adapted conservation measures are required to save the iberian lynx … · saving the iberian lynx...

Saving the Iberian lynx from extinction requires climate adaptation

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Supplementary Methods

Below is a description of coupled niche-population models1 used to integrate Iberian lynx (Lynx pardinus)

range dynamics with that of European rabbit (Oryctolagus cuniculus) population ecology and climate change, to

better understand future extinction threats to Iberian lynx and potential management interventions.

Spatial Data and Ecological Niche Modelling

Location Data

Geographically-referenced occurrence records of the Iberian lynx and European rabbit were obtained from

multiple sources, including unpublished Spanish and Portuguese governmental databases (see below). Location

data, including historical records collected throughout the second half of the 20th century, were used for fitting

ecological niche models, and to characterize the potential future distributions of Iberian lynx and European

rabbits. We did this to more closely approximate climate-physiological limits of the species thus reducing

potential biases in the characterization of the climatic niche of the species2. Such biases are bound to exist

because non-climate factors largely influenced population contraction since 1950, at least for Iberian lynx3. It

follows that ecological niche models (see below) assume that species distributions are in equilibrium with

climate, and departures from this assumption can influence modelled responses to climate change4. This

approach strengthened future forecasts of carrying capacity in our models (see below), but prevented us from

using past location records (i.e., from 1950) to retrospectively validate dynamic mechanisms of our models.

This trade-off was sensible because important spatiotemporal drivers of non-natural mortality in the latter half

of the 20th century are not available; and strong conservation efforts have dampened their influence and

relevance for the future5.

Lynx: Occurrence maps were constructed using records provided by the Subdirección General de Biodiversidad

(Spain) and Instituto da Conservação da Natureza e da Biodiversidade (Portugal). The records for Spain were

Adapted conservation measures are required tosave the Iberian lynx in a changing climate

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based primarily on 2240 presence records constructed using three primary sources of information6-8: (i)

georeferenced records from the scientific and game literature, inventories of hunting trophies, zoological

collections, and private archives; (ii) postal surveys of rangers, hunting associations, nature conservation

associations, and taxidermists, and holders of hunting rights (1310 responses8); (iii) on-ground information,

including sight and death reports from personal interviews with people who had a high probability of detecting

lynx (shepherds, hunters, farmers) (2500 interviews); inventories of physical remains (such as pelts or skulls9)

and a first-hand assessment of habitat and land-uses6,10. Positive reports obtained by postal surveys were

confirmed using on-ground information. The reliability of people interviewed in the field was assessed, and

unreliable reports (40% of total interviews) discarded8. The official maps provided by Subdirección General de

Biodiversidad included some additional records adjacent to occupied cells in the 1950 range map for Spain8.

The occurrence records for lynx in Portugal were obtained using similar approaches and criteria as for Spain11-

13. The quality of the absence records are supported, albeit indirectly, by recent extensive14 and intensive studies

(reviewed by3,5,15) that failed to find past or present lynx occurrences in localities reported as empty in the maps

by Rodríguez & Delibes6-8.

Rabbit: The occurrence records for rabbits were also the result of systematic surveys across Spain16,17 and

Portugal 18,19.Occurrence records came from different published and unpublished sources e.g., volunteer reports

by members of the Spanish Mammal Society20. In Portugal the occurrence records came from published

literature18 and government reports19.”

Spatial Data

Climate data: We identified annual rainfall and mean temperature of the hottest and coolest months (July and

January, respectively) as being likely to have the largest potential climate influence on Iberian lynx and

European rabbit abundance. These variables are often seen as controlling physiological processes limiting the

spatial distribution of species21 and have been shown to effectively discriminate between principal

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environments in the Iberian Peninsula22, and elsewhere in Europe23. The same variables were used to model the

climate suitability of rabbits in Australia with good success24.

Spatial layers describing average July and January daily temperature and annual rainfall (for the period 1961 to

1990) for the Iberian Peninsula were provided by the meteorological institutes of Spain and Portugal.

Specifically, data in Spain were collected from 2713 stations measuring rainfall and 973 stations measuring

temperature, while data from Portugal was obtained from 89 and 51 stations respectively. Interpolation of the

climate variables for the Iberian Peninsula was done using thin plate cokriging 22.

An annual time series of climate change layers for each variable was generated according to two emission

scenarios: a high CO2 concentration stabilising Reference scenario (WRE750)25 and a Policy scenario, assuming

substantive intervention (stabilization at an equivalent CO2 concentration of 450 ppm [MiniCAM LEV1])26. The

procedure consisted of two steps:

1. MAGICC/SCENGEN 5.3 (http://www.cgd.ucar.edu/cas/wigley/magicc), a coupled gas cycle/aerosol/climate

model used in the IPCC Fourth Assessment Report27, was used to generate an annual time series of future

climate anomalies (2000 – 2100) using an ensemble of seven atmosphere-ocean general circulation models

(GCMs)28. Models were chosen according to their superior skill in reproducing seasonal precipitation and

temperature across the Iberian Peninsula. Model performance was assessed following already published

methods29. The seven GCMs were: CGCM3.1 (T47), MIROC3.2 (medres), PCM, UKMO-HadCM3, ECHO-

G, IPSL-CM4, MRI-CGCM2.3.2. Model terminology follows the CMIP3/AR4 multi-model data archive

(http://www-pcmdi.llnl.gov/ipcc/about_ipcc.php). GCM skill assessment results can be quite different

depending on the variable considered, the region studied, the month or season examined, or the comparison

metric used29. However, ensemble forecasts that include greater than 5 GCMs, tend to be more robust to

GCM choice30.





