Download Consequences of low mobility in spatially and temporally

Journal of
Ecology 2004
92, 1025–1035
Consequences of low mobility in spatially and temporally
heterogeneous ecosystems
Blackwell Publishing, Ltd.
GLENN R. MATLACK and JOHN MONDE*
Environmental and Plant Biology, Porter Hall, Ohio University, Athens, Ohio 45701, USA, and *Scientific Software
Applications Group, Room 112, Building 9313, Stennis Space Center, Mississippi 39529, USA
Summary
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 shortlived 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.
Key-words: cellular model, conservation, dispersal limitation, dynamic model, landscape
fragmentation, land-use history, migration, seed dispersal, slow migration
Journal of Ecology (2004) 92, 1025–1035
Introduction
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
© 2004 British
Ecological Society
Correspondence: Glenn R. Matlack (fax +1 740 593 1131;
e-mail [email protected]).
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
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& J. Monde
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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 & GonzalezAndujar 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 dispersalconstrained 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
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 is represented by a square lattice of 50 ×
50 cells. Cells may have two values, habitat (suitable
for colonization, reproduction and dispersal) or nonhabitat (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.
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© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
 
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.
   
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
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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
Trial
Initial
distribution
Habitat
frequency
(%)
Rate of
migration
(m year−1)
Dispersal
mode
Rate of
turnover
1a
1b
1c
2a
2b
3
4
Single cell
Single cell
Single cell
100%
Single cell
100%
100%
0.01–1.0
0.01–1.0
0.01–1.0
0.30
0.30
0.90
0.30, 0.60, 0.90
50
0.5 –5
3
0.1–50
0.1–100
0.1–50
1
c, c + d
c
c, c + d
c
c
c
c, c + d
0
0
0
1–50
1–50
1–50
1–50
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.
Static landscapes
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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 Pcritical c. 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
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Consequences of
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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
 
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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 (Pcritical
c. 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).
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
Fig. 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.
aspects of life history, rate of spread and dispersal
mode, have the potential to limit distribution in a heterogeneous landscape.
 
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
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Fig. 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.
Fig. 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.
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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.
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.
  
P 
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
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Fig. 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.
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.
Extinction was observed in the connected landscape
at rates of movement ≤ 1 m year−1 (Fig. 4b). In slowmoving 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.
 : 
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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
Fig. 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.
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%).
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.
Diagonal movement increased the likelihood of survival by as much as 60% relative to contiguous movement
1032
G. R. Matlack
& J. Monde
Fig. 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.
in the unconnected landscape (Fig. 6b), stressing the
importance of local habitat structure in allowing populations to escape habitat destruction.
Discussion
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
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 geo-
graphical 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 finescale pattern to overall landscape connectivity and
habitat access (Bascompte & Sole 1996; Pearson et al.
1996; With & King 1999).
    
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
1033
Consequences of
low motility
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.
 
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 longrange 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
© 2004 British
Ecological Society,
Journal of Ecology,
92, 1025–1035
Slow dispersal can be placed in a landscape context by
allowing the habitat map to change on the same timescale 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
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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Received 5 December 2003
revision accepted 15 March 2004
Handling Editor: David Gibson