Are spatially correlated or uncorrelated disturbance regimes better for the survival of species?

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1 OIKOS 103: , 2003 Are spatially correlated or uncorrelated disturbance regimes better for the survival of species? Karin Johst and Martin Drechsler Johst, K. and Drechsler, M Are spatially correlated or uncorrelated disturbance regimes better for the survival of species? Oikos 103: The survival of species in dynamic landscapes (characterised by patch destruction and subsequent regeneration) depends on both the species attributes and the disturbance pattern. Using a spatially explicit model we explored how the mean time to extinction of a metapopulation depends on the spatial correlation of patch destruction in relation to the population growth and dispersal abilities of species. Two contrasting answers are possible. On the one hand, increasing spatial correlation of patch destruction increases the spatial correlation of population growth and this is known to decrease metapopulation persistence. On the other hand, spatially correlated patch destruction and regeneration can lead to clustered habitat patches and this is known to increase metapopulation persistence. Therefore, we hypothesised that some species are better off under spatially correlated and alternatively uncorrelated disturbance regimes. However, contrary to this hypothesis, in all kinds of cases spatial correlation reduced metapopulation persistence. We found this to be due to the fact that the spatial correlation of patch destruction causes increasing temporal fluctuations in the regional carrying capacity of the metapopulation and is hence generally disadvantageous for long-term persistence. The main consequence for conservation biology is that reducing spatial correlation in disturbances is likely to be a reliable strategy in a dynamic landscape that will benefit practically all species with a low risk of adverse side effects. K. Johst and M. Drechsler, UFZ-Centre for En ironmental Research Leipzig-Halle Dept of Ecological Modelling, P.O. Box , DE Leipzig, Germany (kajo@oesa.ufz.de). In recent years, much has been done in the way of ecological research on the impact of spatial correlation on the extinction risk of metapopulations (reviewed by Koenig 1999 and Lundberg et al. 2000). In the extensive literature, three types of spatial correlation differing in terms of their environmental causes and their effects on metapopulation persistence are apparent. The first type concerns the spatial correlation of the growth parameters of local populations ( regional stochasticity : Hanski 1991; for other studies see for example Harrison and Quinn 1989, Gilpin 1990, Grimm et al. 1996, Frank and Wissel 1998, Palmqvist and Lundberg 1998). Here attention has mainly been devoted to the synchronisation of population dynamics due to spatial correlation (Heino et al. 1997, Ranta et al. 1997, Earn et al. 1998, Bjornstad et al. 1999, Hudson and Cattadori 1999, Greenman and Benton 2001). Specifically, the relative contributions of disturbances and dispersal to population dynamics have been studied intensively (Lande et al. 1999, Ranta et al. 1999b, Kendall et al. 2000, Ripa 2000). As the synchronising tendency of both forces decreases with distance, disentangling their relative influences has proved difficult (Ranta et al. 1995). All the studies mentioned found that the greater the spatial correlation of population growth, the lower the metapopulation persistence. As the second type of spatial correlation, the spatial distribution of habitat may be correlated (Doak et al. 1992, Adler and Nuernberger 1994, King and With 2002). Adler and Nuernberger (1994) found that the Accepted 23 April 2003 Copyright OIKOS 2003 ISSN OIKOS 103:3 (2003) 449

2 clustering of habitat patches increases persistence as patches linked by costly dispersal still have high average immigration rates even with short- range dispersal. Consequently, habitat clustering may mitigate the negative effects of habitat loss on dispersal success (Doak et al. 1992, King and With 2002). The third type of spatial correlation refers to disturbances that affect not only the populations themselves but also the state (quality and/or size) of the habitat patches. In such dynamic landscapes local population extinction may be caused by patch destruction generated naturally or by man. However, patches (e.g. plant patches) can regenerate and increase in quality again (Thomas 1994, Eber and Brandl 1996, Thomas et al. 1996, Gyllenberg and Hanski 1997, Stelter et al. 1997, Hanski 1999, Keymer et al. 2000). Furthermore, succession after a disturbance may cause the structure and suitability of plant patches to change (Johnson 2000, Amarasekare and Possingham 2001). This third type of spatial correlation is related to both the other types. On the one hand the disturbances usually affect (e.g. destroy) local populations, and thus the increasing spatial correlation of disturbances could be expected to have the same effect as the increasing spatial correlation of