William Gurney

POPULATION PERSISTENCE IN RIVERS AND ESTUARIES

A wide variety of organisms inhabit streams, rivers, and estuaries where they are continually subjected to downstream drift. It is well known that when this is the only transport process, extinction is inevitable (the “drift paradox”). Using a series of analytical and numerical models, representing a range of hydrodynamic scenarios, we demonstrate that the action of diffusive dispersal can permit persistence in an advective environment. The mechanism underlying this phenomenon is that diffusive dispersal can allow a proportion of the population to reproduce close to their natal location. For well- and poorly mixed non-tidal systems we establish approximate analytic conditions for diffusion-mediated persistence both throughout the water column and in a benthic boundary layer. Although tidal forcing results in residual landward flow near the base of the water column, we find that this has little effect on persistence, which is respectably approximated by our analytic results. We apply these analytic results to four hydrodynamically disparate systems: a stream (Broadstone Stream [UK]), a river (Christiana Creek [USA]), a shallow estuary (Ythan [UK]) and a deep fast-flowing estuary (Saco River [USA]). Using parameters derived from published studies we examine the persistence of a number of real and hypothetical organisms in these systems and identify those for which diffusively mediated persistence is a realistic possibility. We note that such persistence is only likely when advection is low or horizontal dispersal is high.

The regulation of inhomogeneous populations

A number of authors have argued that dispersal may play a key role in the regulation of populations of some species. In this paper we examine, on an ecological time scale, mechanisms whereby a population existing in an inhomogeneous environment may use dispersal to regulate its size below the carrying capacity set by the supply of available nutrients. We show that dispersal produced by wholly random motion is incapable of exerting any stabilizing influence, but that the introduction of a suitable non-linearity into the dispersal behaviour of a species whose characteristics are otherwise wholly linear can lead to stabilization under a wide range of conditions.

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.

AN INVULNERABLE AGE CLASS AND STABILITY IN DELAY-DIFFERENTIAL PARASITOID-HOST MODELS

The models were motivated by a study of red scale, an insect pest of citrus in southern California, and its successful parasitoid, Aphytis melinus. The system appears to be stable, but the usual stabilizing mechanisms suggested appear to be absent. We hypothesized that, in combination with overlapping generations, the scales invulnerability to attack by Aphytis at several stages, particularly the long-lived reproductive adult stage, might explain the systems stability. In the model both species have a juvenile and an adult stage. Generations overlap and the host and the parasitoid are not synchronous. The model has the form of coupled, delayed differential equations representing the two populations. The key parameters determining stability are the duration of the juvenile parasitoid stage (the developmental lag) and of the invulnerable adult stage of the scale, relative to the duration of the juvenile scale stage. We conclude that an invulnerable adult stage in the scale is always stabilizing because in its presence some stable parameter space exists that does not occur in its absence. The longer the invulnerable adult stage is relative to the predator developmental lag, the more likely stability is. Stability is unlikely unless the adult scale stage is significantly longer than the juvenile stage. Stability is less likely as adult parasitoids live longer or as scale fecundity increases, but the system is less sensitive to these parameters than to the duration of the invulnerable class. An invulnerable juvenile stage can also add stability, but only for a narrow range of parameter values that are not likely in real systems. Given the parameter values in the red scale-Aphytis interaction in southern California, the invulnerable adult class is not likely to explain the observed stability, but probably contributes to it. This mechanism buys increased stability at the cost of higher pest equilibrium; we discuss the apparent tension between stability and successful pest control.

Interference and generation cycles

In this paper we re-examine the derivation of an interference limited functional response due to Beddington (1975 J. Anim. Ecol. 44, 331–340) and extend his treatment to more realistic models of the interference process. We study the dynamic effects of interference in the context of a structured population model and show that the stabilising effect of interference against paradox of enrichment cycles is unaffected by age-structure. We also demonstrate that single generation cycles are much more weakly affected by interference than prey-escape cycles. Thus the net effect of weak interference is to prevent single generation cycles from being masked by the prey-escape cycles which would otherwise dominate the population dynamics.

The systematic formulation of population models for insects with dynamically varying instar duration

We develop a formalism for insect population dynamics which covers the situation where maturation from one instar to its successor is triggered by weight gain and not by chronological age. We specify assumptions which result in the instantaneous “subpopulations” of various instars obeying delay-defferential equations with time delays (representing instar duration) which are themselves dynamic variables, changing in response to the availability of food. We demonstrate the stabilizing potential of variable time delays by studying an idealised two-stage model in which maturation to the adult stage occurs after absorption of a given (fixed) quantity of food.

Fluctuation periodicity, generation separation, and the expression of larval competition

A suite of models has been formulated to investigate the dynamic consequences of the various routes by which uniform larval competition for food can find demographic expression. It is found that while delayed expression through the vital rates of later age classes gives rise to limit cycles containing multiple overlapping generations, immediate expression via changes in the death or growth rates of the larvae themselves leads to self-sustaining single generation limit cycles. When immediate expression of competition is combined with high adult fecundity and short reproductive lifespan the amplitude of the single generation cycles is so large that they constitute a series of evenly spaced discrete generations, which is maintained indefinitely even in the absence of external cues.

Aggregation and Stability in Metapopulation Models

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.

Modelling compensatory growth

1. We formulate a simple, physiologically based model to investigate the phenomenon of compensatory growth. 2. The model is based upon two key assumptions. First, that an individual partitions net assimilate between two tissue types: those which can and those which cannot be remobilized once laid down. Second, that the individual modulates its behaviour and physiology in response to the instantaneous ratio of mobilizable to non-mobilizable tissues. 3. The model is parameterized for salmonids from published studies of their energetics. Data from aquaculture studies of fish growth under conditions of fluctuating food are used to test the model. Using a common parameter set, the model successfully reproduces the growth patterns observed in 16 different feeding regimes.

The population dynamics of ecosystem engineers

Although the literature contains many examples of habitat modification, there are few systematic studies of the role of such processes in the creation and maintenance of natural habitat, A key element in the development of such models is an understanding of the dynamics of the habitat modifying species, sometimes called ecosystem engineers. In this paper we present a group of strategic models of the population dynamics of a species whose ability to survive depends on modifying its own habitat. We show that such a strategy can lead either to a deterministically stable equilibrium or to endogenous cycles. We identify the conditions leading to both outcomes and discuss their interpretation in the context of examples of habitat modification to be found in the literature. We examine the feasibility of parameterising models of habitat modification from the information currently in the literature, and suggest a number of areas in which new observations or experiments would seem to be required.