Interpretation of R Results to answer 2 Questions about landscape disturbance 600 words

Predicting the Spread of Disturbance across Heterogeneous LandscapesAuthor(s): Monica G. Turner, Robert H. Gardner, Virginia H. Dale and Robert V. O’Neill
Source: Oikos , May, 1989, Vol. 55, No. 1 (May, 1989), pp. 121-129
Published by: Wiley on behalf of Nordic Society Oikos
Stable URL: https://www.jstor.org/stable/3565881
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OIKOS 55: 121-129. Copenhagen 1989
Predicting the spread of disturbance across heterogeneous
landscapes
Monica G. Turner, Robert H. Gardner, Virginia H. Dale and Robert V. O’Neill
Turner, M. G., Gardner, R. H., Dale, V. H. and O’Neill, R. V. 1989. Predicting the
spread of disturbance across heterogeneous landscapes. – Oikos 55: 121-129.
The expected pattern of disturbance propagation across a landscape was studied by
using simple landscape models derived from percolation theory. The spread of
disturbance was simulated as a function of the proportion of the landscape occupied
by the disturbance-prone habitat and the frequency (probability of initiation) and
intensity (probability of spread) of the habitat-specific disturbance. Disturbance
effects were estimated from the proportion of habitat affected by the disturbance and
changes in landscape structure (i.e., spatial patterns). Landscape structure was measured by the number of habitat clusters, the size and shape of the largest cluster, and
the amount of edge in the landscape. Susceptible habitats that occupied less than 50%
of the landscape were sensitive to disturbance frequency but showed little response to
changes in disturbance intensity. Susceptible habitat that occupied more than 60% of
the landscape were sensitive to disturbance intensity and less sensitive to disturbance
frequency. These dominant habitats were also very easily fragmented by disturbances
of moderate intensity and low frequency. Implications of these results for the management of disturbance-prone landscapes are discussed. The propagation of disturbance in heterogeneous landscapes depends on the structure of the landscape as well as
the disturbance intensity and frequency.
M. G. Turner, R. H. Gardner, V. H. Dale and R. V. O’Neill, Environmental Sciences
Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
senberg 1981, Mooney and Godron 1983, So
Pickett and White 1985, Rykiel 1985, Turner
The effects of spatial heterogeneity on ecological profew studies have been done on the relationshi
cesses at broad spatial scales are of current interest inlandscape pattern and disturbance. Landscap
ecological research (Risser et al. 1984, Wiens et al.geneity may enhance (e.g., Turner and Brat
1985, Forman and Godron 1986, Risser 1987, Sala et al. Franklin and Forman 1987) or retard (e.g., Knight
1988, Fahrig and Paloheimo 1988). The spread (i.e.,
1987) the spread of disturbance, and disturbances may
propagation) of a disturbance across a landscape is an generate new landscape patterns (e.g., Pickett and
important example of a functional characteristic that is White 1985, Remillard et al. 1987, Krummel et al.
influenced by spatial heterogeneity (e.g., Romme 1982, 1987). However, a general theory to predict the effects
Romme and Knight 1982, Turner 1987). Disturbance
of spatial heterogeneity on disturbance propagation has
can be defined as “any relatively discrete event in time not yet emerged. This paper presents a conceptual
that disrupt ecosystem, community, or population struc- framework for studying the effect of landscape pattern
ture and changes resources, substrate availability, or the on the spread of disturbance. Generalizations are then
physical environment” (Pickett and White 1985). The developed from simulation experiments based on percogeneral role of ecologial disturbances has received con- lation theory.
siderable attention (e.g., White 1979, Barret and Ro-
Introduction
Accepted 22 November 1988
? OIKOS
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OIKOS 55:1 (1989)
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P=0.4
Conceptual framework
It is useful to distinguish two types of disturbances: (
those that spread within the same cover type (e.g., th
r-i- I
spread of a species-specific parasite through a forest
and (2) those that cross ecosystem boundaries and
spread between different cover types (e.g., fire spreading from a field to a forest). Whether landscape heterogeneity enhances or retards the spread of disturbance
may depend on which of these two modes of propagation is dominant. If the disturbance is likely to propagate within a community, high landscape heterogeneity
^~~ -.
should retard the spread of the disturbance. If the disturbance is likely to move between communities, increased landscape heterogeneity should enhance the
I.