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2. Climate anomalies were downscaled to an ecologically relevant spatial resolution (1km x 1km

longitude/latitude), using the “change factor” method, where the low-resolution climate signal (anomaly)

from a GCM is added directly to a high-resolution baseline observed climatology31. Bi-linear interpolation of

the GCM data (2.5 x 2.5 º longitude/latitude) to a resolution of 0.5 x 0.5º longitude/latitude was used to

reduce discontinuities in the perturbed climate at the GCM grid box boundaries29. One advantage of this

method is that, by using only GCM change data, it avoids possible errors due to biases in the GCMs baseline

(present-day) climate. Fine resolution climate projections (1km x 1km longitude/latitude) were also up-

scaled to a grid cell resolution of 10km x 10km longitude/latitude, by aggregating and then averaging across

fine resolution cell values. This was necessary because suitable baseline climate data was not available at the

coarser resolution. No data values (i.e., sea cells) were identified and excluded from the calculation.

Land cover data: The European Environmental Agency CORINE land cover map

(http://www.eea.europa.eu/publications/COR0-landcover) was accessed for the Iberian Peninsula at a grid

resolution of 250 x 250m latitude/longitude (Supplementary Fig. S4). We used our habitat selection models32

and behaviour data33 to identify CORINE land cover types appropriate for breeding habitat for Iberian lynx and

used this information to generate a binary map of Iberian lynx breeding habitat (see Table S2). We also ranked

CORINE land cover types into 4 categories according to how they influence Iberian lynx dispersal (more details

are provided below). This information was used to construct a categorical map describing the influence of land

cover type on Iberian lynx dispersal. Maps for lynx were up-scaled to a grid cell resolution of 1km x 1km

longitude/latitude by taking the fine scale cell value with the largest proportional presence in a coarse resolution

cell.

We identified CORINE land cover types that are suitable or unsuitable for rabbits; and land cover types that are

highly productive or unproductive for rabbits (see Table S3). This information was used to generate binary

maps of suitable habitat for rabbit occupancy and to identify highly productive habitats. Maps for rabbits were





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up-scaled to a grid cell resolution of 10km x 10km latitude/longitude by aggregating fine resolution points and

averaging across these values. This process produced maps that: (i) provide an index of the proportion of the

cell that is habitable for rabbits; and (ii) the proportion of the cell that not only can be occupied, but is

exceptional rabbit habitat. The reason for a adopting a somewhat coarser spatial resolution for rabbit model

inputs is because of current computational limitations on the number of populations that can be modelled using

metapopulation approaches such as coupled niche-population models (< 7000 discrete populations)24.

Ecological Niche Modelling

Ecological niche models (ENM)34 were used to characterize climatic suitability of Iberian grid cells for the

Iberian lynx and for the European rabbit. The rationale is that ENM-modelled suitability provides a surrogate

for species’ carrying capacity, capturing more than the physiological constraints that define presence/absence at

a given location35, which can then be used in demographic models1. Because projections from alternative ENMs

can vary significantly under climate change36, we computed different models and obtained a consensus among

them37,38.

The Bio-ensembles software39 was used to generate ensembles of ENMs for Iberian lynx and rabbits

(separately) using occurrence records since 1950 (see above). The ensemble included projections with seven

methods: bioclimatic prediction and modelling system (BIOCLIM), Mahalanobis distance (MAH), Euclidean

distance (EUC), Generalized Linear Models (GLM), Random Forest (RF), Maximum Entropy (MaxEnt), and

Genetic Algorithm for Rule-set Prediction (GARP). BIOCLIM, MAH, and EUC are fitted only with the

occurrence records of the species, while MaxEnt and GARP also use the background information. GLM and RF

use the background, assuming it represents true absence of the species. By varying the assumptions regarding

absence data in our models we aimed at characterizing the variability in projections accrued from such

assumption. Cross-validation was used to assess the internal consistency of the model predictions40. To do this

we calibrated models for the climate baseline (1961-1990) using an 80% random sample of the initial data and





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evaluated it against the remaining 20% data. The true skill statistic (TSS)41 was used as the fit statistic and was

calculated for each model based on the confusion matrix expressing matches and mismatches of observed and

predicted occurrences in the validation data set. This matrix was computed after using receiver operation

characteristic (ROC) curves to convert continuous predictions into presence-absence, by applying a threshold

that maximizes AUC36. Ecological niche models were then used to forecast annual time-step probability of

occurrence (2000-2100) according to two emission scenarios (see above).

Demographic Model for the European Rabbit

The demographic model of European rabbits (Oryctolagus cuniculus) was implemented in RAMAS Metapop42.

The model was a cellular/lattice type model, consisting of ~ 7,000 cells (10km x 10km longitude/latitude grid

cell resolution). Each grid cell was modelled with a scalar type stochastic model (see “Rabbit demographic

structure”), which is a simple population projection that has three parameters, the finite rate of population

increase “R”, its variance and carrying capacity43. The carrying capacity and initial abundance of rabbits in each

cell was based on the spatial distribution of habitat suitability (see “Rabbit spatial structure”).

Rabbit Demographic Structure

Scalar models are based on time-series data of population sizes and do not include details of population age or

stage structure43. We used a scalar type approach to model rabbit demographics because the movement between

stage classes (kitten, adult) is rapid (being less than six months) and mortality is high. Thus at an annual time

step, stage classes are largely irrelevant. Furthermore, comprehensive estimates of rabbit vital rates and

associated variances based on capture-mark-recapture type approaches are rare, at least in their native range 44.

Density dependence was modelled using the Ricker equation (“scramble competition” function in RAMAS),

whereby as population abundance in a cell increases, the amount of resources per individual decreases. This

type of density dependence requires estimates of carrying capacity (see “Rabbit spatial structure”) and

maximum rate of population growth in the absence of density effects (Rmax). Time series data for O. cuniculus





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was extracted from the Global Population Dynamics Database

(http://www3.imperial.ac.uk/cpb/research/patternsandprocesses/gpdd) and used to calculate Rmax. There were

seven suitable time series available, ranging from 12 to 71 years in length (the median length was 37 years).

