Download Biological interactions in fish stocks: models and reality

Rit Fiskideildar 16 (1999) 295-305
Biological interactions in fish stocks: models and reality
Kjartan G. Magnússon
Science Institute, University of Iceland
Dunhaga 3, IS-107 Reykjavík, Iceland
ABSTRACT
Three types of biological interactions; predation, competition and cannibalism are discussed in
the context of marine ecosystems. Their effects on stock dynamics are considered and the empirical evidence for biological interactions reviewed. The main predictions from various population
models which include some of these interactions are discussed and compared to empirical observations of stock dynamics, in order to see how well the predictions accord with observations.
Although some limited evidence exists, showing that interactions - predation in particular - can be
important, the fact remains that due to the high level of noise in data from marine ecosystems as
well as the confounding effects of environmental varibility, it has proved difficult to find evidence
demonstrating conclusively that biological interactions play a significant role in regulating stock
dynamics. The purpose of large- scale multispecies models incorporating biological interactions
is discussed, a range of such models for boreal ecosystems is reviewed and the necessary and
desirable features which such models should have are given.
Keywords: Predation, competition, cannibalism, multispecies models.
INTRODUCTION
lakes (Seip 1997), which are relatively constant
and predictable compared to for example pelagic
marine ecosystems. Nevertheless, the results of
Seip (1997), looking at interaction pairs of
phytoplankton and zooplankton in a Norwegian
lake and attempting to relate observations to
prototype predation, competition and mutualism
phase-plane diagrams, were less than conclusive.
There are essentially three types of interspecies interactions: predation, competition and
mutualism. Predation is the one most easily
observed and quantified, since consumption
rates of one species on another can be observed
and calculated from measurements of stomach
contents given suitable models of digestion or
stomach evacuation. Nevertheless, the effect of
Biological interactions in marine ecosystems,
between species as well as within species, may
have a significant influence on stock dynamics and
can contribute to the high variability frequently
observed in recruitment and stock sizes. However, it has proved difficult to determine and
quantify the dynamical effects of biological
interactions since these effects are usually confounded by effects due to environmental variability, the relative importance of the two in
determining abundance being the subject of
much debate. Effects of biological interaction
may be more easily observed and tested in more
stable environments, such as inshore benthic
ecosystems (Branch et al. 1987) or freshwater
Dedicated to Professor Unnsteinn Stefánsson in honour of his contributions to oceonography and education.
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predation on the dynamics and abundance of the
stocks involved is less tangible. Competition is
more difficult to observe and empirical verification of its effects is scarce. Mutualism is probably much rarer in marine ecosystems than predation and competition and evidence for it is even
more difficult to find. It will therefore not be
considered here.
Intra-species interactions may take the form
of competition for resources – as with competition between species – or cannibalism. Again,
empirical evidence for density dependent effects
are hard to come by, but cannibalism has been
observed in a number of species and can play an
important role (Smith and Reay 1991).
The effects of biological interactions can be
studied in two complimentary ways; by looking
for empirical evidence and statistical relationships, and by the investigation of mathematical
models. In this article we will consider three
types of interactions in turn; i.e. predation,
competition and cannibalism, and review, admittedly rather superficially, models and model
results and see how they relate to observations
of the real world.
dependent on capelin abundance is given further
support by the observation that total consumption by cod decreases as the consumption of
capelin decreases, showing that cod is only
partially able to compensate for a decreased
availabilty of capelin by switching to other prey
types (Magnússon and Pálsson 1991).
Mathematical models of populations with predator-prey interactions tend to be of two types:
1. Fairly abstract models where the population
sizes are usually modelled by systems of
coupled differential equations and general
assumptions are made about the nature and
form of the interaction of the predator and
prey. The qualitative behaviour of these
models is usually studied by analytical techniques and computer simulations play a
secondary role.
2. Concrete models, often pertaining to particular species and areas, where the various biological processes involved, such as feeding,
reproduction, mortality, migration, etc. are
modelled explicitly. Such models tend to be
very large and data intensive and cannot be
studied analytically. Computer simulations
are the only option.
