Background

The Joatka area on the Finnmarksvidda plateau in northern Norway (69°45′ N, 24°00′ E) has a long tradition of research on lemmings and voles, their predators and their food resources (see Oksanen et al. 1997 and references therein). The study area encompasses 16 km² and consists of a heterogeneous tundra landscape. Nutrient-poor lichen heaths, dwarf birch Betula nana L. scrublands and bogs dominate. Favourable microclimatic and edaphic conditions create one large central patch of relatively productive habitat types, mainly willow Salix spp. thickets and herb-rich mountain birch Betula pubescens Erhr. ssp. czerepanovii woodlands. Outside this central patch, productive habitats occur as narrow stands only along streams or in small, restricted, patches.

Voles are cyclic in the study area, as in most of northern Fennoscandia (Hörnfeldt 1994; Norrdahl 1995). Grey-sided voles Clethrionomys rufocanus (Sundevall) are habitat generalists (Henttonen & Viitala 1982) but prefer the productive habitat patches occurring in the area with a dense cover of bushes, dwarf shrubs and herbs (Schneider 2000). Norwegian lemmings Lemmus lemmus (L.) show chaotic population fluctuations (Turchin et al. 2000) and in particular inhabit tundra habitats where the vegetation is low (Tast 1982). In the tundra habitats grey-sided voles are not able to build up high densities and have difficulty in surviving the harsh winter conditions (Hambäck, Schneider & Oksanen 1998; Oksanen et al. 1999). The specialist rodent predators stoat Mustela erminea L. and weasel M. nivalis L. feed on lemmings as well as voles. However, as the predators prefer the same habitat types as the voles (Oksanen, Oksanen & Norberg 1992; Oksanen et al. 1999), the latter form the bulk of their diet.

There are indications that lemmings dominate over grey-sided voles in direct interference competition, as they are both aggressive and larger (Henttonen et al. 1977; Tast 1982; Henttonen & Hansson 1984). As lemmings invade the productive habitat patches when densities are high during years of population peaks (Collett 1895; Curry-Lindahl 1980), they should be able to displace grey-sided voles and to build up their own populations. However, this does not happen. Lemming populations outside tundra habitats usually do not persist for longer than a few years. This may be due to high predation on lemmings by small mustelids (Oksanen 1993). The diet of lemmings contains more low-quality forage than that of voles. Hence, the alimentary tract of lemmings is relatively bigger than that of voles, making them more clumsy (Sibly 1981; Hansson 1987; Oksanen 1993) and thus presumably easier to catch, and so lemmings should be favoured by mustelids. Furthermore, the colourful pelage of lemmings is conspicuous in habitats not dominated by lichen, and lemmings do not show any obvious anti-predatory behaviours against mustelids such as have been observed in voles (Ylönen et al. 1992; Norrdahl & Korpimäki 2000).

In the first part of the study, simulating a natural system, the model consisted of two competing prey species (voles and lemmings) and a common predator (small mustelids). One prey species (the lemming) was the superior competitor (because it is better able to exploit the food resources and because it is more aggressive) but more susceptible to predation. The landscape consisted of two habitat types. One type (called vole habitat, i.e. thickets and shrublands) could be used by all species present, but the other (lemming habitat, i.e. tundra heath) was suitable only for lemmings. Therefore, this species had a refuge from predation in the landscape. It has been shown that mustelids are very reluctant to visit open tundra heaths, presumably because of their own exposure to bigger predators (Oksanen et al. 1999).

The second part of the study looked at a landscape altered by human activities. The two habitat types used here were human settlements and remnants of natural habitat (formerly vole habitat and lemming habitat, respectively, as used in the original model). Predators (e.g. house cats) live within human settlements, find high levels of resources there and therefore have a constant and high population level in this habitat. The natural habitat supports a population of natural prey (the lemmings used in the original model). The predators are subsidized in human settlements but hunt in adjacent areas and affect the prey species.

Throughout the study, lemmings were used as a substitute for species of conservation concern. The aim was to understand how loss and fragmentation of refuge habitats may affect population size and viability of endangered species.