The time series abundance data was centred on the mid-19th century (up until 1984). By calculating the

weighted average intercept of Ricker models fitted to each time series we estimated Rmax to be 1.5, which is

similar to that calculated for O. cuniculus for semi-arid landscapes elsewhere45. A standard deviation value of

0.95 around the intrinsic rate of population growth was estimated from the abundance time series data and used

to model population fluctuations driven by environmental stochasticity, including that caused by the viral

disease myxomatosis. Myxomatosis was well established in most populations used in the time series analysis.

In contrast, the time series data predate the emergence and establishment of rabbit haemorrhagic disease (RHD)

in Europe in the 1990’s 46.

Myxomatosis and RHD strongly influence rabbit survival and recruitment44,47. The impact of myxomatosis on

rabbit abundance was modelled implicitly (through environmental stochasticity), while the impact of RHD was

modelled explicitly. The influence of RHD on rabbit mortality was greatest shortly after its arrival on the

Iberian Peninsula, causing an estimated 60% reduction in rabbit population abundance in some areas of Iberia48,

and an additional 22% annual adult mortality49. However, the severity of the RHD impact on rabbit abundance

declines with time following an initial outbreak48,50 and its impact on mortality probably conditions (dampens)

other sources of mortality51. Outbreaks of myxomatosis and RHD tend not to occur simultaneously in the same

year44, allowing its direct influence on survival to be estimated. We model RHD as a catastrophic event that

occurs every two to three years44 causing a 15-25% reduction in abundance49. The assumption here is that when

an outbreak occurs there are a large number of susceptible adults (sero-negative) in the population which results

in additional mortality. Each rabbit population (populated grid cell) was randomly attributed a frequency of

RHD occurrence and severity of RHD impact for each model iteration from within the likely bounds described





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above. We also assume that the timing and frequency of RHD outbreaks is unaffected by global warming,

because there is insufficient data to suggest otherwise.

A local threshold of 5,000 was applied to each cell (equivalent to 50 rabbits per 1 km2). If abundance falls

below this value, the model treated cell abundance as equal to zero. The abundance threshold was based on

observed minimum rabbit densities52 and, in many ways, simulates the impact of an Allee effect, whereby,

below a critical density, the population quickly spirals to extinction53.

Rabbit Spatial Structure

The HS function: Habitat suitability of each lattice cell was defined as the product of 2 components:

1. Climate (output from the ecological niche model) scaled between 0 and 1.

2. Land Cover (scaled between 0 and 1) calculated as the product of the proportion of the cell that is

habitable multiplied by the proportion of the cell that is highly suitable (based on the CORINE criteria;

see Table S3), with a threshold applied (thr). The threshold was developed iteratively, so that the spatial

coverage of occupiable cells maximised the ratio between sensitivity and specificity using field surveys

(see above) and the true skill score metric54. We have used this approach elsewhere55.

Habitat suitability (HS) in the model was defined as

Eq. 1 HS = [Climate]*thr([Land Cover], 0.2)

Carrying capacity: Carrying capacity was calculated iteratively such that: (i) the maximum recorded annual

rabbit abundance per grid-cell did not exceed field based estimates56; (ii) grid-cell abundances (and their spatial

variation) closely approximated on-ground field surveys57 and (iii) estimates of total rabbit abundance for the

entire Iberian Peninsula and sub-regions were sensible. Previously we used this sort of iterative approach to

model the carrying capacity of another lagomorph, Lepus timidus58.

The function used to model cell based carrying capacity was:





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Eq. 2 K0 = ths*30,000

Where the carrying capacity of a cell in a given year is equal to its total habitat suitability (ths) multiplied by 30,000.

Initial abundances: Initial abundance was calculated using a multiplier set at 80% of carrying capacity and a

threshold of 5,000 rabbits per cell. Thus if initial abundance was below 5 000 individuals per cell (i.e., below

annual densities observed in the most marginal habitats: 0.5ha-1), the cell was treated as unoccupied at the initial

time step. We showed elsewhere that setting initial abundance close to carrying capacity is appropriate when a

model burn-in period is then used to generate a stable age distribution and equilibrium initial patch abundance

under the assumption of no future climate change55,59 (see below).

Eq. 3 N0 = thr (ths*24,000, 5,000)

Where the initial abundance of a cell in a given year is equal to its total habitat suitability (ths) multiplied by 24,000 with

a threshold (thr) applied.

A period of 50 years (1,000 permutations), was used to generate a stable age distribution and equilibrium initial

patch abundance under the assumption of no future climate change. Spatial maps of initial abundance were sent

to rabbit experts for external verification based on field observations. There was strong agreement that the maps

provided a good representation of spatial variation in rabbit abundance across the Iberian Peninsula. We have

used a similar approach elsewhere59.

Correlations among grid cells: Environmental variability was correlated between populations depending on

their spatial separation. Thus, individual population fluctuations were highly correlated for closely separated

populations and poorly correlated for disparate populations. Spatial correlations were estimated using historic

weather station data1. Pairwise correlations were calculated for July and January temperature and annual rainfall

for 14 weather stations for the period 1985-2000. All weather stations had complete monthly records and were

chosen to ensure a good spatial representation of Spain. July temperature provided the best distance correlation

relationship.





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An exponential function, P = a.exp(Dc/b), where D is the distance between centroids of population locations, and

a, b and c are function parameters42, was then fitted to the data to calculate the pairwise correlations in vital

rates between populations. Constants were set based on the relationship between distance and July temperature

variation (a = 1, b = 530, c = 1). We used a similar approach for modelling coefficients of correlation for a

lagomorph in the UK and plants in South Africa and Australia1,58,59 .