Predator-prey systems and/or competition
systems of the first type have been extensively
studied as regards existence of long term equilibrium states and their stability properties, existence of oscillatory solutions, existence of
chaotic dynamics and persistence of the system.
The main relevance of these studies in understanding actual predator-prey systems is in
throwing some light on the qualitative dynamics
of such systems, e.g. whether oscillatory behaviour is a common feature and under which conditions is it most likely to occur, which processes
and which functional forms tend to be stabilizing and which destabilizing, how the dynamical
behaviour (stability or oscillations) depends on
the number of predator species and the number
of prey species and on the number and strengths
of the trophic interactions, and so on.
General predator-prey systems with one predator and one prey have been shown to have
either a stable equilibrium or stable sustained oscillations under fairly general and reasonable assumptions (May 1972). Furthermore, if there is
a stable equilibrium state then it is generally a
PREDATION
The main emphasis in theoretical and empirical
studies of species interactions has been on predation since it is relatively easy to observe, and
probably more important than competition. It is
usually straightforward to observe and quantify
predation using stomach content data, together
with a digestion rate model. Mortality rates due
to predation can also be calculated using stomach
contents, catch-at-age data and/or abundance
data; either indirectly as in Multispecies Virtual
Population Analysis (Helgason and Gislason
1985) or directly as in Magnússon and Pálsson
(1989). However, demonstrating that predation
has a measurable and significant effect on stock
dynamics and long-term stock sizes is more difficult. Direct empirical evidence is scarce, but there
are strong indications from Icelandic waters that
the abundance of cod has a significant effect on
the population development of shrimp and that
the abundance of capelin has a significant effect
on individual growth rate of cod (Stefánsson et
al. 1998). The hypothesis that cod growth rate is
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spiral point, i.e. the system will oscillate with
decreasing amplitude towards the equilibrium
state. Existence of stable sustained oscillations
has been demonstrated for a variety of predatorprey models and the existence of chaotic dynamics for Lotka-Volterra type systems with one
predator and two prey and for a three species
food chain was shown in Klebanoff and Hastings (1994, 1994a).
The general conclusion which can be drawn
from these theoretical studies is that oscillatory
behaviour is a common and indeed almost universal feature of predator-prey models, the oscillations being either decreasing with time or sustained. If the model predicts a stable equilibrium, then the stock sizes will tend towards this
equilibrium in an oscillatory manner. For reallife systems, perturbations due to external influence (i.e. environmental) are constantly taking
place. Therefore, an otherwise stable system will
in general not be in a steady state, i.e. it is constantly being perturbed from its equilibrium state,
oscillating back only to be perturbed away once
more. Oscillations are therefore predicted to be
the “natural state“ of predator-prey systems.
It has not been easy to verify these predictions.
Oscillations are a common feature of marine fish
stocks, but it is difficult to separate the effects of
biological interactions and environmental variability.
Fairly simple predator-prey models with one
predator and two prey species can predict the
suppression of one of the prey species. A predator and a prey species can coexist in a stable
long-term steady state, but the presence of a
second prey species may disrupt this co-existence and result in the suppression of the original prey species, since a high predator abundance
can be maintained due to the alternative food
source. Some examples of this phenomenon exist
for terrestrial mammals (e.g. wolf-caribou-moose,
lynx-snowshoe hare-arctic hare, see Bergerud
(1983)), but no definite cases are known for
marine ecosystems. However, the cod-capelinshrimp complex in Icelandic waters appears to
be a possible candidate.
The purpose of theoretical models is to gain
some insight into the qualitative dynamics of
predator-prey systems. However, it is usually
only possible to draw general conclusions and it
is not easy to relate such models to specific
ecosystems. Large-scale models, aiming for
more “ecological and biological realism“, have
therefore been developed to deal with a variety
of situations and areas, modelling the various
processes – biological and environmental –
which are thought to be important, e.g. migration, recruitment, predation etc., explicitly.
