result suggests that maximizing food intake per unit time may not be the goal of well—fed fish, and that different criteria may determine the profitability of prey at different prey densities.

A recent monograph by Hurlbert raised several problems concerning the appropriate design of sampling programs to assess the impact upon the abundance of biological populations of, for example, the discharge of effluents into an aquatic ecosystem at a single point. Key to the resolution of these issues is the correct identification of the statistical parameter of interest, which is the mean of the underlying probabilistic "process" that produces the abundance, rather than the actual abundance itself. We describe an appropriate sampling scheme designed to detect the effect of the discharge upon this underlying mean. Although not guaranteed to be universally applicable, the design should meet Hurlbert's objections in many cases. Detection of the effect of the discharge is achieved by testing whether the difference between abundances at a control site and an impact site changes once the discharge begins. This requires taking samples, replicated in time, Before the discharge begins and After it has begun, at both the Control and Impact sites (hence this is called a BACI design). Care needs to be taken in choosing a control site so that it is sufficiently far from the discharge to be largely beyond its influence, yet close enough that it is influenced by the same range of natural phenomena (e.g., weather) that result in long-term changes in the biological populations. The design is not appro- priate where local events cause populations at Control and Impact sites to have different long-term trends in abundance; however, these situations can be detected statistically. We discuss the assumptions of BACI, particularly additivity (and transformations to achieve it) and independence.

If a predator eats more prey at higher prey densities, grows more as a consequence, and then kills more prey because of its larger size, this produces a developmental response to prey density. In its functional response a predator sea shore snail caused a decreasing percentage mortality as prey (barnacle) density increased (type 2 response). This causes instability in prey numbers. However, when account was taken of the developmental response in a hypothetical pseudosnail, the prey mortality caused over a year by a single—predator as a function of prey density, was different from that expected on the basis of the functional response alone. There is a tendency for the mortality to be a fairly constant percentage of prey density over a rather large range of prey densities. This results in the reduction of the destabilizing effect. Problems of integrating these responses with the numerical response and of generalizing the results are discussed. See full-text article at JSTOR

The predatory behavior of a ladybird, Coccinella, was examined as it preyed upon varying ratios of two aphid species, Acrythosiphon pisum and Aphis fabae. Experiments were done in petri dishes and on bean plants. The ladybirds attacked the two prey species in direct proportion to their relative abundance. There was little variability among predators in a given treatment. Training had no effect on the subsequent diets of the predators, and all treatments provided a very good fit to a simple no—switching" model. Predation on each species was density independent. This simple type of predation contrasts markedly with the results of earlier experiments on predatory snails in which variability among predators and a strong training effect produce switching. See full-text article at JSTOR

Regulation is defined as the return of a population to equilibrium density. An operational definition of regulation is convergence to a single density by subpopulations which have been manipulated previously to different densities. The equilibrium density may be fixed or variable. If the equilibrium is variable then regulation may produce instability (numerical inconstancy) and non-density-dependence. Population inertia is the tendency for a population to resist changes away from its current density. If speed of regulation is defined as Isi, the speed of convergence to equilibrium, then inertia is 1/IsI. The evolution of mechanisms of inertia involves changes in the demographic functions, mediated through physiology or behavior, which keep the rate of numerical change low. It is not clear if populations are control systems or non-control systems, which makes the convergence experiment difficult to interpret the- oretically. Experiments and observations are needed which will try to distinguish, among stable populations, between those with tight regulation and those with high inertia. In this note, I examine the concept of regula- tion, and I compare ways in which a population may maintain a rather constant density. Regula- tion may sometimes be the most important pro- cess, but in some circumstances, what I call in- ertia will be of prime importance. I assume that some stable populations exist, though it seems

The plants and Homoptera on three old fields in southeast Michigan were sam- pled. Within fields, correlations between plant and insect diversity were generally weak. But using all samples from three fields, evenness (J) and diversity (H) of the insects were highly correlated with plant evenness and plant diversity, respectively. For example, 72% of the variance in insect H could be accounted for by variation in plant H. Number of species (S) showed a positive but weaker correlation. When correlations were based on the pooled sam- ples from each field, all three statistics for insects were highly correlated with those for the plants. Insect H was also highly correlated with plant structure (foliage height diversity, FHD) over all three fields. These two measures of plant diversity (H and FHD) were highly correlated and were equally good correlates of insect H. Together they accounted for 79% of the variance in insect H. This extends to insects a correlation between plant and animal diversity, already well established for birds and possibly true for lizards and rodents. It leaves open the unresolved question as to whether plant structure or plant species diversity is more important. The diversities of different components of a com- munity seem to be correlated, in the few cases studied, and in particular, animal diversity has been correlated with aspects of the plant diversity. It is not surprising that a greater variety of plants should lead to a greater variety of plant-eaters. However, the reasons for observed correlations between plant structural diversity and animal species diversity are less obvious. In one group of animals the reason ap- pears obvious; different bird species nest and forage at different heights and their diversity is related to the structural diversity of the vegetation (e.g., MacArthur and MacArthur 1961, Recher 1969). In this paper we explore these relationships in in- sects. Plant-sucking bugs (Homoptera) of several old fields were studied because they form a dominant group of insect herbivores in these communities, and because their diversity might be expected to be closely tied to that of plants. Since these insects feed directly on the green plants, unlike the other groups that have been studied, and since at least some of them are host specific (DeLong 1948, Whitcomb 1957), we expected to find correlations with plant species di- versity, but we also measured foliage height diversity (structure). To avoid geographic effects on diversity, and to keep in the same kind of habitat, we sampled several old fields, all within a 1-km radius and all abandoned for the same period of time.