Chapter 1 Why Quantitative Population Ethology?
Since the advent of theoretical population biology, there have been a number of attempts to simulate and predict the states of various biological systems using any number of sophisticated analytical, statistical, and numerical techniques. In some cases such techniques have been extremely successful, while in other applications the same approaches have failed miserably. We shall briefly discuss some of the general properties of theoretical population biology and then examine two biological systems as they might be viewed by a field biologist. From this study we conjecture some of the properties that an individual in a small population may exhibit. Based on these properties we suggest a possible modeling technique that is uniquely dependent on the information that the biologist observes.
Knowledge about animal behavior comes from two intrinsically different types of research. Ethology involves extensive examination of the physical and behavioral properties of an individual and its relationship to other members of its community. At the other end of the spectrum, population biology studies the general characteristics and dynamics of whole communities. We propose to combine these as quantitative population ethology, modeling the population structure by accounting for the dynamics and behavior of each individual within that population. This approach is quantitative in two senses: it can be based on field measurements, and it can summarize information over time and over populations of individuals. In this paper we examine some model requirements for simulating the properties and dynamics of populations through events that occur to individuals.
An ethologist’s description of individual behavior builds quantitative and qualitative data into an intriguing mosaic. Each member of a community responds to its unique history, environment, health and social position, possibly affecting the success or failure of other segments of that community. Important facets of an individual’s behavior, such as predator search patterns, prey evasion tactics and protective coloration, can shift the balance between species. Reduced reproductive success by a dominant male may threaten the survival of a local population. Limited adaptability of a group of individuals in a changing environment may threaten an entire population.
The major problem with using properties of individuals to describe an entire biological system is that individuals respond uniquely to stimuli in ways not easily characterized by `density response’ summaries. In addition, modeling a population of individuals, unless done judiciously, ultimately leads to substantial dimensionality problems. The complex operational properties of an individual preclude elegant analytic solutions at the population level. On the other hand, simulations that closely mimic individual behavior tend to be weak in mathematical structure and computationally intractable. How can we establish simulations having a balance of attention to biological details and sufficient mathematical structure to yield meaningful results?
1.1 Maleable Tools for the Field Biologists
The primary focus of modeling is the `information'' that is derived from examining attributes and their relationship to acceptance, and not the specificbest’ model selected. It is important for the
researcher to not be distracted from that objective in the pursuit to
develop a `best’ model. Modeling results should report the
information as a clear set of recommendations for product improvement,
and not focus on any specific mathematical model or function.
During model development several valid models should and will be
identified, a result potentially offering convergent learning and
convergent validation of important attributes. Convergent learning is
the basis for identifying important guideline' variables not represented in the selectedbest’ model. Convergent validation is
useful for providing low risk product development direction. Where
different models provide contradictory information, the researcher
uses statistical, practical and experiential criteria to resolve the
conflict.
1.2 Simulating Millions of Organisms
1.4 Discussion from QPE
The researcher interested in exploring the structure and dynamics of a population is faced with an extremely difficult problem of connecting classical modeling techniques to realistic biological processes. Serious problems arise in any brute force, component process approach.
The fundamental problem in an event-driven approach is how to interconnect relationships after an event has occurred. Any a priori approach would grow a model beyond bounds of computing time and complexity. The way that time is handled is crucial. While the biological system comprised of individuals is parallel in time, the event-driven model structure is sequential, with each new event modifying a complex hierarchical structure. This transfers attention from an explicit, static representation of the state-space to a dynamic, implicit one, with events driving time asynchronously. This transformation yields efficient computations while allowing complex interactions to be decomposed into coupled events. Future events are quasi-independent given the current state of the biological system. This allows us to focus on the next scheduled future event and have the model simulation reassemble itself after that event is processed.
If we analyze the structure and dynamics of a population at the individual level, the researcher faces an inherently probabilistic simulation that is complex and may be operationally intractable, with the following properties:
The inherently probabilistic structure at this level of description is central. The biological structure emerges over many individual events. The high dimensionality of the biological system forces the researcher to sample individuals and events. Any description is necessarily incomplete and stochastic.
In view of this inherent complexity, prediction of the future state of given individuals, or groups of individuals, is laced with uncertainty. Predictions on global properties tend to concern aspects that are not directly measurable, and hence cannot be validated.
Implicit in our modeling approach is the philosophy that any mathematical or numerical technique should not dictate the biology, but instead should mimic the biological process as much as possible. Our event-driven quantitative population ethology does not dictate how that process is done. We suggest that the actual simulation be driven by how the biologist perceives the system and chooses to structure the simulation around key research questions.
We propose the concept of quantitative population ethology modeling as an alternative to traditional population ecology models. This provides both a practical model approach as well as a philosophy that gives the field biologist tools and a perspective to analyze processes and structure observed in the field. Simulations can be designed to mimic the perceived structure and dynamics observed in the field. In addition, the approach suggested here has the potential of providing a tool for analyzing emerging properties of self-organizing systems (Kauffman 1993,1995; Paczuski and Bak, 1999; Paczuski et al. 1995).