2027
Ecology, 83(7), 2002, pp. 2027–2036
q 2002 by the Ecological Society of America
ECOLOGICAL-NICHE FACTOR ANALYSIS: HOW TO COMPUTE
HABITAT-SUITABILITY MAPS WITHOUT ABSENCE DATA?
A. H. HIRZEL,
1
J. HAUSSER,
1
D. CHESSEL,
2
AND N. PERRIN
1,3
1
Laboratory for Conservation Biology, Institute of Ecology, University of Lausanne, CH-1015 Lausanne, Switzerland
2
UMR CNRS 5023, Laboratoire de Biome´trie et Biologie Evolutive, Universite´ Lyon I, 69622 Villeurbanne Cedex, France
Abstract. We propose a multivariate approach to the study of geographic species dis-
tribution which does not require absence data. Building on Hutchinson’s concept of the
ecological niche, this factor analysis compares, in the multidimensional space of ecological
variables, the distribution of the localities where the focal species was observed to a
reference set describing the whole study area. The first factor extracted maximizes the
marginality of the focal species, defined as the ecological distance between the species
optimum and the mean habitat within the reference area. The other factors maximize the
specialization of this focal species, defined as the ratio of the ecological variance in mean
habitat to that observed for the focal species. Eigenvectors and eigenvalues are readily
interpreted and can be used to build habitat-suitability maps. This approach is recommended
in situations where absence data are not available (many data banks), unreliable (most
cryptic or rare species), or meaningless (invaders). We provide an illustration and validation
of the method for the alpine ibex, a species reintroduced in Switzerland which presumably
has not yet recolonized its entire range.
Key words: Capra ibex; ecological niche; GIS; habitat suitability; marginality; multivariate
analysis; presence–absence data; specialization; species distribution; Switzerland.
INTRODUCTION
Conservation ecology nowadays crucially relies on
multivariate, spatially explicit models in all research
areas requiring some level of ecological realism. This
includes population viability analyses (Akc¸akaya et al.
1995, Akc¸akaya and Atwood 1997, Roloff and Haufler
1997), biodiversity-loss risk assessment (Akc¸akaya and
Raphael 1998), landscape management for endangered
species (Livingston et al. 1990, Sanchez-Zapata and
Calvo 1999), ecosystem restoration (Mladenoff et al.
1995, 1997), and alien-invaders expansions (Higgins
et al. 1999). Such studies often conjugate the power of
Geographical Information Systems (GIS) with multi-
variate statistical tools to formalize the link between
the species and their habitat, in particular to quantify
the parameters of habitat-suitability models.
Most frequently used among multivariate analyses
are logistic regressions (Jongman et al. 1987, Peeters
and Gardeniers 1998, Higgins et al. 1999, Manel et al.
1999, Palma et al. 1999), Gaussian logistic regressions
(ter Braak and Looman 1987, Legendre and Legendre
1998), discriminant analyses (Legendre and Legendre
1998, Livingston et al. 1990, Manel et al. 1999), Ma-
halanobis distances (Clark et al. 1993), and artificial
neural networks (Manel et al. 1999, O
¨
zesmi and O
¨
zes-
mi 1999, Spitz and Lek 1999). All these methods share
largely similar principles:
Manuscript received 27 March 2000; revised 4 March 2001;
accepted 26 July 2001; final version received 12 November 2001.
3
Corresponding author.
E-mail: Nicolas.Perrin@ie-zea.unil.ch
1) The study area is modeled as a raster map com-
posed of N adjacent isometric cells.
2) The dependent variable is in the form of presence/
absence data of the focal species in a set of sampled
locations.
3) Independent ecogeographical variables (EGV) de-
scribe quantitatively some characteristics for each cell.
These may express topographical features (e.g., alti-
tude, slope), ecological data (e.g., frequency of forests,
nitrate concentration), or human superstructures (e.g.,
distance to the nearest town, road density).
