Chapter 1 Hypothesis Testing in Ecology Charles J. Krebs Ecologists apply scientific methods to solve ecological problems. This simple sentence contains more complexity than practical ecologists would like to admit. Consider the storm that greeted Robert H. Peters’s (1991) book A Cri- tique for Ecology (e.g., Lawton 1991; McIntosh 1992). The message is that we might profit by examining this central thesis to ask “What should ecologists do?” Like all practical people, ecologists have little patience with the philoso- phy of science or with questions such as this. Although I appreciate this senti- ment, I would point out that if ecologists had adopted classical scientific meth- ods from the beginning, we would have generated more light and less heat and thus made better progress in solving our problems. As a compromise to prac- tical ecologists, I suggest that we should devote 1 percent of our time to con- cerns of method and leave the remaining 99 percent of our time to getting on with mouse trapping, bird netting, computer modeling, or whatever we think important. A note of warning here: None of the following discussion is origi- nal material, and all of these matters have been discussed in an extensive liter- ature on the philosophy of science. Here I apply these thoughts to the partic- ular problems of ecological science. ᭿ Some Definitions Let us begin with a few definitions to avoid semantic quarrels. Scientists deal with laws, principles, theories, hypotheses, and facts. These words are often used in a confusing manner, so I offer the following definitions for the descending hierarchy of generality in science: 2 CHARLES J. KREBS Laws: universal statements that are deterministic and so well corroborated that everyone accepts them as part of the scientific background of knowledge. There are laws in physics, chemistry, and genetics but not in ecology. Principles: universal statements that we all accept because they are mostly definitions or ecological translations of physicochemical laws. For example, “no population increases without limit” is an important eco- logical principle that must be correct in view of the finite size of the planet Earth. Theories: an integrated and hierarchical set of empirical hypotheses that together explain a significant fraction of scientific observations. The theory of island biogeography is perhaps the best known in ecology. Ecology has few good theories at present, and one can argue strongly that the theory of evolution is the only ecological theory we have. Hypotheses: universal propositions that suggest explanations for some observed ecological situation. Ecology abounds with hypotheses, and this is the happy state of affairs we discuss in this chapter. Models: verbal or mathematical statements of hypotheses. Experiments: a test of a hypothesis. It can be mensurative (observe the sys- tem) or manipulative (perturb the system). The experimental method is the scientific method. Facts: particular truths of the natural world. Philosophers endlessly discuss what a fact is. Ecologists make observations that may be faulty, and consequently every observation is not automatically a fact. But if I tell you that snowshoe hares turned white in the boreal forest of the south- ern Yukon in October 1996, you will probably believe me. Ecology went through its theory stage prematurely from about 1920 to 1960, when a host of theories, now discarded, were set up as universal laws (Kingsland 1985). The theory of logistic population growth, the monoclimax theory of succession, and the theory of competitive exclusion are three exam- ples. In each case these theories had so many exceptions that they have been discarded as universal theories for ecology. Theoretical ecology in this sense is past. It is clear that most ecological action is at the level of the hypothesis, and I devote the rest of this chapter to a discussion of the role of hypotheses in eco- logical research. Hypothesis Testing in Ecology 3 ᭿ What Is a Hypothesis? Hypotheses must be universal in their application, but the meaning of univer- sal in ecology is far from clear. Not all hypotheses are equal. Some are more universal than others, and we accept this as one criterion of importance. A hypothesis of population regulation that applies only to rodents in snowy envi- ronments may be useful because there are many populations of many species that live in such environments. But we should all agree that a better hypothe- sis would explain population regulation in all small rodents in all environ- ments. And a hypothesis that applies to all mammals would be even better. Hypotheses predict what we will observe in a particular ecological setting, but to move from the general hypothesis to a particular prediction we must add background assumptions and initial conditions. Hypotheses that make many predictions are better than hypotheses that make fewer predictions. Popper (1963) emphasized the importance of the falsifiability of a hypothesis, and asked us to evaluate our ecological hypotheses by asking “What does this hypothesis forbid?” Ecologists largely ignore this advice. Try to find in your favorite literature a list of predictions for any hypothesis and a list of the obser- vations it forbids. Recommendation 1: Articulate a clear hypothesis and its predictions. If we test a hypothesis by comparing our observations with a set of predictions, what do we conclude when it fails the test? There is no topic on which ecolo- gists disagree more. Failure to observe what was predicted may have four causes: the hypothesis is wrong, one