Download Spatial heterogeneity and biotic interactions – scaling from

Spatial heterogeneity and biotic interactions
– scaling from experiments to natural systems
Ulf Bergström
2004
Department of Ecology and Environmental Science
Umeå University
Sweden
AKADEMISK AVHANDLING
som med vederbörligt tillstånd av rektorsämbetet vid Umeå universitet för
erhållande av filosofie doktorsexamen i ekologi kommer att offentligen
försvaras torsdagen den 3 juni 2004, kl. 13 i Stora hörsalen, KBC
Examinator: Professor Lennart Persson, Umeå universitet
Opponent: Professor Sebastian Diehl, Ludwig Maximilians Universität
München, Tyskland
ISBN 91-7305-639-1
Printed by VMC KBC, Umeå University
© Ulf Bergström 2004
Cover: Predator and prey – the isopod Saduria entomon and its main prey in the Baltic
Sea, the amphipod Monoporeia affinis. Layout by Ulf Bergström
Organisation
Umeå University
Dept of Ecology and Environmental Science
901 87 Umeå, Sweden
ISBN 91-7305-639-1
Language English
Document name
Doctoral dissertation
Date of issue
May 2004
Number of pages 38 + 4 papers
Author Ulf Bergström
Title Spatial heterogeneity and biotic interactions – scaling from experiments to
natural systems
Abstract
Much of current ecological theory stems from experimental studies. These studies
have often been conducted in closed systems, at spatial scales that are much smaller
than the systems of interest. It is known that the outcome of these experiments may be
seriously affected by artefacts associated with the caging procedures, as well as by
the actual difference in spatial scale between experimental and target system. Yet,
quantitative methods for estimating and removing artefacts of enclosure and for
extrapolating experimental results to the scales of natural systems are largely lacking.
The aim of this thesis was to confront some of the problems encountered
when scaling from experiments to nature in studies on predator-prey systems, with
focus on effects of changes in spatial heterogeneity. Specifically, I examined
mechanisms that may cause consumption rate estimates to depend on the size of the
experimental arena. I also studied methods for scaling up these process rate estimates
to natural predator-prey systems. The studies were performed on invertebrate
predator-prey systems found in the northern Baltic Sea. Initially, a descriptive study of
small-scale distribution patterns was performed, in order to get background information
on how the behaviour of the organisms was manifested in the spatial structure of the
community. Experimental studies of two predator-prey systems exposed an artefact
that may be widespread in experiments aiming at quantifying biotic interactions. It is
caused by predator and prey aggregating along the walls of the experimental
containers. This behaviour affects the encounter rate between predator and prey,
thereby causing consumption rates to be scale-dependent. Opposing the common
belief that larger arenas always produce less biased results, this scale effect may
instead be reduced by decreasing arena size. An alternative method for estimating the
magnitude of, and subsequently removing, the artefact caused by aggregation along
the arena wall was presented.
Once unbiased estimates of process functions have been derived, the next
step is to scale up the functions to natural systems. This extrapolation entails a
considerable increase in spatial heterogeneity, which may have important implications
for the dynamics of the system. Moment approximation provides a method of taking
the heterogeneity of natural populations into account in the extrapolation process. In
the last study of the thesis, the concepts of moment approximation and how to
estimate relevant heterogeneity were explained, and it was shown how the method
may be used for adding space as a component to a dynamic predator-prey model. It
was concluded that moment approximation provides a simple and useful technique for
dealing with effects of spatial variation, and that a major benefit of the method is that it
provides a way of visualising how heterogeneity affects ecological processes.
Key words aggregation, Baltic Sea, heterogeneity, moment approximation, process
rates, scale effects, scaling models, spatial patterns, zoobenthos
Signature
Date 2004-04-04
Contents
1. Introduction ________________________________________ 7
1.1 Quantifying scale-dependent spatial variation ___________ 9
1.2 Scale effects in experimental studies _________________ 9
1.3 Scaling models for extrapolating experimental results
to natural systems ______________________________ 11
1.4 Study area and studied species ____________________ 13
2. Aims of the thesis and main approaches _______________ 15
3. Small-scale spatial patterns and structuring processes
in zoobenthos (Paper I) _____________________________ 16
4. Spatial scale and heterogeneity in predation experiments
(Papers II and III) ___________________________________ 18
5. Adding space to predator-prey models using moment
approximation (Paper IV) ____________________________ 22
6. Conclusions _______________________________________ 25
7. Acknowledgements _________________________________ 26
8. References
_______________________________________ 27
Tack _______________________________________________ 35
Svensk sammanfattning _______________________________ 37
Appendices : Papers I-IV
List of papers
This thesis is based on the following papers, which will be referred to in the
text by their Roman numerals:
I. Bergström U., Englund G. and Bonsdorff E. 2002. Small-scale spatial
structure of Baltic Sea zoobenthos - inferring processes from patterns.
Journal of Experimental Marine Biology and Ecology 281: 123–136.
II. Bergström U. and Englund G. 2002. Estimating predation rates in
experimental systems: scale-dependent effects of aggregative
behaviour. Oikos 97: 251-259.
III. Bergström U. and Englund G. 2004. Spatial scale, heterogeneity and
functional responses. Journal of Animal Ecology 73: 487-493.
IV. Bergström U., Englund G. and Leonardsson K. Plugging space into
predator-prey models: an empirical approach. Manuscript.
Papers I-III are reproduced with due permission from the publishers.
Contributions
In papers I-III I have been responsible for planning and performing the field
studies and the experiments, as well as for analysing the data and in paper II
also for the modelling. In paper IV my contributions have been planning the
study, and developing the methods and the model together with Englund,
while Leonardsson has mainly contributed with field and experimental data, as
well as model parameters. I have been responsible for writing all the papers.
It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
Though all of them were blind,
That each by observation
Might satisfy his mind.
The First approached the
Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
"God bless me! but the Elephant
Is very like a wall!"
The Second, feeling of the tusk
Cried, "Ho! what have we here,
So very round and smooth and
sharp?
To me `tis mighty clear
This wonder of an Elephant
Is very like a spear!"
The Third approached the animal,
And happening to take
The squirming trunk within his
hands,
Thus boldly up he spake:
"I see," quoth he, "the Elephant
Is very like a snake!"
The Fourth reached out an eager
hand,
And felt about the knee:
"What most this wondrous beast is
like
Is mighty plain," quoth he;
"'Tis clear enough the Elephant
Is very like a tree!"
The Fifth, who chanced to touch
the ear,
Said: "E'en the blindest man
Can tell what this resembles most;
Deny the fact who can,
This marvel of an Elephant
Is very like a fan!"
The Sixth no sooner had begun
About the beast to grope,
Than, seizing on the swinging tail
That fell within his scope.
"I see," quoth he, "the Elephant
Is very like a rope!"
And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the
right,
And all were in the wrong!
Buddhist parable set in verse by
John Godfrey Saxe (1816-1887)
1. Introduction
Discerning patterns in the seeming chaos of nature, and explaining their
causes, is the essence of ecology. A fundamental problem in all ecological
research is that of scale and heterogeneity, in that the description of pattern
means quantification of variation, which in turn entails identification of scales
(Levin 1992). If we do not handle the scales of study carefully, we will, just like
the blind men of the Buddhist story, end up with pieces of information that
seemingly do not fit together to give a picture of the system.
The first studies revealing the importance of scale and spatial
structure for the functioning of populations and communities were done on
experimental predator-prey systems (Gause 1934; Huffaker 1958; Luckinbill
1974). Since then, the study of pattern and scale has grown to become a
central field in ecological research (Wiens 1989; Levin 1992; Hanski and
Gilpin 1997; Thrush et al. 1997; Tilman and Kareiva 1997; Dieckmann et al.
2000; Kemp et al. 2001; Englund and Cooper 2002). The potential
consequences of scale and spatial variation for population dynamical
outcomes such as stability and persistence, mediated through predatory or
competitive interactions, have been thoroughly explored theoretically (Hassell
et al. 1991; Goldwasser et al. 1994; Pacala and Tilman 1994; Bolker and
Pacala 1997; Chesson 1998; de Roos et al. 1998; Nisbet et al. 1998;
Donalson and Nisbet 1999; Pascual et al. 2001; Keeling et al. 2002; Hosseini
2003). Empirical examples are less abundant, and primarily come from smallscale conceptual experiments (Huffaker et al. 1963; Luckinbill 1974; Holyoak
and Lawler 1996; Ellner et al. 2001). Conducting experiments aiming at
coupling scale and/or heterogeneity to population dynamics is for logistic
reasons seldom possible for natural systems. The best way to approach this
problem for large-scale natural populations is instead to develop empirical
spatial population models, in which the effects of space on population
processes may be explored. These models combine small-scale experiments
for measuring process functions with field measurements of spatial variability.
The methods are only beginning to be used, and there is an obvious need for
developing a conceptual framework for how to measure relevant
heterogeneity in natural systems and how to add this information to the
models.
In this thesis, I will attempt to illuminate some aspects of the
procedures involved when developing this kind of empirical spatial models,
exemplified by studies on predator-prey systems. Specifically, I will illustrate
how experiments for measuring predation rates may be affected by scaledependent spatial variation, and how data on heterogeneity in natural
populations may be plugged into predator-prey models to make them spatial.
A field study on small-scale heterogeneity in a benthic community in the
northern Baltic Sea provided background information on how biotic
interactions may affect spatial distributions.
-7-
Definitions of some central concepts in the thesis
Scale, grain, lag, and extent. The term scale as used in ecology can either
simply refer to the dimensions of an object or process (also the temporal
dimension), or, more strictly, to the extent relative to the grain of
measurement (Turner and Gardner 1991; Schneider 1994). Grain is, for a
series of observations in space, the size of an individual sample or of the
experimental arena. Extent denotes the total range over which samples are
collected, while the intersample distance is referred to as the lag (Wiens
1989; Legendre and Legendre 1998). Strictly, the results of a study are
constrained by the grain and extent. We cannot detect any elements of
patterns below the grain, and we should not generalise beyond the extent of
a study without developing scaling models.
