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Keywords:

  • cellular model;
  • conservation;
  • dispersal limitation;
  • dynamic model;
  • landscape fragmentation;
  • land-use history;
  • migration;
  • seed dispersal;
  • slow migration

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  • 1
    Spatially explicit landscape models have revealed the importance of spatial arrangement of habitat patches in the behaviour of mobile organisms. Such models fail to account for creation and destruction of habitat, which may interrupt the movement of slowly migrating species such as forest herbs.
  • 2
    To explore the interaction of habitat turnover and population migration, we present a dynamic landscape model inhabited by a dispersing species. The landscape is represented as a square lattice in which individual cells may be either habitat or non-habitat, and a hypothetical species may spread among habitat cells. Rate of species spread, habitat frequency and habitat clearance and regeneration are allowed to vary.
  • 3
    In static landscapes, the fraction of the landscape occupied by the species is limited by connectivity among habitat patches and rate of population migration. Slow species often cannot reach all available habitat despite the presence of continuous paths to it.
  • 4
    In dynamic landscapes, slow-moving species show reduced map-scale frequency and high risk of extinction due to the cumulative effects of habitat patch destruction and the failure to colonize newly created habitat. Such species decline cannot be predicted based on static descriptions of habitat connectivity or migration rate.
  • 5
    Fast-moving species may be reduced in dynamic landscapes by the cumulative effect of numerous local isolation events. Fast-moving species may also experience a modest range expansion in low-connectivity landscapes due to the cumulative effects of short-lived patch adjacency.
  • 6
    These results suggest a novel mechanism that could account for species impoverishment in fragmented landscapes. They emphasize the importance of maintaining habitat connectivity on a time-scale that accommodates slow-migrating species such as forest herbs.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

The geographical distribution of a species is a reflection of the spatial pattern of habitat and the migration history of populations. Spatial pattern influences the likelihood that one habitat patch is near another and, hence, the ability of a moving organism to locate and gain access to patches (Saunders et al. 1991; Pulliam et al. 1992; Wiens et al. 1993). Valuable insight into the consequences of habitat arrangement has been provided by recent work with spatially explicit map-based models (e.g. Gardner et al. 1987; O’Neill et al. 1992; Pearson et al. 1996; With & King 1999). In model landscapes, access to habitat is dependent on map-scale habitat frequency, degree and scale of habitat clustering, and the hierarchical structure of clustering. Field studies confirm modelling results: spatial organization of habitat often determines the movement patterns of animals in heterogeneous landscapes (Noss 1987; Bennett et al. 1994; Dunning et al. 1995; Brooker et al. 1999).

Most attention has been given to landscapes with static spatial patterns, implicitly assuming that an organism moves through habitat much more rapidly than the spatial arrangement of habitat changes. Such models are appropriate to large vertebrates and generally correspond to the human experience of landscapes. However, many species explore space very slowly relative to the scale of human observation; indeed, at rates slow enough to interact with processes of habitat disturbance and regeneration. Slow-moving species are faced with a changing pattern of habitat distribution creating demographic effects not easily described in static landscape models. All terrestrial ecosystems are subject to change in local habitat quality over time due to disturbance and successional processes (Watt 1947; Connell & Slatyer 1977; Connell 1978; Harmon et al. 1983; Turner et al. 1997). It is reasonable to conclude that most terrestrial species must cope with temporal variation in habitat distribution at some scale, suggesting a limitation on the predictive power of static models.

Few ecological models have considered both spatial and temporal variation in habitat (Wiens 1997; Gustafson 1998). Metapopulation models stress the importance of dispersal among spatially discrete, temporally limited populations (Levins 1969; Lande 1987; Hanski & Gilpin 1991) and allow predictions of local and regional dynamics based on species mobility. In general, habitat fragmentation has been found to threaten metapopulation persistence by limiting recolonization of vacated patches (Bascompte & Sole 1996; Travis & Dytham 1999; With & King 1999). Interpatch dispersal is favoured by temporal variation in habitat quality (Gadgil 1971; Olivieri et al. 1995; Ronce & Olivieri 1997). Metapopulation models are vague with regard to spatial pattern, however, and therefore inappropriate to studies of spatial/temporal interactions. Metapopulation models also fail to take account of shifting habitat availability; population extinction is generally linked to stochastic processes within populations rather than habitat disappearance.

