Landscape Characterization / Forest Fragmentation / Quantifying forest fragmentation with indices / Description of specific indices
Quantifying forest fragmentation with indices
Description of specific indices
In this section we provide an introduction to some indices commonly used
to quantify landscape structure. Each index is explained in the context
of forest fragmentation and formulas are given for the more complicated
indices.
I) Composition
Proportion of Watershed as Forest (P forest).---This
is simple the total area of forest divided by the total area of the landscape
under consideration.
Matrix cover type (Mi).---The matrix cover type for watershed
i is defined as the most abundant cover type in the watershed.
II) Spatial Configuration
Contagion (Probability of adjacency, C).---Contagion
measures the degree to which cells of like and different landscape types are
clumped or evenly dispersed across the landscape. When the landscape is made
of a few large patches the probability of cells of two different landscape types
being adjacent to each other will be low and the probability of cells of the
same landscape type being next to each other will be high; i.e., the probability
of adjacency among combinations of patch types is uneven (Fig. ?). In this case
contagion would be high. In contrast, if the landscape is made up of many small
patches the probabilities of adjacent cells being of the same or different types
will be more even and contagion will be low. The index we are using is that
proposed by Li and Reynolds (1993). The index ranges from 0 when patches of
certain landscape types are clumped to 100 when the probability of patch adjacency
of all combinations of landscape types are equal. Contagion is calculated based
on the probability of two randomly selected adjacent cells belonging to landscape
type i and j using the following formula:
where Pi is the proportion of the landscape occupied by landscape
type i, gik
is the total number of times a cell of landscape type i is next
to a cell of landscape type k, and m is the number of landscape
types found in the landscape.
Total Number of Patchs (N), Mean Patch Size (  )
and Area Weighted Average Patch Size (
).-Total number of patches and average patch size are simply the total number
of forest patches and their average size within a watershed. Average patch size
is sensitive to the number of small patches in the landscape. Weighted average
patch size is not as sensitive to small patches and is calculated as,
where Sk
is the size of the kth patch.
Connectivity (relative patch size, RSi).-A simple index of connectivity
can be calculated as the relationship between the largest size forest patch
and total area of forest cover type. The formula for connectivity is:
where LC forest is the size of the largest forest patch
and A forest is the total area of forest in the watershed.
Average Proximity of Patches (  ).-Although
remaining forest areas may not be joined as one or a few large patches, movement
of animals and seeds among patches will be greater if the remaining forest patches
are in close proximity to one another. An index of the isolation of a forest
patch from other forest patches is given by the proximity index, which is calculated
for the ith patch as
where Sk
is the area of forest patch k within a specified buffer width,
and nk is the distance from
patch i to patch k. The average proximity index
for a watershed,
provides a measure of the overall isolation of patches within
the watershed.
Average Fractal Dimension (
).-The fractal dimension of a patch is a measure of patch shape complexity
and is calculated as
where Ai and Pi
are the area and parameter of the ith patch, respectively.
The average fractal dimension,
is a measure of the general shape complexity of all patches within
a landscape.
| 