population growth parameters, with metapopulation persistence decreasing. On the other hand, the spatial correlation of disturbance often affects habitat (e.g. by leading to the destruction and regeneration of patches in a spatially correlated way), and so increasing spatial correlation could be expected to have an effect similar to the clustering of habitat patches: metapopulation persistence would be increased. The question is which of these two effects outweighs the other, i.e. whether the increasing spatial correlation of disturbances increases or decreases metapopulation persistence, and whether this depends on the characteristics of the disturbance regime, the response of the patches to the disturbance and the species traits. In our study we consider a dynamic landscape where habitat patches are destroyed by disturbances and can regenerate. The disturbance pattern is characterised by the strength, frequency and spatial correlation of patch destruction. A disturbance event may occur depending on the current state of the patch (e.g. fire, windstorms, drought, harvesting) or independent of it (e.g. lava flow, flood, landslide, iceberg scouring on the sea floor). We consider both cases here. The regeneration of the patches is described by a patch growth rate. The species or species groups affected by these patch dynamics are characterised by the population growth rate, strength of density regulation, emigration rate, mean dispersal distance and survival during dispersal. One interesting question that arises in this respect is whether some species are better off under spatially correlated and alternatively uncorrelated disturbance regimes. For example, short-range dispersers which according to the above-cited literature are better off in landscapes with clustered patch distribution could thrive in a dynamic landscape with spatially correlated patch destruction as well. This question is highly relevant for conservation management: if biodiversity is to be maintained, it is important to know what species suffer and what species benefit from management activities that change the spatial correlation of disturbances. Model Spatial pattern and spatial correlation of disturbances We considered a metapopulation of 50 patches in an explicit spatial configuration using a two-dimensional lattice of cells. The patches were randomly distributed over the cells and their imum carrying capacities were randomly chosen from a uniform distribution between K i =500 and K i =1500. To create patch turnover we introduced patch destruction with a probability f pd. The actual carrying capacity of a disturbed patch i was set to K i =1 and the local population size to N i =0. Thus, both the patches and the populations living on them were destroyed and the local extinction risk depends closely on the landscape dynamics. Patch destruction was followed by patch recovery from K i =1uptoK i (see next section). The selection of a disturbed patch i within the metapopulation was completely random or depended on the state of the patch (see below) and the total number of destroyed patches per time step was drawn from a binomial distribution with mean 50 f pd. The spatial correlation of patch destruction was generated by a probability c(i, j) that a patch j in the vicinity of a disturbed patch i j was disturbed as well in the corresponding time step. c(i, j) was assumed to decrease exponentially with the distance d ij of patch j from the disturbed patch i: c(i, j)=exp( d ij ) q(k j ) (1) The parameter characterises the inverse mean length of the spatial correlation of patch destruction. A low corresponds to highly spatially correlated disturbances with destroyed patches being aggregated in space. A high corresponds to local disturbances acting only on patch i and its adjacency. Note that a very high corresponds to spatially uncorrelated patch destruction with destroyed patches being randomly distributed across the whole metapopulation. In this correlated way, patches were selected randomly to be disturbed until the total number of destroyed patches was reached. Consequently, the mean number of destroyed patches was the same under both uncorrelated and correlated disturbance regimes. 450 OIKOS 103:3 (2003)

3 In reality, the impact of disturbances often depends on the state of the patch. To investigate such disturbances, we assumed that a patch s probability of being destroyed per time step was determined not only by the spatial correlation but also by the patch quality. This means that in Eq. (1) the factor q(k j )=1 (disturbances do not depend on the state of the patch) had to be transformed into a function dependent on patch quality. We used two different functional relationships: q(k j )=(K j /K j ) and q(k j )=1 (K j /K j ) 1/. The first functional relationship was chosen to describe disturbances where the probability of patch destruction rises with increasing carrying capacity (i.e. with increasing time since the last disturbance); the second was chosen to describe disturbances where this probability decreases with increasing