Essay for doktorgradskurs i vitenskapsteori (MNVIT401), Universitetet i Oslo. Av Torbjørn Ergon,
Januar 2000:
Questions, approaches and paradigm in studies of small
rodent population cycles; a search for the Holy Grail
INTRODUCTION .................................................................................................................................. 1
QUESTIONS AND APPROACHES IN SMALL RODENT CYCLES ............................................. 2
GENERALITY – “ALL CYCLES ARE CAUSED BY THE SAME MECHANISMS!” ............................................. 3
THE COMPARATIVE METHOD ................................................................................................................. 6
THE REDUCTIONISTIC SYSTEM ORIENTATED APPROACH ........................................................................ 7
APPROACHES IN THE STUDY OF POPULATIONS; TOP-DOWN OR DOWN-UP? ............... 8
HOLISM VS. REDUCTIONISM IN ECOLOGY .............................................................................................. 8
“SYSTEM UNITS” IN NATURE ................................................................................................................. 9
LEVELS OF KNOWLEDGE ...................................................................................................................... 10
KNOWLEDGE AT THE POPULATION LEVEL ........................................................................................... 12
KNOWLEDGE AT THE DEMOGRAPHIC LEVEL ........................................................................................ 13
MECHANISTIC KNOWLEDGE AT THE INDIVIDUAL LEVEL ...................................................................... 13
SUMMING UP ..................................................................................................................................... 14
REFERENCES ..................................................................................................................................... 14
Introduction
Man in the north has probably during all times been puzzled by the regular outbreaks of
lemmings and other small rodents. The Italian priest Francesco Negri who visited Norway in
1664-65 said, “what lemmings show us, is that lightning is by far not the most mysterious in
the clouds, since in between them fully developed animals are born, which together with rain
fall down in tremendous numbers, and within only one day they flood large areas and
completely destroy grain and grasses”1. Such an explanation of the lemming out-breaks was
typical for the time, and was also relayed by the Swedish priest Olaus Magnus in his book
from 1555 about the Nordic people2. Charles Elton from University of Oxford is often cited
as the first who gave a scientific description of the periodic fluctuations of animal populations
in his work from 19243, although this work was largely based on publications by the
Norwegian naturalist Robert Collett who did not seem to acknowledge the significant
periodicity of the fluctuations4. However, neither Elton nor Collett was aware of the account
of the phenomenon by the Finnish naturalist Ehrström who in 1852 introduced his report on
1
Cited from Seldal 1994.
2
Olaus Magnus published his book ‘Historia de gentibus septentrionalibus’ (‘The account of the septentrional people’) in latin
in Rome in 1555. He added to the text a spirited woodcut of the lemmings actually falling from the clouds with spouts of rain.
That animals could self-generate was a common belief in the Middle Ages. It was for example thought that mice and flies were
developed from dirty laundry and refuse.
3
Elton, 1924
4
Elton, 1942
1
the mass movements of lemmings by saying: “We are not aware of the causes of pronounced
periodicity, while smaller fluctuations occurring in nature, we understand only
incomplete…”5. Elton’s first publications were the start of an enormous amount of work on
population dynamics. Much of this work specifically addresses the question: What causes
cyclic fluctuations of small rodent populations? However, although we have gained much
knowledge about population dynamics over the last century, this basic question has remained
unanswered. Rudy Boonstra begins his paper of 1994 where he presents a new hypothesis, the
senescence hypothesis, by saying: “The cause of population cycles in microtines (voles and
lemmings) remains an enigma”. The same could have been said today.
Why are scientists today asking the same questions as they did in the beginning of the
century? No one can of course give an incontestable answer to this question, but the question
should be of great interest to scientists in the field, as well as to philosophers of science. In
this essay I will take a closer look at the questions, paradigm and approaches in the science of
small rodent population dynamics, which has especially focused on explaining the cyclic
dynamics. There is an enormous amount of publications about the ecology of small rodents.
All of this is more or less relevant for the population dynamics. Hence, I will not try to be
comprehensive. Instead I will focus on a few ideas that have caught my interest. There are
many lines of thought in this science. I will take a critical look at some influential review
work that has been put forward by people who represent what is sometimes referred to as the
‘Chitty-Krebs school’ in Canada. Although there are several other traditions in small rodent
research, especially in the Nordic countries, the United States and Russia, the methodological
concepts that I will criticise are by and large adopted by all these traditions. I will especially
question the top-down phenomenological approach in this science, and point out some
historical explanations for this approach. At the risk of being pretentious, I will even dare to
suggest which directions I think will be awarding for the science to take in the future. I realise
that this is a large and difficult task. Rather than just reviewing what other people have said, I
will often try to rethink things from scratch. By doing so, I lay bare my naked worldview
open for criticism. This is a goal. My motivation is just as much to provoke criticism that will
correct my own worldview, as it is to try to affect the worldviews of others6.