Homogeneity, heterogeneity and autocorrelation. If no spatial organisation of
a variable can be recognised, its distribution is said to be homogeneous.
Thus, the term homogeneity usually also includes random distributions.
Heterogeneity denotes a non-random distribution, i.e. that discernable
patterns exist at the scale of study (Dutilleul and Legendre 1993; Platt and
Sathyendranath 1994). Autocorrelation stands for the phenomenon when it is
possible to predict (at least partly) the values of a variable at some points in
space or time from the known values at other sampling points, whose spatial
or temporal positions are also known (Legendre 1993). Autocorrelative
patterns are common in most variables along time series or across
geographic space, as neighbouring points in time or space are usually more
similar than points farther apart due to physical or biotic processes (Barry
and Dayton 1991; Thrush 1991; Legendre 1993).
Geostatistics. Geostatistics refers to a group of statistical methods that
emerged around 1980 as a hybrid discipline of mining engineering, geology,
mathematics and statistics, originally developed for ore reserve estimation.
The strength of these methods is that they, by making use of the spatial
information of a data set, describe spatial variability at a continuity of scales.
This can be opposed to for example hierarchical analysis of variance, which
captures variation only at a few discrete, predetermined scales.
Geostatistical methods are thus well suited for describing autocorrelated
structures, such as most ecological phenomena (Isaaks and Srivastava
1989; Cressie 1993; Legendre 1993).
Process resolution. The resolution of an ecological process is the smallest
scale of spatial variation in a driving variable that is “detected” by, and thus
affects the outcome of, the process (Englund and Cooper 2002). The
process resolution corresponds to the “scale of density dependence” as
defined by Chesson (1998).
-8-
1.1 Quantifying scale-dependent spatial variation
Describing patterns and scales of variation in the distribution of species is a
challenge, because spatial structures are usually scale-dependent across
broad ranges of scale, with separate processes operating at different scales
(e g Legendre and Fortin 1989; Wiens 1989; Thrush 1991; Cooper et al. 1998;
Hewitt 2003). Working with marine organisms, and especially with animals
dwelling in bottom sediments, increases the challenge further, since you have
to do without one of the most powerful instruments for detecting patterns, the
eyesight. Instead you have to rely completely on high-quality sampling
programs.
There are two main, conceptually different approaches to describing
spatial patterns – hierarchical analyses and geostatistical, continuous
methods. Conventional study designs involve hierarchical sampling and
nested analysis of variance, analysis of covariance or maximum likelihood
techniques, which allow detection of variability at a few, predetermined spatial
levels (Searle et al. 1992; Underwood 1997). The benefits of this approach is
that the spatial extent of a study may be large, because sampling need not be
continuous. Also the relative importance of different scales for the overall
variability may be assessed. The ability to partition variance and covariance
components between scales is important for example in moment
approximations, a method that may be used in calculating effects of
heterogeneity when scaling up experimental results to natural populations
(Chesson 1998). The weakness of hierarchical analyses is that they generate
a relatively coarse description of variability, why important patterns may
remain undetected.
Geostatistical methods, such as autocorrelation, semivariance or
fractal analyses, represent an alternative approach for describing patterns,
which has proven useful in ecology (Legendre and Fortin 1989; Rossi et al.
1992; Cressie 1993; Cooper et al. 1997). In these methods, the spatial
information of each data point is utilised in describing continuous variation
over space – a continuity that is an essential characteristic of many natural
phenomena, these being spatially autocorrelated. The geostatistical structure
functions generate more accurate descriptions of scales of variation than
hierarchical methods, and may be used for identifying scales of spatial
dependence. Such high-resolution information on the spatial arrangement of
species can provide information about regulating processes. However, since
geostatistical methods entail data intense sampling programs, the range of
scales that may be covered is limited. Hierarchical methods are thus
appropriate when a large spatial coverage is essential, while geostatistical
methods should be adopted when detailed information on patterns is required
(Rossi et al. 1992; Underwood and Chapman 1996; Bellehumeur and
Legendre 1998).
1.2 Scale effects in experimental studies
Much of our current knowledge of how species dynamically interact with each
other and their environment originates from experimental studies.
-9-
Experiments in ecology are by necessity mostly performed at smaller spatial
(and/or temporal) scales than the natural systems of interest (Duarte et al.
1997; Petersen et al. 1999; Englund et al. 2001; Pace 2001). This practice,
however, raises a question of generality – what can these small, and often
caged, pieces of nature tell us about how populations, communities or
ecosystems function?
In many cases, the results of small-scale experiments have been
directly applied to the systems of interest, assuming that the processes
studied are scale-independent. However, comparisons of small-scale and
whole system experiments not surprisingly reveal that the results of smallscale experiments often deviate substantially from the system-scale
treatments (Barica et al. 1980; Carignan and Planas 1994; Sarnelle 1997;
Wilhelm et al. 2000). These observations suggest that direct extrapolation of
experimental results without prior knowledge of the scale-dependence of the
system should be avoided (Carpenter 1996; Englund and Olsson 1996;
Englund 1997; Schindler 1998; Pace 2001).
In cases when it is not possible to perform experiments at the scale of
interest, two main approaches for dealing with scale effects remain. One
solution is dimensional analysis, in which the experimental system is designed
to respond to manipulations like their natural counterparts using
nondimensional scaling relationships (Legendre and Legendre 1998;
Petersen and Hastings 2001; Englund and Cooper 2002). This method has
been little explored within ecology, and will not be treated further in this thesis.
The other method for dealing with the problem is to develop mechanistic
scaling models. These models describe how the studied response is affected
by the scale of the (experimental) system, and can thus be used for
extrapolating results across scales (Frost et al. 1988; Pace 2001; Englund
and Cooper 2002).
Using scaling models requires that we understand the mechanisms
that cause the experimental systems to function differently from the systems
of interest. These mechanisms have been categorised as related to 1)
exchange processes, 2) spatial heterogeneity, 3) organisational complexity, 4)
number-dependent processes, 5) interactions between system size and
response time, and 6) wall effects (Englund and Cooper 2002). Of these, the
first five groups are fundamental scaling relationships (Petersen et al. 1997),
which occur not only in experimental systems, but also in natural systems of
different size. The last group, the wall effects, occur only in enclosure
experiments, and are directly or indirectly related to the walls of the
enclosures. In this thesis, I will primarily deal with two of these classes of
scale effects, spatial heterogeneity and wall effects. The wall effects in our
studies are also related to spatial heterogeneity, as the walls affect the spatial
distribution of organisms within the experimental systems
- 10 -
1.3 Scaling models for extrapolating experimental results to
natural systems
Many scaling models developed to date are primarily qualitative tools, useful
for identifying scale domains with weak or no scale-dependence (Englund and
Cooper 2002). Thus, findings at one particular scale may be directly
applicable to other scales within the domain, although in other scale domains
within the system they may not be relevant. This can be exemplified by
systems where the scale effects disappear in large experimental systems, so
that systems above a threshold size lie within the same scale domain as the
natural system (e g Marrasé et al. 1992; Chen et al. 1997; Englund 1997;
Petersen et al. 1997).
A universal problem when scaling up experimentally determined
process functions to large-scale natural systems is that changes in spatial
heterogeneity have to be taken into account in the extrapolation process, to
avoid what is called an aggregation error. Aggregation errors arise when we
have nonlinear functions in combination with spatial variation of the
independent variable(s), and this spatial structure is ignored (Rastetter et al.
1992; Chesson 1998). This procedure of only using the mean value of the
variable(s) when calculating a regional-scale average is called the “mean field
approximation”. In the mean field approximation we calculate the function of
the average f (N ) , while the exact solution for a heterogeneous system is
given by the average of the function f (N ) , as illustrated in Fig. 1. The
magnitude of the aggregation error depends on the degree of nonlinearity of
the function and the amount of spatial variation in the distribution of the
independent variable in the population. The problem described here is often
referred to as a nonlinear averaging problem. Nonlinear averaging is a
pervasive problem in ecology – most functions describing ecological
processes are nonlinear, since they are density-dependent, and spatial
variation is also ubiquitous in nature (Melbourne et al. in press). To eliminate
or minimise aggregation errors it is thus imperative to incorporate effects of
spatial variation when scaling up experimentally determined process
functions. There are several scaling methods that can be used to modify
small-scale functions so that they apply to regional-scale, heterogeneous
systems. In contrast to most other scaling models in ecology, these methods
are quantitative. I will briefly describe the methods: extrapolation by expected
value, explicit integration, partitioning, calibration and moment approximation.
- 11 -
f(N2)
f(N)
f(N)
Aggregation
error
f(N1)
N1
N
N2
Fig. 1. Illustration of how spatial variation and nonlinearity may give rise to
“aggregation errors”. In this example we have a habitat consisting of two
patches. The response variable is a decelerating function of the driving
variable, for example a type II functional response. N is the mean density of
the driving variable in the habitat, and N1 and N 2 are the densities in the two
patches. f (N ) is the estimate obtained if variation is not taken into account
(mean field approximation), while f (N ) is the exact function, which is given by
the mean of f ( N1 ) and f ( N 2 ) . The difference between the mean field estimate
and the spatial average is the aggregation error.
Extrapolation by expected value means that spatial variation is
quantified using a probability density function and that the small-scale function
is known, whereby the regional-scale (population-scale) function is derived
using a statistical expectation operator. This method is based on integration,
and may for complex functions become insoluble or too elaborate to be useful
(Rastetter et al. 1992; Englund and Cooper 2002). Small-scale functions may
also be extrapolated by explicit integration, with space as the variable of
integration (King 1992). This requires that the small-scale function is defined
as a function of space, which may be difficult. As for the expected value
method, the integral may in some cases become insoluble. In partitioning the
variability among the components to be aggregated is reduced by dividing the
regional-scale area, for example the area within which a population is found,
into relatively homogeneous subareas. Scaling up is then done in two steps,
first to the subareas, and then to the regional scale by calculating a weighted
mean of the subareas (Rastetter et al. 1992). This method is often applied in
ecology. It can, however, become computationally intense if the regional-scale
- 12 -
data has to be divided into many subareas to acquire the wanted precision.