..
I
spread of disturbance. Furthermore, the rate of disturbance propagation should be directly proportional to
landscape heterogeneity for disturbances that spread
P=0.6
between communities, but inversely proportional for
disturbances that spread within the same community.
The movement of disturbances across landscapes can
be studied within the framework of percolation theory
(Stauffer 1985, Orbach 1986, Gardner et al. 1987). Percolation theoretic methods provide a means of generating and analyzing patterns of two-dimensional arrays,
which are similar to maps of landscape patterns. These
= |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
random maps can be used to generate an expected
pattern in the absence of specific processes and thereby
|~ ~ ImI~
identify landscape-dependent departures from expected
patterns. A two-dimensional percolating network within an m by m array is formed by randomly choosing the
occupation of the m2 sites with probability p. For large
arrays, pm2 sites are occupied while (1-p)m2 sites are
empty (Fig. 1). A cluster is formed by a group of occupied sites that have at least one common edge along the
P= 0.8
vertical and horizontal directions of a square lattice but
not along the diagonals. The number, size, and shape of
clusters of occupied sites change as a function of p.
Cluster characteristics change most rapidly near the critical probability, pc, which is the probability at which the
largest cluster “percolates” or connects the grid continuously from one side to the other (Pc = 0.5928 for very
large arrays). On large grids, the shape of the largest
cluster, as measured by the fractal dimension (Mandelbrot 1977, 1983), has also been shown to affected by
p. Percolation maps at finite scales (m = 50 to 400),
similar to the spatial scales common in landscape analyses, have been characterized in terms of cluster size,
fractal dimension, and edges (Gardner et al. 1987).
The simple nature and properties of percolation arrays make them particularly useful for landscape studA landscape can be characterized in terms of habitat
Fig. 1. Sample percolation maps with the probability ofies.
occursusceptible to a particular disturbance (e.g., pine
rence of disturbance-susceptible habitat, p, being 0.4,that
0.6, is
and
0.8. The arrays depicted are 20 x 20 portions of the 100
x 100susceptible to bark beetle infestations) and habforests
arrays used in this study. The dark areas are habitatsitat
suscepthat is not susceptible to the disturbance (e.g., hardtible to the disturbance, and the white regions are not suscepwood forests, grasslands). The spatial arrangement of
tible.
the disturbance-susceptible habitat can be randomly
generated at probability p on an appropriately scaled
Bti
–
3
_i
|i
P
:~~~~~ I I
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ized by frequency and intensity. Disturbance frequency,
f, is the probability that a new disturbance will be initiated in a unit of susceptible habitat at the beginning of
the simulation (e.g., the probability of lightning striking
a hectare of pine forest during a particular storm event
or time period). Disturbance intensity, i, is defined as
the probability that the disturbance, once initiated, will
spread to adjacent sites of the same habitat (e.g., the
probability of fire or a pathogen spreading to an adjacent site of susceptible forest). In the first set of simulations, disturbance frequency was set at f = 0.01 and
c.
was not varied; the actual number of discrete disturb-
ances per simulation is given by fpm2. Ten replicates
were simulated for each paired combination of disturb(a) Undisturbed Habitat
0.0
0.2
0.4
0.6
0.8
1.0
12UU
a
Disturbance Intensity
Fig. 2. Mean (n = 10) percent of susceptible habitat affected by
disturbance of different intensities in landscapes with different
initial probabilities of occurrence (p) of susceptible habitat.
