Individuals die, populations disappear, and species become extinct. That is one view of the world. But another view of the world concentrates not so much on presence or absence as upon the numbers of organisms and the degree of constancy of their numbers. These are two very different ways of viewing the behavior of systems and the usefulness of the view depends very much on the properties of the system concerned. If we are examining a particular device designed by the engineer to perform specific tasks under a rather narrow range of predictable external conditions, we are likely to be more concerned with consistent nonvariable performance in which slight departures from the performance goal are immediately counteracted. A quantitative view of the behavior of the system is, therefore, essential. With attention focused upon achieving constancy, the critical events seem to be the amplitude and frequency of oscillations. But if we are dealing with a system profoundly affected by changes external to it, and continually confronted by the unexpected, the constancy of its behavior becomes less important than the persistence of the relationships. Attention shifts, therefore, to the qualitative and to questions of existence or not. Our traditions of analysis in theoretical and empirical ecology have been largely inherited from developments in classical physics and its applied variants. Inevitably, there has been a tendency to emphasize the quantitative rather than the qualitative, for it is important in this tradition to know not just that a quantity is larger than another quantity, but precisely how much larger. It is similarly important, if a quantity fluctuates, to know its amplitude and period of fluctuation. But this orientation may simply reflect an analytic approach developed in one area because it was useful and then transferred to another where it may not be. Our traditional view of natural systems, therefore, might well be less a meaningful reality than a perceptual convenience. There can in some years be more owls and fewer mice and in others, the reverse. Fish populations wax and wane as a natural condition, and insect populations can range over extremes that only logarithmic

/pdf/resilience-and-stability-of-ecological-systems-1l48x9fw3m.pdf

Resilience and Stability of Ecological Systems

First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

Simple mathematical models with very complicated dynamics

This review organizes ideas on the evolution of life histories. The key life-history traits are brood size, size of young, the age distribution of reproductive effort, the interaction of reproductive effort with adutl mortality, and the variation in these traits among an individual's progeny. The general theoretical problem is to predict which combinations of traits will evolve in organisms living in specified circumstances. First consider single traits. Theorists have made the following predictions: (1) Where adult exceeds juvenile mortality, the organism should reproduce only once in its lifetime. Where juvenile exceeds adult mortality, the organism should reproduce several times. (2) Brood size should maximize the number of young surviving to maturity, summed over the lifetime of the parent. But when optimum brood-size varies unpredictably in time, smaller broods should be favored because they decrease the chances of total failure on a given attempt. (3) In expanding populations, selection should minim...

Life-history tactics: a review of the ideas.

The author challenges the traditional approach to dealing with uncertainty in the management of such renewable resources as fish and wildlife. He argues that scientific understanding will come from the experience of management as an ongoing, adaptive, and experimental process, rather than through basic research or the development of ecological theory. 

The opening chapters review approaches to formulating management objectives as well as models for understanding how policy choices affect the attainment of these objectives. Subsequent chapters present various statistical methods for understanding the dynamics of uncertainty in managed fish and wildlife populations and for seeking optimum harvest policies in the face of uncertainty. The book concludes with a look at prospects for adaptive management of complex systems, emphasizing such human factors involved in decision making as risk aversion and conflicting objectives as well as biophysical factors. Throughout the text dynamic models and Bayesian statistical theory are used as tools for understanding the behavior of managed systems. These tools are illustrated with simple graphs and plots of data from representative cases. 

This text/reference will serve researchers, graduate students, and resource managers who formulate harvest policies and study the dynamics of harvest populations, as well as analysts (modelers, statisticians, and stock assessment experts) who are concerned with the practice of policy design.

http://www.swrcb.ca.gov/waterrights/water_issues/programs/bay_delta/docs/cmnt081712/dfg/cdfgwalters1986.pdf

Adaptive Management of Renewable Resources

Body size is manifestly one of the most important attributes of an organism from an ecological and evolutionary point of view. Size has a predominant influence on an animal's energetic requirements, its potential for resource exploitation, and its susceptibility to natural enemies. A large literature now exists on how physiological, life history, and population parameters scale with body dimensions (24, 131). The ecological literature on species interactions and the structure of animal communities also stresses the importance of body size. Differences in body size are a major means by which species avoid direct overlap in resource use (153), and size-selective predation can be a primary organizing force in some communities (20, 70). Size thus imposes important constraints on the manner in which an organism interacts with its environment and influences the strength, type, and symmetry of interactions with other species (152, 207). Paradoxically, ecologists have virtually ignored the implications of these observations for interactions among species that exhibit size-distributed populations. For instance, it has been often suggested that competing species

https://www.jstor.org/stable/pdf/2096954.pdf

The ontogenetic niche and species interactions in size-structured populations

Plotting net reproduction (reproductive potential of the adults obtained) against the density of stock which produced them, for a number of fish and invertebrate populations, gives a domed curve wh...

W. E. Ricker

Papers

Stock and Recruitment