4) A function of the EGV is then calibrated so as to
classify the cells as correctly as possible as suitable or
unsuitable for the species. The details of the function
and of its calibration depend on the analysis.
Sampling the presence/absence data is a crucial part
of the process. The sample must be unbiased to be
representative of the whole population. Absence data
in particular are often difficult to obtain accurately. A
given location may be classified in the ‘‘absence’’ set
because (1) the species could not be detected even
though it was present (McArdle 1990, Solow 1993; for
example, Ke´ry [2000] found that 34 unsuccessful visits
were needed before one can assume with 95% confi-
dence that the snake Coronella austriaca was absent
from a given site), (2) for historical reasons the species
is absent even though the habitat is suitable, or (3) the
habitat is truly unsuitable for the species. Only the last
cause is relevant for predictions, but ‘‘false absences’’
may considerably bias analyses.
Here we propose a new approach specifically de-
signed to circumvent this difficulty. Requiring only

2028 A. H. HIRZEL ET AL. Ecology, Vol. 83, No. 7
FIG. 1. The distribution of the focal species on any ecogeographical variable (black bars) may differ from that of the
whole set of cells (gray bars) with respect to its mean (m
S
± m
G
), thus allowing marginality to be defined. It may also differ
with respect to standard deviations (s
S
± s
G
), thus allowing specialization to be defined.
presence data as input, the Ecological-Niche Factor
Analysis (ENFA) computes suitability functions by
comparing the species distribution in the EGV space
with that of the whole set of cells. In the present paper,
we expose the concepts behind the ENFA, develop the
mathematical procedures required (and implemented in
the software Biomapper), and illustrate this approach
through an habitat-suitability analysis of the Alpine
ibex (Capra ibex).
MARGINALITY,SPECIALIZATION, AND THE
ECOLOGICAL NICHE
Species are expected to be nonrandomly distributed
regarding ecogeographical variables. A species with an
optimum temperature, for instance, is expected to occur
preferentially in cells lying within its optimal range.
This may be quantified by comparing the temperature
distribution of the cells in which the species was ob-
served with that of the whole set of cells. These dis-
tributions may differ with respect to their mean and
their variances (Fig. 1). The focal species may show
some marginality (expressed by the fact that the species
mean differs from the global mean) and some special-
ization (expressed by the fact that the species variance
is lower than the global variance).
Formally, we define the marginality (M) as the ab-
solute difference between global mean (m
G
) and species
mean (m
S
), divided by 1.96 standard deviations (s
G
)of
the global distribution
zm 2 m z
GS
M 5 . (1)
1.96s
G
Division by s
G
is needed to remove any bias intro-
duced by the variance of the global distribution: a cell
randomly chosen from a distribution is a priori ex-
pected to lie that much further from the mean as the
variance in distribution is large. The coefficient weight-
ing s
G
(1.96) ensures that marginality will be most
often be between zero and one. Namely, if the global
distribution is normal, the marginality of a randomly
chosen cell has only a 5% chance of exceeding unity.
A large value (close to one) means that the species
lives in a very particular habitat relative to the reference
set. Note that equation (1) is given here mainly to ex-
plain the principle of the method; the operational def-
inition of marginality implemented in our software is
provided by equation (10), which is a multivariate ex-
tension of (1).
Similarly, we define the specialization (S ) as the ratio
of the standard deviation of the global distribution (s
G
)
to that of the focal species (s
S
),
s
G
S 5 . (2)
s
S
A randomly chosen set of cells is expected to have
a specialization of one, and any value exceeding unity
indicates some form of specialization. We reemphasize
that specific values for these indexes are bound to de-
pend on the global set chosen as reference, so that a
species might appear extremely marginal or specialized
on the scale of a whole country, but much less so on
a subset of it.
Extending these statistics to a larger set of variables
directly leads to Hutchinson’s (1957) concept of the
ecological niche, defined as a hyper-volume in the mul-
tidimensional space of ecological variables within
which a species can maintain a viable population
(Hutchinson 1957, Begon et al. 1996). The concept is