Spatial scale, heterogeneity and functional responses - BES journal

Journal of Animal Ecology 2004 73, 487– 493

Spatial scale, heterogeneity and functional responses

Blackwell Publishing, Ltd.

ULF BERGSTRÖM and GÖRAN ENGLUND Department of Ecology and Environmental Science, Umeå University, SE-901 87 Umeå, Sweden

Summary 1. In a laboratory experiment, we studied the effect of arena size on the functional response of the mysid shrimp Neomysis integer preying on the cladoceran Polyphemus pediculus. The aim of the study was to examine mechanisms that cause the functional response to be scale-dependent, by documenting the spatial distribution and the movement behaviour of predator and prey. 2. The attack rate was significantly higher in large arenas, while the handling time did not differ between arena sizes. The difference in attack rate could be explained by differences in aggregative behaviour of predator and prey and in swimming activity of the predator. It is suggested that distributions of animals are often affected by the walls of the experimental arenas and that this spatial heterogeneity is scale-dependent, which may have a considerable impact on estimates of ecological process rates. 3. A method of correcting attack rate estimates for artefacts caused by such spatial heterogeneity is presented. Key-words: consumption rate, encounter rate, Neomysis integer, Polyphemus pediculus, scale effects. Journal of Animal Ecology (2004) 73, 487–493

Introduction During recent decades, substantial effort has been devoted to exploring ecological relationships through experimental studies. These experiments have, as a rule, been performed on much smaller scales than the target systems. None the less, methods that may be used in extrapolating results across scales and mechanisms that may cause ecological processes to be scale-dependent, both in natural systems and their experimental mimics, remain largely unexplored. Learning more about such scaling relations and rules for extrapolation is one of the most urgent tasks in the process of turning ecology into a quantitative science (Wiens 1989; Englund 1997; Kemp, Petersen & Gardner 2001; Bergström & Englund 2002). One mainstay of population ecology is the functional response of predators, which describes the relationship between prey density and the consumption rate of predators. It has attracted much attention, both theoretically and empirically, and a wide variety of response functions have been derived (reviewed in Jeschke, Kopp & Tollrian 2002). Most empirical studies of functional responses have been performed in

© 2004 British Ecological Society

Correspondence: Ulf Bergström, National Board of Fisheries, Gamla Slipvägen 19, SE-74071 Öregrund, Sweden. Tel: + 46 173 46485; Fax: + 46 173 30949; E-mail: [email protected], [email protected]

enclosed experimental systems. Such laboratory-derived functional responses have been used in predator–prey models, whose predictions have been tested against empirical data on dynamics of populations (e.g. Hassell 1978; Crowley et al. 1987; Gurney et al. 1990; de Roos & Persson 2001). However, these functional responses contain a considerable element of uncertainty, as it is known that consumption rates of predators can be affected by the size of the experimental arena used in the measurements (e.g. Cooper & Goldman 1982; de Lafontaine & Leggett 1987; Bergström & Englund 2002). Scale effects on estimates of functional response parameters are in many cases caused probably by the actual caging of individuals (Petersen, Chen & Kemp 1997; Englund & Cooper 2002). Examples of such experimental artefacts are effects of containment on the foraging or escape behaviour of the organisms (Tang & Boisclair 1993; Christensen 1996; Dodson et al. 1997; Buecher & Gasser 1998), or on the distribution of predator and prey within the enclosures, which affects encounter rates (Kaiser 1983; de Lafontaine & Leggett 1987; O’Brien 1988; Wilhelm, Schindler & McNaught 2000; Bergström & Englund 2002). The mechanisms behind these experimental artefacts and their impacts on parameter estimates are not well known. The aim of this study was to examine how our ability to measure functional responses in laboratory settings may be improved by studying explicitly how spatial scale affects the distribution and behaviour of predator and prey. This was conducted by observing the functional

488 U. Bergström & G. Englund

response of a mysid shrimp preying on a cladoceran in two different container sizes. By documenting the spatial distribution and movement behaviour of the animals during the experiments, two mechanisms that caused attack rate estimates to increase with spatial scale were identified.