Submodels of these processes are combined to
form a large-scale model representing the
ecosystem. Such models are generally termed
multispecies models, but usually the primary
interaction between species is via predation. The
purpose of multispecies modelling is manifold:
1. As a tool for formal testing of whether or not
certain interactions or effects exist. Formal
statistical testing of the presence of interactions and effects involves estimating parameters, carrying out sensitivity studies and
comparing log likelihood values (in order to
see if the fit is improved). Thus, some idea
of the importance of various features (such as
predator-prey relationships, environmental
conditions, area structure, variable migration
rates etc.) can be obtained.
2. As a simulation tool to answer “what if“ questions and to provide insight into the system.
The model should be able to reproduce
observed time series of variables deemed to
be of importance. This does not mean that
large-scale multispecies models are to be
regarded as a “true“ representation of the real
system. Many such models have sufficient
degrees of freedom to be able to reproduce
most time series by selecting appropriate parameter values. However, by a suitable parameterization of the model and estimating
parameters in a statistically sound manner,
some degree of confidence may be obtained
that the model is a reasonable representation
of the actual system.
3. To obtain parameter estimates which can be
used as input in other management procedures or to provide direct or indirect management advice. Such models will in general be
a very simplified representation of the real
world with few parameters to estimate.
4. As a system model (operating model) for use
as a representation of the real system. This
type is used to generate data for testing mana-
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gement procedures. This has been done by the
Scientific Committee of the International
Whaling Commission to test proposed
management procedures (Kirkwood, 1992).
The management procedures must be tested
under a variety of assumptions about the various
processes modelled, and it is therefore not
necessary to get the formulation and parameter values in the processes precisely right. The
model must necessarily include a stochastic
component in the data-generating procedure.
Several multispecies models have been developed in the past two decades or so. The models
mentioned here are primarily those with some
applicability to Arcto-boreal regions.
MSVPA (Multi Species Virtual Population Analysis) was developed in the early eighties (Helgason and Gislason 1985). The main purpose was
to calculate predation mortalities in a VPA-like
manner, in addition to the fishing mortalities as
obtained in single species VPA, based on formulations by Anderson and Ursin (1977). MSVPA
can also be used in a forward mode (when it is
referred to as MSFOR) to simulate the effects of
changes in for example mesh size, effort etc.
Predation mortalities are modelled in MSVPA
but feeding rates and predator growth are taken to
be constant, which is an unrealistic assumption
for Arcto-boreal systems. In its present form,
MSVPA does not include area structure and
migration, and in fact migration may be difficult
to model backwards in time.
The continuum model of Reed and Balchen
(1982) is probably the first attempt to construct
an ecological model of an Arcto-boreal system.
It includes many of the features required for a
multispecies model of such a system, that is
predation – on capelin by cod and marine
mammals- and area structure, which is of fundamental importance in Arcto-boreal models. In
the MULTSPEC model (Bogstad et al. 1997),
developed at the Institute of Marine Research in
Bergen, Norway, area structure and migrations
are considered explicitly and feeding rates are
variable, depending on total food abundance
according to formulations adapted from Anderson
and Ursin (1977).
The Arcto-boreal model BORMICON (BORreal MIgration and CONsumption) was developed at the Icelandic Marine Research Institute
(Stefánsson and Pálsson 1997). This model relies
to some degree on MULTSPEC, but has the
advantage of being more recent and therefore
being coded using more recent programming
methodology and making use of the experience
gained in the development of MULTSPEC.
BORMICON is more general and more flexible
than MULTSPEC, for example as regards components included in the model, types of data
which can be utilized and likelihood functions.
The ECOPATH and ECOSIM models (Walters
et al. 1997) consider all components of the ecosystem (not just a selection as for example
MULTSPEC) in a holistic way. The former is a
stationary model. It sets up mass balance equations for the flow between the various components of the system. On the other hand, ECOSIM
is a dynamic model which replaces the mass-balance equations by sets of differential equations
for the various components. The equilibrium assumptions of ECOPATH are used to obtain values
for some of the parameters used in ECOSIM.
