William W. Murdoch

DIVERSITY AND PATTERN IN PLANTS AND INSECTS

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.

Conserving biodiversity efficiently: What to Do, Where, and When

Conservation priority-setting schemes have not yet combined geographic priorities with a framework that can guide the allocation of funds among alternate conservation actions that address specific threats. We develop such a framework, and apply it to 17 of the worlds 39 Mediterranean ecoregions. This framework offers an improvement over approaches that only focus on land purchase or species richness and do not account for threats. We discover that one could protect many more plant and vertebrate species by investing in a sequence of conservation actions targeted towards specific threats, such as invasive species control, land acquisition, and off-reserve management, than by relying solely on acquiring land for protected areas. Applying this new framework will ensure investment in actions that provide the most cost-effective outcomes for biodiversity conservation. This will help to minimise the misallocation of scarce conservation resources.

WHY DO POPULATIONS CYCLE? A SYNTHESIS OF STATISTICAL AND MECHANISTIC MODELING APPROACHES

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.

Community Structure, Population Control, and Competition-A Critique

The paper by Hairston et al. (1960) is examined critically with regard to its premises, logic and internal consistency, and its methodology. It is suggested that, either as conclusions or hypotheses, the major points made in the paper are not acceptable. In the present paper the importance of testability and of operational definitions in ecological hypotheses are stressed.

CYCLIC AND STABLE POPULATIONS: PLANKTON AS PARADIGM

We analyzed over 20 study-years of data from populations of Daphnia and algae in a wide variety of field situations. These systems display three types of dynamic behavior: both populations stable; both populations cyclic; and Daphnia cyclic but algae stable. The last pattern occurs whether we analyze the total amount of algae or only edible algae. There is evidence that this range of dynamics arises from the interaction between Daphnia and its food supply, occurring in systems that are structurally the same; that is, differences in biological rates or time delays, alone, can explain the existence of different dynamic classes. This is particularly the case when different classes occur in the same species in the same environment in different years, or in similar and adjacent habitats at the same time. The cycles thus appear to be internally driven, rather than resulting from external, cyclic, forcing factors. These findings support a basic premise of most mathematical models in ecology. The broad dynamic patterns in cyclic field populations of Daphnia are similar to those found in laboratory populations. The two sets of cycles have very similar periods and (small) amplitudes; both are single-generation cycles (i.e., the period of a cycle is one generation); and both are caused by dominance and suppression, whereby each cohort suppresses reproduction until its density declines sufficiently to allow production of another cohort. The demographic features of laboratory and field cycles are also similar in detail. Since algae are dynamic in the field but not in the laboratory, we cannot conclude that the mechanisms driving laboratory and field cycles are identical. Our hypothesis is that the presence or absence of cycles is determined by the relationships between time delays in Daphnia and other rates in the interacting populations. There is, however, no obvious environmental factor affecting these rates and delays, thereby determining which dynamic class a particular system fits at a particular time. It does not appear that change in the average temperature is the critical factor. Similar single-generation cycles appear to occur in other systems and may be driven by similar dominance-and-suppression mechanisms.

FUNCTIONAL RESPONSE AND STABILITY IN PREDATOR-PREY SYSTEMS

We propose two measures of how stabilizing a functional response is. We suggest that predation be regarded as stabilizing at a prey density of H if the predation rate is increasing then-i.e., if f(H)/H is increasing where f is the functional response. This is equivalent to asking that an increase in prey density results in an increased chance of a given prey being killed by the predator. With Hm as the maximum value of H for which this criterion holds, our measures are Hm and f(Hm). We relate this criterion and these measures to local stability and also to structural stability in a modified Lotka-Volterra model and a general multispecies model. The criteria will be used in detailed models of switching in predators (in the following paper in this issue) and of patchiness.

Aggregation by Parasitoids and Predators: Effects on Equilibrium and Stability

Predators and insect parasites (parasitoids) sometimes aggregate in patches containing high prey (host) densities because they search longer there, causing higher death (parasitism) rates in patches with more prey (hosts). This behavior can stabilize the otherwise unstable, discrete-time, Nicholson-Bailey model, typically at the cost of increasing the host equilibrium density. The key feature that produces both effects in this model appears to be the absence of within-generation dynamics; in particular, parasitoids are not able to reaggregate in response to changes in local host density within the generation. We examine the effects of aggregation on the otherwise neutrally stable Lotka-Volterra model. We allow the parasitoid to reaggregate continually as local host density changes. Aggregation appears as positive covariance between the parasitoid and host density across patches. It affects the model by altering the initially linear functional response. Aggregation always increases parasitoid efficiency and hence reduces host equilibrium density. We examine the effects of aggregation on model stability in several circumstances: (1) the parasitoid responds to a signal ranging from absolute to relative difference in local host density; (2) aggregation is linear or accelerating in response to this signal; (3) the variance of the host distribution is related in various ways to the mean host density (the host may have a Poisson, negative-binomial, or unspecified distribution). When account is taken of the probable limits set on parameter values by theoretical considerations and field conditions, it appears that aggregation is typically destabilizing. Although aggregation reduces host equilibrium density, h*, stability conditions usually require h* to be large. Stability is not affected by the magnitude of the spatial variance of host density, per se, but rather by the rate of change of the variance with respect to the mean. The chances of stability are increased if the parasitoid or predator has an accelerating aggregative response and possibly if it responds to absolute differences in local host density over a wide range of host densities, though the stabilizing effects in the latter case are likely to be weak or limited to small perturbations. We also examine aggregation that is independent of local prey (host) density. The Nicholson-Bailey model can be stabilized if, for example, the distribution of parasitism among patches is highly heterogeneous but unrelated to host density in the patch. Again, strong aggregation increases the Nicholson-Bailey host equilibrium density. Such aggregation has no effect on stability or host equilibrium in our continuous-time model. We discuss critical assumptions in the models. The results point to the need for more information about the signal to which aggregating predators actually respond and about the form of the response in the field.

Theory for Biological Control: Recent Developments

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.

SWITCHING, FUNCTIONAL RESPONSE, AND STABILITY IN PREDATOR-PREY SYSTEMS*

We consider a model for the functional response of a predator feeding on two species of prey. We assume that the predator searches randomly, at constant speed, for randomly distributed prey, but that whether it attacks a contacted prey will depend on the species of the prey, the species of the last meal, and the time since the last meal. We establish a formula for the expected time between meals on species 1, and take the functional response on species 1, the number of species 1 eaten per unit time by a single predator, to be the reciprocal of this. The general formulae are somewhat complicated, but if it is assumed that the probability of attack is independent of time, it is possible to obtain a fairly simple expression for functional response. This functional response is not necessarily stabilizing; it will be if there is a sufficiently strong (relative to the handling times) tendency for the predator to be more likely to attack a contacted prey if it is the species that was eaten last. (More detail is given at the end of the section Switching and Stability.) We then consider relative attack rates (still assuming that preference is independent of time since the last meal) first by taking the ratio of the two functional responses (for species 1 and species 2) and next by regarding the sequence of meals as a Markov chain. The answers are the same: the relative attack rate is a function only of relative density, and switching occurs provided only that the product of the probabilities of attacking the same species as last eaten is greater than the product of the probabilities of attacking the other species. It is possible to have switching and yet not have a stabilizing functional response.

THE PHYSIOLOGICAL ECOLOGY OF DAPHNIA: DEVELOPMENT OF A MODEL OF GROWTH AND REPRODUCTION'

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 Daphnias 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.