Materials and methods   The predator used in the functional response experiment, Neomysis integer (Leach), is a euryhaline mysid shrimp, common in coastal waters and many brackish water lakes of western Europe (Enckell 1980; Mauchline 1980). It is hyperbenthic and can be found in shoals in shallow water, where it feeds mainly on zooplankton, detritus, periphyton and benthic algae (Mauchline 1971; Fockedey & Mees 1999). When feeding on zooplankton mysid shrimps catch prey with limited mobility by suspension feeding, while more mobile prey are caught raptorially (Mauchline 1980; Viitasalo & Rautio 1998). The prey, the littoral cladoceran Polyphemus pediculus (L.) is mainly a freshwater species. It is also found in brackish water, and in the northern Baltic Sea it is found in the same habitat as Neomysis (Enckell 1980; Sandström 1980). It is a fast swimmer, and forms swarms readily (Butorina 1986; Englund & Harms 2001). Polyphemus has a well-developed visual system, which it uses when orientating itself both within the habitat and within the swarm (Butorina 1986).

 

© 2004 British Ecological Society, Journal of Animal Ecology, 73, 487–493

The functional response of Neomysis to varying densities of Polyphemus was determined in containers of two sizes. Preliminary studies had shown that both predator and prey aggregated in the area close to the container wall. In such cases the aggregative behaviour may be scale-dependent, thus affecting the encounter rate between predator and prey (see Bergström & Englund 2002). Based on this observation, we hypothesized that the attack rate coefficient would be higher in the larger containers, due to a stronger coaggregation of predator and prey. The experiment was conducted in white plastic containers, 15 and 32 cm in diameter, both with 10 cm high walls. The containers were filled with filtered (20 µm) Baltic Sea water up to 6 cm height, giving volumes of 1·1 and 4·9 l, respectively. The salinity of the water was 3·5 psu, the temperature 17 ± 1 °C, and the light irradiance 1 µE m−2 s−1 (illumination from above). Both males and females of Neomysis were used in the experiment, with a length range of 11–16 mm (mean 13·3 mm). The animals were collected at the coast of the Gulf of Bothnia, Baltic Sea. They were kept in aerated containers for 5 days at most, and were fed daily with Polyphemus. Before an experimental run, they were starved for 12 h. New individuals were used in each run.

Fresh Polyphemus specimens were collected from a fresh water lake in the morning before each experimental run. The mean size of the individuals used in the experiments was 0·70 mm, with a size range of 0·4– 1·1 mm. The response to prey densities of 13–180 ind l−1 was studied. The small containers were replicated eight times and the large containers four times, except for the highest density, which was replicated five and two times. The density of predators was constant, 1·9 ind l−1, corresponding to two and nine individuals in small and large containers, respectively. The smaller number of replicates of large containers is motivated by more precise estimates of consumption rates being expected in these units, due to the higher number of predators (Bergström & Englund 2002). Before starting an experimental run, which was carried out by adding the predators to the containers, Polyphemus was allowed to adapt to and to distribute over the experimental containers for at least 15 min. Generally Neomysis started feeding almost immediately after being added. The experiments were terminated after 1 h, and remaining prey were counted under a stereo microscope. Estimates of the functional response parameters attack rate and handling time were obtained by fitting the ‘random predator equation’ (Royama 1971; Rogers 1972): Ne = N0 (1 − exp(−aP(T − hNe /P)))

eqn 1

where Ne is the density of prey eaten, N0 is the initial prey density, a is the attack rate, P is the predator density, T is the duration of the experiment and h is the handling time. This model is the integrated form of Holling’s (1959) ‘disk equation’ for type II functional responses. The random predator equation accounts for prey depletion, and is thus appropriate in cases where captured prey is not replaced. Curve fitting was performed with the  module in SAS (non-linear least squares), by adapting the procedure described by Juliano (1993). The two container sizes were treated separately in the analyses, and parameter estimates of a and h for small and large containers were compared with a t-test.

        During the experiments, the horizontal distribution of Neomysis and Polyphemus was studied by photographing the containers from above. The vertical distribution was not recorded, as preliminary studies indicated that it did not change with container size or prey density (Polyphemus was mainly found in the uppermost 2 cm of the water column, while Neomysis had a relatively homogeneous vertical distribution). During a run, three to five pictures were taken of each small and one to three pictures of each large container, at a resolution

489 Scale, heterogeneity and functional responses

of 3·34 million pixels, and the positions of all individuals were digitized. For each container size and prey density, at least 36 records of Neomysis and 300 records of Polyphemus positions were gathered. The data on the distributions were used for calculating an index that is proportional to the rate of encounters between predator and prey (see below). Predator movement patterns were recorded by video taping each replicate container for 30 s. From these video clips three replicates of each container size and density were chosen randomly. The movements of two individuals were digitized by recording their positions at 0·8-s intervals. Each individual was followed for 20 steps: that is, for 16 s. From the digitized positions the mean swimming speed of each predator was calculated. Effects of prey density, container size and container identity on the swimming speed of Neomysis were analysed with a nested .