A small number of studies have considered population flux in environments that are both spatially and temporally heterogeneous. Matlack (1994), based on field observations, suggested that low-mobility forest herbs are lost from a dynamic post-agricultural landscape due to weak dispersal and the pattern of forest clearance and regeneration. In simulations, low-mobility species are generally found to decline in frequency in disturbed landscapes (Colasanti & Grime 1993; Perry & Gonzalez-Andujar 1993). Conversely, broad dispersal mitigates the negative effects of habitat disturbance (Travis & Dytham 1999). If population longevity is determined by habitat destruction, reproductive rate is often more important to regional survival than dispersal range (Lande 1987; Fahrig 1992). Although these models highlight the difficulties faced by time- and dispersal-constrained species in heterogeneous landscapes, they do not explicitly consider spatial arrangement of habitat patches, a serious omission considering the importance of spatial pattern suggested by static landscape models.

In simulations of metapopulation persistence in spatially explicit landscapes, connectivity among patches (inferred from the proportion of habitat) strongly influences regional species frequency (Bascompte & Sole 1996; Keymer et al. 2000). These results suggest an interaction of spatial and temporal pattern consistent with observations of real populations in fragmented landscapes (Peterken & Game 1984; Matlack 1994; Brunet & von Oheimb 1998; Verheyen & Hermy 2001; Verheyen et al. 2003).

We present a landscape model that is both spatially explicit with regard to patch arrangement and dynamic in allowing patch creation and destruction. Our goal is to explore the interaction of species mobility and habitat turnover across a range of turnover and migration rates. In particular we consider ‘slow’ species, defined here as species for which there is a non-trivial chance that habitat quality will change before a population can expand across the width of one habitat unit. We explore the consequences of dynamic landscape pattern for distribution of a species using two pattern-defining parameters, habitat frequency and species dispersal mode.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

Spatial and temporal heterogeneity is explored with a simple cellular map model in which habitat patches appear and disappear, and populations disperse among them. Populations expand across the map through the cumulative effect of many local dispersal events. As a result of local dispersal, the presence of a species in a single cell is dependent on the character of neighbouring cells, so the model can be considered a ‘cellular automaton’ (Hogweg 1988; Bar-Yam 1992; Molofsky 1994). The model was written in the Visual C++ programming language.

landscape

Landscape is represented by a square lattice of 50 × 50 cells. Cells may have two values, habitat (suitable for colonization, reproduction and dispersal) or non-habitat (unsuitable for occupation). Real landscapes are rarely binary in habitat quality (Janzen 1986; Wiens et al. 1997; Szacki 1999) and habitat types are rarely separated by geometrically straight ecotones (Matlack & Litvaitis 1999), but a simplified landscape model allows conceptual questions to be addressed more directly. Landscape maps are constructed by randomly assigning habitat to a specified number of cells. A proportion of habitat is removed at each time-step and a proportion of non-habitat is converted to habitat (analogous to forest clearance and regeneration). Cells are selected randomly for clearance and regrowth. The proportion regenerating is set equal to the proportion cleared such that overall habitat abundance remains constant. This allows the proportion of the landscape occupied by habitat (‘habitat frequency’) to vary independently of the proportion of habitat cleared and regenerated (‘habitat turnover’). Turnover may vary from 0 to 50% per 10-year time-step. Values of 40 and 50% turnover are probably unrealistic in most terrestrial ecosystems, but they are included to fully explore the behaviour of the model.

populations

Populations of a hypothetical species may occupy habitat cells and may spread to adjacent cells if they are habitat. Non-habitat cells cannot be colonized. When a cell first becomes habitat it is not occupied by a population until colonized. When an occupied cell is converted to non-habitat, its population becomes extinct. Population and habitat states are tabulated separately in two parallel arrays allowing the dynamics of populations and landscape to be manipulated independently. Each cell in the landscape array is divided into four equal subcells in the population array. All four subcells share the same habitat designation (habitat or non-habitat, tabulated in the corresponding landscape cell), but occupation of each subcell by a population is independent of the state of the other subcells.

A population spreads by colonizing adjacent subcells, which may be within the same landscape cell or in adjacent cells. Before it is permitted to colonize further subcells a population must occupy a subcell for a period equivalent to subcell transit time, i.e. subcell width divided by the rate of spread. Nesting of subcells inside cells divides spread across the cell into two phases, allowing spatially realistic colonization of subsequent cells. If a population spreads to a subcell that is already occupied, the late-arriving population is not recorded.