0-
0
a
a
0o-
100
0
80 ‘0 –
0
0
o
0
D
percolation map, and the propagation of disturbances N50
that spread within the susceptible habitat may then be
E
studied.
z
Ecological disturbance regimes can be described by a
variety of characteristics, including spatial distribution,
frequency, return interval, rotation period, predictability, area, intensity, severity, and synergism (e.g., White
and Pickett 1985, Rykiel 1985). This study focuses on
two disturbance characteristics, intensity and frequency, as they interact with landscape pattern. We
define disturbance frequency as the probability that a
new disturbance will be initiated in a unit of susceptible
habitat during the time period represented by the simulation. Intensity is defined as the probability that the
disturbance, once initiated, will spread to adjacent sites
of the same habitat. We predict the spread of a disturbance across a landscape as a function of (1) the proportion of the landscape occupied by the disturbance-prone
cover type, (2) disturbance intensity, and (3) disturb- t)0
o
ance frequency.
.- p. S -*
60
40
0-~~~0
20
‘0
0
z
Methods
Two-dimensional landscape maps (100 x 100) were randomly generated for the disturbance-susceptible habitat
at different values of p. The probability, p, for maps this
large represents the proportion of a landscape occupied
by a susceptible habitat. The remainder of the land-
0.0
0.2
0.4
0.6
0.8
1.0
scape is considered unsuitable for propagation of the
simulated disturbance. Thus, the maps are composed of Fig. 3. Mean (n = 10) number of clusters remaining of undis10,000 cells, each of which is randomly designated as turbed habitat (a) and disturbed habitat (b) after simulating the
Disturbance Intensity
propagation of disturbances of varying intensities (i) through
landscapes with different initial probabilities of occurrence (p)
that could propagate through the habitat was characterof susceptible habitat.
suitable or unsuitable for a disturbance. A disturbance
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then randomly propagated with an intensity, i, to an
adjacent disturbance-prone cell. The process was repeated until the disturbance could not spread any farther. The disturbed landscape was then analyzed, and
(a) Undisturbed Habitat
the number, sizes and shapes of clusters of the disturbed
habitat and of the remaining undisturbed habitat were
summarized.
0
X
Results
z
Disturbance intensity
0
The proportion of the available habitat that was disturbed varied with both i and p (Fig. 2). A greater
proportion of habitat was affected at the same disturbance intensity for high values of p than for low values.
The percent of available habitat affected by a disturbance increased rapidly above the percolation threshold,
Pc, when the largest cluster could span the entire map.
When the habitat susceptible to disturbance was rare
(e.g., p = 0.4), less than 20% of the habitat was dis-
(b) Disturbed Habitat
.0
104
E
z
turbed, even when the intensity of the disturbance reac-
hed 1.0. When the susceptible habitat was common
(e.g., p = 0.8), a relatively low disturbance intensity led
to the widespread propagation of the disturbance.
The number of clusters of undisturbed habitat also
varied with p and i (Fig. 3). For cover types below the
percolation threshold (e.g., p = 0.4 and 0.5), the
amount of undisturbed habitat remained relatively high,
showing little change in the number of clusters as disturbance intensity increased (Fig. 3a). Above the percolation threshold (e.g., p > 0.6), the number of remaining clusters increased with moderate disturbance intensities and then declined (Fig. 3a). For example, for p
0
0.0
0.2
0.4
0.6
0.8
1.0
Disturbance Intensity
Fig. 4. Mean (n = 10) size of the largest remaining cluster of
undisturbed habitat (a) and disturbed habitat (b) after simulating the propagation of disturbances of varying intensities (i)
through landscapes with different initial probabilities of occurrence (p) of susceptible habitat.
c
o
ance intensity (i = 0.25, 0.4, 0.5, 0.6, 0.75, 0.9, and 1.0)cx
andp (p = 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9). In the second
U.