     


The encounter rate is a central measure in this study, as it is proportional to the attack rate (a) of the functional response (Jeschke et al. 2002). The encounter rate for a single predator (e) is determined by the densities of predators (P) and prey (N ), their movement speeds (VP, VN) and the encounter radius (r). The relationship is described by e = πr 2 PN ((3VP2 + VN2 )/VP )/3 (Gerritsen & Strickler 1977). The swimming speed of Neomysis was about 10 times that of Polyphemus, which means that VN can be ignored, and the relationship simplifies to e = πr 2PNVP. Thus, e is linearly dependent on predator and prey densities and predator movement speed (Gerritsen & Strickler 1977). In order to measure the effect of the heterogeneous distributions of predator and prey on the encounter rate, predator and prey distributions in different parts of the containers were quantified. This was performed by dividing the containers into 2-cm-wide concentric zones, from the centre outwards, and recording predator and prey densities in each zone. This representation was considered appropriate, as there was a clear gradient in the distribution of both predator and prey along the radius of the containers, with increasing densities towards the container wall. The width of the zones was set to 2 cm, because Neomysis of the size used in the experiment detects prey with their antenna within an approximately 2-cm-wide area (Viitasalo et al. 1998). Using narrower zones would capture small-scale heterogeneity that does not affect the encounter rate, while using wider zones would leave relevant heterogeneity undetected. The predator and prey distribution data was then used to calculate an encounter index (E), which is directly proportional to the encounter rate (e) between predator and prey (Voit 1984) and thus to the attack rate (Jeschke et al. 2002). The encounter index for a zone is given by the densities of predator and prey within the zone (Ez):

Ez = PN * A

eqn 2

where P is the density of predators, N is the density of prey and A is the area of the zone. Here area was used instead of volume, as two-dimensional representations of the distributions were used. The encounter index for the average predator (Ep) within a container provides an estimate of the effect of spatial heterogeneity on the attack rate of the functional response, and is given by: Ep = ( Σ Ez)/ p

eqn 3

where p is the number of predators within the container.

    In preliminary studies it was noticed that the aggregative behaviour of Polyphemus seemed to disappear in darkness. If, as hypothesized, coaggregation would give rise to a scale effect in the functional response experiment in light, then the scale effect should be much weaker or absent in darkness. Using similar procedures as described above, the predation rate was therefore observed in darkness, using two prey densities, 25 and 60 ind l−1. Small containers were replicated six times and large three times. The distributions of Neomysis and Polyphemus were recorded by photographing, as in the functional response experiment. In this experiment we were not able to measure the movement rates of the predator.

Results The functional response of Neomysis preying on Polyphemus differed between small and large containers (Fig. 1). Fitting the random predator equation to the data yielded similar estimates of handling times, while attack rate estimates were 119% higher in the large containers (Table 1). The effect of container size on the attack rate estimates seemed to be the result of two interacting mechanisms, scale-dependent coaggregation of predator and prey and scale-dependent predator activity. Data on the distributions of Neomysis and Polyphemus within the containers showed that both preferred the area along the container wall, and that the densities close to the wall were higher in the larger containers (Fig. 2a,b). The encounter index for each zone (Ez) indicates that these distributions resulted in much higher encounter rates along the wall than in the centre of the arenas. In small containers the area-specific encounter index (Ez /A) in the zone closest to the wall was 20 times higher than in the central zone, and in large containers 300 times higher (Fig. 2c). To quantify the contribution of coaggregation to the observed scale effect on the attack rate, the encounter index for the average predator, Ep (eqns 2, 3), was calculated from the distribution data for each prey density and container size, and then regression lines for both


Fig. 1. The mean prey consumption rate of Neomysis preying on Polyphemus in small and large containers. The hatched lines show the fitted type II functional response functions.