Calibration, in turn, means that parameter values are estimated by fitting the
small-scale model to the population-scale data (Rastetter et al. 1992; Schmitz
2000; Pascual et al. 2001). A major disadvantage of this method is that
regional-scale data is required to perform the calibration, while it is often the
absence of such data that is the actual motivation for scaling up the smallscale function.
Moment approximation is a mathematical method which may be used
to extrapolate experimentally obtained process functions to natural
populations, by including the effects of spatial variation on the functions as
statistical moments (variance, skew, etc). The moment approximation is
derived from a Taylor series expansion, which approximates a function close
to a known point. The resulting moment equation contains expressions that
measure spatial variation in the independent variables, as well as the
nonlinearity of the function. The input data on spatial variation is easily
determined from field data (Rastetter et al. 1992; Chesson 1998; Melbourne
et al. in press). The major benefit of the method is its conceptual value – it
provides a way of visualising the effects of different aspects of heterogeneity,
such as variance and covariance effects. Another exciting possibility of the
method is that it may be used to bring space as a component into dynamic
population models, without substantially increasing model complexity as
compared to their nonspatial equivalents.
1.4 Study area and studied species
The Baltic Sea is one of the world’s largest brackish water seas, with a salinity
ranging from 1 psu in the north to about 10-12 psu in the surface waters of the
southern parts. It is geologically young, and has during the last 10 000 years,
since the end of the last glaciation, undergone several dramatic shifts in
salinity. Its present state of low salinity has prevailed for about 3000 years
(Voipio 1981). In general, few species are well adapted to living in brackish
waters, and this, together with the young age of the Baltic Sea, makes its
biota unusually poor in species (Bonsdorff and Blomqvist 1993; Elmgren and
Hill 1997; Bonsdorff and Pearson 1999). The low number of species makes
the Baltic Sea an ideal environment for testing ecological theory, as the
number of possible species interactions is low.
In my studies, I have primarily worked with the community found in
soft sediment habitats in the Gulf of Bothnia, which is the northernmost part of
the Baltic Sea (Fig 2; papers I, II and IV). At shallow bottoms, the community
is relatively complex, with some ten common animal species living in or at the
unvegetated bottoms from 4-5 m downwards. Here the clam Macoma balthica
(L.), the amphipods Monoporeia affinis (Lindström) and Corophium volutator
(Pallas), the isopod Saduria entomon (L.) and Oligochaeta dominate the
communities (Kuparinen et al. 1996). Below the halocline, from 40-50 m
downwards, the macrofaunal community is extremely simple, essentially
consisting of two of these species, Monoporeia and Saduria (Leonardsson
1991a) (Fig. 3). The deposit-feeding Monoporeia is common on soft bottoms
of all depths throughout the Baltic Sea. It can be very abundant, with densities
- 13 -
2
frequently reaching 10 000 ind/m (Leonardsson 1991a; Hill and Elmgren
1992; Sparrevik and Leonardsson 1998). Saduria is a predator and scavenger
with a similar distribution as Monoporeia, which in the northern Baltic Sea is
its most important food source (Green 1957; Haahtela 1990; Leonardsson
1994; Ejdung and Elmgren 2001). As other predators, such as benthivorous
fish, are scarce at deep bottoms (Leonardsson 1991b), Saduria and
Monoporeia make up a tightly coupled predator-prey system, where predation
from Saduria appears to have a strong influence on the dynamics of
Monoporeia (Sparrevik and Leonardsson 1999).
In one experimental study (paper III), I examined a predator-prey
system consisting of the mysid shrimp Neomysis integer (Leach), and the
cladoceran Polyphemus pediculus (L.). Neomysis is a euryhaline,
hyperbenthic species, which is very common in shallow coastal waters of the
Gulf of Bothnia. It is often found in shoals in the littoral zone, where it mainly
feeds on zooplankton, phytoplankton, detritus and benthic algae (Mauchline
1971; Fockedey and Mees 1999). Neomysis is considered to be an important
link between the pelagic and benthic system (Zouhiri et al. 1998; Albertsson
2001). The prey species, Polyphemus, lives in the littoral zone of fresh and
brackish waters (Enckell 1980).
Fig. 2. The study area in the
Gulf of Bothnia in the northern
Baltic Sea.
Fig. 3. The isopod predator Saduria
entomon and its main prey, the
amphipod Monoporeia affinis.
- 14 -
2. Aims of the thesis and main approaches
In this thesis, I have focused on questions of how heterogeneity at different
spatial scales may affect biotic interactions, both in experimental and in
natural systems. I have studied spatial patterning of natural populations, scale
effects in laboratory experiments, and mathematical models for incorporating
effects of heterogeneity when extrapolating results from experiments to
nature. I have done these studies on animal species that live in, on or close to
soft bottoms of the northern Baltic Sea. Specific questions that I have
confronted, and the approaches I have used, are:
What is the spatial distribution of zoobenthic species in the northern
Baltic Sea at small scales? Can the distribution patterns of different
species be coupled to biotic interactions? (Paper I)
In this field study, I did an extensive sampling of the faunal community on two
soft bottom localities, at scales ranging from centimetres to metres. Spatial
patterns of the dominating species and the relationships between taxa and
size classes were analysed with geostatistical methods and correlations at
different scales.
How are spatial distributions within experimental systems affected by
arena size? How may this heterogeneity affect the consumption rate in
predator-prey systems? (Papers II and III)
In paper II, I approached these questions using a multiscale experimental
setup where the consumption rate of the benthic isopod Saduria entomon
feeding on the amphipod Monoporeia affinis was studied. The observed
difference between arena sizes was related to scale-dependent aggregative
behaviour. In a simulation model I further explored the suggested mechanism.
In paper III, I studied the effect of arena size on the functional
response of the mysid shrimp Neomysis integer preying on the cladoceran
Polyphemus pediculus. The spatial distributions and movement behaviour of
the species were documented, and related to differences in the observed
attack rate of the functional response. A method for correcting the attack rate
for effects of spatial heterogeneity was developed.
Is moment approximation a useful method for extrapolating
experimentally obtained functional responses to natural systems? Can
the method be used for incorporating spatial heterogeneity into dynamic
predator-prey models? (Paper IV)
In this study, we scaled up a laboratory derived functional response of
Saduria entomon feeding on Monoporeia affinis to estimate the consumption
rate in a natural, heterogeneous system using the technique of moment
approximation. The spatial functions were used in developing a dynamic
spatial predator-prey model. The dynamics of this model was compared to a
nonspatial model, and to the dynamics observed in the natural system. The
potential value of moment approximation for ecological applications was
discussed.
- 15 -
3. Small-scale spatial patterns and structuring processes in
zoobenthos (Paper I)
Marine soft sediment communities are largely controlled by physical
processes at large spatial scales, while the structuring effect of species
interactions increases as scales get smaller (e g Pearson and Rosenberg
1987; Barry and Dayton 1991; Thrush 1991; Bonsdorff and Blomqvist 1993;
Legendre et al. 1997). The mechanisms through which patterns are
expressed also differs with scale - at large scales patterns are established
through differences in recruitment and mortality, while at small scales
behavioural responses and movements of the organisms generate patterns
(Hewitt et al. 1996; Englund et al. 2001; Norkko et al. 2001). The spatial
distribution of different species within a community may provide information
about structuring processes. But inferring processes from patterns is a
delicate task, demanding high-quality field data and a careful handling of
scales. In this study, I performed an extensive grid sampling at two sites at
scales ranging from 6 cm to 5 m. The major objective was to examine whether
the spatial patterns could be used to identify key biotic processes structuring
the community at these scales. Another purpose was to gather background
information on the small-scale spatial distribution of the benthic community in
the Gulf of Bothnia, northern Baltic Sea, for coming studies on how spatial
heterogeneity affects predatory interactions. The two sites differed in their
hydrodynamic regime, while they were unusually homogeneous with respect
to the within-site environment. Therefore, similar patterns appearing at both
sites were likely to have originated from biotic interactions. The distributions of
all numerically important taxa were studied simultaneously, which increased
the chances of matching pattern with process, and sorting out causal
relationships from mere correlations.
The multiscale sampling design and the geostatistical methods
employed in the study proved to be efficient tools for analysing spatial
patterns, and revealed structures that would have remained unnoticed with
conventional sampling techniques. The results showed that juveniles of the
amphipods Monoporeia affinis and Corophium volutator both were patchily
distributed, at 1-2 m and 30-40 cm scales, respectively. The probable cause
of these patterns was positive intragroup interactions, since their distributions
were not correlated with any other faunal group. This conclusion is supported
by observations of similar patchiness of Corophium at marine tidal flats, which
was also ascribed to intraspecific aggregative behaviour (Lawrie et al. 2000).
The most conspicuous patterns at the localities were the both positive
and negative correlations between several taxa at the metre scale. All these
correlations could potentially be explained by one mechanism – a common
avoidance of areas with high densities of adults of the bivalve Macoma
balthica by juvenile Macoma and adults of Monoporeia and Corophium.
Experimental studies have indicated that Macoma may be an efficient
competitor for food in the Baltic Sea (Bonsdorff et al. 1986; Olafsson 1989;
Kotta et al. 2001), but this has not been related to the spatial structure of
communities before. We hypothesised that the observed correlations were
- 16 -
caused by food competition, since all these species are mainly deposit
feeders. We were able to test this hypothesis a posteriori in two ways, using a
“natural experiment” approach: by calculating the total potential feeding areas
of Macoma and by correlating the amount of organic material with Macoma
density. Macoma feeds by “vacuuming” detritus from the sediment surface
using its inhalant siphon. The potential feeding area is determined by the
length of the siphon, which is related to the size of the individual (Brey 1991).