Dispersal: In this model, dispersal refers to movement between lattice cells. Dispersal was modelled as a

declining function of centre-to-centre distance between cells. A negative exponential function was used to

determine the proportion of each population that disperses between lattice cells at each time step: P = exp(-D/b),

where D is the distance between patch centroids (in km) and b is a constant set at 2.5. When D exceeds 15km (a

maximum dispersal distance: Dmax), P is set to zero42. The dispersal function permitted ~1.8% of the population

to move annually between cells that share a border and ~ 0.30 % of the population moved between cells sharing

a corner. The dispersal rate closely approximated dispersal estimates used elsewhere (1% movement at

distances >3km)60.

Rabbit Model Simulations

100 rabbit demographic models were generated (following steps described above) and each run for a single

iteration under: (i) a high-CO2 concentration stabilising Reference scenario (WRE750); (ii) a Policy scenario

that assumes strong mitigation of greenhouse-gas emissions (LEV1); and (iii) a no-climate change scenario

where temperature and precipitation remains unchanged from the year 2000. Rabbit density in each 10km

x10km cell was then mapped for each year (2000-2100) based on the results from each run of the demographic

model. A total of 30,000 maps of rabbit density were generated (i.e., 100 models x 100 years x 3 climate

scenarios). We mapped output from single model runs to appropriately capture stochasticity in interactions

between rabbit demography, disease and habitat suitability. Maps were disaggregated to a 1km x 1km grid cell





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resolution (using nearest neighbour assignments) so that they aligned with the climate and environmental spatial

inputs used in the lynx model.

Demographic Model for the Iberian Lynx

The demographic model of the Iberian Lynx, like the European Rabbit, was implemented in RAMAS

Metapop42. The general model structure, density dependence, and model parameters were based on Gaona et al.

1998 (see 61), Palomares et al. 2005 & 2012 (see 62,63) and Ferreras et al. 1992 & 2004 (see 64,65). The model is

a spatially structured metapopulation model. Each subpopulation is modelled with a sex-structured, stage-

structured, stochastic model (see “Lynx Demographic Structure”). The spatial structure of the metapopulation

(size and location of subpopulations) is based on the spatial distribution of habitat suitability (see “Lynx Spatial

Structure”). Data used for demographic models are for current refugial populations in the autonomous region of

Andalucía in Spain (Supplementary Fig. S2).

Lynx Demographic Structure

We built an age- and sex-structured model, parameterized according to a pre-reproductive census. Gaona et al.

1998 60 used an age-and-stage structured model for Iberian lynx that included separate stages for reproductive

individuals with and without territories; the same dynamics are modelled here by calculating, at each time step,

the proportion of individuals (and females) with territories and modifying survival and fecundity values in the

stage matrix based on these proportions (see Density dependence below for details). Thus, the survival and

fecundity values for the breeding (reproductive) stages were for individuals with territories; and fecundity does

not incorporate the proportion of females breeding, or the availability of males (see Survival rates and

Fecundity rates below). Total fecundity in a population is modified to incorporate availability of males (see

below), and the density-dependence sub-model makes the modification for individuals without territories. The

density-dependence sub-model also modifies survival and fecundity as functions of rabbit (because the carrying

capacity is based, in part, on rabbit density) and lynx density. In addition, the stage matrix was for a population





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in a protected area. Populations outside protected areas were modelled with relative survival and fecundity

values that reflect additional mortality (see Populations outside protected areas below for further details).

Survival rates: S0 (survival from 0 to 12 months): Palomares et al. 2005 62 estimate 10-month survival as 0.69.

Based on this, we estimate 12-month survival as 0.6406 (= 0.691.2). This value is consistent with 75% cub

survival (from 0-3 months) and 57% survival from birth to dispersal, which happens after the first year. Note

that because the model is parameterized according to a pre-reproductive census, S0 is used in the stage matrix

only for calculating fecundity.

• SF1 (female survival from 12 to 24 months): This period includes dispersal in search of a territory.

Palomares et al. 2005 62 estimate female survival from birth to dispersal as 0.55. Thus survival from 12

months to dispersal can be estimated as 0.55/0.64 = 0.86. Survival during dispersal is 0.7865, so SF1 =

0.86*0.78 = 0.67.

• SM1 (male survival from 12 to 24 months): Palomares et al .2005 62 estimate male survival from birth to

dispersal as 0.59. Thus survival from 12 months to dispersal can be estimated as 0.59/0.64 = 0.92. Survival

during dispersal is 0.39 (see 65), so SM1 = 0.92*0.39 = 0.36.

• SF2 (annual survival of females, from 24 months to 9 years)64: 0.79

• SM2 (annual survival of males, from 24 months to 9 years)64: 0.88

• SF9 (annual survival of females, from 10 years): 0.6

• SM9 (annual survival of males, from 10 years): 0.6

We assigned old lynx a survival value similar to that for juveniles in the pre-dispersal phase (age: 10 months to

2 years)62. This is because territory holders ≥ 9 yr old (and older) are often supplanted by younger adults of the

same sex66. They have a high probability to become floaters without engaging in the long movements and low

survival associated with natal dispersal65.





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Survival could have also potentially been modelled directly as a function of rabbit density, because starvation is

suspected as a source of Iberian lynx mortality65, but there is no established information available to define this

function.

Fecundity: Because the model is parameterized according to a pre-reproductive census, the first age class is 12-

month-old individuals, and fecundity is calculated as the product of average litter size and survival rate from

birth to 12 months, then divided into two for male and female offspring.

• Age of first reproduction = 3 years62

• Age of last reproduction = 9 years62

• Average litter size = 3.162

• S0 (survival from 0 to 12 months) = 0.6406 (see above)

• Proportion of females at birth = 0.5

• F3+ (fecundity) = 3.1 * 0.6406 * 0.5 = 0.993

We modelled a polygamous mating system, with each male mating with a maximum of 4 females per time step.

