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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. 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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 -