The total potential feeding areas of adult Macoma were well above the
sampled areas. This suggests that the bivalves should be able to reduce the
concentration of detritus at the sediment surface, considering that soft bottom
communities of the Baltic Sea are generally food limited (Sarvala 1986;
Leonardsson 1994). Further support for the hypothesis was obtained from an
analysis of the relationship between organic content of the sediment and
Macoma density, as this was clearly negative. Macoma also evidently had a
structuring effect on Oligochaeta, as there was a strong positive correlation
between these two at the metre scale. This pattern can probably be ascribed
to a “gardening effect”, as some meiofaunal species are known to feed on the
bacteria utilising excretions of Macoma (Reise 1983; Olafsson 1989).
Taken together, this study clearly suggests that biotic interactions are
manifested in the small-scale spatial patterns of infaunal communities in the
northern Baltic Sea. Besides providing several hypotheses about structuring
processes, the information on the spatial arrangement of species in their
natural habitat was used when planning and evaluating the results of the
studies presented in papers II-IV.
- 17 -
4. Spatial scale and heterogeneity in predation experiments
(Papers II and III)
It is known from predation experiments in aquatic systems that the
consumption rate of predators may be affected by the size of the experimental
arena. These results have been attributed to artefacts due to the caging of the
animals, which all are related to the walls of the enclosures. The magnitude of
these wall effects vary with arena size as a consequence of the changing
perimeter to area ratio. Two major categories of wall effects may be
distinguished: 1) effects on the foraging and escape behaviour of predator
and prey (Cooper and Goldman 1982; Christensen 1996; Buecher and
Gasser 1998), and 2) effects on the distribution of predator and prey within
the enclosures (de Lafontaine and Leggett 1987; O'Brien 1988; Wilhelm et al.
2000). The mechanisms behind these effects are, however, poorly studied,
and cannot be used for quantitative assessments of how arena size affects
consumption rate estimates. Once the mechanisms are known, there are two
methods for dealing with these scale artefacts – they may either be minimized
by avoiding scales where the artefacts are large, or their effect may be
estimated and removed from the consumption rate functions by developing
scaling models (Frost et al. 1988; Cooper et al. 1998; Petersen et al. 1999;
Englund et al. 2001; Pace 2001).
In paper II, I tested the hypothesis that coaggregation of predator and
prey along the arena wall gives rise to increasing consumption rates with
arena size. The hypothesis rests on the notion that when the arena size
increases, the relative amount of available wall decreases, why densities of
predator and prey along the wall will increase with arena size. This
presumably raises the per capita encounter rate between predators and prey,
and thus also the consumption rate. I evaluated the hypothesis using a
multiscale laboratory experiment and a conceptual simulation model. In the
experiment, I studied how the instantaneous mortality rate of the amphipod
Monoporeia affinis preyed on by the isopod Saduria entomon changed with
the size of the experimental arena. As hypothesised, I found that the mortality
rate increased with arena size. At the end of the experiment, I documented
the distribution of predator and prey along the wall and in the interior of the
containers. These data showed that the aggregation of both predator and prey
along the wall increased with arena size, in accordance with the hypothesis.
Using the distribution data in a linear predation model, I evaluated whether the
aggregative behaviour could account for the observed difference in prey
mortality. This analysis provided support for the hypothesis that scaledependent aggregation of predator and prey caused the consumption rate to
increase with arena size. It also indicated that most of the prey consumption
should take place in the area close to the wall.
To further explore the mechanisms behind scale-dependent
consumption rates in experimental systems, I developed a general individualbased model for studying how the aggregative behaviour of predator and prey
may affect the observed scale effect. In the simulations I used encounter rate
as a proxy for consumption rate. The main result of the simulations was that
- 18 -
the consumption rate can be expected to be humpshaped when both predator
and prey aggregate along the arena wall, with the highest consumption rates
at intermediate scales. The tested hypothesis, as well as the results of the
Saduria-Monoporeia experiment, where predation rates increased with arena
size, will thus not hold for large spatial scales. The initial increase in
consumption rates with arena size is caused by increasing densities in the
area along the wall, which is a consequence of the decreasing proportion of
the preferred wall area compared to the total area. At larger arena sizes, the
densities in the wall area will increase more slowly, because each individual
spends progressively more time in the interior habitat between wall
encounters. This decelerating increase in densities along the wall will at some
point cause the per capita consumption rate to drop, and the curve turns
downward.
Since the increase in predation rate is an artefact caused by the
enclosure walls, this leads to the conclusion that the least biased estimates of
prey consumption rates will be obtained using either very small or very large
containers. By relating the total path length of the individuals in the
simulations to the arena diameter we got a dimensionless ratio (Petersen and
Hastings 2001), that provided a measure of the size of the arena relative to
the mobility of the animals. This ratio suggested that experiments aiming at
measuring ecological process rates often cannot be performed at scales large
enough to remove this artefact for mobile animals. This result, together with
the humped shape of the curve, are robust predictions of the model, and have
important implications for how to deal with scale effects in experiments aiming
at measuring ecological process rates. For organisms with very low mobility,
scale effects may be avoided by performing experiments at large scales. For
most animals, however, the artefact can only be reduced by doing the
measurements in small experimental arenas. This contradicts the prevailing
paradigm that artefacts of enclosure can always be reduced by increasing
arena size (e g Cooper et al. 1998; Petersen et al. 1999). Minimising wall
effects by using small experimental arenas, however, raises the risk of
introducing other artefacts, such as impaired hunting or flight behaviour due to
the walls (Cooper and Goldman 1982; Buecher and Gasser 1998).
An alternative technique for dealing with the problem is to develop
scaling models for estimating the magnitude of the artefacts caused by
aggregation along the wall of the experimental arena. In paper III, the aim was
to develop such a method for correcting consumption rate estimates for the
effect of coaggregation. In contrast to the setup in paper II, where I only used
one prey density, in this experiment I documented the effect of arena size on
the functional response of the predator, that is, the function describing the
change in consumption rate with prey density. The functional response is the
heart of models describing predator-prey systems, and has attracted a lot of
attention (see Jeschke et al. 2002). In predator-prey models aiming at
explaining the dynamics of natural systems, functional responses have
usually been parameterised in enclosures (e g Hassell 1978; Crowley et al.
1987; Gurney et al. 1990; de Roos and Persson 2001). Given the importance
of this process, it is essential to learn more about how these measurements
may be affected by artefacts such as aggregation along container walls. In
- 19 -
this study, I chose to examine the functional response of the mysid shrimp
Neomysis integer preying on the cladoceran Polyphemus pediculus, in two
container sizes. Preliminary studies had shown that both species aggregate
along the container wall, just like Saduria and Monoporeia, with the important
difference that these species do not burrow in bottom sediments and are thus
much easier to observe. During the experimental runs, I documented the
spatial distribution and the movement behaviour of the animals.
The results of the experiment showed that Neomysis exhibited a type
II functional response in both container sizes, but that the attack rate estimate
was significantly higher in the larger containers. Although the difference in
container size was no more than fivefold, the attack rate estimate of the larger
containers was twice as high as that of the small container size. The key to
understanding this scale effect lies in explaining differences in the encounter
rate, because the attack rate is linearly dependent on encounter rate (Jeschke
et al. 2002). Further, when the movement speed of the predator is much
larger than that of the prey, as was the case in the Neomysis – Polyphemus
system, the encounter rate is linearly dependent on predator density, prey
density, as well as on predator movement speed (Gerritsen and Strickler
1977). These three variables provide the input data for two mechanisms that
together could explain the scale effect on the attack rate: scale-dependent
predator activity and scale-dependent coaggregation of predator and prey.
Data on the swimming speed of Neomysis showed that the predators had a
significantly higher mean speed in the large containers. This effect seemingly
was an effect of the predators triggering each other’s hunting behaviour. This
activation was stronger in large containers, simply due to the higher number
of predators. Whether this mechanism was an experimental artefact or an
effect that occurs in nature was not possible to determine from the
experiment.
In this study, I had detailed data on the distributions of predator and
prey, which clearly demonstrated that both species aggregated along the
container wall, with the effect that most of the predator-prey encounters took
place in the centimetres closest to the container wall. Just like in paper II, the
densities in the wall area were higher in the larger containers, which caused
consumption rates to be scale-dependent. The contribution of coaggregation
to the observed scale effect on the attack rate was estimated by calculating
an encounter index for each container size and prey density. The spatial
distribution of predator and prey in relation to the container walls were taken
into account in the calculations, thus generating index values that were
proportional to the per capita encounter rate. Regression lines were fitted to
the index values for each container size separately. The difference in slope of
the lines between small and large containers gave a measure of the effect of
coaggregation on the encounter rate, and thus on the attack rate. The
regression lines fitted the data well, which indicated that this method of
estimating the scale effect caused by aggregation was highly operational. The
analyses showed that together the effects of coaggregation and movement
speed could account for most of the difference in attack rate of the functional
response.
- 20 -
The method for calculating the effect of coaggregation on the attack
rate is an example of a quantitative scaling model. A measure of the scale
effect caused by coaggregation may be obtained by comparing the slope
calculated for an experimental arena to the slope calculated for random
distributions of predator and prey. These calculations estimated the effect of
coaggregation to 55% in the larger containers, which is a strong effect,
considering the small size of the containers (32 cm diameter) relative to the
mobility of both Neomysis and Polyphemus. This illustrates how important the
choice of arena size may be, a question that is usually more or less ignored
when planning an experimental study.