All aspects of species demography are combined into a single rate of population spread. Population spread approximates a travelling wave passing from cell to cell consistent with diffusive spread generated by an exponentially bounded dispersal kernel (Weinberger 1982; Clark et al. 2001). Long-distance dispersal events are not allowed. Diffusion-based models are generally considered inferior to individual-based (demographically explicit) models because the former do not take account of density-dependent processes, individual responses to environmental gradients, or stochastic effects in finite populations (Wiens et al. 1993; Higgins et al. 1996; Clark et al. 2001). Diffusion models are appropriate to sedentary organisms such as forest herbs, however, because herbs are insensitive to most density effects above the scale of the individual plant neighbourhood (Mack & Harper 1977; Matlack & Harper 1986). By selecting a spatial scale that is very broad relative to the size of individual organisms, we remove the need to consider local effects on individual reproduction and dispersal. Using a rate of population spread based on long-term observations of migration distance avoids stochastic variation inherent in observations of individual-plant reproduction and dispersal (Roughgarden 1986; Neubert & Caswell 2000), permitting simulation as a diffusion process. Because the model considers the spread of populations rather than organisms, and population expansion assumes multiple generations, there is no resource limit to population spread as sometimes required in organism-based models (e.g. Gustafson & Gardner 1996; Brooker et al. 1999). Population spread continues as long as suitable habitat is available for colonization.

Rate of population spread can be varied experimentally. Here, we consider rates of 0–5 (and in one model, 10) landscape cells per time-step, with most attention given to rates of 0–0.5 cells step−1. For purposes of the model, ‘slow’ species are defined as those having rates of < 5.0 cell per time-step. Where the movement rate exceeds one subcell per time-step, the population spreads to neighbouring subcells, then on to tertiary subcells following the same adjacency rule.

Two dispersal modes are examined. The population may spread to contiguous subcells (four colonizable neighbours in a square lattice), or to contiguous subcells plus diagonally adjacent subcells (eight colonizable neighbours). In real biological terms, addition of diagonal movement represents a slight increase in local dispersal capacity, giving access to habitat patches at a greater distance, in this case cells inaccessible by reason of non-contiguity in a square lattice. Movement within subcells proceeds at the specified rate regardless of dispersal mode, making dispersal mode independent of migration rate. Edges of the landscape map connect (‘wrap’) to the respective opposite sides of the map to create a toroidal landscape surface. A population spreading to one edge continues colonization of habitat cells at the opposite edge. Wrapping at map edges provides a reasonable approximation to an infinitely large map if the model map is large (Haefner et al. 1991; Bar-Yam 1992). The method is clearly superior to reflecting or absorbing edges, or linear expansion from a centred population. Wrapping is widely used in cellular automata for operational simplicity and economy of processing time.

operation of the model

The model is parameterized to approximate forest fragments in the post-agricultural matrix of south-eastern Pennsylvania and northern Delaware, USA (Matlack 1997a,b). Landscape cells are set at 100 × 100 m and revisited with a 10-year time-step. Rates of migration are within the range of field observations published by Matlack (1994). Realistic parameterization is not necessary to address the conceptual questions, but the result is easily visualized and becomes convenient when comparing the model with field observations. Henceforth, time will be given in units of years and rates will be given in metres year−1.

Habitat frequency, species frequency, rate of spread, turnover rate and dispersal mode are specified at the beginning of each run. The model allows either of two initial distributions: (i) the initial population occupies a single habitat cell, and is allowed to expand through the landscape; or (ii) the population begins occupying all habitat cells and subsequent reduction is recorded. At each time-step the model first clears the specified proportion of habitat, then randomly regenerates habitat cells and allows colonization within and between cells. At the end of each run the model tallies the number of landscape cells occupied by populations (‘species frequency’). If the species has gone to extinction, the time-step at which extinction occurred is noted (‘time to extinction’).

Each model run proceeds for 100 time-steps, equivalent to 1000 years. In static landscapes, 100 steps curtailed the migration process in some cases (see below). In dynamic landscapes, however, replicated trial runs always showed species frequency stabilizing well before 100 time-steps, demonstrating that 100 steps were a reliable basis for comparison of landscape and dispersal variables. Relative to frequency values at 100 steps, transient effects were minor in amplitude and limited to the first 20–30 steps. Stochastic variation was present with these parameterizations, but was substantially less than any other form of variation.