carrying capacity. The parameters and determine the strength of the dependence. The larger and, the more pronounced the influence of the patch quality on the disturbance pattern. For example, = =1 describes a linear increase and decrease, respectively, of the probability of patch destruction with increasing carrying capacity K j (see also the insets in Fig. 3). = =0 corresponds to disturbances independent of the state of patches (q(k j )=1). The factor (close to 1) in the second relationship was necessary to avoid patches that have reached imum carrying capacity K j not being disturbed anymore (this would eventually lead to a partly static landscape). Dynamics of populations and patches The dynamics of a local population N i (t) were described by: R N i (t+1)= 1+(R 1)(N i (t)/k i (t)) N i(t) (2) This form of density dependence was originally introduced by Maynard Smith and Slatkin (1973) and proposed by Bellows (1981) to describe a wide range of data. R is the reproductive rate of the species considered in the absence of competition, while characterises the strength of density dependence (low R and correspond to compensatory, high R and to overcompensatory density dependence; Earn et al. 1998, Johst et al. 1999, Dennis et al. 2001). To include demographic stochasticity we used integer individual numbers and drew the actual population size from a Poisson distribution with mean N i (t+1) (Gabriel and Bürger 1992). After a disturbance a patch was able to recover and the local carrying capacity K i increased in time t with a patch growth rate R K to K i according to the equation R K K i (t+1)= 1+(R K 1)(K i (t)/k i ) K i(t) (3) Thus, population dynamics (Eq. (2)) included patch dynamics through K i (t) explicitly. We assumed an equal R K for all patches. Dispersal Dispersal within the lattice was described by an exponentially decreasing probability m(i, j) that an individual dispersed from cell i to cell j over the distance d ij (Neubert et al. 1995): m(i, j)=exp( d ij )/ exp( d ij ) (4) j The actual number of dispersers from i to j follows a binomial distribution with mean m(i, j)m tot N i (t). m tot is the total fraction of the local population emigrating. Thus, short-range and long-range dispersal differ only in the mean dispersal distance but not in the emigration rate. Individuals dispersing to empty cells (without patches) died. Alternatively, we considered a scenario in which dispersers were more likely to find patches. This was modelled by increasing the probability of dispersing to cells with patches by a factor of ten compared to dispersing to empty cells. As in the former scenario more dispersers end in empty cells and die, this scenario was denoted as low survival of dispersers to distinguish it from the latter scenario denoted as high survival of dispersers. The parameter characterises the mean dispersal distance. A high results in very short mean dispersal distances (short-range dispersal) where dispersers are distributed almost exclusively across the nearest neighbour cells. At =0 (long-range dispersal) dispersers are distributed uniformly across the lattice. To avoid edge effects we used periodic boundary conditions (i.e. simulations were performed on a torus). Furthermore, the units of patch distances were arbitrary and there was no preferred direction of dispersal. Results Firstly, we examined the relative influence of spatially correlated disturbances versus spatially correlated patch distribution on metapopulation persistence measured as the mean time to extinction of the metapopulation (Johst and Wissel 1997, Stelter et al. 1997). We considered a global disperser ( =0) and two local dispersers ( =1 and =2 in Eq. (4)) and the spatial correlation of the disturbances was varied from =0.005 to 5 (strong to low spatial correlation of patch destruction, see Eq. (1)). Fig. 1a shows that in a landscape with OIKOS 103:3 (2003) 451

4 Fig. 1. Mean times to extinction versus the spatial correlation of patch destruction in a landscape with (a) random and (b) clustered patch distribution. The frequency of patch destruction was set to f pd =0.20, and patches regenerate with a rate ln(r K )=1. The population growth and dispersal properties of species were set to ln(r)=1, =1 in Eq. (2), and m tot =0.3. The spatial extent of dispersal ranges from long-range to short-range-range dispersal (triangles: =0, circles: =1, squares: =2). random patch distribution the mean time to extinction increases with the decreasing spatial correlation of patch destruction. This also holds in a dynamic landscape where the patches have not been arranged randomly but spatially clumped (Fig. 1b). Thus, not even the spatial clustering of patches could eliminate the negative impact of the increased spatial correlation of disturbances. Comparing Fig. 1a and 1b, the spatial clustering of patches increased metapopulation persistence, especially when dispersal was short-ranged and the spatial correlation of disturbances was high. Secondly, we checked the influence of species traits other than the dispersal distance. We varied the