Extinction Debt at Extinction Threshold

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1 Contributed Papers Extinction Debt at Extinction Threshold ILKKA HANSKI* AND OTSO OVASKAINEN Metapopulation Research Group, Department of Ecology and Systematics, P.O. Box 65, Viikinkaari 1, FIN University of Helsinki, Finland Abstract: To allow for long-term metapopulation persistence, a network of habitat fragments must satisfy a certain condition in terms of number, size, and spatial configuration of the fragments. The influence of landscape structure on the threshold condition can be measured by a quantity called metapopulation capacity, which can be calculated for real fragmented landscapes. Habitat loss and fragmentation reduce the metapopulation capacity of a landscape and make it less likely that the threshold condition can be met. If the condition is not met, the metapopulation is expected to go extinct, but it takes some time following habitat loss before the extinction will occur, which generates an extinction debt in a community of species. We show that extinction debt is especially great in a community in which many species are close to their extinction threshold following habitat loss because the metapopulation-dynamic time delay is especially long in such species. A corollary is that landscapes that have recently experienced substantial habitat loss and fragmentation are expected to show a transient excess of rare species, which represents a previously overlooked signature of extinction debt. We consider a putative example of extinction debt on forest-inhabiting beetles in Finland. At present, the few remaining natural-like forests are distributed evenly throughout southern Finland, but the number of regionally extinct old-growth forest beetles is much greater in the southwestern coastal areas, where human impact on forests has been lengthy, than in the northeastern inland areas, where intensive forestry started only after World War II. Ignoring time delays in population and metapopulation dynamics will lead to an underestimate of the number of effectively endangered species. Deuda de Extinción y Umbral de Extinción Resumen: Para permitir la persistencia de una metapoblación a largo plazo, una red de fragmentos de hábitat debe satisfacer ciertas condiciones en cuanto a número, tamaño y configuración espacial de los fragmentos. La influencia de la estructura del paisaje en las condiciones del umbral puede ser medida por una cantidad llamada capacidad de la metapoblación, la cual puede ser calculada para paisajes reales fragmentados. La pérdida de hábitat y la fragmentación reducen la capacidad metapoblacional de un paisaje y hacen menos probable que se puedan reunir las condiciones de umbral. Si las condiciones no son alcanzadas, se espera que la metapoblación se extinga, pero tomará algún tiempo después de la pérdida del hábitat para que la extinción ocurra, lo cual genera una deuda de extinción en una comunidad de especies. Mostramos que una deuda de extinción es especialmente grande en una comunidad en la cual muchas especies están cercanas a su umbral de extinción después de ocurrir una pérdida de hábitat debido a que el tiempo de retraso en la dinámica metapoblacional es especialmente largo en estas especies. Una consecuencia es que se espera que los paisajes que han experimentado recientemente una pérdida sustancial de hábitat y fragmentación muestren un exceso transitorio de especies raras, lo cual representa una indicación de la deuda de extinción que anteriormente se había pasado por alto. Consideramos un ejemplo putativo de deuda de extinción en los escarabajos que habitan los bosques de Finlandia. Actualmente, hay igualmente pocos bosques naturales a lo largo de sur de Finlandia, pero el número de escarabajos de bosques maduros regionalmente extintos es mucho mayor en las áreas costeras del Suroeste, las que presentan un impacto humano más fuerte en los bosques, que en las áreas interiores del noreste, con una actividad forestal intensa iniciada solo después de la Segunda Guerra Mundial. El ignorar el historial de las dinámicas poblacionales y metapoblacionales resultará en una pobre estimación de un número de especies realmente en peligro. * Paper submitted August 8, 2000; revised manuscript accepted August 15, , Pages

2 Hanski & Ovaskainen Extinction Debt at Extinction Threshold 667 Introduction Current interest in metapopulation ecology has brought into sharp focus two concepts of great importance for conservation biology: extinction threshold and extinction debt. According to the metapopulation theory, a network of habitat fragments must satisfy a certain necessary condition in terms of number, size, and spatial configuration of fragments to allow for long-term persistence of the focal species. The extinction threshold distinguishes networks that satisfy that condition from those that do not. To calculate the extinction threshold, a model is required that quantifies the relevant properties of the landscape and species. The threshold condition is fundamental to conservation biology, but it must be realized that this condition refers to the equilibrium state and therefore to a particular structure of the landscape. In