Each run is replicated 100 times, each replicate with a new randomly generated landscape map. Many studies of landscape structure have used only one or a few landscape configurations, so their findings are map-specific. In the present study extensive replication with re-randomization of habitat generalizes and strengthens our conclusions. Results are presented as means of the 100 replicate runs. Standard errors were quite small (usually less than the size of the graph symbols) so they are not presented in most figures.

The model is used in four sets of trials (Table 1). First, population expansion is considered in a static landscape (i.e. no habitat turnover) while varying habitat frequency and migration rate. In the second set, we use dynamic landscapes to consider the interaction of habitat turnover and migration rate at low habitat frequency (30%, i.e. P = 0.30). Thirdly, habitat turnover and migration are examined at high habitat frequency (P = 0.90). Finally, rate of spread is held constant while habitat connectivity is varied by manipulating habitat frequency and allowing diagonal movement.

Table 1.  Combinations of variables used in nine trials of the landscape model. All combinations were replicated 100 times and run for 100 10-year time-steps. Symbols: ‘c’ = contiguous dispersal; ‘c + d’ = contiguous + diagonal dispersal
TrialInitial distributionHabitat frequency (%)Rate of migration (m year−1)Dispersal modeRate of turnover
1aSingle cell0.01–1.050c, c + d0
1bSingle cell0.01–1.00.5–5c0
1cSingle cell0.01–1.03c, c + d0
2a100%0.300.1–50c1–50
2bSingle cell0.300.1–100c1–50
3100%0.900.1–50c1–50
4100%0.30, 0.60, 0.901c, c + d1–50
Static landscapes

To examine the effects of spatial heterogeneity on the spread of populations, the model was run without clearance or regeneration of habitat. The population was randomly assigned to a single habitat cell at the beginning of each run and allowed to spread to any cell accessible through contiguous linkages. The naive expectation is that the species will eventually occupy all available habitat, and the number of cells occupied will equal the amount of suitable habitat in the landscape (species frequency = habitat frequency). In practice this is not observed due to isolation of individual habitat patches at low density. In a square lattice above a habitat frequency of Pcriticalc. 0.59, any randomly placed habitat patch has a high probability of being adjacent to similar patches, causing extensive habitat connectivity (‘percolation’) throughout the landscape (Plotnick & Gardner 1993). Below this threshold, there is a low probability of adjacency and habitat patches tend to be isolated. As such, P describes the spatial structure of a landscape as well as measuring habitat frequency. P has been widely used as an index of landscape connectivity and therefore accessibility of habitat to a moving organism (Gardner et al. 1987; Gustafson & Gardner 1996).

We examined spread in a static landscape allowing contiguous and contiguous + diagonal movement (Trial 1a). Habitat frequencies (P) varied from 0.1 to 1.0 at 0.1 intervals, plus 0.01. Rate of spread was set initially to 50 m year−1 (equivalent to five landscape cells per time-step, a very fast rate of movement). In a second static trial rate of movement was varied while dispersal mode was limited to contiguous cells (Trial 1b). Movement was allowed at 0.5, 1, 2, 3, 4 and 5 m year−1. Finally, dispersal modes were re-examined at a slow rate of movement (3 m year−1) to examine mode–rate interactions (Trial 1c).

Dynamic landscapes

In dynamic landscapes, persistence of species was considered at two levels of habitat frequency. One frequency (P = 0.30) was chosen below Pcritical to produce a dissected habitat consisting of many isolated cells and small cell clusters. In the first trial, the landscape began at 100% occupancy and species frequency was recorded after 1000 years (Trial 2a). Rates of spread and habitat turnover were varied experimentally. To explore the interaction of turnover and dispersal the trial was repeated starting from a single randomly chosen cell (Trial 2b). Starting from a single cell was not intended to simulate behaviour of a population in a real landscape (although it may approximate the spread of an introduced species) but only to emphasize dispersal effects at low connectivity.