U
set of simulations, disturbance frequency was simulated
at three levels (f = 0.01, 0.10, and 0.50). For each
I
frequency level, ten replicates were simulated for paired
combinations of disturbance intensity (i = 0.25, 0.50,
0.75) and p (p = 0.4 and 0.8).
The number of clusters, the size and shape of the
largest cluster, and the amount of edge in the landscape
0.2
0.4
0.6
0.8
1.0
were calculated for each landscape before disturbances
began. Landscape disturbance was then simulated as
Disturbance
In
follows. Sites were randomly disturbed at a given freFig.
5.
Mean
(n
=
10
quency until exactly fpm2 disturbances were initiated. disturbed habitat
Each disturbed cell was changed to a state that was no landscapes with dif
longer vulnerable to disturbance. The disturbance was of susceptible habi
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5
Tab. 1. Mean number (n = 10) of inner and outer edges in undisturbed and disturbed habitat by p and disturbances intensity (i).
Simulated landscapes are 100 x 100 arrays.
Disturbance Undisturbed habitat Disturbed habitat
intensity (i)
Inner edge Outer edge Inner edge Outer edge
p = 0.4
0.00
176
9533
0.25
153
9491
0
0.50
151
9403
0
0.75
153
9193
6
1.00
131
8735
46
0
0
205
286
438
812
p = 0.6
0.00
5731
3998
0
0
0.25
5080
4670
0
354
0.50
4042
5500
9
650
0.75
2193
5856
421
1806
1.00
148
2175
5240
2157
p
=
0.8
0.00
5961
662
0
0
0.25
6172
713
0
558
0.50
5219
1489
202
1745
0.75
29
1970
5514
755
1.00
0
71
5992
583
=
0.9
i = 0.5 and i = 0.75.
the
peak
in
th
dominate.
Disturbances of low intensity
(i < 0.5) tend to decrease the number of inner edges in an undisturbed The number of clusters of disturbed habitat also difhabitat that is rare or moderately common (p < 0.8), fered for habitats below and above Pc (Fig. 3b). Belowbut they increase the inner edges for p > 0.8 (Tab. 1).
Pc, the number of disturbed clusters showed little
Disturbances of high intensity (i > 0.5) cause both the
change with disturbance intensity. Above Pc, low dis-inner and outer edges of undisturbed habitats to decline
turbance intensity created many clusters; the number of
for all values of p. Clusters of disturbed habitat resulting
disturbed clusters then declined as i increased (Fig. 3b).from low-intensity disturbance contain more outer
This decline was most rapid in landscapes with high edges than inner edges for all values of p. Clusters of
values of p.
disturbed habitat resulting from high-intensity disturbThe size of the largest cluster was also influenced by ance
i
respond differently in landscapes with different p
and p, with qualitative differences above and below Pc
values (Tab. 1). For p < Pc, outer edges continue to (Fig. 4a). Largest cluster size was not affected by dis-exceed inner edges, even with i = 1.0. For p > pc,
turbances of any intensity below Pc. Above Pc, the size
however, inner edges exceed outer edges.
of the largest undisturbed cluster decreased rapidly The reversal in the relative importance of inner and
when i > 0.5 (Fig. 4a). The decline was sharpest for the
outer edges (Fig. 6) at certain combinations of p and i
highest values of p. The size of the largest disturbedindicates qualitative changes in the habitat. For p < Pc, cluster increased with both i and p (Fig. 4b). The maxiouter edges exceed inner edges in both the undisturbed mum cluster size was approached asymptotically withand disturbed habitats. For p 2 pc, a qualitative change increasing disturbance intensity at high p, whereas clus-is observed. The undisturbed habitat initially has more ter size appeared to increase linearly at low values of p. inner edges, but a disturbance of moderate to high The largest disturbed cluster tended to be simple inintensity (i > 0.5) causes outer edges to dominate.