The model

A stochastic one-layer cellular automaton model was constructed to investigate populations of predators and prey under changing spatial configuration and size of habitat patches. The model was written in Visual Basic in Microsoft Excel. The model landscape consisted of 27 × 27 cells (Fig. 1). Each cell represented a certain area of land surface and could be interpreted as in reality, including a whole population of animals rather than single individuals. The model did not, however, make any assumptions on within-cell population size.

Each cell could have one of five qualitative states. In the original model, these included empty, only lemmings present, only voles present, only mustelids present, or both voles and mustelids present. In the model dealing with house cats, in the remnant natural habitat the states used were empty, only lemmings present (i.e. endangered prey), only voles present (i.e. primary prey for cats), only cats present, or both cats and their primary prey present. In the cat model, human settlements could have only one state, and they always harboured both cats and their primary prey.

Periodic boundary conditions were used in the simulation, placing the landscape on a torus. That means that the bottom line of cells used the top line as neighbours and vice versa, and the column of cells at the left border of the landscape used the column at the right border as neighbours, and vice versa.

The simulation of population dynamics in any given cell was divided into two parts. The first part dealt with the dynamics within the cell, without any influence of the surrounding cells. This resembled the situation during winter, when the animals do not move very much but do have a certain probability of succumbing due to shortage of food or adverse climatic conditions. The second part of the simulation took into account the states of neighbouring cells. Inter-cell influences were local, encompassing a 3 × 3 neighbourhood and thus including only the eight cells sharing an edge or a corner with the cell in focus (Appendix 1). This part of the simulation resembled summer conditions, when animals can easily move from one habitat patch to another one.

A table of transition rules was set up, separated into winter and summer, that for a given cell included the probability of changing from one state to another one, or of not changing state at all (Appendices 2 and 3). Under summer conditions, the simulation weighed together the influences of all the eight neighbouring cells to determine the direction of change of state (Appendix 1). For each year in the simulation, summer dynamics were modelled followed by winter dynamics.

For all aspects studied (see below) the model was run 10 times for each scenario. Each simulation run lasted 100 years. This time interval was sufficiently long to allow populations to reach their final (equilibrium) level. Equilibrium was defined as existing when, at visual inspection, the number of cells in each state, plotted against time, was at a constant level by year 70.

Competition between prey

To look at competitive interactions of the two prey species, voles and lemmings, landscapes consisting of lemming or vole habitat only were used. At the beginning of each simulation run, empty cells, lemmings and voles were distributed randomly over the landscape. Mustelids did not occur in this scenario. Each set-up (only lemming habitat or only vole habitat) was run 10 times for 100 years and it was noted when the voles went extinct and how many cells were occupied by lemmings at the end of the run.

Lemming population dynamics

To investigate population dynamics of lemmings, each simulation started with a certain amount of lemming habitat present in the landscape, divided into a certain number of patches (Table 1). In each scenario, all patches were about the same size and their shape was as close to a square as possible (Fig. 1). The initial distribution of states over all cells was random.

Spill-over predation

To study the mechanism of spill-over predation in more detail, a landscape containing 20% lemming habitat in one quadratic patch (Fig. 2) was used. This patch was divided into different parts, each representing a belt of cells at a certain distance from vole habitat. The number of cells not occupied by lemmings was counted in each belt at the start and after 1 year as well as every tenth year (10, 20 … 100) during each simulation run. Which belts of the lemming patch were invaded by mustelids, both during summer and in winter, was also checked. This enabled the temporal and spatial pattern of predator impact upon the patch of lemming habitat to be determined, as well as the severity of this impact as a function of distance from the edge of vole habitat.

House cats

To look at the impact of subsidized predators (e.g. house cats) hunting in remnants of natural habitat adjacent to human settlements, the model was changed in several ways. Cells assigned to predator habitat (formerly vole habitat, now called human settlements) never changed state and always contained predators and their primary resource (i.e. subsidies from humans). From there, predators moved into the surrounding natural habitat (formerly lemming habitat) and preyed upon populations of natural prey. Different fractions of the model landscape (2, 5, 10, 20,…, 90%) were assigned to human settlements and cells of this habitat class were distributed randomly.