or more of the background assumptions or initial conditions were not satisfied, we did not measure things correctly, or the hypothesis is correct but only for a limited range of conditions. All of these rea- sons have been invoked in past ecological arguments, and one good example is the testing of the predictions of the theory of island biogeography (MacArthur and Wilson 1967; Williamson 1989; Shrader-Frechette and McCoy 1993). A practical illustration of this problem is found in the history of wolf con- trol as a management tool in northern North America. The hypothesis is usu- ally stated that wolf control will permit populations of moose and caribou to increase (Gasaway et al. 1992). The background assumptions are seldom clearly stated: that wolves are reduced to well below 50 percent of their origi- nal numbers, that the area of wolf control is large relative to wolf dispersal dis- tances, that a sufficient time period (3–5 years) is allowed, and that the 4 CHARLES J. KREBS weather is not adverse. The only way to make the predictions of this hypothe- sis more precise is to define the background assumptions more clearly. With respect to moose, at least five tests have been made of this hypothesis (Boutin 1992). Two tests supported the hypothesis, three did not. How do we interpret these findings? Among my students I find three responses: The hypothesis is falsified by the three negative results; the hypothesis is supported in two cases, so it is probably correct; or the hypothesis is true 40 percent of the time. All of these points of view can be defended, so in this case what advice can an ecolo- gist give to a management agency? We cannot go on forever saying that more research is needed. I recommend that we adopt the falsificationist position more often in ecol- ogy as a way of improving our hypotheses and advancing our research agenda. In this example we would reject the original hypothesis and set up an alterna- tive hypothesis (for example, that predation by wolves and bears together lim- its the increase of moose and caribou populations). Indeed, we would be bet- ter off if we started with a series of alternative hypotheses instead of just one. The method of multiple working hypotheses is not new (Chamberlin 1897; Platt 1964) but it seems to be used only rarely in ecology. Recommendation 2: Articulate multiple working hypotheses for anything you want to explain. Two cautions are in order. First, do not assume that you have an exhaustive list of alternatives. If you have alternatives A, B, C, and D, do not assume that if A, B, and C are rejected that D must be true. There are probably E and F hypotheses that you have not thought of. Second, do not generalize the method of multiple working hypotheses to the ultimate multifactorial, holis- tic world view, which states that all factors are involved in everything. Many factors may indeed be involved, but you will make more rapid progress in understanding if you articulate a detailed list of the factors and how they might act. We need to retain the principle of parsimony and keep our hypotheses as simple as we can. It is not scientific progress for you to articulate a hypothesis so complex that ecologists could never gather the data to test it. ᭿ Hypotheses and Models A hypothesis implies a model, either a verbal model or a mathematical model. Analytical and simulation models have become very popular in ecology. From Hypothesis Testing in Ecology 5 a series of precise assumptions you can deduce mathematically what must ensue, once you know the structure of the system under study. Whether these predictions apply to the real world is another matter altogether. Mathematical models have overwhelmed ecology with adverse consequences. The literature is now filled with unrealistic, repetitive models with simplified assumptions and no connection to variables field ecologists can measure. You can generate models more quickly than you can test their assumptions. In an ideal world there would be rapid and continuous feedback between the modeler and the empiricist so that assumptions could be tested and modified. This happens too infrequently in ecology, partly because of the time limitations of most studies. The great advantage of building a mathematical model is to enunciate clearly your assumptions. This alone is worth a modeling effort, even if you never solve the equations. Recommendation 3: Use a mathematical model of your hypotheses to articulate your assumptions explicitly. Many mathematical models, such as the Lotka–Volterra predator–prey equa- tions, begin with very general, simple assumptions about ecological interac- tions. Therefore, they are useless for ecologists except as a guide of what not to do. If we have learned anything from the past 50 years it is that ecological sys- tems do not operate on general, simple assumptions. But this simplicity has been the great attraction of mathematical models in ecology, along with gener- ality (Levins 1966), and we need to concentrate on precision as a key feature of models that will bridge the gap between models and data. Precise models con- tain enough biological realism that they make quantitative predictions about real-world systems (DeAngelis and Gross 1992). One unappreciated consequence for ecologists who build realistic and pre- cise models of ecological systems is that numerical models cannot be verified or validated (Oreskes et al. 1994). A verified model is a true model and we can- not know the truth of any model in an open system, as Popper (1963) and many others have pointed out. Validation