reality, landscapes are not static but change in the course of time. In most modern landscapes, human-caused habitat loss and fragmentation have long been dominant processes and have led to a directional environmental change that is detrimental to most species. From the viewpoint of most species, many landscapes are in the process of crossing, or have recently crossed, the boundary between the states in which they are and are not able to support a viable metapopulation of the focal species. Nonetheless, especially if the environmental change has been fast, it takes time following habitat loss before the species has reached the new equilibrium corresponding to the current structure of the landscape. Considering a community of species, Tilman et al. (1994) coined the term extinction debt to refer to situations in which, following habitat loss, the threshold condition for survival is no longer met for some species, but these species have not yet gone extinct because of the time delay in their response to environmental change. More precisely, extinction debt at a particular moment is the number of extant species predicted to go extinct eventually because the threshold condition is no longer satisfied in their case. Extinction debt can be paid by either allowing the species to go extinct or by improving the landscape structure sufficiently, and before the species have gone extinct, such that the threshold conditions are met again. Our purpose is to draw attention to a particular feature of the time delay in metapopulation response to environmental change: the time delay is expected to be especially long if the species is located close to its extinction threshold following habitat loss and fragmentation. If a community includes many such species, the extinction debt will be great, and a transient change will occur in the shape of the commonness distribution of species, with an overabundance of rare species following environmental change. This is a general but previously overlooked signature of extinction debt. We illustrate these results with a spatially realistic metapopulation model, which demonstrates how a realistic description of fragmented landscapes can be included in the calculation of the extinction threshold. In the next section, we describe the threshold condition for persistence in the spatially realistic metapopulation theory. A detailed description of the landscape structure and how it affects metapopulation dynamics can be included in the model without loss of clarity, because the behavior of the spatially realistic model can be approximated by a simple metapopulation model with the parameters properly interpreted. In the following sections, we outline the results of the time delay and the shape of the commonness distribution in a community of species paying up the extinction debt. In the discussion, we describe a putative example of forest-inhabiting beetles in Finland. The Threshold Condition This section presents a short description of how the threshold condition for metapopulation persistence can be constructed for species living in fragmented landscapes consisting of a finite number of habitat fragments with given areas and spatial locations (for details see Hanski and Ovaskainen [2000]; for a rigorous mathematical analysis see Ovaskainen and Hanski [2001]). Let us start with Lande s (1987) modification of the familiar Levins (1969) model, in which the dynamic variable is p, the fraction of habitat patches occupied at time t. The instantaneous rate of change in p is given by dp dt = cp( h p) ep, (1) where c and e are the colonization and extinction rate parameters, and h is the fraction of the habitat fragments suitable for occupancy (Hanski 1999). At equilibrium, fraction p* h e/c of the fragments is occupied. Calculating the occupancy probability only for those fragments suitable for occupancy (h) and denoting the ratio of the extinction and colonization rate parameters by ( e/c), we obtain p* 1 /h. Therefore, in this simple model the threshold condition for persistence ( p* 0) is h, and it depends on h and on the extinction and colonization rates of the focal species (Lande 1988; Hanski 1999). A general spatially realistic metapopulation model is defined by the set of equations dp i dt = ( colonization rate) i ( 1 p i ) ( extinction rate) i p i, (2) where p i is the probability of fragment i being occupied at time t. The colonization and the extinction rates are specified as functions of connectivity of fragment i to the existing populations and the area (and possibly quality) of fragment i, the latter being used as a surrogate for