Random vs. predefined habitat patches

To investigate whether a random and a uniform distribution of human settlements would result in different outcomes of the simulations, a fraction of 30% human settlement in the landscape was chosen. This habitat was subdivided into between 1 and 219 (i.e. single cells) settlement patches that were equally large and as close to a square as possible, and that were uniformly distributed over the landscape.

Predator management

The impact of hunting, to control predators spilling over from human settlements, on the persistence and population size of the natural prey species was also studied. To do this, different survival probabilities of the predators in the natural habitat during winter (i.e. the probability of a cell containing predators changes to the state ‘empty’ during winter) were used. Probabilities were between 0·5 and 1·0. For each probability, 16, 36 and 219 patches of settlement were used, a range that yielded interesting results in the previous analysis.

Competition between prey

When mustelids were absent from the system, voles were out-competed by lemmings within a few years (Table 2). There was a (statistically non-significant) tendency for voles to persist longer in vole habitat (t-test, P = 0·065). The total number of cells in the landscape occupied by lemmings gave an index of total lemming population size. The model did not make any assumptions on the size of populations within single cells.

After 100 simulated years, lemmings occupied a significantly higher number of cells when living in vole habitat than when living in lemming habitat when mustelids were absent (Table 2; t-test, P < 0·001).

Lemming population dynamics

When mustelids were present in the system, after 100 years the number of lemming cells was strongly dependent on the total amount of lemming habitat in the landscape as well as the number of patches of this habitat (Fig. 3). The more lemming habitat there was, the more cells were occupied by lemmings, which was not very surprising. However, the more habitat patches there were for a given amount of lemming habitat, the fewer cells were occupied at the end of the simulation period.

This general pattern changed when lemming habitat made up 70% of the total area. Here, the number of cells occupied by lemmings increased when the area was split up into more than four patches (3, 4). After 100 years, there were more lemmings in the landscape including 16 patches than in the landscape with one single large habitat patch. In the same scenario, the number of cells occupied by mustelids (alone or together with voles) decreased by about 50% from the four-patch landscape to the 16-patch landscape. After 100 years, the predators occupied fewer cells than after 50 years.

With no lemming habitat present in the landscape, the lemmings disappeared from the system in less than 10 years (Fig. 5). Increasing the amount of lemming habitat to 2% made the lemmings persist for about 20 years. At 5% or more lemming habitat, the lemmings persisted for 100 years if the habitat was in one patch. However, fragmentation of the habitat into several patches led to a decrease in lemming persistence. This decrease occurred faster the less lemming habitat there was and the higher the level of fragmentation. At the level of 70% lemming habitat, fragmentation did not have any effect on lemming persistence within the range of patch numbers (1–16) investigated.

Spill-over predation

The distance covered by mustelids spilling over into lemming habitat patches was different under summer and winter conditions. During summer, mustelids moved on average a distance of two cells into lemming habitat [mean of 10 replicates (± 1 SE) after 100 years: 1·70 ± 0·15]. During winter, this distance was only one cell (1·00 ± 0·15). This spill-over had consequences for the lemmings. Adjacent to vole habitat, a high percentage of cells were not occupied by lemmings at all (Fig. 6). With increasing distance from vole habitat, lemming frequency increased. In the belts three cells or further from vole habitat, the percentage of empty cells was consistently low (10–20%). This meant the closer a lemming cell was to vole habitat, the higher its probability of being affected by spill-over predation, and this probability was higher in summer than in winter.

House cats

When predators were subsidized by human settlements, and when cells assigned to settlements were randomly distributed over the entire landscape, lemmings had a high probability of surviving for 100 years when human settlements covered 20% or less of the landscape (Fig. 7a). Between 20% and 40% coverage of human settlements, persistence decreased rapidly. When 40% or more of the landscape was covered by settlements, lemmings survived only for a short period of time.