In summary, artefacts caused by aggregative behaviour can be
expected to be widespread in ecological experiments, because a wide variety
of aquatic taxa exhibit a preference for the area close to the walls of
experimental enclosures (e g Savino and Stein 1982; Stephenson et al. 1984;
Uryu et al. 1996; Fernandes et al. 1999, papers II and III). The effect of the
aggregations is that the densities of the independent variable of the function
(prey, competitors etc) perceived by the organisms differ from the mean
density within the experimental arena. In other words, when the resolution of
the process is smaller than the size of the experimental arena, the withinarena heterogeneity will affect the observed function. If this heterogeneity is
ignored we may get seriously biased estimates. By documenting the
distribution of the organisms within the experimental arenas it may, however,
be possible to correct the functions for this artefact.
- 21 -
5. Adding space to predator-prey models using moment
approximation (Paper IV)
Scaling up ecological process functions from small-scale experimental
systems to natural populations generally involves a substantial increase in
spatial heterogeneity, which may have important effects on process rates and
ultimately on population dynamics. Moment approximation is a mathematical
method that can be used to incorporate empirically observed spatial variation
into the extrapolation procedures (Chesson 1998; Englund and Cooper 2002;
Melbourne et al. in press). In ecology, moment approximation has been used
in theoretical models (e g Bolker and Pacala 1997; Bolker et al. 2000;
Chesson 2000; Keeling et al. 2002), while the technique has found little use
so far in empirical studies (Melbourne et al. in press). In paper IV, we outlined
the procedures of moment approximation and how to estimate relevant
heterogeneity in natural populations (Table 1). We exemplified the use of
moment approximation in a study of the Saduria-Monoporeia system, and
developed a dynamic spatial model of the system using moment
approximation.
Table 1. General scheme for the process of making a dynamic population
model spatial using moment approximation
1. Define the nonspatial model
2. Make the model spatial using moment approximation for each
function that is affected by spatial variation
3. Determine the ecological process functions experimentally and
remove artefacts of aggregation (as described in paper III)
4. Measure spatial variation in the independent variables of the functions
in the target system
a) if experimental scale process resolution: measure at
experimental scale
b) if experimental scale < process resolution: measure at resolution
scale
5. Develop functions for variances and covariances based on the
variables tracked by the model
6. Compare the dynamics of the spatial and the non-spatial model to the
dynamics of the target system
- 22 -
In order to study how the spatial variation in a predator-prey system
may affect the interactions, a laboratory derived functional response of
Saduria preying on Monoporeia (Aljetlawi et al. 2004) was scaled up to a
natural system that had been monitored for 12 years. This was done by
developing second-order moment equations for the functional response. This
moment approximation included correction terms for the variance in prey
density and for the covariance in prey and predator density. For the functional
response, the variance and covariance effects may be related to well-known
biological mechanisms: the variance effect is coupled to predator satiation,
while the covariance effect is coupled to the encounter rate between predator
and prey. Data on variances and covariances were obtained from the field
data. The moment approximation showed that the variance and covariance
effects could each alter the prey consumption rate in the system with 40-50%
compared to a situation without spatial variation. Since the variance effect
was generally positive and the covariance effect negative, the net effect of
these mechanisms was, however, relatively small in most years. The analysis
of variance and covariance components showed that most of the variation
came from the larger of the two scales sampled. Thus, in this predator-prey
system the choice of resolution scale for the functional response was of minor
importance for the outcome of the moment approximation.
The calculations of the effects of heterogeneity on the consumption
rate only produced snap-shot pictures of the system. In order to study how
spatial variation affected the Saduria-Monoporeia system over longer time
scales a Lotka-Volterra type, continuous-time model was developed. To make
this model spatial using moment approximation, we had to express the
variance and covariance as dynamic functions of the variables tracked by the
model, that is, of prey and predator densities. A common property of the
variance of population densities is that it often depends on the population
mean (Taylor et al. 1980; Hanski 1987; Downing 1991; Chesson 1998). The
variance in Monoporeia density was, quite in accordance with these previous
observations, nicely modelled as a function of mean density. Finding a model
for the covariance was more challenging, since there are no empirical studies
on its density-dependence available. It has, however, been shown
theoretically that the covariance in systems with a strong coupling between
predator and prey may be modelled by including past densities in the model,
thereby introducing a time-lag in the system (Keeling et al. 2000). We were
able to confirm this modelling prediction by developing a linear model that
included the prey density from the previous year, together with current prey
and predator densities. This model reproduced the covariance for the twelve
years very well, which shows that the covariance in this unstable system has
the remarkable property that it carries information on past densities.
The dynamics produced by the nonspatial model (without the moment
approximation) were stable for the whole parameter space explored. Adding
spatial variation to the model was clearly destabilising, as the spatial model
also generated oscillatory dynamics for part of the parameter space. The
results of the spatial model thus agreed with the dynamics observed in the
natural system. A detailed analysis of the spatial model revealed that the
dynamics of the covariance gave rise to the oscillations, while the variance
- 23 -
effect did not affect stability. This result contradicts the generally approved
finding from theoretical population models that spatial heterogeneity stabilizes
consumer-resource dynamics (Murdoch et al. 2003). It also apposes the
hypothesis presented by Hosseini (2003), that negative covariance would
generally be stabilising. The results also show that the extent of the study
2
(300 km ) was not large enough to give rise to statistical stabilization (sensu
Jansen and de Roos 2000). This might be explained by large-scale
movements of prey or predator, or by regional stochasticity synchronising the
dynamics in the area, i e a Moran effect.
In summary, second-order moment approximation provides a simple
and useful technique for scaling up experimentally derived process functions
to natural systems. It may also be used for plugging spatial information from
field data into population models, by developing variance and covariance
functions that are based on the variables tracked by the model. The main
advantage of the technique is that it provides a way of visualising how
heterogeneity affects ecological processes, by providing explicit estimates of
variance and covariance effects. The method is largely unexplored in
empirical ecology, but our results suggest that it may be a handy tool for
exploring how heterogeneity shapes population dynamics.
- 24 -
6. Conclusions
Ecology is turning into a quantitative science, where the questions addressed
are changing from “does-does not” to “how much”. Given the vast impact of
human activities on nature, we urgently need to promote this development.
We need quantitative population and community models for a sustainable
management of natural resources, and for minimising adverse effects on
biodiversity. But capturing the complexity of nature in mathematical functions
is a demanding task, and most models today are too simplified to be used as
predictive instruments. One such simplification is that the effects of spatial
heterogeneity are often omitted. The fundamental importance of spatial
heterogeneity for the functioning of populations and communities is well
recognised today (Hanski and Gilpin 1997; Tilman and Kareiva 1997;
Dieckmann et al. 2000; Murdoch et al. 2003), and the use of nonspatial
models in many cases probably reflects a lack of appropriate techniques
rather than ignorance of the problem.
In this thesis, I have confronted some problems related to
heterogeneity encountered when developing quantitative empirical models,
both when measuring process rates in experimental systems and when
scaling up these small-scale functions to large natural systems. In papers II
and III, I examined how spatial heterogeneity within experimental systems
may affect the parameterisation of functional responses. The results showed
that aggregation along container walls may seriously bias functional response
estimates, and that this problem may be widespread. A technique for
removing this experimental artefact was suggested. In paper IV, I illustrated
how the method of moment approximation may be used for scaling up
experimentally determined process functions to natural, heterogeneous
systems. I also showed how the method may be used for making dynamic
predator-prey models spatial. It was concluded that moment approximation
appears to provide a simple framework for dealing with the effects of
heterogeneity in population modelling. A major strength of the method is that it
can be used to partition the effects of different aspects of heterogeneity, such
as variance and covariance effects. For example, the results of paper IV
together with the theoretical findings of Keeling et al. (2000) emphasise the
importance of covariance dynamics for the functioning of predator-prey
systems. An important question for future studies, both empirical and
theoretical, would thus be to explore whether the covariance affects the
dynamical properties of other systems than the Saduria-Monoporeia system.
It would also be of great interest to examine the relationship between
movement behaviour and covariances at different spatial scales. Moment
approximation also opens up for the possibility to add space to existing
empirical models, as the information needed on natural spatial variation often
can be extracted from existing field data.
We know a lot about how spatial scale and heterogeneity may affect
the dynamics of populations and communities from theoretical studies, while
progress in empirical spatial ecology has to some extent been hampered by
technical difficulties. Considering the pressing need for quantitative ecological
- 25 -
models as a management tool, it is now high time to go from theory to
practice. To facilitate this transition we need to develop methods for
accurately measuring process functions and for scaling up these functions to
heterogeneous populations. Hopefully the studies in this thesis will contribute
to this development.
7. Acknowledgements
I would like to thank Göran Englund, Erik Bonsdorff and Lena Bergström for
helpful comments on this thesis. The studies included in the thesis have been
financially supported by the J.C Kempe Memorial Foundation, the Längman
Cultural Foundation, and Umeå Marine Sciences Centre.
- 26 -
8. References
Albertsson J (2001) Benthic-pelagic interactions mediated by crustaceans in
the Bothnian Sea. PhD-thesis, Umeå University, Umeå, Sweden
Aljetlawi AA, Sparrevik E, Leonardsson K (2004) Prey-predator sizedependent functional response: derivation and rescaling to the real
world. Journal of Animal Ecology 73: 239-252
Barica J, Kling H, Gibson J (1980) Experimental manipulation of algal bloom
composition by nitrogen addition. Canadian Journal of Fisheries and
Aquatic Sciences 37: 1175-1183
Barry JP, Dayton PK (1991) Physical heterogeneity and the organization of
marine communities. In: Kolasa J, Pickett STA (eds) Ecological
Heterogeneity. Springer-Verlag, New York, pp 270-320
Bellehumeur C, Legendre P (1998) Multiscale sources of variation in
ecological variables: modeling spatial dispersion, elaborating sampling
designs. Landscape Ecology 13: 15-25
Bolker B, Pacala SW (1997) Using moment equations to understand
stochastically driven spatial pattern formation in ecological systems.
