Spatial Dynamics in a Metapopulation Network: Recovery of a Rare Grasshopper Stauroderus Scalaris from Population Refuges

ECOGRAPHY 24: 452–460. Copenhagen 2001

Spatial dynamics in a metapopulation network: recovery of a rare grasshopper Stauroderus scalaris from population refuges

Allan Carlsson and Oskar Kindvall

Carlsson, A. and Kindvall, O. 2001. Spatial dynamics in a metapopulation network: recovery of a rare grasshopper Stauroderus scalaris from population refuges. – Ecography 24: 452–460.

A characteristic feature of the spatial distribution of many species is patchiness. This spatial patchiness may be generated by very different processes, e.g. fragmentation, succession and extinction-colonisation dynamics. In this study, we apply a spatial realistic metapopulation model to analyse the occupancy pattern of a rare and endangered grasshopper, Stauroderus scalaris, found in an extensive network of 158 patches. When the study was initiated in 1985 the regional occupancy was 9.3% declining down to 7.1% in 1989. Then there was a spatial expansion of the population and in 1993 as many as 27.3% of the patches were occupied and 32.9% in 1995. During this expansion phase, the dynamics obeyed metapopulation principles; large patches and less isolated ones were more likely to be colonised. In the beginning, local extinction risks were negatively related to patch size and positively inﬂuenced by isolation. However, later on neither area nor isolation affected extinction probabilities. Altogether, 20 extinctions and 56 colonisations were observed. The shift in regional occupancy, with a growth of ca 20%, coincides with perturbations to the patch network and the warmest summer in 140 yr. Our results suggest that S. scalaris persists on a dynamic habitat mosaic, where refuges are crucial during adverse periods, and stochastic environmental factors (disturbances and climate), that are correlated over large areas, are generating population dynamic patterns that are hard to predict using current modelling techniques.

A. Carlsson, Dept of Conser6ation Biology, Swedish Uni6. of Agricultural Sciences, Box 7044, SE-750 07 Uppsala, Sweden.–O. Kind6all (correspondence: os- [email protected]), Dept of Entomology, Swedish Uni6. of Agricultural Sci- ences, Box 7044, SE-750 07 Uppsala, Sweden.

As a consequence of natural distribution of suitable There is empirical evidence that the spatial dynamics habitats and of secondary fragmentation, many species of several species appears to be driven by a dynamic are found as spatially structured populations. Species habitat mosaic rather than stochastic factors. Thus, for may persist in such landscapes as metapopulations in a instance, extinctions are frequently due to habitat dete- balance between local extinction and recolonisation. rioration, i.e. successional changes in vegetation, habi- There is a growing literature reporting the effects of tat loss and habitat management (Harrison 1991, landscape heterogeneity on metapopulation dynamics. Warren 1993, Thomas 1994, Singer and Thomas 1996), Empirical studies have found differences in extinction while colonisations are facilitated when environmental and colonisation probabilities of local populations due conditions are improved for some reasons (Thomas to differences in local population size (Hanski 1999), 1994). Based on such ﬁndings, it has been suggested patch size (Kindvall and Ahle´n 1991, Soule´ et al. 1992), that habitat dynamics rather than stochastic factors are degree of isolation (Harrison et al. 1988, Sjo¨gren 1991), a key to the persistence of many metapopulations and population variability (Pimm et al. 1988, Bengtsson (Warren 1991, Warren and Thomas 1992, Thomas and Milbrink 1995). 1994). One strength with metapopulation models as an