Lemmings were never able to occupy all cells of natural habitat present at the end of the 100-year simulation (Fig. 7b). When 2% of the landscape was covered by settlements, lemmings only occupied c. 70% (instead of the possible 88% as measured in a predator-free landscape; Table 2). With an increase in settlement area, the area occupied by lemmings after 100 years decreased and reached low values at 20% settlement in the landscape. With even more settlement, lemmings could not survive for 100 years. Without the effects of spill-over predation, lemmings would be able to occupy most cells of natural habitat, and they would be able to survive for 100 years in most scenarios (Table 2 and Fig. 6[link]). In the lemming habitat, the model did not make any difference between the two predator groups, mustelids and cats.

Random vs. predefined habitat patches

When human settlements covered 30% of the entire landscape, the number of (predefined) patches had an effect on the persistence of lemmings and on the fraction of habitat occupied after 100 years (Fig. 8). Lemmings persisted for 100 years when human settlements were subdivided into 16 or fewer patches. Persistence decreased strongly when 36 settlements were present in the landscape. A further subdivision (219 single-cell patches) decreased lemming persistence to a very low value.

Lemmings only occupied c. 70% of the natural habitat when human settlements were in one patch. A subdivision of settlements led to a decrease in the fraction of habitat occupied after 100 years. When settlement occupied 36 or more patches, lemmings were absent from the landscape at the end of the simulation runs.

This pattern showed that, at 30% settlement in the landscape, a subdivision of settlements into 36 patches [persistence (mean ± 1 SE): 56·1 ± 4·2 years, area occupied: 0%] had the same effect as a random distribution of settlements (persistence: 58·8 ± 11·9 years, area occupied: 0%). A lower number of predefined habitat patches increased lemming persistence and population size relative to the random situation. A number of patches higher than 36 affected lemmings more negatively than the random distribution of settlements.

Predator management

Reducing predator numbers (e.g. by hunting) in natural habitat (covering 70% of the landscape) during winter had an effect on lemming persistence only when human settlements were subdivided into 16 or 36 patches (Fig. 9a). When 219 patches of settlement were present, even 100% predator reduction did not increase lemming persistence to high levels. The more subdivided the settlements were, the more hunting effort was necessary to increase lemming persistence to 100 years.

The fraction of the landscape occupied by lemmings after 100 years was higher the fewer patches of settlement there were and the bigger the hunting effort was (Fig. 9b). The maximum value of 70% was never reached. When settlements were very much fragmented (219 patches), lemmings were always absent after 100 years, irrespective of hunting effort.

Modelling results

According to this simulation study, total area as well as the degree of fragmentation of the habitat are important determinants of population size and persistence probability of the endangered species. The edge effect created by predator spill-over from adjacent areas affects the prey population negatively. These results agree with the findings of Oehler & Litvaitis (1996) that ‘even moderate levels of habitat fragmentation may elevate predation rates and subsequently alter the composition of prey communities’.

The present results do not agree with the finding of Andrén (1994) and Fahrig (1997, 1998) that a further habitat fragmentation has no effect if the total proportion of a certain habitat in a landscape exceeds about 20% (10–30% reported by Andrén 1994). In this study, fragmentation also had an effect when the lemming habitat covered 70% of the whole landscape. The effects of fragmentation may depend on the distribution of habitat patches in the landscape. Recent neutral landscape models derived from percolation theory (With & King 1997) predict that landscape function is more heavily influenced by habitat abundance than by habitat configuration, especially when habitat is sparse (With, Gardner & Turner 1997; McIntyre & Wiens 1999). However, in this study it could be shown that a species’ survival and population size depend on the spatial location of habitat patches. A few evenly spaced predator sources had less effect than the same proportion of predator habitat that was randomly distributed, which in turn had less effect than many evenly spaced patches.

