Research Techniques in Animal Ecology - Chapter 1 pot

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
Hypothesis Testing in Ecology
11
Oregon and Washington (Bart and Forsman 1992; Carey et al. 1992; Lande
1988; Taylor and Gerrodette 1993). Attempts to predict what habitat config-
uration 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 a
conservation biologist would like, particularly in the mixed logging-partial
preservation strategies.
If ecologists cannot at present achieve long-term predictions, we do have an
extensive storehouse of knowledge about what management policies will not
work. The catalog of disasters is now large enough that, without additional
hypothesis testing, we can provide management agencies with sound advice
about many ecological problems. For example, designating no-fishing zones or
refuges for marine fisheries is an important conservation measure that we can
recommend without detailed studies of the mechanisms of dispersal and com-
munity organization in the marine community affected by overfishing.
Because ecological communities are open systems and are subject to a
changing climate, it is unlikely that we will ever be able to provide broad eco-
logical laws that apply universally in time and space. We should concentrate on
understanding and developing predictions for short-term changes in commu-
nities and populations. This understanding will be local and specific, and we
should not worry that our spotted owl understanding cannot be applied uni-

versally to all owls or all birds on all continents.
Recommendation 6: Concentrate on short-term predictions to solve local
problems. Learn to walk before running.
This recommendation to focus on the local and the particular is the complete
antithesis of what Brown (1995) recommends as a macroecological future for
ecology. There is a sense of frustration among ecologists that their chosen sub-
ject does not advance as rapidly as genetics or nuclear chemistry. Why is it so
difficult to design theory in ecology? Is it because we are not studying the right
questions? Not using the right methods? Do the textbooks we are using teach
us to focus on unsolvable problems, as Peters (1991) suggests? Lawton (1996)
gives an example of what he considers a critical question in biodiversity: Why
are there 2 species of a taxonomic group in one ecosystem, 20 in a second sys-
tem, and 200 in a third? I suggest that this is an unanswerable question, the
ecologist’s analog of angels-on-the-pinhead, and you could waste your scien-
tific 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-
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 7: Address significant problems. Do not waste your thesis
research or your career on trivial issues.
What is trivial to one ecologist is the major problem of ecology to another.
What can we do about this unsatisfactory state of affairs? In the long run, his-
tory sorts out these issues, but for ecologists facing biodiversity issues now, his-
tory will take too long. We cannot escape these judgments and more discus-
sion ought to be devoted to them in ecological journals. If medical research
councils devoted equal amounts of money to acupuncture and schizophrenia
research, we would be alarmed at the poor judgment. We should not hesitate
to make similar value judgments for ecological research. No person or group is
infallible in their judgments, and this call for discussion of the relative impor-

tance of ecological questions must not be misinterpreted as a call for the regi-
mentation of research ideas.
In this chapter I have concentrated on the role of hypothesis testing in ecol-
ogy, 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 biology could profit from a
more rigorous approach to hypothesis testing.
In our haste to become scientists (with a capital S), we should be careful to
focus on what we desire to achieve as ethologists and as ecologists. This debate,
more about values than about scientific facts, is important for you to join. By
your decisions you will affect the future developments of these sciences.
Acknowledgments
I thank Alice Kenney, Rudy Boonstra, and Dennis Chitty for their comments
on the manuscript, and the Canada Council for a Killam Fellowship that pro-
vided time to write. Joe Elkinton helped me at the Erice meeting by summa-
rizing questions and comments on this chapter.
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