In the third set of trials, frequency was set well above Pcritical (at P = 0.90), to give large areas of continuous habitat surrounding small gaps (Trial 3). Trials began with 100% of the habitat occupied by the species. Species frequency, likelihood of survival and time to extinction were recorded after 1000 years at rates of turnover ranging from 1 to 50% per 10-year increment. Variation in habitat connectivity was further examined by considering several values of P while holding the migration rate constant (Trial 4). Migration rate was set to 1 m year−1. Species frequency results were obtained at P = 0.30, 0.60 and 0.90.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

static landscapes

In the static landscape, the population spread to all available habitat above a threshold of habitat availability, as predicted (Fig. 1a). With contiguous movement, there was a transition zone between P = 0.50 and 0.70, consistent with the well-known behaviour of randomly structured square lattices (Gardner et al. 1987; Gardner et al. 1989; Turner et al. 1989; O’Neill et al. 1992). When diagonal movement was added, a similar behaviour was observed, but the threshold value was lower (Pcriticalc. 0.40). This finding is also consistent with previous work: the threshold for connectivity is dependent upon dispersal behaviour of the organism. Lower thresholds and greater functional connectivity are experienced by species capable of broad dispersal (Plotnick & Gardner 1993; Pearson et al. 1996; Wiens 1997; With & King 1999).

image

Figure 1. Static landscapes. Spread of a population from a single point. (a) Spread of a fast species (50 m year−1) to contiguous and contiguous + diagonally adjacent cells. (b) Spread of populations at six rates of migration. Dispersal is allowed to contiguous cells, but not to diagonally adjacent cells. (c) Spread of a slow species (3 m year−1) in two dispersal modes in static landscapes. The dashed line with open circles (‘available’) indicates the frequency of habitat cells in the landscape; other lines indicate those cells actually occupied by populations. Each data point is the mean of 100 replicates.

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If the rate of spread is slow, however, a different result is obtained (Fig. 1b). Species moving at rates below 5 m year−1 (equivalent to 0.5 cells per time-step) were unable to reach all available habitat, even above the P = 0.59 threshold. Even though all habitat was nominally accessible by reason of connectivity, a migrating species could not colonize some areas because distant cells could not be reached in the time allotted. Given more time-steps, all cases would converge to species frequency = habitat frequency, but, in the time-constrained system, some habitat was inaccessible to the slower species by virtue of distance. The well-known graph of habitat frequency and occupation (Fig. 1a) can be regarded as having two sections. In the section below the percolation threshold the distribution of a migrating species is restricted by lack of habitat connectivity. In the section above Pcritical, connectivity is not limiting. Instead, distributions are determined by the migration potential of the species (i.e. its life history), and the time allotted in the model. When diagonal dispersal was allowed (Fig. 1c), a slow species was able to reach a greater proportion of habitat above Pcritical than when the species only colonized contiguous subcells. Thus, two distinct aspects of life history, rate of spread and dispersal mode, have the potential to limit distribution in a heterogeneous landscape.

dynamic landscapes

In the unconnected dynamic landscape (P = 0.30), species frequency stabilized well below habitat frequency, with more severe reduction occurring at higher rates of turnover (Fig. 2a). Species reduction was the result of the failure of cell colonization to keep pace with population loss by cell clearance. It appears that isolation of individual cells prevented colonization of newly formed habitat, even by relatively fast-moving species. Within each rate of spread, frequency declined as a linear function of turnover because population extinction is a direct result of linearly increasing habitat clearance. A rate-of-movement effect is also evident: slow species were reduced by habitat turnover more than fast species and were more likely to reach extinction. We interpret the rate-of-movement effect in terms of brief opportunities for colonization provided by occasional adjacency of habitat cells. A fast species had a greater likelihood than a slow species of colonizing an adjacent cell if it temporarily became habitat. Sufficient connectivity existed at P = 0.30 to allow persistence of rapid colonizers despite habitat destruction and despite habitat frequency well below Pcritical. By contrast, slow-moving species were seriously reduced at rates of turnover as low as 10% in 10 years.

image

Figure 2. Loss of populations from dynamic landscapes at P = 0.30. Trials began with all habitat cells occupied with a population. (a) Species frequencies at five migration rates and six turnover rates. (b) Likelihood of survival anywhere in the landscape at five migration rates. (c) Time to extinction for those trials where extinction occurred.