These results indicate that one critical variable driving lemming persistence and population size in the simulation study was the amount of edge of adjacent predator habitat in the landscape. There is a positive correlation between the number of patches of predator habitat and the length of the edge of this habitat. The greater the fragmentation of the landscape, the more patches of predator habitat there will be. The longer the edge, the more severe predation pressure will be upon a prey population. This is, however, only true when the intensity of predator spill-over is unaffected by patch size. In the original model including lemmings, voles and mustelids, relative spill-over intensity decreased with decreasing patch size, as smaller predator populations had a higher probability of extinction.

This was illustrated when lemming habitat occupied 70% of the entire landscape and was split up into several patches. Interestingly, in this situation the corridors of vole habitat eventually got too narrow to support viable predator populations. This means, when there is a lot of habitat for an endangered prey, it may be better if there are several patches instead of one large patch, keeping predator populations low. This, of course, only holds when the system is closed and predators do not immigrate from outside the study landscape.

In this simulation study, a qualitative threshold appeared to exist between 50% and 70% lemming habitat in the landscape. When lemming habitat covered 50% or less of the landscape, a further fragmentation of the habitat resulted in a decrease of lemming population size, while the lemming population increased when 70% of lemming habitat was subdivided into several patches. This corresponded well with the finding of Andrén (1994) that a formerly continuous habitat will start to break up into isolated patches when the proportion of this habitat in the landscape falls below 60% due to habitat loss and fragmentation. A similar threshold value has been put forward by percolation theory (59·3%; Gardner & O’Neill 1991).

The factors that are crucial for a predator–prey system in a heterogeneous environment include the physical dissimilarity of the two habitat types, the trophic position of the predator (mesopredator or top predator; Souléet al. 1988) and the degree of predator specialization (and hence the predator’s ability to penetrate the habitat of the endangered prey; Bissonette & Broekhuizen 1995). Some predators may be relatively unaffected by landscape composition or alteration (Matthews, Dickman & Major 1999), while others clearly are affected (Crooks & Soulé 1999).

Relevance for conservation

Often predators and their prey share the same habitat. Sinclair et al. (1998) discussed this and predicted the effects of predation on endangered prey. Here, landscape structure is of minor importance in a conservation context. In other cases, size and shape of (remnant) habitat patches are of crucial importance to predation effects on prey (Chapman et al. 1996; Crooks & Soulé 1999; Oksanen et al. 1999). The present findings from the mustelid–rodent system do not relate directly to species of conservation concern. However, the insights into the effect of habitat loss and fragmentation should be applicable to an array of similar predator–prey systems.

One such system that has received much attention during the last decade is that of ground-nesting birds and generalist nest predators in forest–farmland mosaic landscapes (for a recent review see Andrén 1995). Here, generalist predators include the hooded crow Corvus corone (L.) and badger Meles meles (L.) in Scandinavia, as well as the raccoon Procyon lotor (L.), blue jay Cyanocitta cristata (L.) and brown-headed cowbird Molothrus ater (Boddaert) in North America (Andrén 1995 and references therein). These predators depend mainly on food resources in the farmland and can often build up high population levels due to the high productivity of the agricultural landscape. Because the predators are habitat generalists, they visit forest fragments in the landscape regularly and prey upon birds’ nests there. Consequently, increased rates of nest predation have been documented at the edges of forest fragments in agricultural landscapes (Andrén 1992; Angelstam 1992; Andrén 1995), and the population decrease of capercaillie Tetrao urogallus L. in Sweden has been correlated with an increasing population of generalist predators in fragmented forest landscapes (Angelstam 1992; Hjorth 1994). A similar case of generalist predators that are subsidized in one habitat type and hunt in an adjacent habitat type are domestic cats (for a review on cat biology see Turner & Bateson 2000). Domestic cats prey mainly on small mammals and birds (Liberg 1984; Warner 1985; Churcher & Lawton 1987; Pearre & Maass 1998; Fitzgerald & Turner 2000) and have been introduced to most parts of the world (Ebenhard 1988). Two categories of cats are distinguished here according to their dependence on human households. ‘House’ cats are largely dependent on households for food and shelter, while ‘feral’ cats are completely independent of humans (for other categorizations see Pearre & Maass 1998; Liberg et al. 2000).