shape, as measured by the fractal dimension, when the
When this switch occurs, the habitat changes from being
disturbance-susceptible habitat was rare (Fig. 5). Thehighly connected with interior patches of other habitats
fractal dimension of the disturbed cluster also tended to to being fragmented. The disturbed habitat, in contrast,
decrease (indicating less complexity) as i increased inbegins as small isolated patches at low disturbance inthese rare habitats. In contrast, the shape of the largesttensities (i < 0.5), but the disturbed patches coalesce to cluster of disturbed habitat tended to become complexform connected patches with internal holes at higher when disturbance intensity was moderate to high (i >disturbance intensities. The disturbance intensity re0.6) and the disturbance-susceptible habitat was com-quired to effect this shift decreases as p increases.
mon (p > 0.6) (Fig. 5).
Prior to disturbance, the relative amount of outer
Disturbance frequency
edge (e.g., perimeter) and inner edge (e.g., interior
gaps) is a function of p (Gardner et al. 1987). For p Pc, inner edges influenced by disturbance frequency but varied for
OIKOS 55:1 (1989)
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Undisturbed Habitat
turbed and undisturbed habitats peak when both fre-
1. n
quency and intensity are at intermediate levels (e.g., f =
.v
0.1, i = 0.25, 0.50). The number of clusters declines asf
and i increase.
0.8-
When p = 0.4, the size of the largest undisturbed
cluster is not altered by disturbances of low frequency
but decreases with disturbances of high frequency (Fig.
9) When p = 0.8, cluster size decreases with both
intensity and frequency. The size of the largest disturbed cluster increases with disturbance frequency
when p = 0.4, but increases with disturbance intensity
when p = 0.8.
Outer > inner
0.6-
U)
a
.0
40
0.4 –
0
0.2-
0.0
.
I
5
Discussion
0.6
0.4 0.5
0.7
0.8
0.9
P
The simulation results indicate that the propagation of
disturbance and the associated effects on landscape pat-
Disturbed Habitat
1.0
luu
(a)
0.8
P=0.4
80-
-= 0.6
0
c
0
0
.2 0.4
m
*_
0
—
0)
0.2
0 .0 0.4
60-
* i=0.25
* i=0.50
o i=0.75
40-
20-
0.5
0.6
P
0.7
0.8
0.9
Fig. 6. The combination of disturbance intensity (i) and initial
probability of occurrence of susceptible habitat (p) at which
there is a reversal in the relative importance of inner and outer
edges in undisturbed and disturbed habitats. Reversals indicate
a qualitative change in the landscape structure.
0
luu —
(b)
– P=0.8
80-
landscapes above and below pc (Fig. 7). For example,
when p = 0.4, an increase in frequency causes a substantial increase in the proportion of habitat affected, ax
even when intensity is low (Fig. 7a). When p = 0.8,
increasing frequency increases the amount of habitat
affected only when intensity is low (Fig. 7b). If intensity
is sufficiently high (e.g., i = 0.75), more than 90% of
the habitat can be affected by disturbance of very low
frequency.
0 –
C
1-< 0 0 0. 40 - 20 - The number of clusters of both disturbed and undis- turbed habitats is influenced more by disturbance fre0quency than by disturbance intensity forp < pc (Fig. 8). 0.01 0.50 0.10 High disturbance frequencies result in an increase of Disturbance Frequency disturbed clusters, even when intensity is low. The numFig. 7. The percent of habitat disturbed as a fu ber of undisturbed clusters is not affected by low fredisturbance intensity and disturbance frequency for initial quency disturbances, but decreases sharply with high probabilites (p) of occurrence of susceptible habitat of p < pC frequency. For p > pc, the numbers of clusters of dis(a) and p > pc (b).