452 ECOGRAPHY 24:4 (2001) analytical tool is that they can be used to predict the We digitised all potentially suitable habitat patches consequences of possible future management options, based on aerial photographs (IR-film; 1982, 1987 and i.e. explore how size and persistence of a particular 1994) and economic maps (1:10 000) onto which habitat metapopulation is affected by patch removal or the patches were manually drawn during each inventory. potential to recover if conditions improve and new We also carefully described the vegetation and other patches of suitable habitat are created (Thomas and habitat structures in 1995 on each of the identified Jones 1993, Thomas 1994, Hanski and Thomas 1994, patches in order to assess the correspondence between Sjo¨gren-Gulve and Ray 1996). the remote sensing technique and field observations. In this study, we analyse the pattern of presence-ab- Based on the digitised map, it was possible to calculate sence of the grasshopper Stauroderus scalaris in a re- patch sizes (m2) and central co-ordinates (m) on a gional network of habitat patches differing in size and 10×10 m resolution. isolation. For this purpose we apply a spatially realistic metapopulation model, the incidence function model (Hanski 1994), to analyse whether the recorded occu- The incidence function model pancy pattern may be understood by extinction-recolo- nization dynamics. With the model we try to predict The incidence function model of metapopulation dy- observed changes in the number of occupied patches. namics (Hanski 1994) has been shown to give an appro- We also conduct a sensitivity analysis based on the priate description of extinction-recolonisation processes parameterised incidence function model attempting to in vertebrates (Hanski 1991, Cook and Hanski 1995, identify which mechanisms are responsible for the ob- Moilanen et al. 1998) as well as in insects (Hanski et al. served dynamic patterns. 1995, 1996, Kindvall 2000) living in fragmented populations. Detailed descriptions of the model can be found in Hanski (1994), ter Braak et al. (1998) and Moilanen Material and methods (1999). Here we only summarise the model concept and key assumptions. The species Each patch in a patch network is assumed to have two possible states, occupied or empty. Furthermore, Stauroderus scalaris is a large (18–27 mm) grasshopper assuming constant and patch specific colonisation (Ci) (Orthoptera: Acrididae, Gomphocerinae) with discrete and extinction (E ) probabilities, and a possible rescue annual generations. It is widely distributed in the i effect, then the long-term probability (Ji) of a patch i mountains of central and southern Europe but there is being occupied, the so-called incidence, is given by: an isolated relict population on the island of O8land off the south-eastern coast of Sweden. Within the main Ci distribution range of the species it prefers to live in dry, J = . (1) i C +E −C · E stony mountain meadows (Bellmann 1985). The i i i i Swedish fringe population occupies meadows located The extinction probability is assumed to depend on the on poor, dry sandy soils (Kindvall and de Jong 1991). local population size, which is assumed to be correlated These dry meadows are very distinct features in the to patch area (A ), to a certain degree (x): landscape, which has a very simple structure, being i composed of pine forest, agricultural fields and dry e meadows. E =min 1, , (2) i Ax The O8land population is isolated from the main i European distribution, and restricted to an area of 150 where e is a parameter that sets the overall extinction km2 at the northernmost tip of the island. About 500 risk. The probability that a local patch will become ha (3.3% of the landscape) of suitable habitat are found colonised (C ), is assumed to depend on the spatial patchily distributed in the area. i locations of surrounding occupied patches, and their

areas (Aj). This probability is calculated as Censuses 1 C = , (3) We censused all dry meadows for presence or absence i y2 of the species in the entire range during four years: 1+ Si 1985, 1989, 1993 and 1995. The species stridulates in late July–August during warm sunny days. Each year, where y is a parameter that inversely relates to the all patches were acoustically and visually monitored in migrant’s ability to establish on a patch once reaching appropriate weather. If no specimens were detected on it. The number of migrants arriving at patch i is a particular patch, another visit was made some days determined by an index (Si) describing the later. connectedness:

ECOGRAPHY 24:4 (2001) 453 % a 8 Si = (pj · exp(− · Dij) · Aj). (4) island of Oland. Here, the species is found in dry j"i meadows on sandy soils, a resource that is patchily With this index, it is assumed that the number of distributed in the landscape, as is evident from Fig. 1. migrants declines exponentially with increasing inter- There were 140 suitable patches in the first year. Due to a changes in agricultural subsidies, farming practice in patch distance (Dij). The parameter sets the overall migration ability and assumes that migrants move the region changed and the number of suitable patches equally to the inverse of the average dispersal distance. increased to 158 in 1995. The metapopulation was Incidence function model parameters were estimated censused four times, during which the landscape re- from three sets of occupancy data, using two different mained very stable between the first two censuses and methods (MC and NLRB, see Moilanen 1999) depend- between the last two censuses (Fig. 2). However, being on whether the data from a single inventory or two tween 1989 and 1993 as many as 46.4% of the patches inventories were included in an analysis. Estimates were were subjected to disturbances in terms of altered size obtained using the MCE-program (Ver. 1.05. 1998) (Fig. 2). Increased habitat size was usually caused by created by Atte Moilanen. The MCE-program repre- situations where former small remnants of sandy grass- sents a new approach to obtaining parameter values for land occurred next to a crop field which became suit- the incidence function model (Moilanen 1999). In con- able habitat when transformed into a fallow. Similarly, trast to the earlier method (Hanski 1994), it is now reduction of habitat patches usually occurred when possible also to estimate a variable (RV) that describes former dry grassland became arable land, pasture or the amount of regional stochasticity in the metapopula- planted with forest. tion, by using the MC-method (Moilanen 1999). Mean patch size did not change between the first two We performed a sensitivity analysis based on the censuses (1985; 2.794.0 ha, 1989; 2.693.7 ha). Be- incidence function parameterised with data from 1985 tween 1989 and 1993, mean patch size increased from and 1989. In this analysis, repeated simulations with 2.693.7 ha to 3.696.1 ha (t=1.72, pB0.05), in 1995 different sets of parameter values were performed. We mean patch size was 3.195.4 ha. Furthermore, be- investigated the effect of changing the value of each tween 1989 and 1993 the number of patches increased parameter one at a time while keeping the other by 14 and an additional 4 patches were created during parameters constant. We simulated the metapopulation the last period. dynamics over the years until 1995, starting from the The average connectedness (S, eq. 4; a=0.023) of occupancy pattern observed in 1985, using a model suitable habitat patches was 12.4954.8 in 1985/89, adjusted to the landscape changes actually observed. To 82.09230 in 1993 and 53.69133 in 1995. Hence, in run the simulations, we wrote a program that allowed the patch network there is a substantial reduction in us not only to keep track of landscape changes but also isolation between 1989 and 1993 (t-test: t=3.79, pB to alter parameter values in certain time-steps. For 0.001). example, in some simulations parameter changes were imposed only in the time-step corresponding to the observed metapopulation expansion, i.e. 1993. Regional stochasticity was simulated based on the estimate of Occupancy (RV) according to the procedures suggested by In 1985, S. scalaris was present on 9.3% of the patches Moilanen (1999). (n=140), in 1989 the figure was down in 7.1%, rising to 27.3% (n=154) in 1993 and to 32.9% (n=158) in 1995. The effect of patch area on presence was positive and Temperature data significant for all years except 1985 (Table 1). The effect Information on monthly mean temperature, measured of isolation on patch occupancy was significant only in at the meteorological station on the northernmost part 1993 and 1995, when there was a positive relationship. of O8land, was obtained from the Swedish Meteorologi- This means that less isolated patches were more likely cal and Hydrological Inst. Based on these data, we to be occupied (Table 1). calculated the average temperature for the period when the development from eggs to adults takes place, i.e. May–July, annually during the years 1855–1995. Turn-over During the course of this study 20 extinctions were Results recorded. Mean yearly extinction rate was 0.0719 Landscape dynamics 0.061. It was not possible to perform a reliable analysis of extinction probabilities based on data from 1989 and Current distribution of Stauroderus scalaris in northern 1993 separately, due to low numbers of extinctions. Europe is restricted to a relict population found on the However, the joint data set from these two periods

454 ECOGRAPHY 24:4 (2001) Fig. 1. Map of the Swedish distribution of Stauroderus scalaris, the O8land population, based on occupancy data from 1985 and 1995. Open circles represent empty patches and filled circles represent occupied patches of suitable habitat. Circle size is related to patch size. revealed a significant model, where both area and isola- patterns of metapopulation dynamics. When the infor- tion affected local extinction risk (Table 2). In this case, mation from the censuses in 1985 and 1989 was used extinction risk was highest on the relatively smaller and the model failed to predict the metapopulation expan- more remote patches. According to the logistic regression that was observed in 1993 (Fig. 3a). However, this sion analysis, neither area nor isolation influenced extinction probabilities in 1995 (Table 2). We recorded 56 colonisations, all taking place after 1989. Mean yearly colonisation rate was 0.25190.250. Table 3 gives statistics and parameter estimates for the effect of area and isolation on colonisation probabilities. In 1993, both area and isolation had significant effects on colonisation. However, area and isolation had no significant effects on colonisation events observed in the 1995 census.

Sensitivity analysis and simulations The results from the parameterisation of the incidence function model based on data from different periods of the study on S. scalaris are presented in Table 4. It is Fig. 2. Patch dynamics shown as percentage of patches that clear from the simulations of the model that parameter altered in size (increased/decreased) or remained unchanged values from the different periods predict rather different between census periods.

ECOGRAPHY 24:4 (2001) 455 Table 1. Effect of area and connectedness, (S, eq. 4; a=0.023) on patch occupancy in the four years according to logistic regression.