Values of other parameters are basically guesswork. An attractive feature of both models is that
the ecosystem is considered as a whole and,
furthermore, that they are not too complex in the
sense that parameter values can in many situations be obtained and simulations carried out.
ECOPATH has in fact been used on some Arctoboreal systems such as in the Bering Sea and Icelandic waters. However, it is not statistically based
and the empirical foundation for many parameter
values is weak. The ECOSIM model is only designed to answer “what if“-questions, such as
what happens if effort directed towards one group
of species is varied. Unlike MULTSPEC or
BORMICON, these models are not able to give
parameter estimates or to test for the presence of
effects or interactions.
The ecological model for the Barents Sea,
being developed at the University of Bergen, Norway by Giske and others, also deserves a mention
(Giske et al. 1998). The approach taken there is
quite different from that taken in MULTSPEC,
in that the spatial distribution and behaviour of
cod and capelin is predicted using dynamic programming (and other methods) to optimize fitness
functions. Interactions between cod and capelin
are included in the model via spatial overlap.
Other models have been designed for more re-
298
stricted situations, e.g. a model of cod-capelin
interactions in Icelandic waters (Magnússon and
Pálsson 1991) and a simulation model for codcapelin-shrimp interactions based on statistically
obtained empirical relationships (Daníelsson et
al. 1997).
There are some notable differences between
Arcto-boreal systems and temperate systems.
The former have fewer biological components,
a large part of the diet consists of a few key
prey species (in particular capelin) and the
reservoir of other food is probably smaller than
in temperate systems, such as the North Sea
where MSVPA has found its primary application.
Thus “other food“, as defined in the MSVPA
and acts as a buffer to ensure that fish always
obtain the required amount of food, is only available to a much lesser extent in boreal systems.
This means that individual consumption is more
variable and, consequently, so is individual growth.
Another important difference between the two
types of systems is the variability in the environment, which is much greater in Arcto-boreal
systems. This entails the necessity of including
some environmental variables, temperature being
the minimum requirement. Initially, the values
of these variables may not be modelled, but the
values read from an external file.
In general, the number of fleets and their diversity is smaller in Arcto-boreal systems. Modelling the fishing operations should therefore be
easier and, in addition, management strategies
easier to implement since there are fewer participants.
There are a number of features and components which it is necessary or desirable to include
in a simulation model of an Arcto - boreal marine
ecosystem (Stefánsson and Pálsson 1998):
1. Variable environment (e.g. temperature,
nutrients, primary production)
2. Components: Fish predators (e.g. cod, herring),
prey (e.g. capelin, herring, shrimp), apex predators (marine mammals and man).
3. Spatial structure and hence variable overlap
between species
4. Relatively fine temporal structure (e.g. time
interval of one month), as things can happen
fast in time and space (e.g. capelin migration)
5. Stock structure (e.g. age, length, maturity)
6. Sub-models
a) Predation mortalites dependent on predator abundance, prey abundance, abundance
of other prey and on spatial and temporal
overlap. The form of the relationship
between prey abundance and predation rate
is of major importance in models as in real
life: a relationship where the mortality rate
due to predation decreases with decreasing
prey abundance at low prey densities – the
so-called type III functional feeding response (Holling 1959) – will in general
have a stabilizing effect on the predatorprey dynamics, whereas the opposite is the
case for a type II relationship (predation
mortality rate increases with decreasing
prey abundance at all prey densities). The
dynamics of both predator and prey may
therefore be substantially different depending on the functional relationships used.
b) Variable growth rates depending on the
availability of food (prey abundance for
fish predators, plankton density for prey and
on environmental conditions).
c) Migration (and feeding movements). A submodel of migration can for example be based
on transition matrices (Bogstad et al. 1997,
Stefánsson and Pálsson 1997) or partial differential equations (Reed and Balchen 1982).
d) Recruitment as a function of environmental conditions, size and composition of the
spawning stock and might include cannibalism.