126
OIKOS 55:1 (1989)
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rare communities (e.g., cedar barrens, granite outcrops) in a landscape may therefore depend on the
number of disturbances rather than on their intensity. A
locally intense disturbance may eliminate a cluster of
habitat, but have little effect on the persistence of that
habitat in the landscape. In contrast, a large number of
disturbances of low intensity over a large region could
0
o
0
reduce or eliminate the habitat.
Habitats that are common may be easily fragmented
0
by disturbances of only low to moderate intensity. Inter-
0
mediate levels of disturbance intensity and frequency
created greater patchiness in landscapes that were
dominated by a disturbance-prone habitat (Tab. 2). The
interaction among p, i, and f may thus affect the landscape in ways that are counterintuitive. Large tracts of
forest, for example, may be fragmented by disturbances
of relatively low frequency (e.g., Franklin and Forman
1987). Structural changes associated with this fragmen-
.0
z
0
0
?
.0
z
E
x
z
z
0.0
0.2
0.4
0.6
0.8
Disturbance Intensity
Fig. 8. Number of clusters of undisturbed h
high frequency disturbances for initial pro
currence of susceptible habitat of P < Pc ( tern are qualitatively different when t of the landscape occupied by disturba habitat is above or below the percolati Both the distribution and spatial arrangement of the susceptible habitats help explain these differences. Habitats occupying less than Pc tend to be fragmented, with 0( numerous small patches and low connectivity (Gardner 0 et al. 1987). The propagation of a disturbance is constrained by this fragmented spatial pattern, and the sizes z and numbers of clusters are not substantially affected by disturbance intensity (i), the probability of spread. Habitats occupying more than Pc tend to be highly connected, forming continuous clusters (Gardner et al. 1987). Disturbance can spread through the landscape 0.0 0.2 0.4 0.6 0.8 even when frequency is relatively low. 0 x The persistence of rare habitats (p < pc) that are Disturbance Intensity susceptible to disturbance appears to depend upon disFig. 9. Size of the large turbance frequency (f) (Tab. 2). The long-term viability and high frequency di of remnant forest stands or other dispersed patches of occurrence of suscept 127 OIKOS 55:1 (1989) This content downloaded from 70.79.134.0 on Sat, 17 Sep 2022 08:46:16 UTC All use subject to https://about.jstor.org/terms Tab. 2. Summary of landscape structure in response to the spread of a disturbance. Parameter Response Susceptible Disturbance Area of habitat habitat intensity frequency affected Comments Rare Low Low 95% Initial structure of the undisturbed habitat becomes the structure of the disturbed habitat tation, such as the increased number of edges, have a "neutral model" (Caswell 1976). We have used percolation theory as a neutral model to suggest that knowlimportant implications for the susceptibility to other edge of a few parameters describing the heterogeneity disturbances (e.g., windthrow) and for the distribution of the landscape and the propagation of disturbance and abundance of species. The results of these disturbance simulations have im- may provide useful information for estimating the expected landscape effects. However, the structure of plications for the management of disturbance-prone landscapes. If a habitat type is rare, management shouldhabitats within real landscapes differs from a random distribution, and contagion between cells of the same focus on the frequency of disturbance initiation. Disturbances with low frequencies will have little impact, habitat is greater than expected at random (Gardner et al. 1987). Similarly, p, i, and f were all varied independeven at high intensities of disturbance propagation, beently in our simulations, whereas these variables are cause there is insufficient landscape connectivity (Tab. 2). Therefore, new disturbances will tend to be con-likely to be correlated in real landscapes. For example, some disturbances (e.g., fire) exhibit an inverse relatained by the landscape structure. In contrast, high