3 668 Extinction Debt at Extinction Threshold Hanski & Ovaskainen population size. For instance, we may assume that (extinction rate) i e/a i and (colonization rate) i c j i exp( d ij ) A j p j (t), where A i is the area of fragment i, d ij is the distance between fragments i and j, 1/ is the average migration distance, and e and c are constants ( Hanski & Ovaskainen 2000). (For biological justification see Hanski [1999]. For numerical applications in the context of a stochastic version of a related model, called the incidence function model, see Hanski [1994], Wahlberg et al. [1996], Moilanen et al. [1998], and Moilanen [1999]). These assumptions lead to a landscape matrix with elements m ij exp( d ij ) A i A j for j i and m ii 0. In the term m ij, A i comes from the expected lifetime of local populations, which is given by 1/(extinction rate) i and is hence proportional to A i, whereas exp( d ij ) A j comes from the assumption made about the colonization rate. For more details see Hanski and Ovaskainen (2000) and Ovaskainen and Hanski (2001). The model defined by equation 2 and supplemented with the above structural assumptions is complex in the sense that it consists of n coupled equations for a metapopulation living in a network of n fragments. Fortunately for the analysis, the essential behavior of the model is captured by a much simpler one-dimensional approximation ( Hanski & Ovaskainen 2000; Ovaskainen & Hanski 2001). To reduce the spatially realistic model to the onedimensional model, we first define a measure of metapopulation size as the weighted average of the patch-specific probabilities of occupancy, p λ = V i p i. (3) The weights V i ( V i 1) are given by the relative contributions of individual fragments to the long-term persistence of the metapopulation, and they have a clear biological interpretation which will become apparent below. At equilibrium, p is well approximated by p λ = 1 δ λ M, (4) where M is the leading eigenvalue of the landscape matrix, called the metapopulation capacity (Hanski & Ovaskainen 2000). Equation 4 is exactly analogous to the equation giving the equilibrium in the Levins model, with M replacing h, the fraction of patches suitable for occupancy. Even if this spatially realistic model takes into account the influence of the actual spatial configuration of the habitat fragments on metapopulation dynamics, the extinction threshold is given by a simple condition, λ M > δ. (5) Changes in the structure of a fragmented landscape are reflected in the value of the metapopulation capacity M. Habitat loss and fragmentation reduce M and hence make it less likely that the threshold given by equation 5 is met. A particular advantage of the concept of metapopulation capacity is that it takes into account not only how much habitat is lost but also the spatial pattern of habitat loss, which is typically not random and can have a big influence on the consequences of habitat loss for a population (Neuhauser 1998; Hill & Caswell 1999; With & King 1999; Ovaskainen et al. 2002). The weights V i in equation 3 represent the relative contributions of individual habitat fragments to the metapopulation capacity of the entire network. Thus, V i tells how much the metapopulation capacity is reduced by removal of fragment i from the network, which has obvious applications in landscape ecology and conservation biology (Hanski & Ovaskainen 2000). Armed with this model, let us now consider the time delay in metapopulation response to environmental change. Here, we present numerical examples that illustrate the fundamentally important messages for conservation (for a rigorous mathematical analysis, see Ovaskainen & Hanski 2002). Time Delay in Metapopulation Dynamics Using the same approach as in the previous section, we first describe the time delay in the original Levins model, and then use that model with an appropriate interpretation of the parameters as a good approximation of the spatially realistic model. Assume that, initially, fraction p 0 of the fragments is occupied in equation 1, but following a rapid episode of habitat loss the equilibrium moves to the new value p*. First we have to specify how the length of the time delay will be measured. In deterministic models such as those considered here, it actually takes an infinitely long time for the new equilibrium to be reached exactly. In practice, we are interested in the length of time it takes for the metapopulation to move close to the new equilibrium. We hence specify some value p 1, which is close to p*. When the metapopulation has reached p 1 following habitat loss, we consider that it has, for practical purposes, reached the new equilibrium. In the examples below we assume that p* p The time it takes for the metapopulation to move from p 0 to p 1 following sudden habitat loss at time t is denoted by T( p 0, p 1 ). Figure 1 (broken line) gives a numerical example that illustrates an important point about the time delay in the dynamics of classic metapopulations: the time delay is especially long when the new equilibrium p* is close to zero (that is, when the landscape following habitat loss is slightly better or slightly worse than stipulated by the threshold conditions for persistence). This result is conservative, in the sense that we consider the absolute difference p* p 1 rather than the relative difference p 1 /p* in evaluating the length of the time delay. The latter would give an even longer delay for species with small p* than for species with large p*. Return to the spatially realistic model with the colonization and extinction rates given by the assumptions de-