VariableStatistics Year 1985 1989 1993 1995

ln Area Coefficient 0.44 0.71 0.86 0.32 x2 2.95 5.70 20.4 4.22 p 0.09 B0.05 B0.001 B0.05 ln S Coefficient 0.020 0.014 0.20 0.17 x2 3.78 1.79 51.0 44.7 p 0.052 0.18 B0.0001 B0.0001 Constant Coefficient −6.04 −9.23 −8.96 −3.40 Model R2 B1% 1.2% 37.1% 22.4%

Table 2. Effect of area and connectedness (S, eq. 4; a=0.023) on extinction probabilities in the combined data set from 1989 and 1993 and the data set from 1995 according to a logistic regression. Adjusted R2 was 27.7% in the ﬁrst data set and B1% in the latter.

Year Variable Coefﬁcient9SE x2 DF p

1989/93 ln Area −1.5690.65 11.4 1 B0.001 ln S −0.0690.03 7.48 1 B0.01 constant 11.195.23 1995 ln Area −1.8992.25 0.067 1 0.80 ln S 0.05790.22 0.82 1 0.37 constant 0.07490.084

Table 3. Effect of area and connectedness (S, eq. 4; a=0.023) on colonization probabilities in the years 1993 and 1995 according to a logistic regression. Adjusted R2 was 32.5% in 1993 and 16.6% in 1995.

Year Variable Coefﬁcient9SE x2 DF p

1993 ln Area 0.8590.24 16.9 1 B0.0001 ln S 0.2490.06 47.8 1 B0.0001 constant −9.1692.43 1995 ln Area 0.08790.23 0.15 1 0.67 ln S 0.1690.05 24.4 1 B0.0001 constant −1.7692.16

Table 4. Parameter values for the incidence function model obtained from three sets of occupancy data of Stauroderus scalaris using two different methods (MC and NLRB, see Moilanen 1999) in the MCE-program (ver. 1.05. 1998) created by A. Moilanen. Model ﬁtting is based on maximum log-likelihood estimates (Max. l h.). The parameters a and y are related to the colonisation probability (eqs 3, 4), while e and x are related to the extinction probability (eq. 2). A0 is the threshold patch size (m2) where extinction probability equals 1.0. RV is the amount of regional stochasticity. Input variables, i.e. patch size and interpatch distances, are measured in m2 and m, respectively.

Data Method Parameters Max. lh.

a yexA0V

1985–89 MC 0.23 7.24 0.17 0.44 0.018 0.43 257.2 1993 NLRB 0.023 140.60.55 0.72 0.43 – 67.3 1995 NLRB 0.024 93.1 4.85 1.52 2.81 – 73.0 model accurately predicted the extinctions that were from 1993 the predicted increase was not fast enough to observed in 1989. When, instead, the parameters ob- reach more than approximately half of the observed tained from 1993 were used to run the simulation, an occupancy in 1995, on average. All these results (Fig. 3) increase appeared which was great enough to reach the suggest that the degree of regional stochasticity, as metapopulation size observed in 1995 (Fig. 3b). How- described by the variable RV, which was based on ever, in this case the predicted trajectory deviated information only from the 80s, was unable to generate severely from the pattern observed prior to the expan- the dramatic changes in occupancy that occurred in sion. A similar pattern arises when the parameters from 1993. 1995 are used. When a set of simulations starting from Long-term simulations originating from the occu- the occupancy in 1989 was conducted with parameters pancy pattern observed in 1993 or 1995 (unrealistically