fretionship between intensity and frequency, whereas anquencies of disturbance initiation can substantially thropogenic disturbances (e.g., land clearing for urbanchange landscape structure (Tab. 2). If a habitat type is common, management must consider both frequency ization; clear-cutting) tend toward both high intensitites and high frequencies. Our neutral model can be comand intensity. The effects of disturbance can be prepared to data from actual landscapes to test for the dicted at the extreme ends of the ranges of frequency importance of such relationships. Disturbance effects and intensity (Tab. 2). Disturbances of low intensity and on real landscapes might be observed at lower intensilow frequency will have little effect, whereas disturbties than in the random landscapes, because greater ances of high intensity will cause substantial changes. At connectivity is observed in actual landscapes. A comintermediate levels of intensity, however, responses can approach of modeling and empirical study could be quite complicated and more difficult to predict. bined A common habitat type can be easily fragmented andlead to a predictive theory of the spread of ecological disturbances. qualitatively changed by disturbances of low to moderate intensity and low to high frequency. Relationships between pattern and process can beAcknowledgements - Critical comments on this manuscript from D. C. West and W. M. Post were appreciated. This inferred from significant departures from an expected research was funded by the Ecological Research Division, Ofpattern generated in the absence of specific ecological fice of Health and Environmental Research, U.S. Dept of Energy, under Contract No. DE-AC05-840R21400 with Marprocess. This type of expected pattern has been termed 128 OIKOS 55:1 (1989) This content downloaded from 70.79.134.0 on Sat, 17 Sep 2022 08:46:16 UTC All use subject to https://about.jstor.org/terms tin Marietta Energy Systems, Inc., and by an Alexander Hollaender Distinguished Postdoctoral Fellowship, administered by Oak Ridge Associated Universities, to M. G. Turner. Publi- Remillard, M. M., Gruendling, G. K. and Bogucki, D. J. 1987. Disturbance by beaver (Castor canadensis Kuhl) and increased landscape heterogeneity. - In: Turner, M. G. (ed.), cation No. 3229 of the Environmental Sciences Division, Landscape heterogeneity and disturbance. Springer, New ORNL. York, pp. 103-122. Risser, P. G. 1987. Landscape ecology: state-of-the-art. - In: Turner, M. G. (ed.), Landscape heterogeneity and disturbance. Springer, New York, pp. 3-14. References - , Karr, J. R. and Forman, R. T. T. 1984. Landscape ecology: directions and approaches. - Special Publ. No. 2. Barrett, G. W. and Rosenberg, R. (eds) 1981. Stress effects on Illinois Natural History Survey, Champaign, IL. natural ecosystems. - Wiley, New York. Romme, W. H. 1982. Fire and landscape diversity in subalpine Caswell, H. 1976. Community structure: a neutral model analforests of Yellowstone National Park. - Ecol. Monogr. 52: ysis. - Ecol. Monogr. 46: 327-354. 199-221. Fahrig, L. and Paloheimo, J. 1988. Effect of spatial arrange- and Knight, D. H. 1982. Landscape diversity: the concept ment of habitat patches on local population size. - Ecology applied to Yellowstone Park. - BioScience 32: 664-670. 69: 468-475. Rykiel, E. J., Jr. 1985. Towards a definition of ecological Forman, R. T. T. and Godron, M. 1986. Landscape ecology. disturbance. - Aus. J. Ecol. 10: 361-365. Wiley, New York. Sala, 0. E., Parton, W. J., Joyce, L. A. and Lauenroth, W. K. Franklin, J. F. and Forman, R. T. T. 1987. Creating landscape 1988. Primary production of the central region of the patterns by forest cutting: ecological consequences and United States. - Ecology 69: 40-45. principles. - Landscape Ecol. 1: 5-18. Sousa, W. P. 1984. The role of disturbance in natural commuGardner, R. H., Milne, B. T., Turner, M. G. and O'Neill, R. nities. - Ann. Rev. Ecol. Syst. 15: 353-391. V. 1987. Natural models for the analysis of broad-scale Stauffer, D. 1985. Introduction to percolation theory. - Taylor landscape pattern. - Landscape Ecol. 1: 19-28. and Francis, London. Knight, D. H. 