Appendix A
Description of Notation Used in Formulae and Metrics

Description
Subscripts of variables
i, j individual element (point, quadrat, line, or patch) or individual measurement
j, k class of similar elements (species or patch types)
a value of the Hill series
x number of points
v condition of a transition process
General symbols
α, β, γ parameters or coefficients of equations
x, y variables
n number of landscape elements, individuals, or measurements considered in the analysis
t time
m number of classes (patch types) in the landscape
S number of species in the area considered
Xi, Yi Cartesian coordinates of point i
di distance from i to its nearest neighbor
dij distance between i and j
A area
L length of a line or of a patch
P perimeter of a patch
p probability of a certain event
r radius of a circle
pj proportion of class j
pjk proportion of class j in the first group in class k in the second group
Population statistics
N total population size
Nj size of population of species j
Njk size of population of species j in habitat k
N.k size of population of all species in habitat k
K carrying capacity
T e time for local extinction
ε per capita birth rate
μ per capita mortality rate
σ colonization rate
ϕ extinction rate
p eq proportion of equilibrium
General statistics
MEAN average value of the variable in the population observed MEAN = ∑xi/n
VARIANCE variance of the population observed VARIANCE = ∑(xi – MEAN)2/n
SE standard error
E(x) expected value of variable x
z statistic of the normal distribution
χ 2 chi‐square statistic
Metrics Application context Related variables
Line/perimeter metrics
li length of line i Line/Perimeter
Ljk total length of edge lines between classes j and k Class TLA total length of auxiliary lines
TL total length of lines (as edgelines) in the landscape Landscape
D fractal dimension Line/Perimeter/Class/Landscape s size of a ruler or the side of a quadrat used to measure a line, or the size of segments used in auxiliary lines to define crossings with existing lines
Area metrics
ai area of patch i Patch
Aj total area of class j in the landscape Aj = ∑ aij Class aij area of patch i of class j
MPA mean patch area Landscape ACV coefficient of variation of patch areas
TA total area of the landscape Landscape A′ area in different measurement units
Density
λ density or number of elements (points) per unit area Landscape
λ l line density (total length of lines per unit area) Landscape
λ p patch density Landscape
NP number of patches Landscape
Shape metrics
LWRATIO length to width ratio of a patch Patch
SHAPE shape index of a patch Patch P c perimeter of a circle with area A
SHAPE2 a second shape index of a patch Patch
EDGE the area of the patch within a certain distance from its perimeter Patch
CORE the area of the interior of the patch at more than a certain distance from its perimeter Patch
CAI core area index Patch
MSI mean shape index Class/Landscape
AWMSI area weighted mean shape index Class/Landscape
MEDGE mean edge area Class/Landscape EDGECV coefficient of variation of edge areas
MCORE mean core area Class/Landscape CORECV coefficient of variation of core areas
MCAI mean core area index Class/Landscape
IEDGERATIO interior (core) to edge ratio Landscape
LSHAPE landscape shape index Landscape
Pattern metrics
PATTERN1 index of the spatial pattern of distribution of points Class nx number of quadrats with x points
PATTERN2 index of the spatial pattern of distribution of lines Class n′x expected number of quadrats with x points with a random distribution
PATTERN3 index of the spatial pattern of distribution of patches Class CROSS number of crossings between lines and auxiliary lines
VMR variance to mean ratio of the distribution of landscape elements Class L(r) radius of an equivalent circle
f(r) metric of point pattern for the Ripley’s K analysis Class Q number of quadrats
qjj proportion of like adjacencies for class j Class xi number of points in quadrat i
CONTAGj contagion index for class j Class a area of quadrat
EMD expected mean nearest neighbor distance between elements
OMD observed mean nearest neighbor distance between elements
ENR expected mean number of points within a circle or radius r
ONR observed mean number of points within a circle of radius r
PLR percolation from left to right of the landscape map
PTB percolation from top to bottom of the landscape map
p c critical proportion threshold for percolation
R probability of finding at least one occupied cell after k moves
R c critical probability threshold for finding at least one occupied cell after k moves
Proximity
PROX1 proximity index Patch Iij interaction between elements i and j based on a gravity model
PROX2 proximity index based on a gravity model Patch G proportionality gravity coefficient