456 ECOGRAPHY 24:4 (2001) assuming a constant landscape equal to the one de- the ability of the species to colonise once it has reached scribed in 1995), based on model parameters from 1993 the patch. and 1995, predicted a gradual metapopulation increase The predicted metapopulation dynamics was insensi- which, beyond year 2050, will approach equilibrium tive to extinction parameters e and x. No expansion with between 70 and 110 local populations, on average. occurred even when e was set to 0, implying that the These numbers correspond to a 35–200% increase in extinction risk is zero for all local populations. Parame- occupancy from what was observed in 1995. ter x could be set to anything between 0 and 100 The sensitivity analysis reveals that only two parame- without any observed effect on the dynamics. Further- ters trigger an increase in the metapopulation, namely: more, the regional stochasticity, RV, had a very small a and y, i.e. the two parameters that are related to impact on metapopulation dynamics. For example, species migration and colonisation ability. We found when increasing the value of RV three orders of magni- that when a was set to 0.015 the occupancy increased to tude greater than obtained from the parameterisation what was observed in the ﬁeld (Figs 3c and d). This (Table 4), i.e. setting RV=100, the only effect was that value, which corresponds to an average inter-patch the metapopulation became more extinction prone. migration distance equal to 70 m, is close to the value obtained from the parameterisation based on data from 1993 or 1995 and only about one order of magnitude Weather ﬂuctuations different from the value representative for the 80s (Table 4). However, much greater changes must be Mean early summer temperatures (May–July) have made in order to obtain a metapopulation expansion by varied between 8.9 and 15.8°C during 140 yr (mean9 altering the value of y. This only happened when y was SD=13.191.0°C). The warmest temperatures were set to zero. Even values as small as 10−35 revealed no observed in 1992, and similar high values have not been increase at all. The parameter y is inversely related to recorded for \100 yr (Fig. 4).

Fig. 3. Observed (thick line with black dots indicating censuses) and predicted (thin line: average; dotted line: min/max; 1000 replicates) number of patches occupied by Stauroderus scalaris in relation to the total number of habitat patches available in the years 1985–95 (thickest line). All predictions are based on simulations starting from the observed occupancy in 1985, but with different combinations of parameter values (see Table 1): a) 1985–89; b) 1993; c) 1985–89 for all years except in 1993 when the dispersal parameter a was temporarily set to −0.015; d) as in (c), but with parameters from 1993 used from 1993 and onward. Regional stochasticity (RV) as measured from the 1985–89 data was included in all simulations.

ECOGRAPHY 24:4 (2001) 457 habitat-tracking metapopulation (Harrison and Taylor 1997). Patch suitability is determined by the presence of bare sand for egg laying (Kindvall and de Jong 1991), and this is created by some of the agricultural practises used in the region. Suitability declines with succession (Larsson 1999). In this system, extinctions do not make habitat available for recolonisation. In fact, of the 20 observed extinctions none has been recolonised, sug- gesting that patch suitability has declined and was the cause of local extinction, i.e. deterministic extinctions. It is known that several rare species colonise serial stages of particular vegetation types. Some generations later, they become extinct due to habitat deterioration (Menges 1990, Warren 1991, Thomas 1994). For such spatially structured populations the dynamics are su- Fig. 4. Mean temperature during May–July shown for 140 yr at the study site. The extremely hot summer in 1992 is indi- perimposed on a dynamic habitat mosaic. The abun- cated. dance and distribution of such species will track the availability of habitat and remain roughly constant Discussion only if the rates of habitat loss and renewal remain equal (Thomas 1994). At the end of this study, the When we initiated this study, the spatial distribution of growing S. scalaris metapopulation had probably not S. scalaris suggested a relict population withdrawn to a had time to approach equilibrium. A challenge is to few large patches. Because of this limited number of understand the dynamic nature of the habitat mosaic populations and the restricted range, it was classified as and the ability of the species to track succession. endangered in the Swedish Red list (Ehnstro¨metal. As is the case with many insects, population dynam- 1993). The expected future for the species was then ics of grasshoppers is often significantly affected by judged as balancing on the verge of extinction (Kind- various weather parameters (Richards and Waloff 1954, vall and de Jong 1991). Because of the recorded expan- Haes et al. 1990). Both survival and fecundity of sion of the species in the late 80s, the species is today grasshoppers, living in the temperate zone, are known classified as vulnerable (Ga¨rdenfors 2000). to be negatively influenced during wet and cloudy sea- Our analysis of S. scalaris suggests that first order sons, while sunny and dry situations favour population effects of patch area and isolation largely control the growth (Dempster 1963, Pickford 1966, Uvarov 1966, dynamics. During the phase of spatial expansion, the 1977, Begon 1983, Atkinson and Begon 1988). Al- population obeys central tenets of metapopulation the- though weather effects have not been studied on S. ory and thus corroborates empirical findings now scalaris, it is reasonable to assume that the extremely shown in numerous other insect studies (Thomas and high early summer temperatures observed in 1992 could Hanski 1997). Large and less isolated patches were have promoted an extraordinarily high survival rate more likely to be colonised. In the beginning of the and successful reproduction. If this was the case, then study, local extinction risk seemed to be related to the unexpected expansion of the distribution of S. patch size and isolation, as expected from theory. How- scalaris can largely be explained by an extreme weather ever, neither area nor isolation affected extinction prob- situation, which is a rare event (Fig. 4). abilities in 1995, this result being in contrast to other Based on data presented in this study, it is not studies (Hanski 1999). possible to tell whether it was the landscape perturba- From the initial scenario, we were unable to predict tion or the extreme weather situation that actually the observed expansion of the species using the inci- caused the observed increase in the distribution range dence function model. This may not be unexpected and number of local populations of S. scalaris. In fact, since one assumption in the model is that the landscape there is a possibility that the expansion observed be- of suitable habitat patches remains constant, which was tween 1989 and 1993 would never have happened if not upheld in this study. We have two sources of these two factors had not coincided. Regardless of the information that the landscape was ‘‘perturbated’’ be- actual cause, we can conclude that changes in occu- tween the censuses carried out in 1989 and 1993. pancy of metapopulation-like systems of the same order Firstly, farmers told us that due to changes in subsidies, as reported here are very hard to foresee. Current the area of set-aside land had increased. Secondly, our modelling approaches are unable to predict these types analysis shows that 46% of the patches were subjected of scenarios. Still, we should expect natural populations to perturbation in the form of altered size. We envisage to be very dynamic. that disturbance and succession create the spatial dy- Our investigations of the incidence function model namics of S. scalaris; the species is thus a so-called suggest that the only parameter that must change in