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Likelihood of survival was reduced by habitat turnover (Fig. 2b) much as species frequency was reduced; extinction is the extreme example of low frequency. As with species frequency, survival rate is also affected by rate of spread. Although fast-moving species (5–50 m year−1) were reduced in frequency at moderate levels of habitat turnover, their chances of survival somewhere in the landscape were good. By contrast, slow-moving species (0.1 and 1 m year−1) were prone to complete extinction at all but the lowest (1%) turnover. Time to extinction at P = 0.30 reflects likelihood of survival (Fig. 2c). Whereas a species moving 1 m year−1 survived 750 years at 20% turnover, at 30% it was only likely to survive 400 years. Again, migration rate is important; slow species were at greater risk than fast-moving. Because time to extinction covaries closely with likelihood of survival, here and elsewhere, it will not be discussed further.

When the population started from a single cell (Trial 2b), most species only spread to small areas around the point of introduction (Fig. 3). At low turnover (1% every 10 years) species generally spread to < 10 cells because contiguous cells were rarely available for colonization. At high rates of turnover (40–50%) few cells were occupied because occupied cells were rapidly cleared. At intermediate levels of turnover, however, fast-moving species were able to expand their ranges. We interpret range expansion in terms of the transient opportunities for colonization noted above. Connected clusters of habitat were occasionally formed, creating continuous paths to several colonizable cells. Although a path could be broken at the next time-step, its brief existence was sufficient for dispersal of a fast species. By facilitating dispersal, short-lived habitat patches appeared to be acting as bridges, contributing to species frequency out of proportion to their habitat areas. This opportunity was not available to slow-moving species, which could not negotiate habitat bridges within bridge life spans. Rapid movement ceased to be advantageous at high rates of turnover, because populations were destroyed faster than bridges formed.

image

Figure 3. Spread of populations in fragmented dynamic landscapes (P = 0.30) at six rates of migration. Trials began with a single habitat cell occupied. Species frequencies at six turnover rates. Each point is the mean of 100 replicates; bars show one standard error.

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dynamic landscapes above pcritical

At a habitat frequency of 90% (P = 0.90) one might expect that extensive connectivity would allow easy colonization and thereby ensure that species frequency was not affected by habitat turnover, but this was not the case (Fig. 4a). Species moving at 5, 10 and 50 m year−1, which were able to reach all habitat in the static landscape (Fig. 1b), showed reduced frequency in the dynamic landscape. The reduction was dependent on rate of turnover but appeared to be independent of rate of spread, suggesting some form of connectivity effect. We conclude that in highly connected, habitat-dense landscape maps habitat configurations occasionally arise that completely isolate cells making them uncolonizable regardless of movement rate. The cumulative effect of many such isolation events may be substantial. Severe reduction in frequency at high turnover rates suggests that inaccessibility is more common at high levels of habitat turnover. Slow-moving species (≤ 1 m year−1) experienced a more severe reduction than fast species, consistent with the transience of colonization opportunities. We interpret reduction of slow species as a compound effect reflecting both time limitation and cell isolation. Hence, the definition of ‘inaccessible’ habitat must consider the migration potential of the species as well as the geographical arrangement of habitat patches.

image

Figure 4. Loss of populations from dynamic landscapes at P = 0.90. Trials began with all habitat cells occupied with a population. (a) Species frequencies at five migration rates and six turnover rates. (b) Likelihood of survival anywhere in the landscape at three migration rates.

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Extinction was observed in the connected landscape at rates of movement ≤ 1 m year−1 (Fig. 4b). In slow-moving species (0.1–1.0 m year−1), high rates of turnover led to low likelihood of survival, with certain extinction at moderate turnover (20–40%), notwithstanding the extensive connectivity of the landscape.

dynamic landscapes: connectivity

Frequency data reformatted from Figs 2(a) and 4(a), plus values obtained at P = 0.60, are presented in Fig. 5(a). At 1% turnover, species frequencies after 1000 years were still close to the respective habitat frequencies. At 10 and 20% turnover, species frequency was reduced at all values of P, with a greater reduction at P = 0.30 than at P = 0.90. As a null hypothesis of ‘no effect’ one would expect a smaller number of cells to remain occupied at P = 0.30, but we also observed that a smaller proportion of habitat cells remained occupied. Species frequency at P = 0.30 was reduced 80% at 10% turnover, while frequency at P = 0.90 was only reduced 9%. Apparently, greater opportunity for movement in the connected landscape conferred greater resistance to the negative effects of habitat turnover. The intermediate frequency (P = 0.60) fell in between, with species frequency at P = 0.60 disproportionately greater than P = 0.30 at 10% turnover and disproportionately below P = 0.90 at 20% turnover. Connectivity also favoured survival. Likelihood of survival (Fig. 5b) was much greater in the connected landscape than the unconnected at moderate levels of turnover (20 and 30%).

image

Figure 5. Loss of populations from dynamic landscapes at habitat frequencies of 30, 60 and 90%. The species migrates at 1.0 m year−1. Trials began with all habitat cells occupied with a population. (a) Species frequencies at six turnover rates. (b) Likelihood of survival anywhere in the landscape at six turnover rates.