7. Parameter estimation (with a flexible likelihood function, flexibility with respect to the
incorporation of a number of available data
sources) and the ability to test the significance of effects such as interactions.
An interesting result from studies of multispecies models is the demonstration that sometimes changes in one component in the system
can lead to changes in the other components
which are counter-intuitive. An example is
provided by the model of fur seals and hake off
South Africa (Punt 1994). It turns out that if hake
is modelled as one species (it is managed as one
species at present) then a seal cull would lead to
an increased stock of hake. However, if hake is
modelled as two species, the larger preying on the
smaller (which is in fact the case) then predatorprey interactions between the two species of hake
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together with differential predation rates by seals
on the two species, could mean that the result of
a seal cull is a smaller hake stock. This is
contrary to what might be expected.
Bogstad et al. (1997) provide another example
of this phenomenon. It is well known that minke
whales consume capelin, so it is reasonable to
expect that an increased whale stock would lead
to a smaller capelin stock. In fact, model results
indicate that the opposite might be the case. This
is due to strong predator-prey interactions
between herring and capelin and the fact that
herring is also preyed on by whales. An
increased whale stock leads to increased whale
predation on herring which in turn reduces
herring predation on juvenile capelin.
A third example is the effect of mesh size
changes on long-term yield. Single species models
generally predict that a higher yield will result
from an increase in mesh size, but in multispecies models the opposite can occur. The reason
is that the abundance of predators may increase
by increasing the mesh size, leading to higher
predation mortalities especially on younger fish
(both from cannibalism and predation by other
species). This will in turn lead to lower stock
sizes and hence to lower yields. The real possibility of such effects has been demonstrated
using the MSVPA/MSFOR model for the North
Sea (Pope 1991).
From a mathematical point of view, these
results are not very surprising for a system with
many interacting variables, but they nevertheless
draw attention to the fact that ecosystems are
very complex and even the direction of changes
resulting from certain actions is not always easy
to predict. Multispecies models are therefore of
considerable value in demonstrating how ecosystems can behave in ways which are both complex
and at times counter-intuitive.
It is still too early to pass judgement on the
success or otherwise of large-scale multispecies/
ecosystem models. They have in many cases
been shown to be fairly successful in reproducing historical time series such as weights-at-age
for Barents Sea cod (Anon. 1996) and early computer runs of BORMICON are promising (Stefánsson and Pálsson 1997). However, formal statistical comparisons between retrospective predictions from single species models and multi-
species models – e.g. running both models using
historical data such as catch and recruitment
series, and comparing the observed time series
of other variables such as weights-at-age and
stock numbers with the predictions from the two
models, thereby testing rigorously for the presence of predation effects – will be a real test of
the importance of multispecies effects as well as
of the usefulness of multispecies models.
COMPETITION
A range of mathematical models have been
constructed to describe inter-species competition,
ranging from simple ordinary differential equations models of the Lotka-Volterra type to more
elaborate age- and/or size-structured models. A
common feature of these models is the existence
of multiple steady states with one or more species at low stock levels. A change in the abundance of one species due to external effects such
as changing catch rates or different environmental conditions can result in a transition to a
different steady state. Such transitions in a competition system to a state with different stock
levels, with one stock significantly lower and
another stock significantly higher than before,
have been termed competitive species replacements. In order to investigate whether these
model predictions have been observed in real
ecosystems and if there is any empirical evidence
for species replacements, one should look for
cases where a species has apparently filled an
ecological niche which has become vacant due
to a decrease in a competing species. The potential examples are generally of pelagic species.
The best known examples are the pilchard-anchovy pairs in various parts of the world, but
other possible cases are herring-blue whiting and
herring-capelin in the North-Atlantic, and herringAtlantic mackerel off New England and the Canadian Maritime Provinces (Skud 1982).
