STABILITY AND PERSISTANCE OF POPULATIONS AND ASSEMBLAGES: THEORY AND LABORATORY AND FIELD STUDIES A Departmental Thesis Presented to the Faculty of California State University, Hayward In Partial Fulfillment of the Requirements for the Degree Master of Science in Biological Science By Burke A. Strobel .Ttme, 1996 Aknowledgments I would like to thank the Moss Landing Marine Laboratories' librarians Sheila Baldridge and Joan Parker, whose efforts made many important papers available to me. The use ofJay Hager's and Brett Strobel's computers for text and graphics respectively was invaluable to the project. Discussions with Christopher Moyer solidified many of the ideas on disturbances presented. I also thank my committee members for their patience and insights, and, most of all, my wife Katie for her support, understanding, and even courage. 111 Table of Contents Acknowledgments iii Table of Contents IV List of Figures vi I. Introduction 1 IT. Stability Theory: Populations 13 Introduction 13 Carrying capacity 17 Mechanisms 25 Density dependence 29 Detection of density dependence 32 Assumptions 35 Ill. Stability Theory: Paired Interactions 37 Interspecific competition 37 Amensalism 46 IV v Predation 47 Mutualism 66 N. Stability ofMultispecies Interactions 70 Indirect effects 70 V. Stability of Assemblages 76 Considerations 76 Diversity 78 Alternative stable states 81 VI. Conclusion 84 Bibliography 89 List of Figures Figure 1. Gompertz curve of population growth 18 Figure 2. Logistic curve of population growth 19 Figure 3. Holling type I predator functional response 49 Figure 4. Holling type I1 predator functional response 50 Figure 5. Holling type ill predator functional response 51 Figure 6. Lotka-Volterra predator/prey trajectory 53 Figure 7. Predator/prey trajectory (prey: self-limiting; predators: type I1 functional response; d=O.Ol) 57 Figure 8. Predator/prey trajectory (prey: self-limiting; predators: type I1 functional response; d=0.03) 58 Figure 9. Predator/prey trajectory (prey: self-limiting; predators; type I1 functional response, self limiting) 62 vi As many populations persist for long periods, yet remain finite, there can be little doubt that they experience some fonn of density-dependent limitation (Pollard et a!. 1987). I. Introduction Stability of populations and assemblages is a widely assumed trait given the continued presence offamiliar species and associations of species. Holling (1973) identifies two ecological views of natural systems as qualitative and quantitative. The qualitative view concerns itself with presence or absence of populations within an arbitrarily defined system. The continued presence of a species' population within a system is termed persistence. The quantitative view concerns itself with the degree of constancy of numbers of individuals in the species' populations in the system. This concern focuses on two questions: are the observed numbers of individuals constant or fluctuating, and why are they that way, or, stated another way, how do the numbers of individuals respond to forces that could potentially alter them? The first question is a straightforward matter of unbiased observation. Numerical constancy, however, does not, in itself, provide an answer to the second question. The absence of fluctuation can be due to the lack of perturbing forces or the presence of mechanisms that compensate for them. The change in numbers with time is dictated by the strength offorces potentially altering them and the population response to these forces, whether through 1 2 resisting them or recovering from them. Ecologists are divided over which of these predominates in determining population dynamics ( eg. Andrewartha and Birch 1954, Nicholson 1933). It is the population's response to disturbances, when they occur, that defines its stability. References to stability infer the existence of a size that a given population would have in the total absence of disturbance. This is the equilibrium, where the population's per capita rate of increase equals its per capita rate of decrease. The questions whether or not and under what circumstances populations and assemblages are or are not stable or persistant are central to the science of ecology, which attempts to account for organisms' distributions and abundances. As the human species continually occupies new resources and exploits populations of organisms, it becomes increasingly important to consider how other species in an impacted system will respond. They may remain unaltered, increase in number or biomass, decrease, or go extinct. Their numbers could become more or less variable, all to humans' eventual benefit or detriment. Despite the importance of understanding populations' and assemblages' persistance and stability, researchers' conclusions, indeed the entire issue remain vague. Lack of aggreement on definitions for specific terms, nebulous concepts, and preconcieved notions all seem to have added to this lack of clarity regarding ecological persistance and stability. Most of the contributions to stability theory have been by theoreticians. To a lesser extent the predictions made by theory have been investigated in laboratory and 3 field studies, although such predictions have often, without being first demonstrated, formed the basis of investigations of field data (see 'detection of density dependence' below). To some extent field and laboratory studies have in turn guided the development of theory. It is the objective of this review to explore what ecology understands about the dynamics of persistance and stability in populations and assemblages. It will attempt to draw together and give cohesion to the scattered body of theory with the ultimate goal of evaluating the usefulness of the concept of population and assemblage stability. The existence of forces capable of disturbing populations, in the form of environmental variation and catastrophes, is obvious and it is possibly as a result of this observation that the stability qualities of populations and assemblages have traditionally been invoked to explain persistence of populations. Egerton (1973) traces the related concept of the "balance of nature" back to Greek philosophy. The existence offossils of unknown organisms in the geological record first introduced the possibility of extinction to human thought in the 19th century (Egerton 1973). The assumption of stability continued into the 20th century and became central to plant ecology, where it was incorporated into Clement's view of the plant assemblage as a superorganism (Mcintosh 1982). One of the distinguishing traits of such a superorganism was homeostasis, or self regulation that maintains an equilibrium of its parts and processes. 4 Although H. A Gleason advanced an opposing view of populations undergoing separate dynamics and more or less coincidentally co-occuring, his "individualistic concept" was not fully appreciated until the 1950's by such researchers as Whittaker (1956), who examined plant species' distributions along environmental gradients. The assumption of homeostasis in "mature" assemblages of organisms continued ( eg. Margalef 1963, 1974) and many researchers assume that ecological systems are best described by the stability principles of engineers (eg. Berryman 1991). The mathematical formulations ofLotka (1925) and Volterra (1926) stimulated interest in describing situations when interacting populations might be expected to be stable or proceed to extinction. Similar modeling of laboratory insect populations by Nicholson (1933), in conjunction with Lotka-Volterra theory, gave rise to the field of theoretical ecology. Much of theoretical ecology examines models of populations assumed to react in specific ways to their environment. Stability of these models is determined by looking for equilibria. Some researchers have opposed the extrapolation of findings in this body of theory to real systems. They suggest that environmental variation renders the entire equilibrium concept next to useless. Such criticisms, appearing as early as the 1930's, were acknowledged by Nicholson (1933) and countered by the concept of an equilibrium being the point approached but often never attained by a population as it varies under different environmental conditions. Similar arguments are echoed in more recent debates (Dennis and Taper 1994, Berryman 5 1991). Clearly the continuing controversy revolves around the issue of the predominance of the mean equilibrium, given environmental "noise", or the variance about the mean in determining population and assemblage dynamics. The opinions are likely to be as diverse as are the positions along the continuum between the two extremes occupied by real populations and assemblages. A myriad of ecological terms have been used in reference to stability. Populations and assemblages have been shown to respond to disturbances in various ways that have been claimed to indicate stability. The most fundamental distinction is between persistence and stability as described above. These two population responses have been confused in the past (Connell and Sousa 1983). The tendency for certain populations to remain relatively constant through time as seen in time series data has been referred to as stability (eg. Matthews eta!. 1988). This has also variously been referred to as constancy (Orians 1974, Whittaker 1974), conservatism (mentioned in Connell and Sousa 1983), endurance (Margalef 1969), and stabilization (Reddingius and Den Boer 1987). For the sake of clarity I will use the term constancy. Consistent