4 Hanski & Ovaskainen Extinction Debt at Extinction Threshold 669 Figure 1. Time delay in metapopulation response to habitat loss plotted against the value of the equilibrium fraction of occupied habitat following habitat loss (p *). The continuous line shows the time delay in the 30-patch landscape, shown in Fig. 2 and predicted by the spatially realistic model. The broken line gives the Levins-model approximation with appropriately interpreted parameters (see text). Values of p * 0 correspond to metapopulation extinction (p * 0), but the negative values (obtained from p * 1 / M ) are shown here to illustrate how far below the threshold the calculated metapopulation equilibrium is located. scribed below equation 2. The dynamics of the n-dimensional model are well approximated by the Levins model, with the following interpretation of the colonization and extinction parameters: c c M / and ẽ e/, where V i A i (Ovaskainen & Hanski, unpublished data). Thus, the result in Figure 1 applies to the spatially realistic model when the parameters are interpreted in this manner. We illustrate this result with a numerical example based on the patch network shown in Fig. 2. Out of the original 30 habitat fragments, 9 were removed such that the remaining 21 fragments contained two-thirds of the metapopulation capacity of the original network. There is a close correspondence between the time delay in the numerical results for the spatially realistic model and in the approximation (Fig. 1). To reiterate, in the present context the key conclusion is that the time delay becomes increasingly long when the new equilibrium p*, which includes the consequences of habitat loss and fragmentation, approaches the extinction threshold. We next consider the implications of this result for the extinction debt in a community of species. An Example of Extinction Debt Assume that, which is a species parameter, is normally distributed in a community of species (Fig. 3, upper Figure 2. A hypothetical 30-patch network with patch areas log-normally distributed. Patch areas have been scaled to yield M 1. Habitat loss was brought about by randomly removing individual patches (crossed) until two-thirds of the original metapopulation capacity remained. Parameters: 1 and (in the reduced network). panel). Therefore the commonness of the species in the community, as measured by p *, is also normally distributed (Fig. 3, lower panel), with common species being characterized by small, and vice versa (recall that p * 1 / M ). We again use the example in Fig. 2, in which prior to habitat loss the value of M is sufficiently large to allow all the species to persist (Fig. 3, continuous line). Habitat loss and fragmentation reduce M to two-thirds of its original value, and the threshold condition given by equation 5 is no longer met for some of the species (Fig. 3, broken line). Figure 4 shows the predicted change in the commonness distribution in the course of time, both for the full model and for its approximation. What is apparent is an initial change in the shape of the distribution: the frequency of rare species (small p ) greatly increases, while for some time only a few species go extinct. In the course of time, however, a large fraction of the newly rare species goes extinct. The initial accumulation of rare species is due to the long time delay in the response of species whose new equilibrium is close to the threshold for long-term persistence (Fig. 1). Once again, the Levins model with parameters appropriately interpreted gives an excellent approximation of the behavior of the full spatially realistic model. This correspondence de-

5 670 Extinction Debt at Extinction Threshold Hanski & Ovaskainen in Fig. 4, typical fragments in the network have experienced several (but not tens of ) turnover events. At this stage the extinction debt is great, representing around 20% of the species number in the original community. Discussion Figure 3. (a) The distribution of values in a hypothetical community. The straight lines give the size of the metapopulation, p * 1 / M, before (continuous line) and after (broken line) habitat loss. Before habitat loss, the threshold condition (equation 5) is satisfied for all species, whereas after habitat loss the condition is not satisfied for a large fraction of the species (those with 0.67). (b) The respective distribution of metapopulation sizes (p *). The position of one species has been highlighted with a dot to illustrate that a rare species has a large value of. rived by Ovaskainen and Hanski (unpublished data) is important, because we can thereby, using the theory available for the simple Levins model, establish the generality of this example. We emphasize that the shape of the distribution of the original p * values is immaterial to the predicted temporary excess of rare species (with respect to the assumed distribution). One might be tempted to assume the lognormal distribution for p *, but this is not necessarily a realistic assumption, as it would be for the distribution of species abundances in a local community. To get an idea of the actual length of time it takes for the commonness distribution to reach the new equilibrium in Fig. 4, note that the characteristic turnover time of the metapopulation in the network following habitat loss is 1/ ẽ /e Therefore, at times t 1 and 2 The theoretical framework we used is best suited to describe spatial dynamics in highly