While feral cats occupy the same habitat as their prey, domestic cats return regularly to their homesteads at human habitations. The distance travelled by cats from their home (i.e. home range size) is negatively correlated with cat density, which in turn depends on resource levels (Liberg et al. 2000). Therefore, foraging house cats may cover a large proportion of the landscape when cat homes are close together, irrespective of population density. Domestic cats may reach high population densities that are sustained by food supplied by humans. There is great variation in the densities of domestic cats reported in the literature, ranging from one animal km⁻² in feral populations to 14 000 animals km⁻² in Rome (Liberg et al. 2000 and references therein). Liberg et al. (2000) presented three categories of cat density: more than 100 animals km⁻² are found in urban areas only where cats are intensively fed; intermediate densities of 5–100 animals km⁻² are found on farms and in rural feral populations with good food supply; low cat densities (< five animals km⁻²) ‘were found only in rural feral populations subsisting on widely dispersed prey’. The European wildcat Felis silvestris Schreber occupies the same ecological niche as the domestic cat (Hemmer 1993) but only reaches densities of 1·0–1·7 km⁻² in Germany (Piechocki 1990) and up to 3 km⁻² in Scotland (Corbett 1979; cited in Liberg et al. 2000).

House cats are subsidized carnivores, and predator–prey theory predicts that predators that are not dependent on a given prey can suppress the population of this prey to very low densities (Crawley 1992). These cats can continue to take wildlife in habitat patches long after the density of prey is too low to sustain natural predators (Souléet al. 1988). Because of this, and because their density is often high, house cats have the potential to affect populations of natural prey, and they are often accused of doing so by the general public (M. F. Schneider, personal observation).

In this simulation study, spill-over predation from human settlements with a constant and high population of predators affected the persistence as well as the size of lemming populations in natural habitats. Predator influence was low when the fraction of human settlement in the landscape was low (≤ 20%). When human settlements covered much of the landscape (≥ 40%), cats had a large influence. Here again the number of settlement patches was important, and lemming persistence and population size were higher when settlements were concentrated in few patches. The model thus predicts that cats should have relatively little influence in rural areas where villages cover only a small fraction of the landscape and where settlement boundaries are well defined. In suburban areas, on the other hand, humans cover a large fraction of the landscape, and settlement boundaries are often fragmented. In these areas, cats should have a pronounced effect on prey populations in remnants of natural habitat. Empirical studies on house cat predation showed that small mammals can be affected in rural Sweden (Erlinge et al. 1984; Hansson 1988). Cat predation has also been discussed as one important edge effect causing local extinction of bird and mammal species in patches of shrub habitats fragmented by urbanization in southern California (Souléet al. 1988; Bolger et al. 1997). However, the influence of house cats on bird populations remains unclear in continental areas where prey could adjust to these predators (as opposed to islands where cats often have great impacts upon naive prey) (Fitzgerald & Turner 2000). The current modelling results suggest that cats do affect bird populations in the vicinity of human settlements, and the next step should be to test this hypothesis empirically.

Predator hunting as a management tool

Managers can reduce predator populations using a range of methods, e.g. baiting, shooting, trapping and fencing (Litzbarski 1998; for a review on mammalian predators see Reynolds & Tapper 1996). In the current model, decreasing the number of predators in natural habitats decreased the impact of spill-over predation. However, this measure was only effective when source habitats of predators covered a small fraction of the landscape and when they were concentrated in a few patches. Also, most of the predators had to be killed, and predator removal was conducted every year. In real life, this approach requires an intensive effort and in most cases is effective only at a local scale and for a short period of time (Smith, Pressey & Smith 1994). Furthermore, it may be ethically problematic and not acceptable by society (Reynolds & Tapper 1996). In the long run, predator management will be expensive and it may be difficult to guarantee continuity. The results of the simulation indicate that predator management is not a viable strategy to conserve endangered prey in landscapes where predator density is high and where predators are subsidized by humans.

Received 25 November 1999; revision received 11 January 2001