Questions and approaches in small rodent cycles
The motivation for the early work on the ecology of small rodents by Charles Elton, Dennis
Chitty and others in the Bureau of Animal Population was a fascination for the massive
outbreaks and regular fluctuations of lemmings in Scandinavia and other small mammals. As
fluctuations with seemingly regular periods were discovered in other populations and species,
the natural question to ask was: “What causes the cycles?” Implicit in this question is a notion
that the demarcation between ‘cyclic’ and ‘non-cyclic’ population dynamics reflects
5
6
Cited from Klemola (1999) who referred to Ehrström (1852).
I welcome criticism of any sort: torbjorn.ergon@bio.uio.no
2
fundamentally different processes and mechanisms. Among many biologists who caught
interest in the population cycles, questions of the type “Why are some populations seemingly
stable?” and “What causes the variation in the dynamics between populations in general?”
have been subordinate. Questions at the individual level like “In what way do reproductive
traits vary?” and “What causes the variation in the individuals performance?”, have to a large
extent only been asked in order to understand “what causes cycles?”.
In natural science, and maybe especially in biology, one have through all times
classified and structured the view on nature in order to understand it. This is maybe especially
so in biology, where we are dealing with millions of life forms in an immensely complex
environment. For early ecologists that were faced with such a complex nature, which they
knew little about, the best approach seemed to be to describe and classify their observations.
Ecologist before the time of Elton was also mainly taxonomists engaged in classifying and
naming parts in nature. It is thus hardly surprising that ecologists have made such
phenomenological categorisations also about population dynamics. By all means, the
recognition that some populations are cyclic (fluctuate regularly), and that some populations
are not, has been fruitful as it made us appreciate the importance of delayed density
dependence in the regulation (see box).
Generality – “all cycles are caused by the same mechanisms!”
Krebs & Myers (1974) state in probably the most influential review article about small rodent
cycles: “We believe that a universal explanation must be sought for population fluctuations in
voles and lemmings until we have evidence that two or more distinct explanations are
required.” Krebs is faithful to this approach in his review 26 years later, after considerable
more variation in the dynamics of small rodent populations had been described: “I believe
that we ecologists should seek the underlying generalities about cycles and not get lost in
describing differences among cycles” (…)”In my view, these differences [within and between
populations] will be interesting and possibly explicable once we understand the underlying
generalities.” The generalities that he here refers to are not of a mathematical or system
theoretical nature, but he refers to generalities in the biological mechanisms. That is, the
individual level mechanisms are assumed to be essentially the same for all cycles.
This assumption has been, and still is, a part of the paradigm. In articles, evidence for
different “views” is commonly collected from a variety of species belonging to several
genuses and living in widely different environments. It is often not even mentioned what are
the species or environment that is being referred to. The main question has simply been: What
causes the small rodent cycle? It has been assumed that everyone is talking about the same
thing. The research on small rodent cycles has very much been a “pursuit of the ecological
Holy Grail”7. Several examples of this can be found in the history of the science. For
7
Dennis Chitty, who started working with Charles Elton only few years after the founding of the Bureau of Animal Population
at Oxford, uses this phrase himself in his book about his life in the “cycle science”, Do Lemmings Commit Suicide? (Chitty,
1996).
3
example, Dennis Chitty was for some time engaged in investigating the possibility that
epidemics of a protozoan parasite, Toxoplasma, cause the populations to decline. Several
observations indicated that this might be the case. However, when it was discovered that
some populations declined without the presence of Toxoplasma he shifted his research
interests towards something else8.