458 ECOGRAPHY 24:4 (2001) order to fit observed changes in occupancy is a.Itis will not mechanistically generate all expected dynamic therefore reasonable to conclude that the migration behaviours. We suggest that it might be better to behaviour altered in some way in the early 90s. The estimate also the variation of each model parameter value obtained from the occupancy patterns in 1985 and the temporal co-variation among parameters. and 1989 (a=0.23) corresponds to an average migra- There are certainly reasons to believe that parameters tion distance equal to B5 m, which is unrealistically that promote local extinction risks are negatively corre- small compared to what is demonstrated for other lated with parameters promoting colonisations (Sol- insects. It is also very small compared with observations breck 1991). Studies focusing on describing temporal from other species of Orthoptera, e.g., for the bush variation in many of the relevant parameters are cer- cricket Metrioptera bicolor a-values corresponding to tainly needed. For example, there is very little informa- average dispersal distances between 170 and 500 m were tion on temporal variation of, e.g. migration distances obtained when applying the incidence function model (or values of a). Nonetheless, some studies indirectly (Kindvall 2000). However, Appelt and Poethke (1997) suggest very skewed frequency distributions of migra- assumed that the grasshopper Odiepoda caerlescens tion rates (e.g. Kindvall 1995). only migrates between 7 and 100 m, on average. Simi- Another improvement of the current method of esti- larly, the average dispersal distance estimated from mating parameters of the incidence function model occupancy data of the wart-biter, Decticus 6erruci6orus, would be to allow also changes in patch sizes and was only 40 m (Hjermann and Ims 1996). Nevertheless, configuration. With the current software we had to use it seems as if S. scalaris has the potential of moving the MC-method on data from the 80s only. Landscape much greater distances than was indicated from the changes were too great between the other censuses to occupancy patterns during the 80s, and therefore we enable us to apply the MC-method in its present form believe that the emigration rates, or the population on these data sets. densities, were too low to enable any significant migration at all in that period. The fact that only extinctions Acknowledgements – We thank I. Hanski and C. D. Thomas and no colonisations were observed before 1993 sup- for instructive comments on the manuscript, and A. Moilanen for some technical clarifications. This research has been possi- ports this hypothesis. The weather situation in 1992 ble by fundings from Swedish Council for Forestry and Agri- might have triggered an increased emigration rate, ei- cultural Research to AC and from Oscar and Lili Lamm’s ther because of higher population densities, or because Memorial Foundation to OK. of the drought that was observed to enforce specimens of the bush cricket Metrioptera bicolor to move into alternative habitats (Kindvall 1995). As an interesting coincidence, that observation was also made in 1992. References The new method of parameterisation of the incidence Appelt, M. and Poethke, H. J. 1997. Metapopulation dynam- function model that was described by Moilanen (1999) ics in a regional population of the blue-winged grasshopper (Oedipoda caerulescens; Linnaeus, 1758). – J. 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