Thus, we modelled total fecundity as a function of the number of breeding females only as long as there was at

least 1 male for every 4 females in adult stages. Fecundity was not directly modelled as a function of rabbit

density, because there is no correlation between the number of cubs born or number of breeding females and

population size of European rabbits62.

Populations outside protected areas: Survival rate was modelled as a function of the protection status of an

area. Iberian lynx are subject to high levels of non-natural mortality (trapping and shooting)10, especially when

moving outside protected areas. Animals in unprotected patches were modelled as having an additional 10%

mortality67. Thus, for each population, the survival rates were multiplied by (0.9+PropProtected/10), where

PropProtected is the proportion of the area of that population that is under protection. Because fecundity





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includes cub survival, which also depends on protection, fecundity values were also multiplied with the same

number.

Thus, in “Link to Metapopulation” 42, relative survival (RelSurv) and relative fecundity (RelFec) were:

Eq. 4 RelSurv = 0.9 + PropProtected/10;

Eq. 5 RelFec = 0.9 + PropProtected/10;

And, the stage matrix in the template Metapopulation file was for a protected population.

Environmental Stochasticity: We estimated temporal variability in survival rates based on a radio-tracking study

of 30 Iberian lynx from 1983 to 1989, which included juvenile (under one year old), subadult (1-2 years old),

and adult (over two years old) lynx64. This analysis resulted in an estimate of standard deviation of 0.266. After

removing variance due to demographic stochasticity68, the standard deviation was estimated as 0.252, and

coefficient of variation (CV) of survival rate as 0.41. We used this CV estimate for all age classes.

Available data allowed us to estimate a major component of temporal variability in fecundity for the Iberian

lynx. Based on data on Iberian lynx litter size from 1993 to 200062,63, we estimated the CV of litter size to be

0.42. Fecundity variation would also incorporate variation in survival from age 0 to age 1 (S0), but these data

were not available, so we used CV = 0.42 for fecundity. This value was slightly higher than what we estimated

for the European lynx (Lynx lynx) (CV of 28-34%) based on established data69.

Density dependence: The density dependence sub-model was based on Gaona et al. 1998 61 and implemented as

a “user-defined function” in RAMAS Metapop42. When the number of reproductive-age adults exceeds the

carrying capacity (K) of a population, (i) only those individuals with territories in that population can breed, and

(ii) individuals (in reproductive age classes) without a territory suffer 10% additional mortality. To simulate

these effects, the model multiplies fecundity with the proportion of individuals (in reproductive age classes) that





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hold territories in that population (T), and multiplies survival rates with T+(1-T)*0.9. The density dependence

source code is available from the authors on request.

Carrying capacity and initial abundance: In this model, carrying capacity (K) of each population was the

number of territories in that population. Thus at equilibrium, K was smaller than total population size. Carrying

capacity was estimated as a function of total habitat suitability (ths), which is a function of the average rabbit

density in that population (based on the rabbit model results), climate suitability, protection status, whether

there is active lynx management, and whether the land is suitable for breeding (see Spatial Structure below).

The carrying capacity function was:

Eq. 6 K = thr(ths*0.5,4)

The thr constant in this function was generated iteratively, to approximate the number of females with

territories in Doñana and Sierra Morena populations based on 2004-2010 surveys5,66,70 and expert advice. This

was done by generating a new constant based on the performance of the previous constant. We have used a

similar approach elsewhere58.

Initial abundances were calculated in a similar way to K, but with a different scaling factor (0.5/0.41, instead of

0.5) because K is based only on the number of individuals in the reproductive age classes, and the proportion of

individuals in these classes is 0.41:

Eq. 7 N0 = ths*0.5/0.41*0.8

An additional multiplier (0.8) is used to reflect the assumption that 80% of territories are occupied at t1. The

initial abundance of currently unoccupied populations was set to zero. The first 15 time steps of the model

simulation (i.e., 2000-2015) were used to generate a stable age distribution and equilibrium initial patch

abundance59. Number of animals and territories in 2015 closely approximated the most recent census (data not

used to parameterize the model) under a Reference climate change scenario.





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Disease: We modelled the probability of an outbreak of Feline Leukemia Virus (FeLV) as a catastrophe71,72.

Probability of a disease was modelled as a per population catastrophe.

Eq. 8 Probability of catastrophe = obs/(yrs*no. pops)

where number of observed outbreaks (obs) is proportional to the number of years of population monitoring (yrs)

multiplied by the number of populations being monitored (no. pops).

Both extant populations (Doñana or Sierra Morena) have been intensively monitored for the past twenty years 3

and a single outbreak was observed in Doñana over this period71,72. Disease prevalence during the Doñana

outbreak was estimated at 27% (see 72) and 29% (see 71) causing 54%-58% mortality71,72. We modelled FeLV

occurring at a rate of 1 in 40 years (0.025) amplifying the mortality of lynx (≥ 1 year), through a decrease in

survival rates (multiplier = 0.15); and the potential for a disease outbreak to occur owing to a pro-virus

immigrant.

Spatial Structure

The spatial structure is based on the distribution of lynx habitat requirements defined by a habitat suitability

model as the product of 4 components:

1. Rabbit: Rabbit densities per 10 x10 km cell were converted to rabbit density per ha by dividing each cell by

10000. A threshold of 1 rabbit per ha was used to remove areas of effective territory where rabbit abundance

was too low to support Iberian lynx reproduction in a given year 56. An upper estimate of annual average

rabbit abundance (10 per ha) was used to scale rabbit densities between 0 and 1.

2. Climate: Ecological niche model output with a threshold of occurrence applied (0.4; based on an AUC

threshold, see above) and scaled between 0 and 1.

3. Management: A multiplier that accounts for the additional day-to-day management supplement feeding,

habitat restoration, disease monitoring; 3,72,73 that presently goes into supporting the viability of the two

extant populations 5. A function was applied to a binary map of the two extant lynx populations (Doñana or

Sierra Morena = 1; all other areas of the Iberian Peninsula = 0) to reduce the suitability of non-actively





17

managed lynx populations by 50%. This figure was chosen iteratively to maximise the fit between field data

and model estimates of patch area and population abundance for the two extant populations in the year 2000.

4. Breeding: A binary mask of lands suitable/not-suitable for breeding (see Table S2).

Thus, habitat suitability (HS) for Iberian lynx was defined by the following equation:

Eq. 9 HS = (thr(([Rabbit]/10000),1))/10)*thr([Climate],0.4)*max([Management],0.5)*[Breeding]

Where a threshold function (thr) is applied to Rabbit and Climate and a maximum of two arguments function (max) is

applied to Management. Each component of the HS function in parenthesis is described in detail above.

A threshold of 0.2 was applied to HS. The threshold was calculated based on quantiles of occurrence records

from the decade leading up to the year 2000. We explored 2.5, 5 and 10% quantiles and found 5% gave results

that best matched the present-day occurrence records (i.e., maximised sensitivity41) . The approach is described

in detail elsewhere59.

Our predator-prey model, with a slanted predator isocline, whereby prey abundance determines the predator's K:

is functionally similar to other models74; is seen as an improvement on the Lotka-Volterra model75; is more

supported by data than Lotka-Volterra models76; and has been used for modeling a variety of predator-prey

systems, including wolf-moose77, lynx-hare78, bark beetles79, and others. Alternatively, modelling the effect of

rabbits on Iberian lynx via fecundity and survival would have required a function linking Iberian lynx survival

and fecundity to rabbit abundance at different Iberian lynx densities. This is because we modelled Iberian lynx

abundance with a density-dependent model. No such empirical data exists for rabbits and Iberian lynx.

Subpopulations and potential habitats are identified as patches based on the habitat suitability map for each

year, using a habitat suitability threshold parameter and a neighbourhood distance parameter 42. Patches were





18

identified as clusters of grid cells that had a HS greater than 0.2 (see above) and were within 4 grid cells (~ 4

km) of each other. A threshold of 4 grid cells was used to approximate the typical territory size66.

Correlations among grid cells: The correlation distance function was identical to the function used in the rabbit

model (see above).

Dispersal: In this model, dispersal refers to movement among subpopulations. Dispersal was modelled as a

declining function of edge-to-edge distance between subpopulations. Distances between subpopulations (d in

the equation below) were based on “friction” values that represented the difficulty of movement through

different land-cover types. A value of 1 indicates “normal” or standard habitat types. Habitats that present a

higher difficulty for dispersal have higher values. Friction values were assigned considering the results of

habitat selection analyses on detailed behavioural data of subadult lynx during their natal dispersal phase33,67,80,

habitat-related risk of mortality during dispersal65, and patterns of occurrence records that revealed habitat types

usable by dispersing individuals7. We constrained CORINE land-cover polygon values into 4 categories using

behavioural studies33,81: very good for dispersal (Friction value = 1); appropriate for dispersal (5); unsuitable for

dispersal (10); highly unsuitable for dispersal (50) (see Table S2). The spatial layer is available from the authors

on request.

Dispersal was calculated as:

Eq. 10 dispersal = 0.15 exp (-d/18.8), if d ≤ 45 km and as 0 if d>45 km

Where mean dispersal distance equals 18.8 km (Coto del Rey subpopulation =25.8 km ; Reserva Biologica de Doñana

subpopulation=11.9 km)65 and maximum dispersal distance = 45 km (Junta de Andalucia, unpublished data ). See Ferreras

et al. 2001 for a similar estimate of maximum dispersal81. There is anecdotal evidence that Iberian lynx may achieve

dispersal distances > 45km, but this has never been reported in natural conditions (i.e., for non-translocated individuals),

even in the nearly saturated lynx population of Sierra Morena.





19

Stage-specific dispersal: Stage 1 individuals (12+ months old) are able to disperse over the next 12 months. All

adults can disperse, but dispersal probability is low for those holding territories, thus, we assumed that adults

(stages 2 and above) disperse at half the rate of juveniles (first stage) i.e., half the rate given by Eq. 10.

Density-dependent dispersal: Because only individuals without territories disperse, dispersal from a population

is expected to be greater when that population has a larger number of breeding-age individuals. This was

approximately modelled using density-dependent dispersal rates. The dispersal rate calculated as described

above is assumed to be the dispersal rate when the population is at carrying capacity. The dispersal rate was

modelled to change linearly with the number of breeding aged individuals with no dispersal when N = 0 (for a

practicle example, see 82).

Lynx Model Scenarios

Scenario 1 − Influence of Climate Change

We compared the influence of climate change severity on extinction risk for Iberian lynx by modelling

population persistence under a high CO2 concentration stabilising Reference scenario, a more conservative

Policy scenario that assumes substantive intervention and a No Climate Change scenario, where it is assumed

that present-day climate conditions (or more specifically, those in the year 2000) remain unchanged. For each

climate scenario 100 Iberian lynx demographic models were built, with each model drawing on a unique time

series (2020 – 2090) of rabbit maps (output from a single run off the stochastic rabbit model) for that specific

climate scenario. Models were run for 100 iterations and the first 15 years of the simulation was discarded.

Thus model results were based on the period 2015 to 2090.