It is worth to notice that the “Chitty-Krebs school” asks no question about the
objectivity of their phenomenological categorisations of cycles/non-cycles. Generalisations on
the causes of our defined phenomena rest on the assumption that the categorisations capture
the essence of how nature is truly organised9. Chitty writes in the introduction to his book,
which is written as a guide to the scientific methods: “Having chosen a phenomenon to study,
we next have to discover the relevant (or necessary) factors.” He does not stop to reflect over
that the definition of the phenomenon is not given by nature but is made by the researcher. He
does not contemplate that specific materialisations of the defined phenomenon in nature may
have fundamentally different causations. Simplistic categorisations of complex systems that
are poorly understood, like population dynamics, are almost bound to not reflect the
mechanisms very well. The history of science is full of examples of concepts and “labels” of
nature that have had a large influence on the science, but which later have been proven to be
fallacious10. Today we know that, even in very simple models of population dynamics, a
minute change in the value of one parameter can completely change the superficial dynamics
of the model. For example, a model yielding regular fluctuations with large amplitude may
also, with a minute change in one parameter value, cause constant population size over time
or irregular fluctuations. Likewise, two completely different models may yield not only
similar dynamics in the population size that fits with the definition of ‘cycles’, but the
dynamics may yield virtually identical fluctuations11. Thus, one ‘cyclic’ and one ‘non-cyclic’
population may have more in common in terms of the underlying mechanisms for population
regulation than two ‘cyclic’ populations (or two populations that have seemingly identical
fluctuations for that matter). One cannot judge how similar the mechanisms are just by
looking at the population level patterns.
It is rather paradoxical, when considering this strong focus on dichotomy between
cyclic and non-cyclic populations, to see that scientists in the field have not agreed on the
definition of the cycles. ‘Cycles’ has been defined in at least three ways. The different
8
From Chitty’s book, Do Lemmings Commit Suicide? (Chitty, 1996), most of my later references to Chitty’s work are from this
book.
9
For example, early philosophers may have defined water as “a transparent liquid that boils when it is heated”. Today we know
that many substances fit with this definition. Another example is polyphyletic groups in taxonomy.
10
A classical example is the concept of “phlogiston” which, prior to the discovery of oxygen, was believed to be a substance
that left the material during combustion. This concept was a part of chemistry in the 18 th century, and explanations of
observations were made to fit with this concept. For example, the discovery that metals gained weight when heated (and formed
oxides) led many to believe that ‘phlogiston’ had a negative mass. A more resent example is the dualism reflected in the concept
of an “autonomous nervous system” which is no longer a part of modern neuroendocrinology.
11
see McCauley & Murdoch (1987) and Murdoch et al. (1992).
4
definitions emphasise respectively the variability in numbers, the periodicity of the
fluctuations or variations in individual level criteria such as body mass and reproductive rates.
Nevertheless, it has always been assumed that they are talking about the same things. Hence,
as a compromise the ‘problem definition’ has become very complex; one are looking for
mechanisms that can explain a wide range of phenomena. Elton undertook an even wider
problem definition in his early days when he assumed that the cause of the cycles necessarily
had the same cause as large-scale synchrony. In his 1924 paper he concludes that, since the
lemming fluctuations are synchronous over large areas they must be caused by fluctuations in
the climate because it is “the only possible factor which is acting in a similar way all over
these regions” 12. Today, such an argument is considered to be a logical flaw since we know
that stochastic fluctuations in the climate, which influence demography, will tend to
synchronise the population dynamics within the climatic domain independent of the
mechanisms of the cyclic fluctuations13.
Krebs and Myers’ approach of assuming generality is not mainly motivated by a
belief that this is the actual case in nature, but rather on a argument that this is the best
approach. They say, “The multiple-factor hypothesis is particularly dangerous as a
methodological argument.” (…) “But if we adopt this hypothesis as a research strategy, we
lose one of the most important checks of scientific speculation – the testability of hypothesis.
Suppose that we adopt the hypothesis that the absence of disease x is a sufficient condition for
population growth for Microtus ochrogaster in Kansas. We cannot test this hypothesis on
Microtus ochrogaster in Nebraska because this is a different situation.” (…) “If carried to an
extreme, we cannot even test the hypothesis on the next cycle of M. ochrogaster in Kansas.”
This is a confusing set of arguments in many ways. True, it is difficult to validate a model that
says, “anything can happen”. However, this is not a very interesting hypothesis in itself either.
There is no need to view a research strategy (the term they also are using) as a hypothesis that
needs to be tested. A starting point that the mechanisms for all cycles may be different is
certainly more open- minded than an ‘a priori’ assumption that all cycles are caused by the
same mechanisms. You can test any hypothesis on any population, but, strictly speaking, the
results only apply to the system studied. Generalisations can only be built on evidence of
such. Krebs adopts the generality assumptions “for reasons of simplicity to maximize the
testability of hypothesis”14. That is, by adopting his assumption, you can test hypothesis about
the Kansas voles on a different species in Finland. It is difficult to understand his argument
that this is a good research strategy. That the important mechanisms may change over time in
the same population complicates the problem. Nevertheless, this may be the case15. The only
12
He claims to have evidence that populations in Norway and Canada are synchronous. Today we know that this is not the case.