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Results in the static landscape suggest that diagonal movement should be viewed as a slight increase in functional connectivity caused by a change in local dispersal behaviour. In both connected and unconnected dynamic landscapes (Fig. 6a) diagonal movement allowed greater species frequency than contiguous movement alone, presumably by creating additional paths among habitat patches, thereby providing more opportunities for colonization. The advantage of diagonal over strictly contiguous movement at P = 0.90 and 20% turnover supports the conclusion that poor local connectivity acts as a constraint even in landscapes extensively connected at the map scale. Diagonal movement also allowed higher frequency in the unconnected landscape (P = 0.30), again emphasizing the importance of local habitat connectivity. Species frequencies in unconnected landscapes remained much lower than in connected landscapes, however, demonstrating that map-scale connectivity is also important (in this case, dominant) in dynamic landscapes.

image

Figure 6. Loss of populations from dynamic landscapes at two habitat frequencies in two dispersal modes (adjacent and diagonal). The species migrates at 1.0 m year−1. Trials began with all habitat cells occupied with a population. (a) Species frequencies at six turnover rates. (b) Likelihood of survival anywhere in the landscape at six turnover rates.

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Diagonal movement increased the likelihood of survival by as much as 60% relative to contiguous movement in the unconnected landscape (Fig. 6b), stressing the importance of local habitat structure in allowing populations to escape habitat destruction.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

The model confirms the observation that dispersal-limited species are at a disadvantage in frequently disturbed landscapes (Lande 1987; Colasanti & Grime 1993; Perry & Gonzalez-Andujar 1993; Ronce & Olivieri 1997). Final frequency in the landscape was determined by a species’ rate of spread relative to the dimensions and longevity of habitat patches. Survival depended on achieving a balance between population establishment by patch colonization and elimination by patch destruction. Simulated species that spread slowly often dropped to extinction. Although this general result is anticipated by previous work, the present model shows several non-intuitive behaviours that can be interpreted in terms of species mobility and the spatial arrangement of habitat.

In static landscapes map-scale connectivity of habitat was the dominant feature determining species frequency. Below a threshold of habitat frequency (Pcritical) population spread in the static landscape was limited by isolation of habitat, consistent with simulations of the spread of disturbance (Turner et al. 1989). Above Pcritical, fast-moving species reached all habitat cells in the static landscape, indicating widespread connectivity. Slow-moving species, however, failed to reach all habitat due to the artificial time limit specified in the model. It appears that time limitation imposes a de facto geographical limit on the distribution of a slow species analogous to resource limitation in a fast-moving species (e.g. Aborn & Moore 1997). The geographical limit may be extended by diagonal movement, which serves to increase habitat connectivity by creating more-direct paths between habitat patches. It is notable that connectivity at the scale of the landscape map (P > Pcritical) does not necessarily allow access to all habitat in the static landscape. Rate of spread, dispersal mode and available time must also be considered. Because rate of spread and dispersal mode vary among life histories, the severity of time limitation and, ultimately, frequency in the landscape, may be expected to vary among species.

Dynamic landscapes differ from static landscapes in that local extinction occurs with the clearance of habitat cells. Habitat connectivity is critical to survival in dynamic landscapes because it provides access to newly formed habitat patches, compensating for extinction by clearance of existing patches. Map-scale connectivity (P > Pcritical) promotes high species frequency, as in static landscapes, and increases the likelihood of survival. In addition to map-scale phenomena, our results suggest two local connectivity effects arising from the interaction of migration rate, habitat frequency and habitat turnover. Local effects have the potential to strongly influence species frequency and survival, in some cases counteracting effects predicted at the map scale, an important finding of this study. They involve the relative position of habitat patches within small clusters, and appear to act independently of map-scale habitat frequency (P). These findings are consistent with studies of static landscapes that stress the importance of fine-scale pattern to overall landscape connectivity and habitat access (Bascompte & Sole 1996; Pearson et al. 1996; With & King 1999).

local connectivity effects

In the first type of local effect, a species expands its range by crossing ephemeral ‘bridges’, taking advantage of habitat linkages only briefly available in the changing landscape pattern. The bridge effect is an expression of time limitation in which the time limit is defined by habitat turnover. Rapid spread is at a premium, allowing broader exploration of habitat than a slow species would enjoy. The ephemeral-bridge effect is particularly noticeable when it allows a fast species to expand its range below Pcritical, but in reality the effect is universal. All landscape linkages are temporary in a dynamic landscape, and all colonization events take place across such linkages.