fragmented landscapes, in which the fragments of suitable habitat are discrete and generally sufficiently small to justify the presence/ absence description of local dynamics (Hanski 1999). For many species, real landscapes are highly fragmented in this sense, but there are clearly also other sorts of landscapes, in which habitat quality varies in space but in a more continuous fashion, making the present models less appropriate. In the case of highly fragmented landscapes, another prerequisite for the use of the metapopulation theory is that the spatial scale be appropriate to the focal species. If the spatial scale is very large, other processes apart from the extinction-colonization dynamics assumed in these models may become decisive, whereas if the spatial scale is very small the relevant processes are likely to be related to individual foraging behavior rather than to metapopulation dynamics. Finally, a caveat should be added about the deterministic nature of the present models. Very rare species for which the deterministic threshold condition of equation 5 is met are liable to go extinct for stochastic reasons within the time frame relevant to conservation. Nonetheless, there is no reason to assume that, with the exception of the increased extinction risk of rare species (small positive p *), the results of the deterministic theory would not be qualitatively consistent with the predictions of an appropriate stochastic theory. The finding that the time delay in metapopulation response to environmental change is longest near the extinction threshold is not surprising, because an analogous result would apply to all comparable population models. This result is not widely recognized, however, and it is especially noteworthy for conservation because the long time delay in species located close to the extinction threshold implies that the extinction threat is likely to be underestimated in changing environments in exactly those cases where it matters most. We have shown that this result applies also in a spatially realistic model, which incorporates a realistic description of how the landscape structure influences the extinction threshold. This line of modeling, which can be applied to real metapopulations, allows one to assess the consequences for metapopulation persistence of specific changes in landscape structure (Hanski & Ovaskainen 2000). Our results also undermine the common criticism of the Levins model that it is overly simple, unrealistic, and of little importance for conservation ( Harrison

6 Hanski & Ovaskainen Extinction Debt at Extinction Threshold 671 Figure 4. Temporal changes in the distribution of metapopulation sizes (p ) in the community of species shown in Fig. 3 following the loss of habitat depicted in Fig. 2 at time t 0. Continuous and broken lines show the result for the spatially realistic model and for the onedimensional approximation, respectively (the lines agree so closely that the broken line is difficult to see). The dots (initially equally spaced along the x-axis) illustrate the shift toward rarity and, in the rarest species, eventual extinction of particular species. The bars on the left show the current extinction debt (pattern) and the number of species that have gone extinct ( black). According to our analysis, species with p* 0.05 are considered extinct, so the width of the bar is Parameter e ). Although it is true that the original model is very simple, it now appears that, given an appropriate interpretation of the model parameters, it can be used as an excellent approximation of much more complex models, involving an equation for the rate of change in the probability of occupancy of each habitat fragment in a network of n fragments. Apart from the increasing length of the time delay with decreasing distance to the extinction threshold, Ovaskainen and Hanski s (2002) mathematical analysis shows that the length of the time delay depends on three other factors: strength of the perturbation, characteristic turnover time of the species (1/e), and the value of, the latter two of which combine to give the characteristic turnover time of the specific metapopulation (1/ ẽ /e). The length of the time delay increases with all these factors. We have every reason to believe that the time delay in population and metapopulation responses to environmental changes, as well as the extinction debt, are real and important phenomena to which conservation biologists should pay more attention. But it is unfortunately an almost insurmountable task to obtain the necessary empirical information on large spatial and temporal scales to come up with quantitative estimates of the magnitude of extinction debt in real metacommunities. Most examples of extinction debt in fact refer to the time lag in the loss of local populations from individual habitat fragments rather than from a fragmented landscape. For instance, Brooks et al. (1999) describe extinctions of bird species from isolated fragments of tropical forest in Kenya. Assuming an exponential decay of populations from isolated fragments, they estimated that populations in a fragment of roughly 1000 ha have an approximate half-life of 50 years. Other studies of tropical bird populations