The question of whether these and other pelagic fish species compete with one another and
whether the reduction of one species led to its
replacement by another has attracted considerable attention. However, pelagic fish occupy regions where environmental fluctuations are high
and therefore evidence for such inter-specific
competition has proved elusive. What little evi-
300
dence there is, is circumstantial. Stocks of California pilchard, Peruvian pilchard, Far Eastern
pilchard, and South African pilchard have all collapsed and have been followed by apparent increases in the size of anchovy stocks. This has
led to speculations that the increases in anchovy
stocks were due to reduced competition by
pilchard (Kawasaki 1983). The possible competitive replacement of South African pilchard by
anchovy in the Benguela ecosystems off Southern Africa has been extensively studied. Models
of this interaction show that a decrease in one
stock is followed by an increase in the other,
either in an alternating way (Silvert and Crawford 1988), or the anchovy stock increasing
when the pilchard stock was reduced by overfishing, and pilchard again becoming dominant
when the fishing pressure on it is reduced
(Korrubel 1992). However, data supporting the
theory of competitive species replacement is
limited. Admittedly, there is a strong negative
relationship between the catches of the two
species, but the interpretation of this is
confounded by a number of other factors (Branch
et al. 1987). Furthermore, the estimates of
anchovy biomass show it to have been fairly
constant after the collapse of the pilchard stock
and far from replacing the lost biomass of pilchard. In this case, the suggestion of competitive replacement is therefore ambiguous and the
supposed replacement of pilchard by anchovy
could simply be a reflection of the collapse of
the former species due to overfishing and the
subsequent switch of effort to the latter. Evidence of replacement is even weaker in most of
the other possible cases. A review of the literature by Daan (1980) identified only one possible example of species replacement, i.e. in the
Californian anchovy-pilchard pair, and even this
is uncertain. However, the lack of evidence does
not imply that competition between species is
non-existent, only that evidence for it is hard to
find, perhaps because the effects of environmental variability dominate and the effects of competition are of secondary importance (Branch et al.
1987).
The possibility of competition for food between herring and capelin in northern waters has
been suggested (Nikolsky and Radakov 1968).
Based on commercial catches, it might be hypo-
thesized that competitive species replacement
took place in Icelandic waters with the capelin
stock increasing following the collapse of the
herring stock in the 1960’s. There is however, no
evidence to support this hypothesis since the size
of the capelin stock prior to the collapse of herring is not known. The stock of capelin may in
fact always have been large and there are indications of large stock sizes of capelin earlier in
this century (Hjálmar Vilhjálmsson pers. comm).
The possible replacement of the Atlanto-Scandian herring by blue whiting is more plausible,
but the evidence for that is circumstantial (Daan,
1980, Hjálmar Vilhjálmsson pers. comm.). The
competition between herring and capelin in the
Barents Sea has been suggested, i.e. grazing by
juvenile herring on low stocks of zooplankton in
the mid-1980’s may have caused food shortages
for capelin (Skjoldal and Rey 1989), and the
reduced food competition due to a low herring
stock in the 1970’s may have contributed to the
high stock of capelin in this period (Dragesund
and Gjøsæter 1988). However, this is highly speculative and the real effect of herring on capelin
dynamics may in fact be through predation by
juvenile herring on capelin larvae and juveniles
(Hamre and Hartlebakk 1998).
It would therefore appear that the predictions
of competition models are not substantiated by
observations. There seems to be little direct evidence for inter-species competition among fish.
There are some suggestions or indications, based
either on general considerations such as two species occupying a similar trophic niche or on changes
in commercial catches , i.e. a decline in the catch
of one species was followed by an increase in
the catch of the other. The more obvious explanation for the changes in catches is simply a
change in the relative fishing effort due to one
of the species being reduced by overfishing.
However, inter-species competition may be
observed indirectly by responses to changing
environmental conditions. A dominant (i.e.
more abundant) species may respond positively
to environmental conditions such as temperature, whereas the subordinate species responds
negatively. The negative response of the subordinate species may be a reaction to a change in
the abundance of the dominant species, and
hence increased competitive pressure, rather
301
than a direct effect of the physical environment.