Theoretical Population Biology 52: 179-197
Bolker BM, Pacala SW, Levin SA (2000) Moment methods for ecological
processes in continuous space. In: Dieckmann U, Law R, Metz JAJ (eds)
The geometry of ecological interactions. Cambridge University Press,
Cambridge, pp 252-270
Bonsdorff E, Blomqvist EM (1993) Biotic couplings on shallow water soft
bottoms - examples form the northern Baltic Sea. Oceanography and
Marine Biology: an Annual Review 31: 153-176
Bonsdorff E, Mattila J, Rönn C, Österman C-S (1986) Multidimensional
interactions in shallow soft-bottom ecosystems; testing the competitive
exclusion principle. Ophelia 4: 37-44
Bonsdorff E, Pearson TH (1999) Variation in the sublittoral macrozoobenthos
of the Baltic Sea along environmental gradients: A functional-group
approach. Australian Journal of Ecology 24: 312-326
Brey T (1991) Interactions in soft bottom benthic communities - quantitative
aspects of behavior in the surface deposit feeders Pygospio elegans
(Polychaeta)
and
Macoma
balthica
(Bivalvia).
Helgolander
Meeresuntersuchungen 45: 301-316
Buecher E, Gasser B (1998) Estimation of predatory impact of Pleurobrachia
rhodopis (cydippid ctenophore) in the northwestern Mediterranean Sea:
in situ observations and laboratory experiments. Journal of Plankton
Research 20: 631-651
Carignan R, Planas D (1994) Recognition of nutrient and light limitation in
turbid mixed layers: three approaches compared in the Panamá
floodplain (Argentina). Limnology and Oceanography 39: 580-596
Carpenter SR (1996) Microcosm experiments have limited relevance for
community and ecosystem ecology. Ecology 77: 677-680
- 27 -
Chen CC, Petersen JE, Kemp WM (1997) Spatial and temporal scaling of
periphyton growth on walls of estuarine mesocosms. Marine Ecology
Progress Series 155: 1-15
Chesson P (1998) Making sense of spatial models in ecology. In: Bascompte
J, Solé RV (eds) Modeling spatiotemporal dynamics in ecology.
Springer- Verlag and Landes Biosience, pp 151-166
Chesson P (2000) General theory of competitive coexistence in spatiallyvarying environments. Theoretical Population Biology 58: 211-237
Christensen B (1996) Predator foraging capabilities and prey antipredator
behaviours: Pre- versus postcapture constraints on size-dependent
predator- prey interactions. Oikos 76: 368-380
Cooper SD, Barmuta L, Sarnelle O, Kratz K, Diehl S (1997) Quantifying
spatial heterogeneity in streams. Journal Of The North American
Benthological Society 16: 174-188
Cooper SD, Diehl S, Kratz K, Sarnelle O (1998) Implications of scale for
patterns and processes in stream ecology. Australian Journal Of Ecology
23: 27-40
Cooper SD, Goldman CR (1982) Environmental factors affecting predation
rates of Mysis relicta. Canadian Journal of Fisheries and Aquatic
Sciences 39: 203-208
Cressie NAC (1993) Statistics for spatial data. John Wiley & Sons, Inc., New
York
Crowley PH, Nisbet RM, Gurney WSC, Lawton JH (1987) Population
regulation in animals with complex life-histories: formulation and analysis
of a damselfly model. Advances in Ecological Research 17: 1-59
de Lafontaine Y, Leggett WC (1987) Effect of container size on estimates of
mortality and predation rates in experiments with macrozooplankton and
larval fish. Canadian Journal of Fisheries and Aquatic Sciences 44:
1534-1543
de Roos AM, McCauley E, Wilson WG (1998) Pattern formation and the
spatial scale of interaction between predators and their prey. Theoretical
Population Biology 53: 108-130
de Roos AM, Persson L (2001) Physiologically structured models - from
versatile technique to ecological theory. Oikos 94: 51-71
Dieckmann U, Law R, Metz JAJ (2000) The geometry of ecological
interactions. Cambridge University Press, Cambridge
Donalson DD, Nisbet RM (1999) Population dynamics and spatial scale:
Effects of system size on population persistence. Ecology 80: 2492-2507
Downing JA (1991) Biological heterogeneity in aquatic ecosystems. In: Kolasa
J, Pickett STA (eds) Ecological Heterogeneity. Springer-Verlag, New
York, pp 160-180
Duarte CM, Gasol JM, Vaque D (1997) Role of experimental approaches in
marine microbial ecology. Aquatic Microbial Ecology 13: 101-111
Dutilleul P, Legendre P (1993) Spatial heterogeneity against
heteroscedasticity: an ecological paradigm versus a statistical concept.
Oikos 66: 152-171
Ejdung G, Elmgren R (2001) Predation by the benthic isopod Saduria
entomon on two Baltic Sea deposit-feeders, the amphipod Monoporeia
- 28 -
affinis and the bivalve Macoma balthica. Journal of Experimental Marine
Biology and Ecology 266: 165-179
Ellner SP, McCauley E, Kendall BE, Briggs CJ, Hosseini PR, Wood SN,
Janssen A, Sabelis MW, Turchin P, Nisbet RM, Murdoch WW (2001)
Habitat structure and population persistence in an experimental
community. Nature 412: 538-543
Elmgren R, Hill C (1997) Ecosystem function at low biodiversity - the Baltic
example. In: Ormond RFG, Gage J, Angel M (eds) Marine biodiversity:
Patterns and processes. Cambridge University Press, Cambridge, pp
319-336
Enckell PH (1980) Kräftdjur. Signum, Lund
Englund G (1997) Importance of spatial scale and prey movements in
predator caging experiments. Ecology 78: 2316-2325
Englund G, Cooper SD (2002) Scale effects and extrapolation in ecological
experiments. Advances in Ecological Research 33: 161-213
Englund G, Cooper SD, Sarnelle O (2001) Application of a model of scale
dependence to quantify scale domains in open predation experiments.
Oikos 92: 501-514
Englund G, Olsson T (1996) Treatment effects in a stream fish enclosure
experiment: Influence of predation rate and prey movements. Oikos 77:
519-528
Fernandes TF, Huxham M, Piper SR (1999) Predator caging experiments: a
test of the importance of scale. Journal of Experimental Marine Biology
and Ecology 241: 137-154
Fockedey N, Mees J (1999) Feeding of the hyperbenthic mysid Neomysis
integer in the maximum turbidity zone of the Elbe, Westerschelde and
Gironde estuaries. Journal of Marine Systems 22: 207-228
Frost TM, DeAngelis DL, Bartell SM, Hall DJ, Hurlbert SH (1988) Scale in the
design and interpretation of aquatic community research. In: Carpenter
SR (ed) Complex interactions in lake communities. Springer Verlag, New
York, pp 229-258
Gause GF (1934) The struggle for existence. Williams & Wilkins, Baltimore,
Maryland, USA
Gerritsen J, Strickler JR (1977) Encounter probabilities and community
structure in zooplankton: a mathematical model. Journal of Fish
Research Board of Canada 34: 73-82
Goldwasser L, Cook J, Silverman ED (1994) The effects of variability of
metapopulation dynamics and rates of invasion. Ecology 75: 40-47
Green J (1957) The feeding mechanism of Mesidothea entomon (Linn.)
(Crustacea: isopoda). Proceedings of the Zoological Society of London
129: 245-254
Gurney WSC, McCauley E, Nisbet RM, Murdoch WW (1990) The
physiological ecology of Daphnia: A dynamic model of growth and
reproduction. Ecology 71: 716-732
Haahtela I (1990) What do Baltic studies tell us about the isopod Saduria
entomon (L.). Annales Zoologici Fennici 27: 269-278
Hanski I (1987) Cross-Correlation in Population-Dynamics and the Slope of
Spatial Variance - Mean Regressions. Oikos 50: 148-151
- 29 -
Hanski IA, Gilpin ME (1997) Metapopulation biology: ecology, genetics, and
evolution. Academic, San Diego
Hassell MP (1978) The dynamics of arthropod predator-prey systems.
Princeton University Press, Princeton
Hassell MP, May RM, Pacala SW, Chesson PL (1991) The persistence of
host-parasitoid associations in patchy environments: I. A general
criterion. American Naturalist 138: 568-583
Hewitt JE (2003) Using multi-scale spatial and temporal information to explain
soft-sediment macrofaunal heterogeneity. PhD thesis, Åbo Akademi
University, Åbo, Finland
Hewitt JE, Thrush SF, Cummings VJ, Pridmore RD (1996) Matching patterns
with processes: predicting the effect of size and mobility on the spatial
distributions of the bivalves Macomona liliana and Austrovenus
stutchburyi. Marine Ecology Progress Series 135: 57-67
Hill C, Elmgren R (1992) Predation by the isopod Saduria entomon on the
amphipods Monoporeia affinis and Pontoporeia femorata: Experiments
on prey vulnerability. Oecologia 91: 153-156
Holyoak M, Lawler SP (1996) Persistence of an extinction-prone predatorprey interaction through metapopulation dynamics. Ecology 77: 18671879
Hosseini PR (2003) How localized consumption stabilizes predator-prey
systems wit finite frequency of mixing. American Naturalist 161: 567-585
Huffaker CB (1958) Experimental studies on predation: dispersion factors and
predator-prey oscillations. Hilgardia 27: 343-383
Huffaker CB, Shea KP, Herman SG (1963) Experimental studies on
predation: complex dispersion and levels of food in an acarine predatorprey interaction. Hilgardia 34: 305-330
Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics.