in recently isolated forest fragments have produced comparable results (Bierregaard & Stouffer 1997; Terborgh et al. 1997), with a half-life of some decades. As expected, the half-lives are much longer for much larger areas, such as large landbridge islands isolated by the post-glacial rise in sea level (Diamond 1972). Petit and Burel (1998) describe a rare example of time delay in the response of a metapopulation to environmental change. The ground beetle Abax parallelepipedus breeds in small woodlands in the study area in northern France and disperses mostly along hedgerows. Over a period of 41 years, the connectivity of the study landscape, measured from the perspective of the beetle, was reduced by 28% due to the removal of hedgerows. Petit and Burel (1998) demonstrate that the current distribution of the beetle is better explained by the connectivity of the landscape in 1952 than in 1993, a result suggesting a delayed metapopulation response to loss of habitat and connectivity. Considering communities at large spatial scales, the following example of forest beetles in Finland is suggestive

7 672 Extinction Debt at Extinction Threshold Hanski & Ovaskainen of extinction debt. Finnish forests are intensively managed, and the area of natural and seminatural forests in southern Finland is currently 0.5% of the forested land (Fig. 5; Virkkala & Toivonen 1999). Against this background, it is not surprising that approximately 100 forest-dwelling species have already gone extinct in Finland (Rassi et al. 2001; 71 extinctions among the species that have been assessed, representing one-third of all the species). Figure 5 summarizes the numbers of regionally extinct species among 171 well-known endangered forest-beetle species. Among the 101 species specializing in boreal coniferous forests, the fraction of regionally extinct species is already 50% in the southwestern coastal regions with long-term and severe human impact on forests. In contrast, in the northeastern inland areas, the bulk of the endangered species still represents the extinction debt, because only 10 20% have gone extinct regionally. The important point, and the basis for our interpretation, is that this pattern of regional extinctions does not reflect the current state of the forests, because two of the subregions in northeastern Finland (Fig. 5, numbers 5 and 6) with a low fraction of extinct species have currently as few natural-like forests as the southwestern part of the country. In northeast Finland, intensive forestry started only after World War II, so recently that apparently only a relatively small fraction of the extinction debt imposed by the massive habitat loss has been paid up by regional extinctions so far. This interpretation is further strengthened by the pattern of regional extinctions amongst the 70 species that specialize in mixed forests, which typically occur in restricted areas on the most productive soils. Throughout the country, these forests have mostly been cleared for agriculture a long time ago, which means that no large differences in the fraction of regionally extinct species would be expected. In fact, there are no regional differences; roughly 50% of the endangered beetle species specializing in mixed forests having gone extinct across the country (Fig. 5). Rather than examining patterns in the extinction of species, it would be more satisfying to be able to predict and test the magnitude of extinction debt in quantitative terms. Although this ideal is not possible with existing information, we suggest that conservation biologists should become attentive to the issue of large-scale extinction debt and should consider its role in the distribution of regionally extinct and threatened species, as we have done in the example in Fig. 5. In the case of landscapes that have recently experienced substantial habitat loss and fragmentation, it would be a fatal mistake to assume that all extant species would have viable populations if any additional loss and fragmentation of the habitat were to be prevented. The only way to save such living dead species is to improve the quality of the landscape for these species. Acknowledgments We thank D. Tilman, M. Heino, A. Moilanen, J. Sanderson, and two anonymous referees for comments on the manuscript. This study was supported by the Academy of Finland (MaDaMe Programme, grant 50165, Finnish Centre of Excellence Programme , grant number 44887). Figure 5. (a) The incidence of regional extinction among 171 endangered forest-inhabiting beetle species in eight forest regions of Finland (shown on the map). Black bars give percentage of the regionally extinct species among species specializing in boreal coniferous forests (101 species in the pooled material). White bars give the same information for species specializing in mixed forests (70 species; data from Ruuhijärvi et al. [2000], based on analysis by P. Rassi). The numbers on top of the bars give the total number of species. (b) The fraction of the forested land covered by natural or natural-like forests in the eight forest regions (minimum age 140 years, with substantial amount of dead wood or signs of damage; Virkkala et al. 2000). The map shows the eight forest regions.