13
This effect is commonly referred to as the Moran-effect, after the Australian statistician P.A.P. Moran who first described this
phenomenon for the Canadian lynx (Moran, 1953).
14
Krebs, 1996
15
The story about Chitty’s study of Toxoplasma above is one example. That populations of Norwegian lemmings crash over the
winter in some years, almost certainly due to food shortage, but decline over the summer in other years, is another example. Even
5
way to deal with this problem is to carry out long term observational programs on the
demographic mechanisms of the dynamics (see below).
It is also likely that the generality assumption has been driven by a desire to make
general laws and theory about nature. This has maybe been especially motivated by the
success in physics and chemistry where generally accepted laws make up an essential part of
the science. I will later argue that such ‘laws’ first of all should be sought among the most
fundamental and incontestable interactions in the ecosystem16. After all, also in physics the
laws are not formulated at the higher levels of complexity, at the level of geophysical or
meteorological processes.
The comparative method
In line with their phenomenological approach, both Krebs and Chitty applies a comparative
method. In effect they ask “What is typical for cyclic populations?” and “What is typical for
the ‘decline phase’?” etc. Chitty writes in the introduction to his book: “Making comparative
statements is one of the tricks of the scientific trade.” (…) “The control for a regulated
population is an unregulated population – one that is increasing exponentially - and we
understand the former in terms of its difference from the latter.” He later says that we must
compare the phases of the cycle in order to understand why the population increases and why
it declines. His motivation is that without this approach we are left with “an unmanageable
set of variables”. A survey of specific traits between populations may of course be fruitful as
to unravel variation and similarities in nature, but to a priori expect that this variation must fit
into our categorisations of population dynamics at a high level of integration is likely to lead
us astray. The comparative approach may give us an indication about where to look for
essential mechanisms, but I would argue that one are most likely to gain such insight by
detailed physiological, behavioural and life-history studies of individuals.
The elimination method by the comparative approach will, according to Chitty, lead
to a set of conditions that may be ‘necessary’ (must be involved) or ‘sufficient’ (on its own) to
cause cycles. A set of ‘necessary’ conditions may be ‘sufficient’. To determine whether a
factor or a set of factors is ‘sufficient’ to cause, say, a decline, experiments must be carried
out. However, doing elimination experiments is a difficult approach because when removing
one part of the system, you create a new system that may not have much relevance for the
original system. For example, when removing all predators from a system with predator-prey
oscillations, herbivore-plant interactions that are negligible in the original system may come
into play and cause cycles. It is therefor imperative to also study the demographic
mechanisms and not just the superficial population level dynamics in such experiments. Many
simple laboratory systems of Daphnia (a small crustacean) are known to switch back and forth between different dynamical
attractors (McCauley, pers. comm.)
16
A set of such “laws” and postulates for population dynamics has been formulated by Turchin (manuscript for book chapter,
pers. comm.). That animals can not self-generate (see footnote 2) is an example of one such “law”, that there must exist some
upper density bound is another, etc.
6
such experiments with manipulations at the population level have been done without studying
the underlying mechanisms
Generally in biology, there has been a strong emphasis on classification and the
comparative method. Biologists are often criticised for an over-emphasis on statistical
hypothesis testing, and are often ignoring the parameter estimates of the statistical models
they apply. In effect, the hypothesis testing, then, serve only as a rather uncritical
classification criterion in the comparative method. Two individuals, groups of animals or
populations are never equal. Whether there is a statistically significant difference between
them is only a matter of how much effort we put into estimating their values, relative to how
different the values really are17. These aspects are not well reflected on among those who
apply the comparative approach to understand the small rodent cycles.
The reductionistic system orientated approach
Chitty disregards the usefulness of any observational study that does not have a control. He is
harsh in his critique: “That correlations are worthless without controls is one of the features
that makes the critics of population ecology doubt whether it can be regarded as a science”18.
I agree that proper controls are imperative in experimental studies, and much sin has been
committed with respect to this in ecological research. However, observational studies of real
systems, where one acknowledge the co-variation between variables as well as their variation,
is of prime importance for the understanding of any complex ecological system.
An alternative, or rather an additional, approach to understand complex systems is to
seek to identify the smallest relevant parts of the system and find out how they work.
Together with observations about the structure in the interactions between the components,
we can construct mathematical models and analyse the properties of these models. The
predictions of the models may be compared (validated) to population level data (e.g. the
fluctuations in numbers) to assess how good the models are. When we have been able to
construct good predictive models of many individual systems, generalities may be found in
the mechanisms of the systems. Generalities are most likely to be found in the most
fundamental and ubiquitous interactions in the ecosystem. One day when we know the
ecosystems well enough we might be able to construct general models that would work for all
populations. My friend in meteorology tells me that at present different models are used to
predict the weather in polar areas and in the tropics. Of course, the same physical laws apply
in the north and in the tropics. Hence it should be possible to construct general models that
are able to predict the weather in both “environments”. However, because the background
settings (range of sea-temperature, interrelations between land and sea, etc.) are so different,
structurally different models are preferred at present.
17
See David Anderson’s homepage for text, references and hundreds of citations about the theme:
http://www.cnr.colostate.edu/~anderson/null.html
18
p. 174 in Chitty’s book (1996).
7
This ‘reductionistic system oriented approach’, which I will get back to in the next
section, is more commonly adopted to understand population dynamics of other species,
especially fish, birds and fresh-water systems. Workers in these fields are not motivated by a
desire to solve ‘the enigma’ of any particular type of dynamics, but rather to predict the
population change for management purposes. Hence, they have been much less concerned
with phenomenological descriptions and focused more on quantitative predictions. The
methodologies applied in these fields are becoming increasingly more influential in small
rodent research.
Approaches in the study of populations; top-down or down-up?
We structure our view of nature hierarchically so that the units at one level consist of units at
a lower level. Biology deals with complex systems and is therefore maybe more
hierarchically organised than other branches of science. The disciplines in biology follow this
structure. Molecular biologists study molecules within cells, cell biologists study organelles
and cells, and physiologists study organs and processes within the whole organisms. Up to
this point, the limits between the levels are pretty fixed, as they fit with the distinction
between physical entities19. Ecology is the discipline of biology that deals with individuals or
higher units of hierarchical organisation. Also in ecology one refers to hierarchical levels:
individuals, demes, populations, communities, etc. The distinctions are here less exact.
Holism vs. reductionism in ecology
The relations between hierarchical levels in nature have been subject to a great deal of
controversy through the history of science. Early reductionists following Descartes’
philosophy of the scientific method in the 17th century opposed to supernatural explanations
and had a strong faith in that every phenomenon could be understood by studying the smallest
parts of which it consisted, that everything could be explained by laws of physics and
chemistry. At the rise of biology in the 19th century students opposed to the idea of the
reductionists that plants and animals were not essentially different from non-living matter,
and they invoked the concept of a ‘vital force’ to explain life. This ‘vitalism’ was fiercely
debated and challenged by the ‘physicalists’ who had adopted the world view of classical
physics emphasising on essentialism and reductionism. The demise of vitalism in the
beginning of the nineteen hundreds did not lead to a victory of the physicalists, but rather it
led to the rise of a new world-view, ‘orgaincism’20. This paradigm acknowledged that new
characteristics emerge as molecules form new entities and that the characteristics of living
organisms are not only due to their composition but also to their organisation. At higher levels
of integration, the properties of the smallest parts become increasingly less important. In
ecology, this mode of thinking led many to disregard the properties of the elements and rather
emphasised on the dynamics of the whole ecosystem. The most extreme form of holism in
19
Often referred to as “natural kinds” in philosophy.
20
I have more or less copied this historical scenario from Ernst Mayr’s recent book (Mayr, 1997).
8
ecology is represented by the ‘Gaia theory’21 (the theory that the biosphere acts as one
homeostatic super-organism) and the theory of ‘group selection’22 (the theory that
mechanisms in nature have evolved because they are to the best for the population or the
species as a whole). Today such theories are regarded as unscientific and rather theological
because they lack a mechanistic explanation and imply that there is a meaning and purpose of
the ecosystem23.
“System units” in nature
In all of natural science it is a major aim to be able to explain the phenomena under study in
terms of interaction between units at some lower level that are the “building blocks” of the
processes24. I will term these units the ‘system units’. In the study of population dynamics,
individuals are the ‘system units’. It is the individuals that are born, that give birth and die. If
you know what every individual in the population is doing, you also know what the
population is doing. In many ways the individuals in population ecology have the same place
as molecules have in chemistry. Chemists try to build a theory to predict the properties of
mixtures of substances from the properties of the molecules. One may be able to construct
models that, to some degree, can predict the properties of the mixtures from the physical
properties of the substances without going down to the molecular level, but such a theory is
incomplete. Knowledge about units at lower levels than the molecules, or individuals, may
help us to understand the properties of the ‘system units’, but once we know how the ‘system
units’ work in the system under study this knowledge can be ignored. However, there are
some important differences between individuals and molecules in this analogy. Every
individual is different owing to its unique genotype. The characteristic of an individual, its
state, is not a fixed attribute, but changes with the environment and time. Age, size, seasonal
physiological changes, reproductive status, immunological status, social status, etc. are all
ever-changing characteristics of individuals. Individuals give birth to new individuals with
particular characteristics and they die. They may also migrate in or out of a local population.
A population can only increase by births and immigration, and it can only decrease by deaths
or emigration. Hence models of population dynamics can be formulated as a book-keeping of
these individual level processes25. Unlike molecules, individuals seldom form new physical
entities with new emerging characteristics26.
21
See MNVIT-essay by Dag Hjermann: http://www.uio.no/%7ehjermann/gaia.htm
22
Although some forms of group selection may be possible, explanations of the type “birds reduce their clutch size because they
will avoid overpopulation” is by most biologists regarded as false. Whynn-Edvards is usually given the ‘credit’ for such
explanations, and is referred to in most textbooks about evolutionary biology.
23
Mayr gives a rather critical account of the reductionistic method in his two books, The Growth of Biological Thought (1982)
and This is biology: the science of the living world (1997). His view is criticised by Łomnicki (1992) and Caplan (1988).
24
I am here thinking about ‘basic research’. In applied research (management) one are more concerned with what works and
what gives the best predictions.
25
see e.g. DeAnglies & Gross (1992).
26
Molecules form new entities which acts as ‘system units’ at higher levels of organisation. I’m not sure if individuals do when
you group them together in a population. I’m not sure if the ‘population’ concept is necessary to be able to understand dynamics
of communities and ecosystems in an ecological time scale. However, many processes in population genetics are difficult to
explain without the concept of a ‘population’. Population dynamics may also be linked to such population genetics processes (e.g
fluctuating selection and inbreeding). Since, also demographic stochasticity is related to the population size, and since one for
management purposes is interested in the number of animals, the population has at least a heuristic meaning.
9
To be able to make models of the system that the “system units” form, we also need
to make assumptions about how the units fit into the structure of the system. That is, for
population dynamics we must make assumptions about the spatial structure of the population.
Inclusion of spatial structure in the model enables us to build migrations, heterogeneous
environments and local interactions into the model. If we have no spatial structure in the
model, we assume that every individual is experiencing the same environment27.
Levels of knowledge
I think it may be useful to structure our knowledge about population dynamics in the
following levels:
A. Population level. We gain knowledge at this level by studying population level
measurements such as population size (abundance), biomass or frequency
distributions of individual’s state (percent reproducing, weight and age distributions
etc.). At this level it is important to recognise the spatial pattern as well as the
temporal pattern. The population level patterns may give us an indication of what
demographic processes that cause them, but usually several scenarios are possible.
One may add knowledge about the co-variation between numbers in the study
population and the size of assumed interacting populations (e.g. predators) to this
level. From studying the fluctuations at the population level we may be able to
construct non-mechanistic (descriptive) dynamic models to predict the development
of the population although the mechanisms for the population regulation is not
known.
B. Demographic level. Demography is the study of individual processes that relate to
population rate of change. Such processes are age at first reproduction, time between
successive reproductions, fecundity (number of offspring), longevity, and time/age
specific probabilities of survival, maturation, emigration and immigration. To be able
to link these processes to the population regulation we need to know how these
processes relate to present and past population densities. One particular question one
can ask with knowledge at this level is: To what degree is variation in the population
level rate of change due to variation in population structure (e.g. age structure) and to
what degree is it related to variation in individual responses to past and present
densities?
C. Mechanistic individual level. Knowledge at this level is gained by answering
questions relating to: What is the cause of the individual level variation in
demographic traits? In relation to population regulation, we are especially interested
in the proximal causes of direct and delayed density dependence at the individual
level. To understand delayed density dependent regulation it is important to identify
where the memory for delayed density dependence resides. Whereas knowledge at
the higher levels mainly build on observational data, knowledge at this level must
also build on experiments that untangles the proximal causes of individual responses.
27
This assumption is in individual based modelling called “mixing”, see DeAnglies and Gross (1992).
10
Physiological and behavioural knowledge may help us to understand how individuals
respond to changes in the environment, and it may be useful to include physiological
mechanisms in population models at this level. To construct models of the population
from knowledge at this level we also need to include the dynamics of the relevant
environment, such as predators, diseases, vegetation, social structure, etc. Hence, we
also need knowledge at the next level of understanding:
D. Ecosystem interaction level. Important parts of the environment for individual
small rodents in addition to the density of conspecifics are the densities of
predators, parasites and competitors as well as quality and abundance of food
plants. We gain knowledge about these interacting populations (species) in the
same levels as above (A, B and C). It is important to realise that populations
that do not interact directly may interact indirectly because they both interact
with a third population28. Lags may occur in the regulation of one population
because “slowness” in the growth of the interacting populations (e.g. one may
say that it takes some time to convert prey biomass into predator biomass).
These levels are not distinct and independent. Knowledge at one level will help us to gain
knowledge at another level. Specific hypothesis relating to knowledge at one level may be
falsified (tested) by observations or experiments at the same level. Many different
mechanisms at a lower level may lead to the same pattern at a higher level (e.g. X more
individuals that are born will have the same result on the population size as if X less
individuals die). Hence, one cannot draw inferences about the mechanisms at a lower level
from knowledge at a higher level. In contrary, models for population dynamics built on
knowledge at a lower level predict only one pattern at a higher level (with some degree of
uncertainty29). Hence, these models may be validated against observations at a higher level.
However, the crude form of the Popperian hypothetical-deductive method is hampered with
difficulties because we for several reasons do not expect to be able to predict exactly what we
observe. Firstly because the quantitative observations at the population level as well as
estimated model parameters are associated with large uncertainties. Secondly, ecological
processes are inherently stochastic. Thirdly, due to the immense complexity of ecological
systems we can never claim to have found a “true” model. We may reject hypotheses that are
in strong disagreement with the observed data, but we will also certainly fail to falsify
“untrue” hypothesis. All models are ‘untrue’, but there are objective reasons to believe that
some models are closer to the truth than others. Hence, a hypothesis will stand, not until it is
falsified, but until someone comes up with a hypothesis that explain more of the relevant
observed data in the system. A good model for population dynamics builds on justified
mechanisms at a lower level (structure and strength of interactions) and is able to make
precise and accurate predictions at the population level30. We are not looking for true models,
28
Although I am using the term ‘population’ here, I still maintain the view that all interactions are local between individuals of
the same or a different species.
29
Stochastic demographic changes may lead to switching between multiple dynamic attractors (see previous section).
30
In modern applied statistics one rank competing models according to their ‘parsimony’ quantified by the models’ AIC
(Akaike Information Criterion), which builds on Kullback-Leibler information criterion theory. This criterion builds on finding
11
but we are looking for better ones, and we assume that this approach will lead us closer to the
truth. We may be looking for the Holy Grail, but we do not expect to find it. This approach is
rather different than the qualitative approach of Chitty outlined above.
Knowledge at the population level
There has been a rather strong faith in that population level data can tell us a lot about the
mechanisms of the regulation in small rodent science. Hence, many long time-series of snaptrapping data once or twice a year has been collected. Through time-series analysis of these
trapping indexes, i.e. statistical models where population rate of change is modelled as a
function of past and previous densities, one has over the last decade gained much new
knowledge about the dynamics at the population level. Time-series analysis has especially
been used to document geographical gradients in the density dependent structure, detect nonlinearities and separate between density dependence acting over the summer from density
dependence acting over the winter31.
However, population level descriptions of the cycles are nothing new. Descriptions of the
fluctuations have a very central place in Elton’s first work and in early review articles of the
field32. The cycles were characterised in terms of amplitude and periodicity, and especially
characterisations of the phases of the cycle were emphasised. These characterisations was
meant to help answer questions such as “how do the populations increase or decline?” Hence,
the phases of the cycles were defined as ‘increase’, ‘peak’, ‘decline’ and ‘low’ (i.e. the
classification builds on change in numbers and present densities, rather than past densities).
This is a rather different approach than time-series analysis33. On the one hand, the “phasedependency approach” is more mechanistically orientated because it focuses not only on
population size but also on body-mass distributions, frequency of breeders, length of the
breeding season etc. On the other hand, in order to understand how the populations are
regulated we need to know how these things are related to past and present densities, and not
only rate of change. Although life-history theory predicts that it would be optimal for the
individuals also to adjust their strategies according to the population rate of change, it is
difficult to believe that the animals can perceive the rate of change as a proximal cue 34.
Hence, we should assume that population rate of change that is not explainable by past and
present densities are due to random changes in the environment that is not part of the
population regulation.
the optimal trade-off between general models (with low bias but high variance in the predictions) and simple models (high bias
and low variance). Such model selection criterion, which has a strong theoretical foundation (see Burnham and Anderson, 1998),
has become a widely used criterion to select the “best” model in data-based models of demography and population dynamics.
31
In short, population rate of changed is statistically described as a function of past densities. The length of lags and in which
seasons they occur may give an indication of what parts of the system that may “contain” the memory of past densities. For
examples see Hansen et al. (1999) and Stenseth (1999).
32
see Krebs & Myers (1974), Taitt & Krebs (1985) and Chitty (1996, e.g. p. 93).
33
If the population fluctuations were perfectly regular, there would be a one-to-one correspondence between ‘cyclic phase’
defined by the combination of density and population growth and ‘cyclic phase’ defined by past and present densities. However,
the fluctuations are not perfect. There is considerably irregularity in the densities of peaks and the periods between successive
peaks may vary from 3 to 5 years, and the length of each of the phases may vary. This irregularity makes time-series analysis
possible without assuming a priori shapes (e.g. linear) of the density dependence. In statistical terms, in perfect fluctuations there
is a total confounding between density at any lag with densities at any other lag.
34
See McNamara (1996).
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Knowledge at the demographic level
The demographic level of understanding (B above) is maybe the level that has received the
least focus in empirical studies. Although one in the “phase-dependency approach” has
focused on measurements other than population size, these build to a small extent on
estimates of individual demographic traits. Instead, they present frequency distributions of
animals’ state in “snap-shots” of time35. The same frequency distribution of individual states
may be produced by several individual level mechanisms (e.g. many large individuals in the
population may be due to and older age-structure or that young animals grow larger). This
shortcoming of individual level observations together with the qualitative descriptions in a
“phase-dependent” framework has made it difficult to build realistic mechanistic models for
the population fluctuations. However, much data has been collected at this level over the past
decades, and is currently being analysed. A time-series approach to understand variation in
individual measurements of demographic traits has not yet been attempted (that is describe
the individual level variation in terms of past and present densities), but is maybe one of the
most promising avenues for the future.
Mechanistic knowledge at the individual level
Naturally, the ultimate aim in the science of small rodent cycles is to understand the dynamics
as an interplay between all the relevant interacting parts in the ecosystem (level C and D
above). Hence, hypotheses are often labeled with terms like ‘specialist-predator hypothesis’,
‘plant-defence hypothesis’, ‘nutrient-recovery hypothesis’, etc. A great deal of research on
small rodents has been done at the ‘mechanistic individual level’ (C above). Research
interests include physiological responses and life-history (reproduction, survival, etc.)
responses to a wide range of environmental stimuli such as food quality, predator odours,
pathogens, day length, social structure, landscape structure, etc. This research is faced with
the unavoidable trade-off between experimental control and reality in the background
environment. Since knowledge at the ‘demographic level’ (B above) is incomplete it is
difficult to assess the relevance of knowledge at the ‘mechanistic individual level’ for the
population dynamics. It is also, for the same reason, difficult to design experiments that have
relevance for the population dynamics. Although we are starting to get fairly good knowledge
of how individuals respond to their environment (C above), we also need knowledge about
the dynamics of the environment (D above) to construct mechanistic ecosystem models. How
the small rodents affect the relevant parts of the environment we know little about. We know
especially little about interactions involving food plants, vegetation and pathogens, but also
data on predator populations are rather scant36.
35
In the influential review of Krebs & Myers in 1974, even in the section about the “Demographic machinery” there is mainly a
review of population level data collected from snap-trapping or short term live-trapping.
36
There has been strong tendencies to favour hypothesis that include simple interactions that we know are there, eg. predatorprey interactions. The favouring of such hypothesis is not based on any knowledge that other interactions are not important,
neither is it based on a detailed knowledge about the predator-prey interactions.
13
Summing up
How long will we continue to say, “The small rodent cycle remains an enigma”? And if we
stop saying it, will it be because we have solved the puzzle or because we think it is a stupid
thing to say? Krebs said in his 1996 review ”Population ecology is not a baseball game in
which one team wins and another team loses, one team is right and others are wrong”. While
I agree with the first part of the sentence I would change the second part to ”every team will
get somewhere, but some teams will be more successful.” We have come a long way since
Elton, and we will continue to go further…
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