1987. Parasites, lightning, and the vegetation Turner, M. G. (ed.) 1987. Landscape heterogeneity and dismosaic in wilderness landscapes. - In: Turner, M. G. (ed.), turbance. - Springer, New York. Landscape heterogeneity and disturbance. Springer, New - and Bratton, S. P. 1987. Fire, grazing and the landscape York, pp. 59-83. heterogeneity of a Georgia barrier island. - In: Turner, M. Krummel, J. R., Gardner, R. H., Sugihara, G., O'Neill, R. V. G. (ed.), Landscape heterogeneity and disturbance. and Coleman, P. R. 1987. Landscape patterns in a disSpringer, New York, pp. 85-101. turbed environment. - Oikos 48: 321-324. White, P. S. 1979. Pattern, process, and natural disturbance in Mandelbrot, B. B. 1977. Fractals: form, chance, and dimenvegetation. - Bot. Rev. 45: 229-299. sion. - Freeman, San Francisco. - and Pickett, S. T. A. 1985. Natural disturbance and patch - 1983. The fractal geometry of nature. - Freeman, New dynamics: an introduction. - In: Pickett, S. T. A. and York. White, P. S. (eds), The ecology of natural disturbance and Mooney, H. A. and Godron, M. (eds) 1983. Disturbance and patch dynamics. Academic Press, New York, pp. 3-13. ecosystems. - Springer, New York. Orbach, R. 1986. Dynamics of fractal networks. - Science 231:Wiens, J. A., Crawford, C. S. and Gosz, J. R. 1985. Boundary dynamics: a conceptual framework for studying landscape 814-819. ecosystems. - Oikos 45: 421-427. Pickett, S. T. A. and White, P. S. (eds) 1985. The ecology of natural disturbance and patch dynamics. - Academic Press, New York. 9 OIKOS 55:1 (1989) 129 This content downloaded from 70.79.134.0 on Sat, 17 Sep 2022 08:46:16 UTC All use subject to https://about.jstor.org/terms Materials For this lab, you will need: • • • • • A laptop with R & RStudio installed The Excel file (for data entry) A printed version of figure 17.1 (black & white) A ruler (in mm) Something to write with Introduction Fall webworms (Hyphantria cunea), a generalist lepidopteran herbivore (member of the butterfly and moth group), provide an example of insects whose outbreaks interact with landscape structure. The larvae of the Hyphantria moth form silk tents over the foliage of deciduous trees, which they consume until reaching maturity. Work with similar lepidopteran herbivores has shown that many species choose locations in full sun over those in shaded environments (Louda and Rodman, 1996). Also, the severity of tent-forming caterpillar outbreaks is known to increase with forest fragmentation (Roland, 1993). In the summer and fall of 1996, central Oklahoma experienced a severe outbreak of the fall webworm. During this time Wallace et al. performed a study to determine how forest structure influenced webworm distributions on the landscape shown in the aerial photograph in Figure 17.1. The locations of webworm-infested trees are identified with white circles. Edges of the forested areas and forested openings appear as lighter and gray while forested areas are darker gray and have a more “textured” appearance. You will conduct two different spatial analyses using the data collected in that study. 1. Demarcate Axes First, use a ruler to demarcate axes for an x-y-coordinate system along the two edges of Figure 17.1. 2. Generate Coordinates Use a random numbers generator to locate a random point in the photograph: generate a random number for the x-coordinate, and then another random number for the y-coordinate. The range of numbers you select from will depend on how you draw your grid. The set.seed() function sets the starting number used to generate a sequence of random numbers – it ensures that you get the same result if you start with that same seed each time you run the same process. sample takes a sample of the specified size from the elements of x using either with or without replacement. set.seed(312) #the number you use here is arbitrary, as lon g as it's the same every time you run the code #Change the seed, which will change the random numbers you generate #Here I'm generating 15 x and y coordinates between the val ues of 0 and 20 (with replacement) #Change the values (0:20) to reflect the grid you drew x