Oxford University Press, New York
Jansen VAA, de Roos AM (2000) The role of space in reducing predator-prey
cycles. In: Dieckmann U, Law R, Metz JAJ (eds) The geometry of
ecological interactions. Cambridge University Press, Cambridge, pp 183201
Jeschke JM, Kopp M, Tollrian R (2002) Predator functional responses:
Discriminating between handling and digesting prey. Ecological
Monographs 72: 95-112
Keeling MJ, Wilson HB, Pacala SW (2000) Reinterpreting space, time lags,
and functional responses in ecological models. Science 290: 1758-1761
Keeling MJ, Wilson HB, Pacala SW (2002) Deterministic limits to stochastic
spatial models of natural enemies. American Naturalist 159: 57-80
Kemp WM, Petersen JE, Gardner RH (2001) Scale-dependence and the
problem of extrapolation: implications for experimental and natural
coastal ecosystems. In: Gardner RH, Kemp WM, Petersen JE (eds)
Scaling relations in experimental ecology. Columbia University Press,
New York, pp 3-47
King AW (1992) Translating models across scales in the landscape. In: Jones
CG, Lawton JH (eds) Linking species and ecosystems. Chapman and
Hall, New York, pp 479-514
- 30 -
Kotta J, Orav H, Sandberg-Kilpi E (2001) Ecological consequence of the
introduction of the polychaete Marenzelleria cf. viridis into a shallowwater biotope of the northern Baltic Sea. Journal of Sea Research 46:
273-280
Kuparinen J, Leonardsson K, Mattila J, Wikner J (1996) Food web structure
and function in the Gulf of Bothnia, the Baltic Sea. Ambio 8: 13-21
Lawrie SM, Raffaelli DG, Emes CH (2000) Small-scale patterns in the
distribution of the amphipod Corophium volutator on the Ythan estuary,
Aberdeenshire, Scotland. Sarsia 85: 321-327
Legendre P (1993) Spatial autocorrelation: Trouble or new paradigm?
Ecology 74: 1659-1673
Legendre P, Fortin MJ (1989) Spatial pattern and ecological analysis.
Vegetatio 80: 107-138
Legendre P, Legendre L (1998) Numerical Ecology. Elsevier, Amsterdam
Legendre P, Thrush SF, Cummings VJ, Dayton PK, Grant J, Hewitt JE, Hines
AH, McArdle BH, Pridmore RD, Schneider DC, Turner SJ, Whitlatch RB,
Wilkinson MR (1997) Spatial structure of bivalves in a sandflat: Scale
and generating processes. Journal of Experimental Marine Biology and
Ecology 216: 99-128
Leonardsson K (1991a) Effects of cannibalism and alternative prey on
population dynamics of Saduria entomon (Isopoda). Ecology 72: 12731285
Leonardsson K (1991b) Spatial size variation in adult females of Saduria
entomon (Crustacea, Isopoda): A comparison between field observations
and predictions of a life-history model. Ophelia 34: 91-104
Leonardsson K (1994) Multiple density dependence in two sub-populations of
the amphipod Monoporeia affinis: A potential for alternative equilibria.
Oecologia 97: 26-34
Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73:
1943-1967
Luckinbill LS (1974) The effects of space and enrichment on a predator-prey
system. Ecology 55: 1142-1147
Marrasé C, Lim EL, Caron DA (1992) Seasonal and daily changes in
bacterivory in a coastal plankton community. Marine Ecology Progress
Series 82: 281-289
Mauchline J (1971) The biology of Neomysis integer (Crustacea, Mysidacea).
Journal of the Marine Biological Association of the United Kingdom 51:
347-354
Melbourne BA, Sears AL, Donahue MJ, Chesson P (in press) Applying scale
transition theory to metacommunities in the field. In: Holyoak M, Leibold
MA, Holt RD (eds) Metacommunities: Spatial Dynamics and Ecological
Communities. University of Chicago Press, Chicago
Murdoch WW, Briggs CJ, Nisbet RM (2003) Consumer-resource dynamics.
Princeton University Press, Princeton, New Jersey
Nisbet RM, deRoos AM, Wilson WG, Snyder RE (1998) Discrete consumers,
small scale resource heterogeneity, and population stability. Ecology
Letters 1: 34-37
- 31 -
Norkko A, Cummings VJ, Thrush SF, Hewitt JE, Hume T (2001) Local
dispersal of juvenile bivalves: implications for sandflat ecology. Marine
Ecology Progress Series 212: 131-144
O'Brien WJ (1988) The effect of container size on the feeding rate of
Heterocope septentrionalis, a fresh-water predaceous copepod. Journal
of Plankton Research 10: 313-317
Olafsson EB (1989) Contrasting influences of suspension-feeding and
deposit-feeding populations of Macoma balthica on infaunal recruitment.
Marine Ecology Progress Series 55: 171-180
Pacala SW, Tilman D (1994) Limiting similarity in mechanistic and spatial
models of plant competition in heterogeneous environments. American
Naturalist 143: 222-257
Pace ML (2001) Getting it right and wrong: extrapolations across experimental
scales. In: Gardner RH, Kemp WM, Kennedy VS, Petersen JE (eds)
Scaling relationsin experimental ecology. Columbia University Press,
New York, pp 157-177
Pascual M, Mazzega P, Levin SA (2001) Oscillatory dynamics and spatial
scale: The role of noise and unresolved pattern. Ecology 82: 2357-2369
Pearson TH, Rosenberg R (1987) Feast and famine: Structuring factors in
marine benthic communities. In: Gee JHR, Giller PS (eds) Organisation
of communities past and present. Blackwell Scientific Publications,
Oxford, pp 373-395
Petersen JE, Chen CC, Kemp WM (1997) Scaling aquatic primary
productivity: Experiments under nutrient- and light-limited conditions.
Ecology 78: 2326-2338
Petersen JE, Cornwell JC, Kemp WM (1999) Implicit scaling in the design of
experimental aquatic ecosystems. Oikos 85: 3-18
Petersen JE, Hastings A (2001) Dimensional approaches to scaling
experimental ecosystems: Designing mousetraps to catch elephants.
American Naturalist 157: 324-333
Platt T, Sathyendranath S (1994) Scale, pattern and process in marine
ecosystems. In: Giller PS, Hildrew AG, Raffaelli DG (eds) Aquatic
ecology: scale, pattern and process. Blacwell Scientific Publications,
Cambridge, pp 593-599
Rastetter EB, King AW, Cosby BJ, Hornberger GM, O'Neill RV, Hobbie JE
(1992) Aggregating fine-scale ecological knowledge to model coarserscale attributes of ecosystems. Ecological Applications 2: 55-70
Reise K (1983) Biotic enrichment of intertidal sediments by experimental
aggregates of the deposit-feeding bivalve Macoma balthica. Marine
Ecology Progress Series 12: 229-236
Rossi RE, Mulla DJ, Journel AG, Franz EH (1992) Geostatistical tools for
modeling and interpreting ecological spatial dependence. Ecological
Monographs 62: 277-314
Sarnelle O (1997) Daphnia effects on microzooplankton: Comparisons of
enclosure and whole-lake responses. Ecology 78: 913-928
Sarvala J (1986) Interannual variation of growth and recruitment in
Pontoporeia affinis (Crustacea: Amphipoda) in relation to abundance
- 32 -
fluctuations. Journal of Experimental Marine Biology and Ecology 101:
41-60
Savino JF, Stein RA (1982) Predator-prey interaction between largemouth
bass and bluegills as influenced by simulated, submersed vegetation.
Transactions of the American Fisheries Society 111: 255-266
Schindler DW (1998) Replication versus realism: The need for ecosystemscale experiments. Ecosystems 1: 323-334
Schmitz OJ (2000) Combining field experiments and individual-based
modeling to identify the dynamically relevant organizational scale in a
field system. Oikos 89: 471-484
Schneider DC (1994) Scale-dependent patterns and species interactions in
marine nekton. In: Giller PS, Hildrew AG, Raffaelli DG (eds) Aquatic
ecology:scale, pattern and process. Blackwell Scientific Publications,
Cambridge, pp 441-467
Searle SR, Casella G, McCulloch CE (1992) Variance components. John
Wiley and Sons, New York
Sparrevik E, Leonardsson K (1998) Recruitment in the predacious isopod
Saduria entomon (L.): Alternative prey reduces cannibalism. Journal of
Experimental Marine Biology and Ecology 221: 1117-1130
Sparrevik E, Leonardsson K (1999) Direct and indirect effects of predation by
Saduria entomon (Isopoda) on the size-structure of Monoporeia affinis
(Amphipoda). Oecologia 120: 77-86
Stephenson GL, Hamilton P, Kaushik NK, Robinson JB, Solomon KR (1984)
Spatial distribution of plankton in enclosures of 3 sizes. Canadian
Journal of Fisheries and Aquatic Sciences 41: 1048-1054
Taylor LR, Woiwod IP, Perry JN (1980) Variance and large scale spatial
stability of aphids, moths and birds. J. Anim. Ecol. 49: 831-854
Thrush S (1991) Spatial patterns in soft-bottom communities. Trends in
Ecology and Evolution 6: 75-79
Thrush SF, Schneider DC, Legendre P, Whitlatch RB, Dayton PK, Hewitt JE,
Hines AH, Cummings VJ, Lawrie SM, Grant J, Pridmore RD, Turner SJ,
McArdle BH (1997) Scaling-up from experiments to complex ecological
systems: Where to next? Journal Of Experimental Marine Biology And
Ecology 216: 243-254
Tilman D, Kareiva P (1997) Spatial ecology - the role of space in population
dynamics and interspecific interactions. Princeton University Press,
Princeton, New Jersey
Turner MG, Gardner RH (1991) Quantitative methods in landscape ecology:
an introduction. In: Turner MG, Gardner RH (eds) Quantitative methods
in landscape ecology. Springer-Verlag, New York, pp 3-14
Underwood AJ (1997) Experiments in ecology. Their logical design and
interpretation using analysis of variance. Cambridge University Press,
Cambridge
Underwood AJ, Chapman MG (1996) Scales of spatial patterns of distribution
of intertidal invertebrates. Oecologia 107: 212-224
Uryu Y, Iwasaki K, Hinoue M (1996) Laboratory experiments on behaviour
and movement of a freshwater mussel, Limnoperna fortunei (Dunker).