of a numerical model implies that it contains no logical or programming errors. But a numerical model may be valid but not an accurate representation of the real world. If observed data fit the model, the model may be confirmed, and at best we can obtain corrobora- tion of our numerical models. If a numerical model fails, we learn more: that one or more of the assumptions are not correct. Mathematical models are most useful when they challenge existing ideas rather than confirm them, the exact opposite of what most ecologists seem to believe. These strictures on numeri- 6 CHARLES J. KREBS cal models apply more to complex models (e.g., population viability models) than to simple models (e.g., age-based demographic models). Numerical models in which we have reasonable confidence can be used in ecology for sensitivity analysis, a very important activity. We can explore “what-if” scenarios rapidly and the only dangers are believing the results of such simulations when the model is not yet confirmed and extrapolating beyond the bounds of the model (Walters 1993). ᭿ Hypotheses and Paradigms Hypotheses are specified within a paradigm and the significance of the hy- pothesis is set by the paradigm. A paradigm is a world view, a broad approach to problems addressed in a field of science (Kuhn 1970; McIntosh 1992). The Darwinian paradigm is the best example in biology. Most ecologists do not realize the paradigms in which they operate, and there is no list of the com- peting paradigms of ecology. The density-dependent paradigm is one example in population ecology, and the equilibrium paradigm is an example from com- munity ecology. Paradigms define problems that are thought to be fundamen- tal to an area of science. Problems that loom large in one paradigm are dis- missed as unimportant in an opposing paradigm, as you can attest if you read the controversies over Darwinian evolution and creationism. Paradigms cannot be tested and they cannot be said to be true or false. They are judged more by their utility: Do they help us to understand our observations and solve our puzzles? Do they suggest connections between the- ories and experiments yet to be done? Hypotheses are nested within a para- digm and supporters of different paradigms often talk past each other because they use words and concepts differently and recognize different problems as significant. The density-dependent paradigm is one that I have argued has long out- lived its utility and needs replacing (Krebs 1995). The alternative view is that a few bandages will make it work well again (Sinclair and Pech 1996). My chal- lenge for any ecological paradigm is this: Name the practical ecological prob- lems that this paradigm has helped to solve and those it has made worse. In its preoccupation with numbers, the density-dependent paradigm neglects the quality of individuals and environmental changes, which makes the equilib- rium orientation of this approach highly suspect. Consider a simple example of a recommendation one would make from the density-dependent paradigm to a conservation biologist studying an en- Hypothesis Testing in Ecology 7 dangered species that is declining. Because by definition density-dependent processes are alleviated at low density (figure 1.1), you should not have to do anything to save your endangered species. No ecologist would make such a poor recommendation because environmental changes in terms of habitat destruction have changed the framework of the problem. Much patchwork has been applied to camouflage the inherent bankruptcy of this approach to pop- ulation problems. Ecologists find it very difficult to discuss paradigms because they are value- laden and are part of a much broader problem of methodological value judg- ments (Shrader-Frechette and McCoy 1993). Scientists are unlikely to admit to value judgments, but applied areas such as conservation biology have brought this issue to a head for ecologists (Noss 1996). All scientists make value judgments as they observe nature. For example, population ecologists estimate densities of organisms, partly because they value such data more than Figure 1.1 Classic illustration of the density-dependent paradigm of population regulation. In this hypothetical example, populations above density 8 will decline and those below density 8 will increase to reach an equilibrium at density 8 (arrow). If an endangered species falls in density below 8, density-dependent processes will ensure that it recovers, without any management intervention. Of course, this is nonsense. 8 CHARLES J. KREBS presence/absence data. Moreover, they prefer some estimation techniques to others because they are believed to be more accurate. Another example of methodological value judgments is the disagreement about the utility of microcosm research in ecology (Carpenter 1996). Methodological value judgments are particularly clear in conservation biology. Why preserve biodiversity? Some ecologists answer that diversity leads to stability, and stability is a desired population and ecosystem trait. But there are two broad hypotheses about biodiversity and ecosystem function. The rivet theory, first articulated by Ehrlich and Ehrlich (1981), suggests that the loss of any species will reduce ecosystem function, whereas the redundancy theory, first suggested by Walker (1992), argues that many species in a community are replaceable and redundant, so that their loss would not affect ecosystem health. Which of these two views is closer to being correct is a value judgment at present, as is the concept of the balance