# 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

121

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

OIKOS 55:1 (1989)

122

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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

OIKOS 55:1 (1989)

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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

OIKOS

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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

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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
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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)
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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.
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9 OIKOS 55:1 (1989)
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Materials
For this lab, you will need:
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•
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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