Journal Of Molluscan Studies 62: 327-341
- 33 -
Wiens JA (1989) Spatial scaling in ecology. Functional Ecology 3: 385-397
Wilhelm FM, Schindler DW, McNaught AS (2000) The influence of
experimental scale on estimating the predation rate of Gammarus
lacustris (Crustacea : Amphipoda) on Daphnia in an alpine lake. Journal
of Plankton Research 22: 1719-1734
Voipio A (1981) The Baltic Sea Elsevier Oceanography Series. Elsevier,
Amsterdam, pp 418
Zouhiri S, Vallet C, Mouny P, Dauvin JC (1998) Spatial distribution and
biological rhytms of suprabenthic mysids from the English channel.
Journal of the Marine Biological Association of the United Kingdom 78:
1181-1202
- 34 -
Tack
Göran, du har varit en fenomenal handledare! Ditt stora engagemang och din
förmåga att hitta guldkornen bland alla idéer och tankar vi diskuterat har varit
till stor nytta och glädje. Du har satsat fullt ut på handledarrollen, men ändå
varit noga med att inte styra mer än nödvändigt. Du är forskare ut i
fingerspetsarna och tänker gärna på tvären, vilket har lett till många
spännande diskussioner, som vandrat iväg långt från våra gemensamma
skalproblem.
Erik, dig har jag att tacka för att jag överhuvudtaget började
doktorera. Eftersom jag kände dig sedan tiden i Åbo, så tvekade jag inte när
jag väl fick chansen att komma till Umeå för att arbeta med dig. Trots att du
rätt snart drog tillbaka till Åbo, så gav du mig en god start och har hela tiden
hjälpt till när det behövts. Vårt samarbete har varit ett nöje!
Kjell, du har hjälpt mig många gånger med kniviga problem och det är
jag tacksam för. Vår gemensamma studie var rolig, och blev till och med
bättre än vi trodde från början.
Juha, Lotta, Sara och Annika vill jag tacka för hjälp med
experimenterande och provsortering. Ylva och Sussi ska ha ett speciellt tack
för att ni sett till att hålla ordning på mig administrativt. Jag vill också passa på
att tacka alla på UMF som hjälpt mig, främst Mikael, Jonas, Nina, Katarina
och Karin, och alla andra nuvarande och tidigare UMF:are och marina
ekologer för den trevliga stämningen – Tina, Umut, Janne, Agneta, Johan,
Calle, Erik, Sus, Tommy och alla andra. Ett speciellt varmt tack går till Johnny
och Marko, delar av den finlandssvenska enklaven och fiskekompisar - vi
pratade mer fiske än vi fiskade, men visst blev det en och annan middagsfisk,
och framför allt en hel del oförglömliga minnen. Våra gemensamma wappar,
lilla jular och andra fester saknar vi! Fiskevattnen i Öregrund är förresten
väldigt fina. Kom gärna ner och pröva dem.
Nu när jag varit borta från Umeå och universitetsvärlden ett tag är det
vissa saker jag saknar lite extra – att folk alltid har tid att för en pratstund, de
långa fikapauserna, fredagspubarna, festerna, och inte minst innebandyn,
som gjorde måndagarna till en dag att se fram emot. Jag saknar den
avslappnade stämningen och det norrländska gemytet (jodå, visst finns det).
Tack alla för en fin tid!
Jag vill också tacka Kustlaboratoriet och mina nya arbetskompisar för
att ni visat förståelse för min kluvna tillvaro, och gett mig tillräckligt med
spelrum för att avsluta doktorandarbetet. Jag är glad för att jag får arbeta med
er!
Till sist vill jag tacka min familj. Dig Lena, för att du gör mig till en
lycklig människa! Den senaste tiden har varit rätt jobbig, inte bara för mig,
men du har stöttat mig till hundra procent. Ni, Axel och Emilia, har fått mig att
bli vuxen och samtidigt barn igen. Det är spännande att få upptäcka världen
på nytt tillsammans med er! Jag vill också tacka er, mamma och pappa, för att
ni gav mig mitt naturintresse och för att ni alltid ställt upp för mig!
Jag vet att det här är den ojämförligt mest lästa delen av en
avhandling, och vill därför, för er som inte är bekanta med forskarvärlden,
försöka förklara vad som är drivkraften för doktorander och forskare. Vad är
det som får en att med glädje satsa kvällar och helger bara för att få ihop data
- 35 -
till en ny artikel, för att inte tala om att våndas fram densamma framför
datorn? Svaret för min del, och säkert för många andra, är enkelt. Vi drivs av
nyfikenhet. På sätt och vis är vi vår tids upptäcktsresande (jo, jag håller med det var annat på Shackletons tid. Nu finns inga andra faromoment än att tidvis
bli utan finansiering). Vi utforskar inte okända kontinenter utan söker svar på
frågor, men spänningen finns där och tillfredställelsen när man finner det man
sökt. Eller som muminpappan uttryckte det:
”Ni förstår, jag vill komma underfund med om havet har något system
eller om det bär sig åt precis hursomhelst - det är viktigt.”
Ur Pappan och havet, Tove Jansson 1965
- 36 -
Svensk sammanfattning
För att förstå samspelet mellan organismer och deras livsmiljö bygger
ekologer modeller. Idag är dessa modeller ofta rätt grova, helt enkelt för att
det är svårt att matematiskt fånga de komplexa sambanden i naturen.
Eftersom människan har en mycket stor inverkan på naturen är det av största
vikt att utveckla modeller som kan förutsäga hur arter och samhällen
utvecklas framåt i tiden, givet vissa förutsättningar. Sådana prediktiva
modeller är av central betydelse för att vi ska kunna förvalta naturresurserna
på ett långsiktigt hållbart sätt. Vad händer t ex om vi ökar eller minskar fisket
eller jakten på en viss art, både med avseende på arten själv och på
ekosystemet, eller vad händer om vi påverkar arters livsmiljö på ett negativt
sätt?
När man bygger ekologiska modeller beskriver man de olika
processer som tillsammans styr systemet med matematiska funktioner. Man
bestämmer dessa funktioner genom att mäta processerna i experimentella
studier. Dessa experiment utförs i regel på en mindre skala än den vi
egentligen är intresserade av, eftersom ekologiska system oftast är för stora
för att man ska kunna utföra kontrollerade experiment på hela system. När
man på det här viset ”krymper” systemstorleken i experimentella studier
innebär det alltid att man riskerar att förändra systemets egenskaper. En av
de viktigaste frågorna inom ekologin är därför hur man ska kunna extrapolera
resultat från småskaliga studier till regionala eller till och med globala skalor.
Tidigare antog man ofta att resultat från småskaliga experiment kunde
tillämpas direkt på storskaliga naturliga system. Idag vet vi att detta
antagande ofta är felaktigt, men vi vet fortfarande mycket litet om hur man ska
överföra resultat mellan olika skalor. En viktig uppgift är därför att försöka
finna generella mekanismer som skapar skalberoende i ett system. Med
kunskap om sådana mekanismer kommer dagens ekologiska modeller att
kunna utvecklas till betydligt känsligare instrument.
I mitt avhandlingsarbete har jag framför allt arbetat med att försöka
förstå mekanismer som gör att småskaliga experiment fungerar annorlunda
än naturliga system, och därigenom kunna utveckla metoder för att översätta
resultaten till naturen. Predationsprocessen, dvs att ett djur äter ett annat, är
mycket central inom ekologin, och jag har därför valt att studera olika aspekter
av denna. Mina studier har jag gjort på predator-bytessystem som
förekommer i Östersjön. I mina studier har jag visat att när man mäter
predationshastigheter experimentellt, så påverkas resultatet indirekt av
väggarna i akvariet. Genom att både predator och byte ansamlas längs
väggarna kommer fler byten att fångas än om båda hade varit jämnt fördelade
i akvarierna, och om man ej beaktar detta vid mätningarna uppstår ett fel.
Storleken på detta mätfel är dessutom beroende av storleken på de akvarier
man använt, så att mätfelet är större i stora akvarier. När man väl känner till
mekanismen finns det två sätt att undvika denna felkälla. Man kan antingen
designa experimentet så att djuren ej samlas längs kanterna, vilket i många
fall kan vara svårt, eller så kan man utveckla metoder för att matematiskt
- 37 -
korrigera mätfelet. Jag har utvecklat en sådan metod, som bygger på att man
studerar utbredningen av djuren inom akvarierna.
Något av det mest fascinerande med naturen är att den är så
variabel. Variationen i sig har visat sig vara mycket viktig för hur naturliga
system fungerar. Men denna variation utgör ett problem när man bygger
ekologiska modeller, eftersom den ofta inte går att få med i småskaliga
experiment. Därför måste man försöka bygga in denna rumsliga variation i
själva modellstrukturen i stället. Det finns ett flertal metoder för att göra detta,
som alla bygger på att man kopplar modellen till någon slags karta över
systemet. Nackdelen med dessa metoder är att modellerna vanligen blir
mycket komplexa. Jag har studerat en alternativ teknik, som kallas
momentapproximering, och bygger på att man beskriver den rumsliga
variationen statistiskt i stället för med en karta. Jag har visat hur man gör för
att använda momentapproximeringen i en predator-bytesmodell. Metoden
torde vara mycket användbar inom ekologin, eftersom den ger oss ett enkelt
verktyg för att koppla den variation vi observerat i naturen till modellen. Den
låter oss också dela upp variationen i välkända statistiska komponenter, vilket
ökar förståelsen för hur olika aspekter av rumslig variation påverkar
ekologiska processer.
Sammantaget har jag visat att det är viktigt att beakta rumslig
variation både när man gör experiment och när man skalerar upp
experimentresultat till naturliga system. En starkare fokusering på skalor och
heterogenitet kommer att ge en förbättrad förståelse för hur naturen fungerar,
vilket behövs för att vi på sikt ska kunna bygga modeller som utgör kraftfulla
verktyg inom naturresursförvaltningen.
- 38 -