The Ecological Detective: Confronting Models with Data (Monographs in Population Biology) - Softcover

Hilborn, Ray

Softcover

ISBN 10: 0691034974 ISBN 13: 9780691034973

Verlag: Princeton University Press, 1997

Inhaltsangabe

The modern ecologist usually works in both the field and laboratory, uses statistics and computers, and often works with ecological concepts that are model-based, if not model-driven. How do we make the field and laboratory coherent? How do we link models and data? How do we use statistics to help experimentation? How do we integrate modeling and statistics? How do we confront multiple hypotheses with data and assign degrees of belief to different hypotheses? How do we deal with time series (in which data are linked from one measurement to the next) or put multiple sources of data into one inferential framework? These are the kinds of questions asked and answered by The Ecological Detective. Ray Hilborn and Marc Mangel investigate ecological data much as a detective would investigate a crime scene by trying different hypotheses until a coherent picture emerges. The book is not a set of pat statistical procedures but rather an approach. The Ecological Detective makes liberal use of computer programming for the generation of hypotheses, exploration of data, and the comparison of different models. The authors' attitude is one of exploration, both statistical and graphical. The background required is minimal, so that students with an undergraduate course in statistics and ecology can profitably add this work to their tool-kit for solving ecological problems.

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Ray Hilborn & Marc Mangel

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The Ecological Detective

Confronting Models with DataBy RAY HILBORN MARC MANGEL

PRINCETON UNIVERSITY PRESS

Copyright © 1997 Princeton University Press
All right reserved.
ISBN: 978-0-691-03497-3

Contents

Preface: Beyond the Null Hypothesis...................................................................xi1. An Ecological Scenario and the Tools of the Ecological Detective...................................32. Alternative Views of the Scientific Method and of Modeling.........................................123. Probability and Probability Models: Know Your Data.................................................394. Incidental Catch in Fisheries: Seabirds in the New Zealand Squid Trawl Fishery.....................945. The Confrontation: Sum of Squares..................................................................1066. The Evolutionary Ecology of Insect Oviposition Behavior............................................1187. The Confrontation: Likelihood and Maximum Likelihood...............................................1318. Conservation Biology of Wildebeest in the Serengeti................................................1809. The Confrontation: Bayesian Goodness of Fit........................................................20310. Management of Hake Fisheries in Namibia Motivation................................................23511. The Confrontation: Understanding How the Best Fit Is Found........................................263Appendix: "The Method of Multiple Working Hypotheses" by T C. Chamberlain............................281References............................................................................................295Index.................................................................................................309

Chapter One

An Ecological Scenario and the Tools of the Ecological Detective

AN ECOLOGICAL SCENARIO

The Mediterranean fruit fly (medfly), Ceratitis capitata (Wiedemann), is one of the most destructive agricultural pests in the world, causing millions of dollars of damage each year. In California, climatic and host conditions are right for establishment of the medfly; this causes considerable concern. In Southern California, populations of medfly have shown sporadic outbreaks (evidenced by trap catch) over the last two decades (Figure 1.1). Until 1991, the accepted view was that each outbreak of the medfly corresponded to a "new" invasion, started by somebody accidentally bringing flies into the state (presumably with rotten fruit). In 1991, our colleague James Carey challenged this view (Carey 1991) and proposed two possible models concerning medfly outbreaks (Figure 1.2). The first model, MJ, corresponds to the accepted view: each outbreak of medfly is caused by a new colonization event. After successful colonization, the population grows until it exceeds the detection level and an "invasion" is recorded and eradicated. The second model, M2, is based on the assumption that the medfly has established itself in California at one or more suitable sites, but that, in general, conditions cause the population to remain below the level for detection. On occasion, however, conditions change and the population begins to grow in time and spread over space until detection occurs. Carey argued that the temporal and spatial distributions of trap catch indicate that the medfly may be permanently established in the Los Angeles area. Knowing which of these views is more correct is important from a number of perspectives, including the basic biology of invasions and the implications of an established pest all agricultural practices.

Determining which model is more consistent with the data is a problem in ecological detection. That is, if we allow that either model M₁ or model M₂ is true, we would like to associate probabilities, given the data, with the two models. We shall refer to this as "the probability of the model" or the "degree of belief in the mode!." How might such a problem be solved? First, we must characterize the available data, which are the spatial distribution of trap catches of medfly over time (Figure 1.3). We could refine these by placing small grids over the maps and characterizing a variable that measures the number of flies that appear in cell i in year y. Second, we must convert the pictorial or verbal models shown in Figure 1.2 into mathematical descriptions. That is, some kind of mathematical model is needed so that the data can be compared with predictions of a model. Such models would be used to predict the temporal and spatial patterns in detected outbreaks; the mathematical descriptions would generate maps similar to the figures. The models would involve at least two submodels, one for the population dynamics and one for the detection process. Courses in ecological modeling show how this is done. Third, we confront the models with the data by comparing the predicted and observed results. At least three approaches can be broadly identified for such a confrontation.

Classical Hypothesis Testing. Here we confront each model separately with the data. Thus, we begin with hypotheses:

H₀: Model M₁ is true

H_a: Some other model is true

Here the alternate model might be that outbreaks are random over time and space. Using the mathematical descriptions of the models, we construct a "p value" for the hypothesis that M₁ is true. It might happen that we can definitely reject H₀ because the p value is so small (usually less than 0.05 or 0.01). Alternatively, we might not be able to reject H₀ (i.e., p > 0.05), but then might discover that the power of the statistical test is quite low (we assume that most readers are probably familiar with the terms "p values" and "power" from courses in elementary statistics, but we shall explain them in more detail in the following chapters). In any case, we use such hypothesis testing because it gives the "illusion of objectivity" (Berger and Berry 1988; Shaver 1993; Cohen 1994).

After we had tested the hypothesis that model 1 is true against the alternate hypothesis, we would test the hypothesis that model 2 is true against the alternate. Some of the outcomes of this procedure could be: (i) both models M₁ and M₂ are rejected; (ii) model M, is rejected but M₂ is not; (iii) model M₁ is not rejected but M₂ is; and (iv) neither model is rejected. If outcome (ii) or (iii) occurs, then we will presumably act as if model M₁ or M₂ were true and make scientific and policy decisions on that basis, but if outcome (i) or (iv) occurs, what are we to do? Other than collecting more data, we are provided with little guidance concerning how we should now view the models and what they tell us about the world. There is also a chance that if outcome (ii) or (iii) occurs, the result is wrong, and then on what basis do we choose the p level?

Likelihood Approach (Edwards 1992). In this case, we use the data to arbitrate between the two models. That is, given the data and a mathematical description of the two models. we can ask, "How likely are the data, given the model?" Details of how to do this are given in the rest of this book, but read on pretending that you indeed know how to do it. Thus, we first construct a measure of the probability of the observed data, given that the model is true—we shall denote this by Pr{data|M_i}. We then turn this on its head and interpret it...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 1997
• Sprache: Englisch
• ISBN 10: 0691034974
• ISBN 13: 9780691034973
• Einband: Taschenbuch
• Anzahl der Seiten: 336
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar