Population fragmentation and extinction in the Iberian lynx
Alejandro Rodrıguez*, Miguel Delibes
Department of Applied Biology, Estación Biológica de Doñana, CSIC, Avda. Marı´a Luisa s/n, 41013 Seville, Spain
Abstract
We studied the relationship between extinction frequencies of Iberian lynx subpopulations (Lynx pardinus) and their size and
isolation during a 35-year period of strong geographic range contraction. At the end of this period there were fewer fragmentation
events, fewer lynx populations of small size, and less isolation between them, than in simulated geographic ranges derived from a
random distribution of local extinctions. Only small populations occupying < 500 km2 went extinct. Local extinction in large, selfsustainable populations probably resulted from the sole action of deterministic factors, e.g. widespread prey decline. As compared
with large populations, small ones experienced increased contraction per unit occupied area, which may reflect demographic
unstability. The consistent effect of isolation on extinction suggests that such unstability was often prompted by reduced immigration and the subsequent disruption of metapopulation equilibrium. Several practical recommendations could be derived. Provided
that habitat quality was adequate, a lynx population should avoid extinction within 35 years if it occupied an area of at least 500
km2. The persistence of small populations will also be enhanced by minimizing the distances to neighbouring populations within 30
km, and by maximizing the area occupied by these neighbours. Therefore, habitat management, or any other restoration action,
directed to expand the area occupied by a small lynx population should be best located at points of its boundaries oriented towards
other existing nearby populations.
.
Keywords: Extinction; Fragmentation; Geographic range contraction; Lynx pardinus; Metapopulation dynamics
1. Introduction
Fragmented populations, as opposed to continuous
distributions, often occur naturally reflecting the heterogeneity in the distribution of resources. For instance,
population fluctuationsthat track temporal variability
in environmental conditionscause continuous contraction or expansion of the geographic range boundaries
(Brown and Lomolino, 1998), which may result in fragmented distributions at these fringe areas (Curnutt et
al., 1996; Mehlman, 1997). Nowadays, however, population fragmentation in more central partsof the geographic range is usually the consequence of long-lasting
declines, triggered by habitat loss or other deterministic
factorsrelated to human activity (Caughley, 1994).
Metapopulation theory predictsthat, if separation
between discrete populations is within the species’ dispersal distances, larger population size and higher
immigration rates will increase population persistence
(Hanski, 1999). Conversely, if a species with a fragmented distribution suffers further range contraction,
* Corresponding author. Fax: +34-954-621125.
E-mail address: alrodri@ebd.csic.es (A. Rodrıguez).
we expect that vulnerable small and/or isolated populations will go extinct first. There is, therefore, conservation interest in determining the size and proximity of
populationsin order to minimize their probability of
extinction (Bright et al., 1994; Rodrıguez and Andren,
1999). Thisinformation may be used to decide where
habitat management will best improve population
persistence.
There are many field studies either inferring or
demonstrating the relevance of population size and
migration (or itsabsence) between populations to
explain patterns of fragmented distributions. Case
studies often refer to small species with high potential
for turnover (e.g. Peltonen and Hanski, 1991; Kuussaari
et al., 1996; Driscoll, 1997). There are fewer field studies
on larger, long-lived species (e.g. Berger, 1990; Newmark, 1995) for which the extinction of isolated populationsmight be delayed, for example when adults
survive but no longer reproduce. Large species may need
longer observation periods to show metapopulation
equilibrium, which dependson the rescue (or reinforcement) of extinct (or weak) populationsby immigrants.
Recently we have reconstructed the contraction of
geographic range in the Iberian lynx (Lynx pardinus)
during a 35-year period. Lynx distributional patterns
and the contraction process can be described by four
main features(Rodrıguez and Delibes, 2002). First, lynx
distribution was already discontinuous in 1950. A large
central or ‘‘mainland’’ population was surrounded by
smaller satellite or ‘‘island’’ populations, some of which
could receive immigrantsfrom the ‘‘mainland’’ (see
Harrison, 1994). Second, highly vulnerable small populationswere present in 1950 and new oneswere generated through fragmentation later on. Thisallowed usto
measure extinction frequencies in populations of different age and degree of isolation. Third, range contraction
was steady and successful colonization of previously
extinct populationsdid not occur during the study period. Finally, the contraction had a similar impact on
both the central and satellite populations across the
whole range. Rodrıguez and Delibes(2002) have proposed that this contraction was initially precipitated by
myxomatosis causing a widespread and persistent
reduction in rabbits(Oryctolagus cuniculus), which were
the main lynx prey.
The original aim behind thiswork was to develop
criteria to decide where conservation measures should
be best allocated in order to maximize the persistence of
lynx populations. We first consider if extinctions were
spatially correlated to assess whether they were only
caused by deterministic factors operating in particular
regions(Harrison and Quinn, 1989). Second, we compare the geometry of populationsat the end of the 35year contraction with that of virtual populationsresulting from a simulated random distribution of extinctions
across the lynx range. Third, we examine whether
extinction frequenciesdecreased with increasing population size and immigration, and set the population size
above which extinction risk approaches zero. A similar
threshold for immigration will depend on the method
employed to estimate isolation. Therefore, we finally
evaluate how well can extinction ratesbe predicted by
different estimates of isolation. In particular we investigate the relative effect on extinction of three potential
determinantsof immigration, namely number, size, and
distance of neighbouring populations.
larger than the maximum foraging movementsof settled
adults(Ferreraset al., 1997). Therefore, lynx presence
within a cell is unlikely to be sensitive to changes in the
occupancy of individual breeding territories, whereas
lynx absence will indicate that the population (or a part
of it) hasbecome extinct. Consequently, a ‘local population’ refersto each single occupied cell in the grid.
Note that thisdefinition only agreeswith the usual
meaning in the metapopulation literature (discrete subpopulation connected with othersby migration) in the
particular case of single cell populations. Thus, ‘local
extinction’ meansthe loss of a local population during a
given period, while ‘population extinction’ impliesthe
local extinction of all cellsmaking up a population.
‘Area loss’ denotes the number of local extinctions in a
2. Methods
2.1. Distribution maps
The study was based on the eight distribution maps of
lynx at 5-year intervalsfrom 1950 to 1985 reconstructed
by Rodrıguez and Delibes(2002), and plotted on a 10km UTM projection grid (Fig. 1). Here we define a
‘population’ asa continuum of occupied adjacent cells
connected either by sides or corners. The area within
each cell allowsup to 13 lynx breeding territories, and
the distance between populations (510 km) ismuch
Fig. 1. Sketch of the Iberian lynx distribution at the first and last
stages of a 35-year period of geographic range contraction, plotted on
a 10-km grid. Modified from Rodrıguez and Delibes(2002).
specified population or group of populations. ‘Range
loss’ is the number of local extinctions in the whole
geographic range. ‘Fragmentation’ refers to the fission
of a population caused by area loss. When we observed
this ‘event’, by comparing maps, we assigned the identity of the original population to the largest resulting
fragment and new identities were assigned to the others.
We call ‘short-term extinction rate’ the fraction of extinct
populationsbetween two consecutive mapsat 5-year
intervals. ‘Long-term extinction rates’ were calculated
between the first and last distribution maps (Fig. 1).
2.2. Spatial attributes of populations
Large isolated populations tend to persist longer than
small ones (Pimm et al., 1988) in a more than linear
relationship with the area they occupy (Gaston et al.,
2000). Nevertheless, we opted for modelling a linear
relationship between distribution and density. Population size (variable SIZE) was set equal to the number of
occupied cells, and average density was assumed to be
similar across populations. For each population, we
also recorded the number of neighbouring populations
(NEIG), defined as those having at least one cell within
three grid unitsaway. Thisdistance is30 km, the maximum natal dispersal distance recorded for the Iberian
lynx (Ferreras, 1994). Finally, we measured the distances(DIST, given in grid units) to each neighbouring
population, defined asthe length of the line connecting
the centresof the closest cellsof the focal population
and itsneighbour.
Immigration rates have been implicitly (Whitcomb et al.,
1981; Buechner, 1987) or explicitly (Hanski et al., 1994)
modelled by different functions of distance to neighbouring populations. We estimated isolation in three ways:
1. asthe number of neighbouring populations,
NEIG, under the hypothesis that all neighbours
contribute equally to reduce isolation regardless
of their size and distance.
2. asthe distance to the nearest neighbour, NEAR.
Using this variable we assume that immigration
ratesdecrease
geometrically with distance
(Waser, 1985; Buechner, 1987), i.e. the nearest
neighbour contributesmost immigrantsregardless of its size. A geometric distribution with
parameter P=0.071 describes adequately the
distribution of lynx maximum dispersal distances
(km) recorded in the field (Ferreras, 1994, p.
111). For distances within 30 km, the probability
of dispersal beyond a given distance predicted by
the inverse of this geometric distribution can be
approached by an exponential distribution.
Thus, we used exp(NEAR) to estimate immigration from the nearest neighbour.
3. asthe weighted distance index ISOL,
ISOL ¼
k
X
wi eDi
i¼1
St
where k=NEIG, D=DIST, and St isthe sum of all the
neighbours’ sizes. This formula for isolation assumes
that (1) all neighbourscontribute immigrants, (2) the
contribution of each neighbour decreases geometrically
with distance (estimated again by an exponential function), and increases linearly with neighbour size, (3)
immigrant contribution isadditive, and (4) the effect of
distance is weighted (w) by neighbour size, where
wi=SIZEi/St. Thisway of modelling isolation is conceptually similar to that used by Hanski (1994, 1997).
2.3. Analyses
We represented lynx distribution and measured
population attributes with a GIS (Idrisi32; Eastman,
1999). We simulated the lynx distribution in 1985 by
randomly removing 183 cellsfrom the 1950 map, i.e. a
number of cellsequal to the overall long-term range loss
(Rodrıguez and Delibes, 2002). By comparing real and
simulated maps we examined how likely it was to obtain
the observed population attributes if the lynx range had
contracted at random places. The spatial attributes
measured were number, size, shape, and isolation of
populations, aswell asthe number of fragmentation
events. Shape was expressed as the compactness ratio,
C=(A/Ac)0.5, where A isthe number of cellsoccupied
by a population, and Ac isthe area of a circle having the
same population perimeter. For each population, isolation wasmeasured on an area of N cellswhich contained the focal population plusthree grid unitsaround
it, by using the indices ISOL and patch cohesion,
"
#
1
SP
1
;
1 pffiffiffiffi
PC ¼ 1
- pffiffiffiffi
S P A
N
where, for each population, A isthe number of cells
occupied and P isitsperimeter in cell sides(Schumaker,
1996).
3. Results
Out of 32 populationsthat were present in 1950, 17
had disappeared 35 years later, which gives a long-term
population extinction rate of 0.53 during the study period (mean annual rate=0.015; Fig. 2). The ratesat
which the 32 populationspresent in the initial map went
extinct in successive 5-year periods were < 0.07 during
the first 20 years (mean annual rate=0.005) and > 0.07
during the last 15 years (mean annual rate=0.032;
Fig. 2). A significant increase in extinctions took place
between the periods1970–1974 (mean annual
rate=0.006) and 1975–1979 (mean annual rate=0.042;
G=4.64, df=1, P=0.031; Fig. 2).
Overall we observed 21 extinction events. Most of
them occurred in the periods1970–1974 (six) and 1980–
1984 (eight). Since extinction ratesdid not differ
between these two periods (Fig. 2), we used the 1970
and 1980 mapsto analyse the differencesbetween attributes of extinct and surviving populations in the short
term (see below). Pooling populations of both maps did
not result in pseudoreplication because range contraction between 1970 and 1980 was so intense (Rodrıguez
and Delibes, 2002) that only one out of 59 populations
kept the same values of size and isolation over that
period.
3.1. Spatial correlation of extinctions
Only populationswith 43 cellswent extinct in any of
the 5-year periods (see below). Thus, it seems that these
small populations were especially vulnerable. If adverse
environmental factorshad operated over one region,
most or all vulnerable populations in the region would
have gone extinct, and extinctionswould aggregate.
Hence, the average distances between extinct populations would have been shorter than the distances
between these extinctions and extant vulnerable populations outside the affected region. However, the distance between extinctionsthat took place in the same 5year period waslarge ( > 100 km for 88% of pairs;
Table 1). Moreover, for any focal extinction, up to 15
extant vulnerable populationswere counted within the
distance to the nearest contemporary extinction (V in
Table 1), while none wasexpected to occur that close.
For each 5-year period, the mean distance between
extinctionswaseither similar to, or higher than, the
mean distance between pairs of vulnerable populations
randomly chosen (Table 1). We conclude that there
were no signs of spatially correlated extinctions.
3.2. Geometry of populations
At the end of the 35-year period, the geometric attributesof lynx populationsdiffered in many waysfrom
those of populations resulting from a simulated random
distribution of local extinctions (Table 2). The number
of populationsin 1985 wasmuch lower than expected.
Remarkably, 47% of the observed range in 1985 was
contained in small populations of 2–5 cells, while their
expected percentage was34%. The contribution of
populations in other size classes was significantly lower
than expected (Table 2). There were also fewer fragmentation eventsthan expected. Perimeter length of
populationsin 1950 explained 87% of the variance in
the log transformed number of fragments produced
after 35 years(multiple regression, F1,9=60.4, P
< 0.001). Excluding the influent central population,
which had a very convoluted edge, their compactness
ratio explained 73% of thisvariance (F1,8=22.2,
P=0.002). This showsthat populationswith complex
shapes split up into more fragments than relatively
compact populations. The compactness ratio of popu-
Fig. 2. Cumulative extinction rate of the 32 lynx populations present in the 1950 map (line). Short-term extinction rates (circles) represent the ratio
between the number of populations present in 1950 that disappeared (bars) and the number of extant populations five years before (n).
lationsin 1985 washigher than in simulated populations
of the same size (Table 2). Values of isolation in the
observed map were significantly lower than in artificial
populations (Table 2), even when we assumed larger
dispersal capabilities of the Iberian lynx by redefining
neighbouring populationsasthose within five grid units.
3.3. Effects of size on population extinction
Long-term extinction rateswere 0.75, 0.63, and 0.00
for populationsof size 1, 2–5, and > 5 cells, respectively
(Fig. 3). Populationsof 45 cellshad a significantly
higher extinction risk than larger ones (G=15.26, df=1,
P < 0.001). Among the population attributesexamined,
size in 1950 had the strongest effect on long-term
extinction rates(69% of the explained variance,
Table 3). Large populations persisted but suffered
extensive area loss during the study period. The Iberian
lynx disappeared from 156 out of 369 cells allocated in
populationsof > 5 cells(42%; Rodrıguez and Delibes,
2002). The same long-term rate of area loss applied to
the 37 cellsthat belonged to populationsof 45 cellsin
1950 would have yielded 16 local extinctions, whereas
the actual number of extinct cellsin small populations
was27 (x2=14.3, df=1, P < 0.001).
In the short-term populations of > 3 cellswere never
observed to go extinct. Population size had a strong
effect on short-term extinction rates (0.38 for one-cell
populations, n=32; 0.06 for larger populations, n=36;
G=11.36, df=1, P < 0.001) and wasagain the most
Table 1
Analysis of the spatial correlation of lynx extinctionsa.
Period
Population
code
Distance to
the nearest
extinction (km)
V
Distance between observed
extinctions(km)
Distance between vulnerable
populationsb (km)
Meanc SD
Mean SD
CI 95%
1955–1959
a
b
91
91
4
2
173 154
62
283
1965–1969
c
d
272
272
15
11
152 105
77
228
1970–1974
Alle
e
f
g
h
i
j
182 81
124
240
112
112
95
95
292
58
3
3
2
4
9
3
All
k
l
m
158 17
260 104
185
335
140
140
158
6
4
4
148
322
6
11
3
2
2
0
6
3
272
290
213
240
317
230
251
274
365
235 122
133
133
89
108
32
1975–1979
1980–1984
All
n
o
p
q
r
s32
t
u
142
150
203
182
204
150
159
350
170
117
130
114
85
92
54
112
131
117
68
136
148
148
148
123
127
td
df
P
0.49
0.01
0.44
0.71
0.50
4.14
0.23
23
13
13
13
13
13
13
0.631
0.990
0.665
0.490
0.627
0.001
0.825
0.78
0.93
0.43
0.08
1.24
0.08
0.24
0.64
2.12
36
15
15
15
15
15
15
15
15
0.438
0.367
0.672
0.936
0.234
0.935
0.815
0.534
0.051
a
Left: lettersidentify each observed extinct population, n isthe number of extinctions per 5-year period. V isthe number of extant vulnerable
populations within a circle with centre in the middle cell previously occupied by the focal extinct population, and radius equal to the distance to the
nearest contemporary extinction. Under the hypothesis of correlated extinctions V should be zero. Right: test of the hypothesis that the mean distance between populationsthat went extinct was equal to the mean distance between 10 pairsof vulnerable populationsdrawn at random from the
same distribution map.
b
Vulnerable populations are those with size 43 cells.
c Sample size is n–1 distances between each focal and all other contemporary extinctions.
d t-test performed only when n > 5.
e
‘All’ refersto the n(n–1)/2 distances between all pairs of extinct populations.
important explanatory factor asrevealed by logistic
regression (Table 3).
processes after complete isolation have probably been
the stochastic component of lynx extinctions.
3.4. Effects of isolation on population extinction
4.2. Fragmentation
Long-term extinction rateswere inversely related to
the number of neighbours(Fig. 3): 0.85, 0.44, and 0.17
for populationshaving one, two, and more than two
neighbours, respectively (G=9.31, df=2, P=0.010).
When the nearest neighbour was as close as possible
(NEAR=2) the extinction rate (0.42) was significantly
lower (G=6.10, df=1, P=0.014) than when it wasfurther away (rate=0.89; Fig. 3). The best regression
model included the exponential of the distance to the
nearest neighbour (Table 3). In contrast, long-term
extinction ratesvaried lessamong the three categoriesof
the weighted distance index ISOL (G=1.52, df=2,
P=0.468; Fig. 3). Among isolation indices, only ISOL
was positively related to short-term extinction rates
after the effect of size was controlled for (Table 3).
The lynx range in 1950 wasmade up of relatively
compact populations which tended to split up less often
than predicted by a random distribution of local
extinctions. Simulated maps featured high fragmentation probably because they were generated as if all cells
went suddenly extinct. In contrast, the real 1985 map is
the product of lasting processes acting differentially on
each cell. Thus, the internal dynamics of large populations, e.g. replacement of vacant territories by surplus
transient individuals, would tend to buffer it against
local extinction from fragmentation or creation of gaps.
Table 2
Descriptive attributes of lynx distribution in 1985, and in 10 simulated
maps resulting from drawing 183 randomly distributed local extinctionsin the 1950 mapa
Simulated maps
4. Discussion
4.1. Effects of size on extinction
One-cell populationswere very unstable in the longterm and went extinct at frequencieshigher than larger
ones. The relatively high vulnerability of small populationsdue to stochastic variation in their demography is
well established (Goodman, 1987; Lande, 1993). Large
populationsare thought to be only vulnerable to deterministic disturbance. Some authors contend that high
extinction of small populations may result only from
deterministic factors as edge effects (Woodroffe and
Ginsberg, 1998). However, edge effects were unlikely to
operate during the study period, given the nature of
deterministic factors involved (e.g. myxomatosis spread
all over the lynx range). Moreover, deterministic factors
that may have been important in the early yearsdid not
affect all areascontaining small populations (hunting;
Rodrıguez and Delibes, 1990). We conclude that deterministic disturbance alone could not explain the high levels
of extinction in areasoccupied by small populations.
Although stochastic factors always operate, they only
have visible effects on small populations (Gilpin and Soule,
1986; Soule and Simberloff, 1986); their size may be a good
predictor of extinction risk irrespective of the pressure
exerted by human disturbance (see Richman et al., 1988).
What kind of stochastic factors may have played a
role? The absence of spatial correlation between extinctions suggests that large-scale environmental fluctuationswere not involved. Range contraction was so rapid
(Rodrıguez and Delibes, 1990, 2002) that the adverse
effectsof a potential genetic impoverishment probably
had no time to influence extinctions. Hence, demographic
Observed
map
Attribute
Mean
CI 95%
Lower
Upper
NUMBER
47.7
45.1
50.3
36b
SIZE
1
2–5
6–20
> 20
23.2
16.2
6.2
2.1
20.4
15.0
4.8
1.7
26.0
17.4
7.6
2.5
14b
17
3b
2
CONTRIBUTION TO TOTAL RANGE SIZE (%)
1
48
44
52
38
2–5
34
31
>5
17
15
20
SHAPEc
5
8
10
12
6 60
ISOLATION
Mean ISOL
Maximum ISOL
Mean PC
FRAGMENTATION
EVENTS
39b
47 b
14b
0.59
0.51
0.47
0.47
0.20
0.56
0.47
0.42
0.38
0.18
0.62
0.54
0.53
0.57
0.22
0.69b
0.56 b
0.56b
0.47
0.28b
1.96
15.54
0.39
1.81
11.86
0.37
2.11
19.22
0.31
1.22b
7.39b
0.47b
37.7
35.5
39.9
32b
a NUMBER of populations; SIZE, number of populations in each
size class (cells); % TOTAL RANGE contributed by populations in each
size class (cells); SHAPE, compactness ratio C for populations of different size (cells); ISOLATION, the mean and maximum of the index ISOL,
and the mean patch cohesion, for all populations in a distribution map;
FRAGMENTATION EVENTS, the total number of fragments generated.
b The observation falls outside the 95% confidence interval for the
mean of each attribute in simulated maps.
c The compactness ratio C is only shown for populations larger than
four cellsas lower sizesallow little variation in C values.
Fig. 3. Frequency distribution of extinct (shaded bars) and extant lynx populations (open bars) after 35 years as a function of their spatial attributes
in 1950. NEIG: number of neighbours. NEAR: distance to the nearest neighbour (x10 km). ISOL: index of isolation (see text for definition).
4.3. Effects of isolation on extinction
The significant effect of isolation suggests that most
small populations may have been maintained by immigration. Extinctionscould be explained by three
mechanisms leading to the disruption of metapopulation
equilibrium (Harrison, 1994): decreased population density at the source of immigrants, increased resistance of the
inter-population space to movement, and reduced chances
of immigrant settlement in the recipient area (Fig. 4).
First, dispersal can be proximately driven by population density (Hansson, 1991; Lidicker and Stenseth,
1992). Iberian lynx dispersal seems to be density-dependent for females(Ferreras, 1994; Gaona et al., 1998). A
local decrease of density may result in lower emigration
and, consequently, reduced immigration in recipient
populations(Fig. 4, case B). Indeed, the contraction of
large lynx populationshasbeen accompanied by a drop
of density inside them (Rodrıguez and Delibes, 2002).
Second, the suitability for dispersal of the habitat
between populationsmay affect the proportion of emigrantsthat reach the target (Taylor et al., 1993; Aberg
et al., 1995; Gustafson and Gardner, 1996). For the
Iberian lynx, Ferreras(2001) hasfound that the proportion of dispersers reaching a given subpopulation
waspartly determined by the quality of intervening
habitats. A reduction in quality of the matrix habitat
can reduce connectivity below a critical threshold and
Table 3
The effects of size and isolation of lynx populations on their long-term (35 year) and short-term (5 year) probability of extinctiona
Intercept
ln(SIZE)
Long-term
STEP 1
STEP 2
1.30 0.58
6.13 5.03
1.30 0.55
1.27 0.63
Short-term
STEP 1
STEP 2
0.54 0.39
1.20 0.50
1.80 0.76
1.90 0.77
a
exp(NEAR)
ISOL
0.92 0.65
Coefficients( SE) of terms in the logistic regression function are given.
0.30 0.15
G
df
P
% explained
deviance
9.00
4.57
1
1
0.003
0.033
24
35
10.90
6.34
1
1
0.001
0.012
18
29
produce absolute isolation (With et al., 1997; Fig. 4,
cases E and F).
Third, if vulnerable populationsinhabit good habitats
they can have a net positive growth and persist without
immigration (Fig. 4, cases A and E). This may explain
the persistence during 35 year of small, highly isolated
lynx populations. In contrast, populations in suboptimal
habitats (i.e. sinks; Pulliam, 1988) may have gone extinct
quickly without consistent immigration (Fig. 4).
Whereas persistence in the long-term increased with
the number of neighbours, the crucial factor was how
far apart and how large they were. The significant
influence of isolation was represented by different variablesin the long- and the short-term. The variables
NEAR and ISOL did not convey the same information,
the former expressing absolute isolation better than the
latter (Fig. 5). When the nearest neighbour was far
away, the contribution of immigration to recipient persistence may have been irrelevant. Therefore,
exp(NEAR) may indicate qualitative isolation, even
being a quantitative variable, because it describes a steep
declining probability function for immigration. Distance
to the nearest neighbour (NEAR) was shown to have an
effect in the long-term since extinction risk increases with
time after absolute isolation (Soule et al., 1988; Berger,
1990). For populations in good habitats, absolute isolation
does not imply immediate extinction (Fig. 4). Habitat
quality was probably high in most areas occupied by lynx
populationsin 1950 because myxomatosishad not entered
the Iberian peninsula then (Fenner and Ross, 1994), its
catastrophic effects were delayed a few years (Rogers et al.,
1994), and adverse changes in land uses also occurred after
1960 (Fernandez-Ales at al., 1992).
Conversely, the weighted distance index ISOL is a
relatively poor indicator of absolute isolation because
even when itsvalue ishigh it ispossible that one neighbour can be close enough to supply some immigrants
(Fig. 5). Given that there isimmigration, thisindex
probably estimates the amount of immigrants more
accurately than the distance to the nearest neighbour
NEAR (Fig. 5). ISOL may explain the quick extinction
of non-isolated sink populations that depend on a
steady supply of immigrants (Fig. 4). In fact, many vulnerable lynx populationsthat were generated during the
fragmentation crises of 1970 and 1980 probably lived in
suboptimal habitats because of prey scarcity (Rodrıguez
and Delibes, 2002). Simultaneously habitat quality in, and
emigration from, source populations may have decreased,
leading to a sudden disequilibrium (Fig. 4, case B).
5. Conservation implications
Predictionsof extinction probability based on our
regression models can help decision making in lynx
conservation. If economic resources for conservation
are expressed in terms of the number of cells where local
extinction isto be avoided, or the number of cells where
suitable conditions for lynx are aimed at recovery,
modelsdeveloped here can be used to determine the
Fig. 4. Possible mechanisms of disruption of metapopulation equilibrium. The central population undergoes contraction and local reduction of
population density. Both distance and isolation increase between the large population and populations A, C, and E. Whereas A and E persist, C
does not receive enough immigrants and goes extinct. Isolation (but not distance) increases in B and F, because of reduced emigration in the
mainland and precluded dispersal across the interposed empty area, respectively.
Fig. 5. The different meanings conveyed by the distance to the nearest neighbour (NEAR) and the weighted distance index ISOL. Open circles
represent focal populations of one cell. Capital letters denote other populations. The semicircle indicates the maximum dispersal distance for the
Iberian lynx. The values of NEAR differ for situations where isolation is almost absolute (a) and where there is some immigration (b), while the
values of ISOL are similar. Where immigration occurs (c and d), ISOL describes the expected amount of immigrants received at the focal population
more accurately than NEAR.
places where these efforts should be concentrated to
maximize persistence at the regional scale.
Despite extensive disturbance throughout the lynx
range during the study period (about 10 lynx generations, Gaona et al., 1998), only a fraction of populations
living in areas smaller than 500 km2 (i.e. five grid cells
and up to 100 adult lynx; Ferreraset al., 1997) went
extinct. These rough threshold estimates of area and
population size may be useful approximations of the
minimum reserve size needed to avoid population
extinction in 35 yearsunder low levels of adverse environmental stochasticity.
However, habitat quality wasprobably much better in
populationsoccupying up to five cellsin 1950 than it is
nowadays. Relatively high lynx densities (more than 16
adults/100 km2, but locally ashigh as90 adults/100
km2) have been associated with little disturbed protected areas(Palomareset al., 1991, 2001). Densitiesof
thismagnitude should have been common in the 1950s
throughout the lynx range, whereas estimated densities
> 8 adults/100 km2 at the end of the 1980swere only
found in 12.3% of the lynx range (Rodrıguez and
Delibes, 1992). Thus, a habitat quality condition should
be added to the minimum reserve size, so that lynx can
live at high densities in them, otherwise the minimum
area needed to avoid extinction in 35 yearswould
increase considerably.
The expected persistence of small populations can be
improved in the long-term by keeping them within 30
km of a stable population, and in the short-term by
minimizing distances to neighbours within the range 0–
30 km. Where possible this should be done by making
suitable for the lynx the major components of its habitat
(e.g. structure of scrubland, rabbit density, mortality
factors, barriers to movement) in the area interposed
between small and other nearby populations. Similarly,
area and density of neighbouring populations should be
maximized in order to favour migration towards
dependent small populations. Acting upon the same
habitat components, this can be achieved by recovering
new adjacent area to allow the natural expansion of
existing populations, and by improving the quality of
areasalready occupied, respectively.
Acknowledgements
We thank H. Andren, U. Breitenmoser, P. Ferreras,
A. Kranz, K. McKelvey, and T. Wiegand for discussing
and providing helpful commentson an earlier version of
the manuscript, G. Crema for producing some of the
illustrations, and B.N.K. Davis for editorial improvement. Thisresearch was partly funded by a Life Project,
through an agreement between the Directorate General
XI of the European Commission and the Spanish
Council of Scientific Research. During the preparation
of thispaper A.R. benefited from both a postdoctoral
grant from the ‘‘Direccion General de Investigacion
Cientıfica y Ensenanza Superior’’ and his stay at the
Grimso Wildlife Research Station, SLU, Sweden.
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