The response might othervise have been positive in the absence of the dominant species. The
abundance of the subordinate species is thus
controlled by the dominant species. This behaviour is easily described and “explained“ by a
competition model consisting of two ordinary
differential equations. Cases where the
response to changing environmental conditions
is positive when a species is dominant and
negative when it is subordinate would strongly
indicate some sort of competition or interaction. Examples of this behaviour are found in
the herring-mackerel pair off the east coast of
USA and Canada as well as in sardines and
anchovies off California (Skud 1982). Similar
phenomena have been observed in freshwater
species.
Occasionally a negative correlation between
the abundance of two candidate competing species is observed. Two “competing“ species may
interact in other ways and the important interaction, as well as the explanation for a negative
correlation in abundance, may be predation rather
than competition. Cases in point are predation of
juvenile herring on capelin larvae mentioned
earlier and predation by pilchard and anchovy on
each other’s eggs and larvae.
tant effect on the dynamics of the cod stock. For
example, there is a significant negative relationship – probably due to cannibalism –
between recruitment in Icelandic cod and the
abundance of immature cod (Bogstad et al.
1994) and including cannibalism gives a better
fit between abundance indices from surveys and
the VPA estimates for cod age groups 1-3 in the
Barents Sea (Tjelmeland and Bogstad 1998). It
is therefore believed that cannibalism is sufficiently important to be taken into consideration
in the assessment and management of the
Barents Sea cod stock (Anon. 1996a) and it is
suggested that cannibalism is a factor contributing to the observed fluctuations in recruitment
of three year old cod (Ulltang 1996; Moxnes
1998).
Some estimates of mortality rates due to cannibalism have been obtained for Icelandic waters
and for the Barents Sea. Stefánsson et al. (1997)
gave a point estimate of 0.19 for the annual mortality rate of 1 year old cod in Icelandic waters
due to cannibalism. By relating observed recruitment for Iceland cod to the abundance of immature cod, Bogstad et al. (1994) estimated that the
value of the cannibalism mortality rate on 0-2
year old cod is 0.71 on the average over the period 1970-1991, i.e. an average annual value of
0.24. Estimates for the Barents Sea are even higher
(B. Bogstad, pers. comm.) and the mortality rate
is probably negatively related to the abundance
of capelin, the main prey of cod. In their analysis
of data up to 1992, Bogstad et al. (1994) found
no evidence that cod cannibalism decreased with
increasing biomass of capelin. However, using
more recent data, Bogstad has found strong indications that increased capelin biomass has a
negative effect on cannibalism in cod (Bogstad,
pers. comm.).
Theoretical studies of population models have
shown that cannibalism can have a considerable
effect on population structure and dynamics.
This effect can even be positive. For example,
Kohlmeier and Ebenhöh (1995) have shown that
cannibalism by the predator can in some cases
lead to a higher long term predator stock size.
Furthermore, cannibalism can enable a population to survive when food for the adults is scarce
– the so-called life boat effect (van der Bosch et
al. 1988).