population growth rates (ln(r)=1, 2, or 3), the emigration rates (m tot =0.3, 0.5, or 0.9), the overall survival during dispersal (low or high), and the strength of the density dependence of the growth rates ( =1, or 10). Systematic combination of these parameter values leads to 1242 different species traits which encompass the plausible range. As a general result, in all combinations of species traits, the mean time to extinction of the metapopulation increased with decreasing spatial correlation of patch destruction. Fig. 2 shows a selection of the results of the systematic analysis. In particular, it shows the effect of spatial correlation for increased population growth rates (Fig. 2a), higher emigration rates (Fig. 2b), increased overall survival during dispersal (Fig. 2c), and complex local population dynamics (Fig. 2d). Simulations including other forms of environmental stochasticity (e.g. fluctuations of R in addition to patch destruction) showed the same trend, albeit with a lower Fig. 2. Mean times to extinction versus the spatial correlation of patch destruction. The parameters of landscape dynamics are the same as in Fig. 1a. The population growth and dispersal properties of species (ln(r), m tot ) were varied as following: (a) 2, 0.3; (b) 1, 0.5; (c) 1, 0.5, high survival of dispersers; and (d) 3, 0.5, =10 in Eq. (2), high survival of dispersers. The spatial extent of dispersal ranges from long-range to short-range-range dispersal (triangles: =0, circles: =1, squares: =2). 452 OIKOS 103:3 (2003)

5 general level of T (Lande 1993, Foley 1997, Johst and Wissel 1997, Ripa and Lundberg 2000). Higher local population growth rates increased the mean time to extinction as populations are able to grow efficiently after colonisation of regenerating patches (compare Fig. 1a and 2a). Increasing the emigration rate (from m tot =0.30 to 0.50) decreased the mean time to extinction due to the significant mortality during dispersal within the metapopulation (compare Fig. 1a and 2b). Increasing the overall survival during dispersal (to high survival of dispersers, see sub-section Dispersal ) increased the mean time to extinction (compare Fig. 2b and c). In all these cases long-range dispersal was superior to short-range dispersal and the spatial correlation of patch destruction reduced the mean time to extinction. As we concentrated on the variation of species attributes we assumed given values for the rates of patch destruction f pd and regeneration ln(r K ) in all figures. Decreasing R K or increasing f pd would lead to small local populations with high extinction rates and the colonisation extinction dynamics of the metapopulation would break down. In this case the spatial correlation of patch destruction had no effect. Alternatively, increasing R K would approach a non-dynamic landscape with local population extinction rate equal to patch destruction rate f pd (Johst et al. 2002). In this case the spatial correlation of patch destruction would act like regional stochasticity which is known to have a negative impact on metapopulation persistence (see Introduction). Thus, deviations from the given values would not qualitatively alter the effect of spatial correlation on metapopulation persistence. In all figures except Fig. 2d we assumed equilibrium population dynamics ( =1 in Eq. (2)). However, even strong overcompensatory density dependence (scramble competition) which can induce complex population dynamics with crashes in the local population size, could not alter the negative impact of spatial correlation of disturbances (Fig. 2d). Note that here intermediate to short-range dispersal can be superior for long-term persistence. Compared to Fig. 1a, Fig. 3 shows the influence of disturbances depending on patch quality (see model description). Irrespective of increasing (Fig. 3a) or decreasing (Fig. 3b) the probability of patch destruction with increasing carrying capacity, the detrimental influence of the increasing spatial correlation of disturbances was retained (albeit sometimes in alleviated form) or the influence of the spatial correlation of disturbances vanished. Irrespective of the degree of spatial correlation, increasing decreased and increasing increased metapopulation persistence compared to the disturbance regime independent of patch quality in Fig. 1a. Discussion We investigated the persistence of a metapopulation in a dynamic landscape subject to stochastic disturbances in the shape of patch destruction and with subsequent patch regeneration. Species living in such landscapes are confronted by a varying number, quality and spatial arrangement of patches over time. An important issue of interest in this respect is the role of the spatial correlation of disturbances on metapopulation persistence. As the response of species to the disturbance regime may depend on the species specific traits, we hypothesised that some species could be better off under spatially correlated and others under uncorrelated disturbance regimes. Therefore, we examined how the spatial correlation of patch