Table 1. Parameter estimates for the functional response of Neomysis preying on Polyphemus in small and large containers (mean ± SE). P-values refer to t-test of differences between parameter estimates in large and small containers Small Attack rate (l pred−1 h−1) Handling time (h) r2 of regression (%)


Large

0·62 ± 0·16

1·36 ± 0·36

0·045 ± 0·006

0·048 ± 0·003

90

P-value 0·018 > 0·3

97

container sizes were fitted (Fig. 3a). The difference in slope of the lines between small and large containers is a measure of the scale effect caused by coaggregation. This difference was 40%. The Ep can also be calculated for random distributions, by using mean abundances of predators and prey. By comparing the slopes in Fig. 3a for random distributions and for observed aggregated distributions, the total effect of coaggregation can be estimated. This comparison showed that the encounter rate was elevated with 11% and 55% for small and large containers, respectively, compared to a random distribution of predator and prey. The swimming activity of the predator, represented by the average swimming speed, did not differ between prey densities within a container size, but was significantly higher in large containers compared to small (Table 2). The average swimming speed in small containers was 23·2 ± 2·3 mm /s and in large 31·0 ± 1·8 mm/s (mean ± SE). This difference (34%) was caused by both a lower proportion of inactive predators in the large containers and a higher swimming speed of the active individuals. In the  the container identity factor was significant, which indicates that individuals within a container tended to exhibit similar movement speed. The combined effect of coaggregation and swimming speed on the attack rate is multiplicative (both linearly affect the encounter rate), so that the expected difference in encounter rate between small and large containers would be 88% (1·40*1·34). This agrees

Fig. 2. Distribution of (a) Polyphemus and (b) Neomysis along the radius of the containers (mean ± SE). The figures represent average distributions for all prey densities in the functional response experiment. (c) Encounter index (eqn 2) per area based on the distributions in (a)–(b) (mean ± SE). The highest index value has been set to 1.

reasonably well with the attack rate estimates, where the difference between container sizes was 119%. As predicted, the prey consumption rate did not differ between small and large containers in darkness, with mean ± SE of 6·2 ± 0·5 and 6·3 ± 0·3 predator−1 h−1 for 25 prey l−1, and 15·1 ± 1·0 and 16·5 ± 0·9 predator−1 h−1 for 60 prey l−1 (P > 0·3 for factor container size in two-factor ). Polyphemus was no longer aggregated along the container wall, while Neomysis exhibited weak aggregation. Regressions of the encounter index against prey density showed that Ep for small and large containers did not deviate from Ep for randomly distributed predator and prey (Fig. 3b).

Discussion In this study, we demonstrate that the size of the experimental arena may have a large impact on the observed functional response. In the experiment with Neomysis and Polyphemus, the increase in attack rate estimates with arena size was probably the joint result of two mechanisms, scale-dependent activity of the predator and scale-dependent coaggregation of predator and prey. Both mechanisms acted to increase the attack rate


Fig. 3. Encounter index for the average predator (eqn 3) regressed against prey density for (a) the functional response experiment and (b) the darkness experiment. The hatched line shows the regression line for randomly distributed predator and prey. The slope of the regression lines are given in (a).

Table 2. The effect of prey density, container size and container identity on the swimming speed of Neomysis, analysed with a three-factor nested 

© 2004 British Ecological Society, Journal of Animal Ecology, 73, 487– 493

Factor

SSQ

d.f.

MSQ

F-ratio

P-value

Density Size Density × size Container (density, size) Error

1212·4 810·2 243·7 4142·3

6 1 6 27

202·1 810·2 40·6 153·4

1·317 5·281 0·265 1·779

0·284 0·030 0·949 0·047

3535·5

41

86·2

coefficient in the larger of the studied container sizes. The importance of understanding mechanisms that may cause these kinds of scale effects in experimental systems is emphasized by the large difference in the attack rate estimates. Although there was less than a fivefold difference in container size in the experiment, the estimates differed 119%. The first mechanism, scale-dependent predator activity, was caused by the actual number of Neomysis in a container. In the larger containers the predators had a higher average swimming speed, which was the combined result of a lower proportion of inactive individuals and a somewhat higher swimming speed of the active individuals. Our observations suggest that the animals were influenced by the activity of the other predators in the container, so that when one individual started feeding, the others also became more active. This meant that in the larger containers, with a higher number of Neomysis, the predators were generally more