Scenario 2 – Efficacy of Present-day Management Efforts

We evaluated whether extending present-day management efforts to conserve Iberian lynx beyond the

autonomous region of Andalucía will decrease extinction risk for Iberian lynx under two different greenhouse





20

gas emission scenarios (Reference and Policy). Active management was modelled by approximating present-

day efforts to boost Iberian lynx numbers in Doñana and Sierra Morena5. To do this we modified the habitat

suitability equation (Eq. 9) so that the max threshold constraining Management increased linearly (from 0.5 to

1) over a thirty year period (2020 to 2050). Thus under this scenario, in 2050 all patches of suitable Iberian lynx

habitat on the Iberian Peninsula received the same positive management benefits as Doñana and Sierra Morena.

We built 100 Iberian lynx demographic models for the Reference and Policy climate scenario, each drawing on

a different time series of rabbit maps (paired to climate scenario) and run for 100 iterations, discarding results

from the first 15 years.

Scenario 3 − Managed Reintroductions

We compared the efficacy of increasing habitat suitability (i.e., based on scenario 2) with and without managed

reintroductions. The Iberian Conservation Breeding Program aims to develop and maintain 60-70 Iberian lynx

as breeding stock for translocation programs83. The program is being developed in such a way that 85% of

genetic diversity presently found in the wild will be preserved84. In 2009 the program consisted of 58 captive

animals, including 22 reproductively active females. Managed introductions of lynx into the wild are presently

being informed by simple habitat models70 that do not explicitly account for the interaction between

metapopulation processes, prey abundance and how these might change under a shifting climate.

We developed a model to determine a sustainable number of younger animals that could be removed annually

from a captive breeding population of 60 lynx − the present relocation scheme, and that planned for the future,

favours removing younger animals from a breeding population of 60 animals83. To do this we: assumed that cub

survival would be 20% higher in captivity than in the wild; that first year male survival (i.e., 12-24 months)

would be similar to that of females, because increased mortality associated with migrating and establishing a

territory would be avoided; and that population growth is not regulated by density. We concluded that removing

6 females and 6 males (aged between 1-4 years) each year, for 100 years, had little influence on population





21

persistence. Median population abundance after 100 years was 46 (based on 1 000 RAMAS simulations).

Similarly, Lacy and Vargas83 showed that 12 to 13 cubs could be supplied for reintroduction per year, while still

maintaining the required (for maintenance of gene diversity) nucleus population of 60 breeders.

In a second step we explored the number of animals and the frequency of releases needed to support a viable

lynx population with an initial abundance of zero. We concluded that releasing 3 females and 3 males (aged

between 1-4 years) each year for 3 years would allow a population to persist, assuming temporal stability in

carrying capacity. Releasing fewer animals in an introduction event, or less frequently introducing animals,

increased the risk of the population failing to establish because of environmental and demographic stochasticity.

Two metrics were used to evaluate and rank which patches to release Iberian lynx into.

• One metric evaluated patches based on carrying capacity, initial population size and relative rate of survival

and fecundity (Eq. 11).

• The second metric also considered the connectivity of favourable habitat within 20km of a release site (a

distance similar to the average distance travelled by a dispersing Iberian lynx), accounting for the influence

of habitat type on movement (see modelling dispersal using friction values, above) − by summing the

suitability of patch i at time t across neighbouring patches, the metric favours release sites that are

surrounded by patches that have a high growth potential (Eq. 12).

Patch suitability was evaluated over a moving three year period, matching targeted reintroductions.

Eq. 11 ��

Eq. 12 �� ∑ ��

where, Si,t is the suitability of patch i at time t; Ki,t is the carrying capacity of patch i at time t; Kmax,t is the maximum

carrying capacity of all patches at time t and Ri,t is the relative fecundity and survival multiplier of i at time t.





22

Patch rankings were quite similar for both metrics. However, because connectivity has been shown elsewhere to

be negatively associated with forecast extinction risk under climate change85, we used Eq. 12 to rank patches for

all simulations.

We simulated two contrasting reintroduction schemes:

1. Geopolitical scenario: Where the underlying aim was to establish viable Iberian lynx breeding populations in

every autonomous region within its recent historical range (Supplementary Fig. S2). This scenario simulates

what is likely to be implemented by policy makers15. To do this, we spread (where ever possible)

introductions evenly across autonomous regions – targeting the most suitable patch of habitat in each of two

autonomous regions, for three consecutive years.

2. Peninsula-wide scenario: Where the underlying aim was to ensure the persistence of Iberian lynx by moving

animals to areas of most favourable habitat regardless of autonomous region. Here we introduced animals to

the two best ranked habitats regardless of regional location for three consecutive years.

The number of patches targeted (n= 2) and animals released (3 females and 3 males aged between 1-4 years

each year for three years) between 2015 and 2080 were the same for the Geopolitical and the Non-geopolitical

scenarios.

For each climate reintroduction scenario, 100 Iberian lynx demographic models were generated, with each

model drawing on a different time series of rabbit maps (paired to climate scenario) and run for 100 iterations,

discarding results from the first 15 years.

Assessing Extinction Risk and Vulnerability

We calculated extinction risk and vulnerability metrics for each scenario. Extinction risk prior to 2090 was

measured using expected minimum abundance (EMA), probability of total population size declining to zero and

median time to extinction 42. Metrics were calculated by averaging across model runs (i.e. 100 model outputs)





23

for each modelled scenario. Measures of vulnerability such as annual average abundance and metapopulation

patch occupancy were also recorded.

Model Sensitivity

We undertook a global sensitivity analyses on the rabbit and lynx models separately to determine: (i) whether

our rabbit model was sensitive to assumptions surrounding disease, carrying capacity and population growth

rates; and (ii) if assumptions surrounding spatial and/or non-spatial parameters largely influenced our lynx

model. To ensure that sampled values covered the entire parameter space, we used Latin hypercube sampling86,

whereby the values for each parameter were selected from uniform increments within set ranges (for a practical

example see 87). Latin hypercube sampling allows model parameters to be varied concurrently, permitting

interactions – in contrast to local sampling methods which vary one parameter at a time88. We used generalised

linear models (GLM) to explore the relative importance of different parameter values on key indicators of

population viability89. We calculated the standardised regression coefficients (coef/S.E.) for each term in the

saturated model (six term model) as a relative metric of prevalence sensitivity to variation in vital rates90.