8 Hanski & Ovaskainen Extinction Debt at Extinction Threshold 673 Literature Cited Bierregaard, R. O., Jr., and P. C. Stouffer Understory birds and dynamic habitat mosaics in Amazonian rainforests. Pages in W. L. Laurence and R. O. Bierregaard Jr., editors. Tropical forest remnants. University of Chicago Press, Chicago. Brooks, T. M., S. L. Pimm, and J. O. Oyugi Time lag between deforestation and bird extinction in tropical forest fragments. Conservation Biology 13: Diamond, J. M Biogeographic kinetics: estimation of relaxation times for avifaunas of Southwest Pacific Islands. Proceedings of the National Academy of Sciences of the United States of America 69: Hanski, I A practical model of metapopulation dynamics. Journal of Animal Ecology 63: Hanski, I Metapopulation ecology. Oxford University Press, Oxford, United Kingdom. Hanski, I., and O. Ovaskainen The metapopulation capacity of a fragmented landscape. Nature 404: Harrison, S Metapopulations and conservation. Pages in P. J. Edwards, R. M. May, and N. R. Webb, editors. Large-scale ecology and conservation biology. Blackwell Science Press, Oxford, United Kingdom. Hill, M. F., and H. Caswell Habitat fragmentation and extinction thresholds on fractal landscapes. Ecology Letters 2: Lande, R Extinction thresholds in demographic models of territorial populations. The American Naturalist 130: Lande, R Demographic models of the Northern Spotted Owl Strix occidentalis caurina. Oecologia 75: Levins, R Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America 15: Moilanen, A Patch occupancy models of metapopulation dynamics: efficient parameter estimation with implicit statistical inference. Ecology 80: Moilanen, A., A. T. Smith, and I. Hanski Long-term dynamics in a metapopulation of the American pika. The American Naturalist 152: Neuhauser, C Habitat destruction and competitive coexistence in spatially explicit models with local interactions. Journal of Theoretical Biology 193: Ovaskainen, O., and I. Hanski Spatially structured metapopulation models: global and local assessment of metapopulation capacity. Theoretical Population Biology 60: Ovaskainen, O., and I Hanski Transient dynamics in metapopulation response to perturbation. Theoretical Population Biology: in press. Ovaskainen, O., K. Sato, J. Bascompte, and I. Hanski Metapopulation models for extinction threshold in spatially correlated landscapes. Journal of Theoretical Biology: in press. Petit, S., and F. Burel Effects of landscape dynamics on the metapopulation of a ground beetle (Coleoptera, Carabidae) in a hedgerow network. Agriculture, Ecosystems and Environment 69: Rassi, P. et al The red data book of Finland. 3rd revision. Report. Ministry of Environment, Helsinki. Ruuhijärvi, R., et al Metsien suojelun tarve Etelä-Suomessa ja Pohjanmaalla. Publication 437. Suomen Ympäristö, Helsinki (in Finnish with English summary). Terborgh, J., L. Lopez, J. Tello, D. Yu, and A. R. Bruni Transitory states in relaxing ecosystems of land bridge islands. Pages in W. L. Laurence and R. O. Bierregaard Jr., editors. Tropical forest remnants. University of Chicago Press, Chicago. Tilman, D., R. M. May, C. L. Lehman, and M. A. Nowak Habitat destruction and the extinction debt. Nature 371: Virkkala, R., and H. Toivonen Maintaining biological diversity in Finnish forests. The finnish environment 278. The Finnish Environment Institute, Helsinki. Virkkala, R., K. T. Korhonen, R. Haapanen, and K. Aapala Metsien ja soiden suojelutilanne metsä- ja suokasvillisuusvyöhykkeittäin valtakunnan metsien 8. Inventoinnin perusteella. Publication 395. Suomen Ympäristö, Helsinki (in Finnish with English summary). Wahlberg, N., A. Moilanen, and I. Hanski Predicting the occurrence of endangered species in fragmented landscapes. Science 273: With, K. A., and A. W. King Extinction thresholds for species in fractal landscapes. 13:

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