destruction affects metapopulation persistence for various species traits including population growth rate, density dependence, emigration rate, mean dispersal distance and survival during dispersal. First of all, we investigated the relative impact of the spatial correlation of disturbances versus the spatial correlation of patch distribution on metapopulation Fig. 3. Mean times to extinction versus the spatial correlation of patch destruction including a patch-qualitydependent probability of patch destruction q(k j ) (see model section). The parameters of landscape dynamics and population dynamics are the same as in Fig. 1a. (a) q(k j )=(K j /K j ), =0; (b) q(k j )=1 (K j /K j ) 1/ 0.9, =2. Note that the results of =0.01 approach those of =0 in Fig. 1a, while the results of =0.002 approach those of =2 in Fig. 1a. The insets qualitatively show q(k j ) for increasing and, respectively. OIKOS 103:3 (2003) 453

6 persistence. As already explained in the introduction, both types of spatial correlation have opposite effects on persistence, prompting the question of which one dominates. We found that in a dynamic landscape with clustered patch distribution the metapopulation persistence is increased (Fig. 1), tallying with the results of those models that consider habitat clumping but no patch dynamics (Doak et al. 1992, Adler and Nuernberger 1994, King and With 2002). This indicates that habitat clumping can have a positive effect irrespective of whether the landscape is dynamic or static. Comparison of Fig. 1a and 1b shows that this effect especially appears in short-range dispersers. Nevertheless, an increasing spatial correlation of disturbances is always adverse irrespective of clumped or random patch distribution. An important species trait in the metapopulation context is the dispersal distance. Apart from correlated patch destruction, dispersal can amplify the spatial correlation of local population dynamics due to immigrants arriving from other populations (synchronisation effect, Ranta et al. 1995, Heino et al. 1997, Lande et al. 1999, Ripa 2000, for an overview of processes causing population synchrony see Bjornstad et al. 1999). On the other hand, long-range dispersal may enhance the colonisation rate between the patches (colonisation effect, Hanski 1991, 1999). If this colonisation effect prevails, long-range dispersal is always superior to short-range dispersal (Fig. 2a c; Grimm et al. 1996, Frank and Wissel 1998 for non-dynamic landscapes). If the synchronisation effect prevails, long-range dispersal becomes disadvantageous compared to short-range dispersal (Heino et al. 1997, Ranta et al. 1999a, Keeling 2000, Johst et al. 2002). Especially, in metapopulations with complex local population dynamics synchronisation over large spatial scales increases the risk of metapopulation extinction (Fig. 2d, Palmqvist and Lundberg 1998). The advantage of long-range dispersal also disappears in a landscape with clustered patch distribution and spatially uncorrelated patch destruction (Fig. 1b, Johst et al. 2002). Then only particular patches of a cluster are destroyed and short-range dispersal allows a sufficient colonisation of regenerated patches within the clusters. Nevertheless, even though there is no unique answer to the question of whether short-range or long-range dispersal is superior in a dynamic landscape, we found no evidence of mean times to extinction increasing with the increasing spatial correlation of patch destruction for specific combinations of species traits. In other words, the more correlated the disturbances are in space, the lower the viability of the metapopulation, irrespective of the species dispersal and growth properties as well as the rates of the landscape dynamics. To find a reason for this unexpected finding, we should direct our attention to the patch dynamics. Fig. 4a shows that in the case of spatially correlated distur- Fig. 4. Fluctuations of the carrying capacity of the metapopulation in a landscape with (a) spatially correlated patch destruction ( =0.005) compared to (b) spatially uncorrelated patch destruction ( =5). bances, the temporal variation of the regional carrying capacity of the metapopulation (sum of all local carrying capacities K i (t)) is much higher than that of weak spatial correlation (Fig. 4b). A higher temporal variability in the regional carrying capacity directly increases the variability in the metapopulation size. This also increases the variability in the number of dispersers and the frequency of small local population sizes enhancing the demographic stochasticity. As population viability closely depends on the environmental and demographic stochasticity (Lande 1993, Wissel et al. 1993, Foley 1997, Johst and Wissel 1997, Drechsler and Wissel 1998), this explains why increasing spatial correlation of patch destruction reduces regional population viability irrespective of the species specific traits. What remains is an explanation for the finding that increasing spatial correlation of patch destruction increases the temporal variation of the regional carrying capacity of the metapopulation. The spatial correlation of disturbances synchronises the destruction and subsequent regeneration of the correlated patches and thus the regeneration state of sub-sets of patches (for the impact of spatial correlation in non-dynamic landscapes see Ranta et al. 1999a). If the disturbance hits a sub-set of patches which are at high carrying capacity K(t) (where the time span since the last disturbance event 454 OIKOS 103:3 (2003)