of nature in conservation planning. Recommendation 4: Uncover and discuss the value judgments present in your research program. These methodological value judgments are a necessary part of science and in articulating and discussing them, ecologists advance their understanding of the problems facing them. There is a very useful tension in community ecol- ogy between the classical equilibrium paradigm and the new nonequilibrium paradigm of community structure and function (DeAngelis and Waterhouse 1987; Krebs 1994). ᭿ Statistical Hypotheses Statistical hypotheses enter ecology in two ways. One school of thought rejects the deterministic hypotheses I have been arguing for and replaces all ecological hypotheses with probabilistic hypotheses. For example, the hypothesis that North American moose populations are limited in density by wolf predation can be replaced by the probabilistic hypothesis that 67 percent of North Amer- ican moose populations are limited by wolf predation. Probabilistic hypothe- ses have the advantage that they remove most of the arguments between oppos- ing schools of thought because they argue that everyone is correct part of the time. The challenge then becomes to specify more tightly the initial conditions of each hypothesis to make it deterministic. For our hypothetical example, if deer are present as alternative food, moose populations are limited by wolf pre- Hypothesis Testing in Ecology 9 dation. If deer are not present, moose are not limited by wolves. Buried in this consideration of probabilistic hypotheses are many philosophical issues and value judgments, but the major thrust is to replace ecological hypotheses with multiple-regression statistical models. Peters (1991) seemed to adopt this ap- proach as one way of making applied ecological science predictive. The more usual entry point for statistical hypotheses in ecology is through standard statistical tests. Ecological papers are overflowing with these statisti- cal hypotheses and their resulting p-values. We spend more of our time instructing students on the mechanics of statistical hypothesis testing than we do instructing them on how to think about ecological issues. I make four points about statistical inference: • Almost all statistical tests reported in the literature address low-level hypotheses of minor importance to the ecological issues of our day, not the major unsolved problems of ecological science. Therefore, we should not get too concerned about the resulting p-values. • Achieving statistical significance is not the same as achieving ecological sig- nificance. You may have strong statistical significance but trivial ecological sig- nificance. You cannot measure ecological significance by the size of your p-values. What matters in ecology is what statisticians call effect size: How large are the differences? There is no formal guidance in what are ecologically sig- nificant effect sizes. Much depends on the structure of your ecological system. For population dynamics we can explore the impact of changes in survival and reproduction through simple life table models. Similar sensitivity analyses are not possible with questions of community dynamics. • The null hypothesis of statistical fame, which suggests no differences between treatments or areas, is not always a good ecological model worth test- ing. We should apply statistics more cleverly when we expect differences between treatments and not pretend total ecological ignorance. We can often make a quantitative estimate of the differences to be expected. One-tailed tests ought to be common in ecology. Testing for differences can often be used, and specified contrasts should be the rule in ecological studies. We should use sta- tistics as a fine scalpel, not as a machete, and we should not waste time testing hypotheses that are already firmly established. • No important ecological issue can be answered by a statistical test. The im- portant ecological issues, such as equilibrium and nonequilibrium paradigms, 10 CHARLES J. KREBS are higher-level questions that involve value judgments, not objective proba- bility statements. Recommendation 5: Use statistical estimation more than statistical inference. There is more to life than p-values. These cautionary notes should not be misinterpreted to indicate that you do not need to learn statistics to be an ecologist. You should learn statistics well and then learn to recognize the limits of statistics as a tool for achieving knowl- edge. Every good study needs explicit null hypotheses and the appropriate sta- tistical testing. ᭿ Hypotheses and Prediction Hypotheses, once tested and confirmed, lead us to understanding but not nec- essarily to predictions that will be useful in applied ecology. Prediction is often used to mean forecasting in a temporal sense: What will happen to Lake Supe- rior after zebra mussels are introduced? At present, applied ecologists can make only qualitative predictions in the medium term and quantitative predictions in the short term. We should focus on these strengths for the present and not berate ourselves for an inability to predict in the long term how disturbed pop- ulations and communities will change. Short-term quantitative predictions are of enormous practical utility. If you know the number of aphids now, the numbers of their predators, and the tem- perature forecast for the next 2 weeks, you can predict aphid damage in the short term (Raworth et al. 1984). Ecologists should exploit the vast store of natural history data to develop these simple predictive models. This is not the route to the Nobel Prize, but it is still one of the most important contributions ecologists can make to society. Medium-term predictions are more difficult, and ecologists often have to settle for qualitative predictions. A good example is provided by the search for habitat models that can be used in conservation planning. Not all habitat patches are occupied by all species, and metapopulation theory builds on this observation. But a habitat can be declared suitable only if it has the food and shelter a species requires and if the species can disperse there. Suitable habitats may have all the structural features needed but become unsuitable if a preda- tor takes up residence (Doncaster et al. 1996). The scale of the difficulty in achieving medium-term predictions can be seen by work on the spotted owl in [...]