In the second local effect, the occasional isolation of individual habitat cells makes them unavailable in a habitat-dense landscape. Isolation occurs despite extensive map-scale connectivity. Although no cell is isolated for long in a dynamic landscape above Pcritical, our results suggest that the cumulative effect of many short isolation events may severely reduce species frequency. The degree of reduction increases as a function of turnover rate because high turnover entails more creation of new habitat than low turnover and, thus, provides more opportunities for cell isolation. From the standpoint of static landscapes these results are counterintuitive. Ephemeral-bridge and ephemeral-isolation effects cannot be determined analytically from observations of static pattern because they involve dynamic interactions of population migration and changing habitat configuration. A static map of habitat will be a poor predictor of species frequency or survival; information on habitat turnover is also required.

caveats

These conclusions are of particular interest because they include habitat turnover, a common property of real ecosystems heretofore not addressed in abstract landscape models. Application to real landscapes is problematic, however. Although our model is based on field observations in real fragmented landscapes (Matlack 1994; Brunet & von Oheimb 1998; Singleton et al. 2001; Verheyen & Hermy 2001; others), it is unclear how closely the model approximates the dynamics of such landscapes. For simplicity the model assumes habitat is distributed randomly, an unlikely arrangement in real landscapes and one that is almost guaranteed to influence species persistence through its effect on habitat connectivity (Lavorel et al. 1993; Pearson et al. 1996; Wiens 1997; Malanson & Cramer 1999). Further, biogeographical (Cain et al. 1998; Clark et al. 1998) and genetic evidence (Ellstrand 1992; Dow & Ashley 1996; Ouborg et al. 1999) suggests that rare long-range dispersal events are disproportionately important in determining species’ regional and continental distributions. Long-range dispersal is not included in our model although it doubtless occurs in the herb species that parameterized the model (Cain et al. 1998). We are presently exploring the properties of non-random dynamic landscapes with and without long-range dispersal.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

Slow dispersal can be placed in a landscape context by allowing the habitat map to change on the same time-scale as populations expand. It becomes clear that survival in a dynamic landscape depends on a species’ rate of spread, and on the opportunities for spread provided by habitat connectivity. Connectivity is most strongly influenced by map-scale threshold effects but unanticipated local effects are also important. Short-lived connections between habitat patches, repeated many times across the landscape map, can boost the regional frequency of a fast-moving species, perhaps explaining the rapid range expansion observed in many non-native species in human-disturbed landscapes. Conversely, short-lived isolation of patches can lead to species decline even among those with rapid spread. Slow species, and species with short-range dispersal, are at a disadvantage in both cases. These appear to be permanent consequences of habitat turnover rather than transient effects within the model.

These results demonstrate the essential role of both spatial and temporal habitat structure in regulating the long-term distribution of species. As such, the model pulls a little closer together the disparate strands of landscape structure, metapopulation function and empirical observation of fragmented systems (Wiens 1997; Tischendorf & Fahrig 2000; With 2002).

Conservation planning has long embraced spatial connectivity of habitat. Present results suggest that conservation efforts also need to address habitat turnover. ‘Slow’ species are most at risk; they need to be identified and accommodated. It is worrying, however, that neither high mobility nor extensive connectivity of the landscape were sufficient to ensure survival in the dynamic model. By implication, protection of diversity requires active management of all habitat-specific species in human-shaped landscapes. Although ‘slow’ species experience habitat turnover most acutely, the potential for loss probably extends to a large portion of the flora and fauna.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

This work greatly benefited from discussions with David Ford and Raymond O’Connor. The work was partially funded by grant 95-37106-2446 from the US Department of Agriculture. Early phases were supported by a Bullard Fellowship at Harvard University. We thank Dean Urban, David Gibson, Lindsay Haddon and two anonymous reviewers for comments on the manuscript.

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  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
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