7 was long enough to allow significant patch regeneration), the regional habitat size (metapopulation carrying capacity) will strongly decrease. In turn, if the disturbance hits a sub-set of patches which are at low carrying capacity (where the time span since the last disturbance event was too short to allow for significant patch regeneration), the other groups of patches can efficiently regenerate and the regional habitat size will increase considerably. As the impact of disturbances may depend on the state of the patch we explored whether the above results and conclusions also hold when not only the distance from a disturbed patch but also the patch quality was decisive for a patch being hit by a disturbance. Fig. 3 revealed that there is generally no deviation from the findings concerning spatially correlated disturbances independent of patch quality. Nevertheless, two things need to be stressed. Firstly, only metapopulations of long-range dispersers can persist in a dynamic landscape where the probability of patch destruction increases with increasing patch quality (Fig. 3a). By contrast, even metapopulations of short-range dispersers can survive in a landscape where the probability of patch destruction decreases with increasing patch quality (Fig. 3b), although they cannot persist under disturbances of the same frequency which are independent of patch quality (Fig. 1a). This is because high-quality patches are rare in the former case but are frequent in the latter, decreasing or increasing the colonisation effect of dispersal. Secondly, the impact of the distance-dependent spatial correlation of disturbances interferes with the impact of patch quality. To illustrate this, we insert q(k j ) into Eq. (1) and write c(i, j)=exp{ d ij + ln(k j / K j )}. Depending on the relative magnitudes of and, the patch quality or distance from a disturbed patch is most relevant for a patch being destroyed. Thus, increasing (or ) can alleviate or remove the influence of the distance-dependent spatial correlation of disturbances on the mean time to extinction but cannot reverse it (Fig. 3). We have shown that the spatial correlation of patch destruction can be expressed by increasing temporal fluctuations of the regional carrying capacity and is hence generally disadvantageous for the long-term persistence of the metapopulation. On the other hand, spatial correlation generated by individual behaviour such as short-range dispersal can be advantageous for long-term persistence if local population fluctuations result from internal dynamics due to strong density dependence (Fig. 2d) or inter-specific interactions (Keeling 2000). Species specific traits such as dispersal distance, survival during dispersal or population growth rate can counteract the detrimental influence of the spatial correlation of disturbances and can ensure species survival even in spatially correlated dynamic landscapes but nevertheless, these species are yet better off in a landscape without spatial correlation of disturbances. Our findings have important implications for conservation management. Commonly, an alteration of environmental conditions by conservation management implies positive consequences for the species of interest but may imply negative consequences for other species. However, our findings suggest that a reduction in the spatial correlation of patch destruction causes all species to benefit or at least not to suffer, regardless of their traits. In this study, we modelled a disturbance regime where disturbance events destroy the habitat. Alternatively, disturbance events may create habitat, such as mowing or grazing meadows for many butterfly species in Central Europe. Furthermore, dispersal can be condition-dependent (Johst and Brandl 1997, Ruxton and Rohani 1998, Saether et al. 1999, Aars and Ims 2000, Ylikarjula et al. 2000), which can influence local and thus global population dynamics. Therefore, we do not want to claim that our hypothesis is true in every situation of spatially structured populations living in dynamic landscapes. Nevertheless, we still wish to point out this issue and present a hypothesis which according to our results is valid in a considerable number of instances. Our results should stimulate further research on this problem highly relevant to species protection in dynamic landscapes, including those disturbed by human activities. Acknowledgements We would like to thank C. Wissel, V. Grimm and L. Fahse for their helpful comments on the manuscript. References Aars, J. and Ims, R. 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