... northern spotted owl (Strix occidentalis caurina) Oecologia 75: 6 01 607 Lawton, J 19 91 Predictable plots Nature 354: 444 Lawton, J 19 96 Patterns in ecology Oikos 75: 14 5 14 7 Levins, R 19 66 The strategy of model building in population biology American Scientist 54: 4 21 4 31 MacArthur, R and E O Wilson 19 67 The theory of island biogeography Princeton, N.J.: Princeton University Press McIntosh, R P 19 92 Whither... multiple working hypotheses Science 14 8: 754–759 DeAngelis, D L and L J Gross, eds 19 92 Individual-based models and approaches in ecology: Populations, communities, and ecosystems New York: Chapman & Hall DeAngelis, D L and J C Waterhouse 19 87 Equilibrium and nonequilibrium concepts in ecological models Ecological Monographs 57: 1 21 Doncaster, C P., T Micol, and S P Jensen 19 96 Determining minimum habitat... Fellowship that provided time to write Joe Elkinton helped me at the Erice meeting by summarizing questions and comments on this chapter Literature Cited Bart, J and E D Forsman 19 92 Dependence of northern spotted owls Strix occidentalis caurina on old-growth forests in the western USA Biological Conservation 62: 95– 10 0 Hypothesis Testing in Ecology Boutin, S 19 92 Predation and moose population dynamics:... Management 56: 11 6 12 7 Brown, J H 19 95 Macroecology Chicago: University of Chicago Press Carey, A B., S P Horton, and B L Biswell 19 92 Northern spotted owls: In uence of prey base and landscape character Ecological Monographs 62: 223–250 Carpenter, S R 19 96 Microcosm experiments have limited relevance for community and ecosystem ecology Ecology 77: 677–680 Chamberlin, T C 18 97, reprinted 19 65 The method... ecologist’s analog of angels-on-the-pinhead, and you could waste your scientific life trying to find an answer to it But you will find in the literature almost no discussion of which types of questions in ecology have proven to be unsolv- 11 12 CHARLES J KREBS able and which have been fruitful, which have contributed to solving practical problems and which have been interesting but of limited utility Recommendation... Monographs 12 0: 1 59 Kingsland, S E 19 85 Modeling nature Chicago: University of Chicago Press Krebs, C J 19 94 (4th ed.) Ecology: The experimental analysis of distribution and abundance New York: HarperCollins Krebs, C J 19 95 Two paradigms of population regulation Wildlife Research 22: 1 10 Kuhn, T 19 70 The structure of scientific revolutions Chicago: University of Chicago Press Lande, R 19 88 Demographic... Entomologist 11 6: 879–888 Shrader-Frechette, K S and E D McCoy 19 93 Method in ecology: Strategies for conservation Cambridge, U.K.: Cambridge University Press Sinclair, A R E and R P Pech 19 96 Density dependence, stochasticity, compensation and predator regulation Oikos 75: 16 4 17 3 Taylor, B L and T Gerrodette 19 93 The uses of statistical power in conservation biology: The vaquita and northern spotted owl... Whither ecology? Quarterly Review of Biology 67: 495–498 Noss, R F 19 96 Conservation biology, values, and advocacy Conservation Biology 10 : 904 Oreskes, N., K Shrader-Frechette, and K Belitz 19 94 Verification, validation, and confirmation of numerical models in the earth sciences Science 263: 6 41 646 Peters, R H 19 91 A critique for ecology Cambridge, U.K.: Cambridge University Press Platt, J R 19 64 Strong inference... as a call for the regimentation of research ideas In this chapter I have concentrated on the role of hypothesis testing in ecology, and one may ask whether any of this applies to ethology as well I am not a professional ethologist, so my judgment on this matter can be questioned In my experience the problems I have outlined do indeed apply to ethology as well as ecology I suspect that much of organismal...Hypothesis Testing in Ecology Oregon and Washington (Bart and Forsman 19 92; Carey et al 19 92; Lande 19 88; Taylor and Gerrodette 19 93) Attempts to predict what habitat configuration will permit the owl to survive are ecologically sophisticated because of the extensive background of descriptive studies on this owl But even with maximum effort, the medium-term predictions are more uncertain than . role of hypotheses in eco- logical research. Hypothesis Testing in Ecology 3 ᭿ What Is a Hypothesis? Hypotheses must be universal in their application, but the meaning of univer- sal in ecology. preda- tor takes up residence (Doncaster et al. 19 96). The scale of the difficulty in achieving medium-term predictions can be seen by work on the spotted owl in Hypothesis Testing in Ecology 11 Oregon. Dependence of northern spotted owls Strix occidentalis caurina on old-growth forests in the western USA. Biological Conservation 62: 95– 10 0. Hypothesis Testing in Ecology 13 Boutin, S. 19 92. Predation