CANNIBALISM
Cannibalism has been observed in a great variety of fish species. It is common among piscivores and can make a significant contribution to
the diet (Smith and Reay 1991). Rates of losses
due to cannibalism can sometimes be very high,
e.g. 60% annual mortality of the 0+ age group
has been observed in walleye pollock in the
Eastern Bering Sea (Dwyer et al. 1987). It has
been demonstrated, that adult Atlantic cod eat
large numbers of their young, especially those
of ages 0 to 2 years (Bogstad et al. 1994), and
that the frequency of occurrence of cannibalism
in the Barents Sea increases with the abundance
of juvenile cod. Although the contribution of
cannibalism to the diet of Atlantic cod is fairly
small – it does not exceed 9% on the average,
even for the largest cod, and is somewhat higher
in the Barents Sea than off Iceland – (Bogstad
et al. 1994), it can nevertheless have an impor-
302
It has been shown that cannibalism can in
some cases have a stabilizing effect on a predator – prey system. Kohlmeier and Ebenhöh
(1995) studied a two-dimensional predator-prey
system of a Lotka-Volterra type with predator
satiation, where cannibalism is incorporated by
letting the total food supply for the predator be
a weighted sum of the prey biomass and the
predator biomass. They show that cannibalism
can stabilize a predator-prey system by eliminating cycles that can otherwise occur in the
absence of cannibalism. These cycles are caused
by the interaction between prey carrying capacity and predator satiation. Recently, van den
Bosch and Gabriel (1997) showed that cannibalism can stabilize a predator-prey system where
the oscillations are due to age structure. Their model
is essentially a system of two differential equations for the adult predator population and the
prey population, with delays in the equation for the
former. This system can oscillate due to the
delays, but the stability region (in a two dimensional parameter space) is enlarged by increasing the “cannibalism pressure“. The results of
those two papers lead van den Bosch and Gabriel
to conclude that „In predator – prey systems,
cannibalism by predators can stabilize both externally generated (consumer-resource) as well as
internally generated (age-structure) fluctuations.“
There are, however, exceptions to this and in
Magnússon (1999) an example is given of a predator-prey system where cannibalism can lead
to oscillations in both predator and prey abundance in a system which is otherwise stable. It
is shown that sustained oscillations are not
possible without a high juvenile mortality rate
and low recruitment rate. For cod, the mortality
rate for juveniles is likely to be high, in particular under harvesting, and the age at maturation
of 6-7 years is high. Thus, only a small portion
of the total juvenile population will be recruited
in any given year and the recruitment rate to the
mature population is therefore fairly low. The
necessary conditions for sustained oscillations
are therefore likely to be satisfied for the cannibalistic predator-prey system consisting of cod
and capelin, but it is not possible at this stage
to draw any firm conclusions whether cannibalism might contribute to the fluctuations that
characterize the dynamics of the stocks of cod
and capelin in the Atlantic. Both stocks are
heavily harvested, also at the juvenile stage in
the case of cod. It is therefore worth noting that
harvesting juvenile fish will make oscillations
more likely, since not only does harvesting
increase the juvenile mortality rate but also
decreases recruitment rate since a smaller fraction of the total juvenile stock will survive to
reach the age of maturity.
The main result in Magnússon (1999) is that
sustained oscillations are not possible for low
levels of cannibalism, but at sufficiently high
levels oscillations can set in. Therefore, cannibalism can be a destabilizing force in a predator-prey system. This is contrary to the results
of Kohlmeier and Ebenhöh (1995) and van den
Bosch and Gabriel (1997). The main reasons for
this discrepancy are the following:
In the Kohlmeier and Ebenhöh model, predators are not separated into juveniles and adults.
All individuals are therefore vulnerable to
cannibalism and all individuals indulge in cannibalism. The model of van den Bosch and Gabriel
is fully age structured, but the only effect of
cannibalism is an increased mortality rate of
juveniles. The adults do not benefit in terms of
increased growth rates. The conversion efficiency of juvenile biomass to adult biomass via
cannibalism is therefore zero. In view of this, it
can be postulated that all of the following
features are necessary for cannibalism to be
destabilizing:
1. Predator population is separated into adults
and juveniles, with adults feeding on juveniles.
2. Low recruitment rates to the adult population,
e.g. due to a high age at maturity and/or high
mortality of juveniles.
3. Cannibalism leads to increased growth rates
of adults as well as increased mortality rates
of juveniles.
However, the effect of cannibalism on the dynamics of predator-prey systems are not straightforward and a number of other factors can be important. Cycles and oscillations can occur in
predator-prey systems without cannibalism and
can indeed also be caused by environmental fluctuations. The main issue is however that cannibalism may be yet another factor contributing to
the variability of fish stocks.
303
SUMMARY
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