active than in the small containers. The significant container effect in the  on swimming speed (Table 2) also indicated that predators within a container influenced each other’s activity. It is not possible from our experiment to judge whether this scale effect should be considered as an artefact of enclosure or if similar behaviour occurs in nature. Neomysis is a shoal-forming species, so this mechanism may potentially have a large impact on the foraging activity of the predators in nature. The other mechanism, scale-dependent coaggregation, was caused by both predator and prey aggregating along the container wall (Fig. 2). As a result, the prey density perceived by the predators was higher than the mean density calculated for the whole container. In the large containers, the favoured area was a smaller proportion of the total area (lower perimeter-to-area ratio), and therefore the densities in the aggregates increased with container size. Consequently, a predator in a large container encountered more prey than a predator in a small container, which thus affected the attack rate estimates. It was verified that coaggregation was an important mechanism causing the functional response to be scaledependent by studying the consumption rate in darkness. In this experiment the encounter rate indices did not differ from that for random distribution, showing that there was no coaggregation. Accordingly, the difference in consumption rate between container sizes was not significant. The swimming speed of Neomysis could not be measured in darkness. However, the fact that the consumption rate was scale-independent suggests that the difference in swimming speed disappeared as well. Observations of the behaviour of predator and prey provided clear indications about the causes of the aggregative behaviour. Polyphemus is very sensitive to differences in light intensity (Butorina 1986) and preferred the darkest area of the containers, which was along the walls. For Neomysis the aggregation seemingly was an effect of the animals following the wall for some time after each wall encounter. These mechanisms were supported by observations of the distributions of predator and prey in darkness (not presented), where Polyphemus was distributed randomly over the arenas while Neomysis was still aggregated along the wall. Scale-dependent aggregation can be expected to be occurring commonly in experimental studies on consumption rates, as animals often are distributed heterogeneously within experimental arenas (e.g. Savino & Stein 1982; Kaiser 1983; Stephenson et al. 1984; Bergström & Englund 2002). Simulations presented in Bergström & Englund (2002) showed that when working with highly motile animals coaggregation is expected to increase with arena size, leading to a positive relationship between consumption rate and arena size. This was the case in the current study. Because the coaggregation was an artefact caused by the container walls, the attack rate estimates obtained in the small containers were less biased than the estimates from the



large containers. This leaves us with two alternative strategies for trying to circumvent this scale effect. Either the scale effect may be minimized by using very small containers, thus running the risk of adversely affecting the behaviour of the animals (e.g. Cooper & Goldman 1982; Buecher & Gasser 1998), or the experiment may be run at larger scales and the functional response can be corrected for the artefact caused by aggregation. A method of achieving the latter, to assess the effect of coaggregation on the attack rate estimates, may be to fit regressions of the encounter index (Ep) against prey density (Fig. 3a). The slope of the regression line for randomly distributed predator and prey presents a baseline, to which the regression lines from the experiment can be compared. As the attack rate is directly proportional to the encounter rate, the difference in slope measures the effect of coaggregation on attack rate estimates. In the larger containers the effect of aggregation was estimated to be 55%, although these containers were no more than 5 L, which can be considered as small for animals as mobile as Neomysis. This demonstrates clearly that the choice of spatial scale can largely affect the outcome of functional response experiments. Ideally, functional responses should be measured in natural environments (Abrams & Ginzburg 2000), either through direct field observations (Anderson 2001) or through gut content analysis (Wilhelm et al. 2000). However, such studies are, in many cases, fraught with practical difficulties, which is why most studies aiming at quantifying functional responses have been performed in enclosures. In light of this, we urgently need to learn more about experimental artefacts and about methods for extrapolating experimentally obtained models of biotic interactions to nature. A major challenge when extrapolating experimental results to real populations is to take into account spatial heterogeneity in the environment and in the distribution of individuals in the natural system (Kemp et al. 2001; Englund & Cooper 2002). In conclusion, we found that the functional response can vary with the size of the experimental arena due to scale-dependent coaggregation of predator and prey and to scale-dependent foraging activity of the predator. The generality of this result is not known, as scale effects on functional response estimates have been investigated in few other systems. However, the fact that a wide range of organisms are known to aggregate along enclosure walls (see Bergström & Englund 2002) suggests that coaggregation of predator and prey is a common phenomenon. Thus, we believe that scale effects caused by this mechanism are more widespread than is currently appreciated.

Acknowledgements We thank Juha Salonsaari and Sara Andersson for assistance in gathering experimental data. The study

was supported by Umeå Marine Sciences Centre and the J. C. Kempe Memorial Foundation.

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© 2004 British Ecological Society, Journal of Animal Ecology, 73, 487– 493

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