MPROX1 mean proximity index Class k constant or parameter
MPROX2 mean proximity index based on a gravity model Class D m distance to mainland
Connectivity
ONL observed number of links in the network Network MNL maximum number of links in a network
V number of vertices (nodes) in a network Network
ICON index of connectivity Network
HI the Harary index of landscape connectivity Network
IIC integral index of connectivity of the landscape Network MAX maximum value of the landscape attribute of interest (e.g., total area of the landscape or total area of a certain patch type)
dIIC connectivity value of the patch, relative difference of connectivity after removal of the patch Patch IICafter integral index of the connectivity of the landscape after removal of a patch
General diversity
SH the original Shannon index Species, landscapes
SI the original Simpson index Species, landscapes
BP the Berger‐Parker index Species, landscapes
Ha “diversity numbers” of the Hill series (equivalent number of classes) Species, landscapes
Ea evenness measures related to the values of the Hill series Species, landscapes
Species diversity
pj proportion of individuals of species j in the total number of individuals of all species Species
SDHk species diversity of habitat k Class
z slope of the log–log species–area plot Class
ASDH average species diversity of a habitat (average for all habitats) Landscape
SDL species diversity of a landscape Landscape
Landscape diversity
pj proportion of class j in the landscape Class
HDL habitat diversity of a landscape Landscape
WHDL weighted habitat diversity of the landscape Landscape wk weight or value of habitat k
Habitat use and selection
HUDSj habitat use diversity of species j Species ukj proportion of habitat k in the distribution of species j
GHUD global habitat use diversity (for all species) Species
AHUD average habitat use diversity of a species (average for all species) Species
SRk selection ratio of habitat k Class
IEk index of electivity of habitat k Class
Landscape configuration
ADL diversity of adjacencies in the landscape Landscape adjk proportion of adjacencies between patch types j and k
AEL adjacency evenness of the landscape Landscape
IP proportion of interior (like) adjacencies Landscape
EP proportion of exterior (edge) adjacencies Landscape
IEDI interior/edge diversity index Landscape
IDL diversity of interior (like) adjacencies in the landscape Landscape
EDL diversity of exterior (edge) adjacencies in the landscape Landscape
EEL edge evenness of the landscape Landscape
EDCON edge contrast index for the landscape Landscape CONjk contrast between patch types j and k (weight)
IJI interspersion and juxtaposition index (a measure of edge evenness) Landscape
Landscape dynamics
V(t) vector of landscape composition at time t Landscape pj(t) proportion of class j in time t
AT absolute transition matrix Landscape atjk elements of the absolute transition matrix indicating the area (or number of cells) that changed from state j into state k
RP relative proportion matrix Landscape rpjk relative proportion of the area of the landscape that was in class j and changed to class k
M relative transition matrix Landscape mjk probability that a cell (or patch) in class j changes to class k
EQ equilibrium vector representing the composition of the equilibrium landscape Landscape eqj proportion of class j in the equilibrium landscape
CI coefficient of inertia (or agreement) between two maps Landscape
CA coefficient of agreement (or inertia) between two maps (Cohen’s kappa) Landscape t d disturbance interval (time between two consecutive disturbances)
Landscape dynamics
TDL transition diversity of the landscape Landscape t r recovery time (time required for recovery after disturbance)
ICT index of complexity of temporal changes (evenness of transitions) Landscape d probability that a disturbance event occurs changing from mature to initial (seral) stages of the succession
DSI disturbance/stability index Landscape dj disturbance probability for class j
e probability that a cell (or patch) changes state with ecological succession to more mature stages
ej probability that a cell (or patch) in class j changes for the next state with ecological succession
M′ transpose of the relative transition matrix
RP′ relative proportion matrix of two random maps with given compositions
rp′jk elements of the relative proportion matrix of two random maps showing the relative proportional changes between classes j and k
CI′ coefficient of inertia between two random maps with given compositions
wv weight (proportion) of the condition v in the transition process
mjkv probability that, under condition v, a cell (or patch) in class j changes to class k
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