Confidence intervals for the coefficients were generated through a bootstrapping procedure (10,000 bootstraps)

that modelled the relationship between the response and predictor variables.

Rabbit Model Sensitivity

We used 100 sampling dimensions drawn from realistic ranges of variation (±10%) for Rmax and its standard

deviation, carrying capacity, probability of a catastrophic rabbit disease outbreak and the strength of its negative

influence on abundance. The sensitivity analysis was run for a Policy climate scenario. Each model was run for

1,000 iterations and we recorded final mean population size of non-terminal runs (i.e., those that did not end in

extinction). We normalised final mean population size using a square root transformation. We used GLMs

(Gaussian distribution and identity link function) to explore the relative importance of different parameter

values on final mean population size. We found that model results were most sensitive to perturbations in the





24

population growth rate (Rmax) and were less sensitive to uncertainties regarding RHD frequency and severity

(see Table S4).

Lynx Model Sensitivity

We used 200 sampling dimensions drawn from realistic ranges of the following parameters: adult survival (±

5%), fecundity (±10%), carrying capacity (± 20%), mean dispersal distance (±20%), environmental variation

(±10%), the probability of a disease outbreak (±10%) and its influence on survival rates (±10%). The

sensitivity analysis was run for a Geopolitical reintroduction management scheme and Policy climate scenario.

For each iteration of randomly selected parameter values, we projected the population to 2090 (based on 100

lynx models each run for 100 iterations each) and recorded mean population size of non-terminal runs. We used

GLMs (Gaussian distribution and identity link function) to explore the relative importance of different

parameter values on mean final abundance in 2090 (for persistent model runs only). The results are reported in

Table S1.

Model Uncertainty

To strengthen climate change forecasts, and account for inter-model differences, we assessed the skill of GCMs

in reproducing seasonal precipitation and temperature across the Iberian Peninsula, and then generated an

ensemble forecast based on seven skilful models28,29. However, our estimates of future change in precipitation

and temperature are still influenced by strong assumptions regarding the strength of climate forcings (such as

aerosols) and climate sensitivity (the equilibrium warming for a CO2 doubling) and future rates of greenhouse

gas emissions.

We also used an ensemble type approach to generate ENM projections. Here we generated consensus

projections based on a subset of skilful ENMs using internal evaluation to rank models (see above). Although

this approach can reduce uncertainty in projections of species’ habitat suitability and/or range91, there is still an





25

assumption that species distributional limits reflect physiological limits (i.e., climate-equilibrium assumption4);

and that climatic niches are stable through time92. Because dispersal limitation often constrains a species from

accessing some habitable areas93, and human impacts can prevent establishment or modify abundances92, we

used occurrence records from the second half of the 20th century to characterize the potential distribution of

Iberian lynx prior to its range collapse. This allowed us to more closely approximate climate-physiological

limits, and better capture the species’ potential niche (see above).

The level of the complexity in the rabbit and Iberian lynx metapopulation models reflect a balance between the

need for management actions to be based on realistic models that do not exclude major factors, and making the

models as robust as possible to underlying uncertainties. Our sensitivity analysis provided important feedback

for future model refinement, by identifying which spatial and non-spatial demographic parameters had the

largest influence on the model results based on uncertainties in their estimates. However, our model framework

did not allow for model error to propagate over time as a result of uncertainties at each step of the modeling

framework i.e., climate projections, ecological niche projections, rabbit model, lynx model. Propagating all

known uncertainties, occurring at each step of the modelling processes into forecasts of Iberian lynx range and

abundance under different management scenarios would be extremely difficult and would require an inordinate

amount of model development and processing time. Recently, it has been shown that niche-population models

can be fitted in a Bayesian framework to explore parameter uncertainty more explicitly94. Bayesian “range

dynamics models” are a promising development that could help improve our theoretical understanding of range

dynamics for species’ with simple demographic characteristics95. However, using Bayesian techniques to

explore uncertainty in complex models, such as the Iberian lynx model, is computationally demanding and

independent evaluation of such models is extremely complicated.

We could not directly assess the ability of our lynx niche-population model to predict lynx occurrence across

time using hindcasting techniques96 because important spatiotemporal records of human impacts (shooting,





26

trapping etc.) on lynx demographic traits are not available during the period of accelerated lynx range

contraction (i.e., after or around 1975). Similarly, it is not possible to validate our 21st century lynx model using

techniques that substitute space for time, because lynx today exist only in two heavily managed areas of

Andalucía.

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Table S1: Results of the Latin-hypercube-sampling sensitivity analysis for expected mean

final abundance in 2090 (for persistent iterations of the stochastic demographic model only)

of Iberian lynx under a Geopolitical reintroduction management scheme and Policy climate

scenario that assumes strong mitigation of greenhouse gas emissions.

Dependent Variable SRC Coeff Lower CI Upper CISurv. 0.281 7539 7189 8144

Fecund. 0.083 2233 2147 2661Env. var. 0.033 -895 -1117 -663

K 0.021 570 59 796Catast. prob. 0.542 -14537 -24149 -6953Catast. mult. 0.036 -974 -1867 696

Dispersal 0.003 77 -167 302

Standardized regression coefficients (SRC; dimensionless and sum to 1), actual model

coefficients (Coeff) and their upper and lower confidence intervals (0.025 and 0.975

bootstrap percentiles) for final mean population size of non-terminal runs according to the

saturated generalized linear model, with the independent variables: adult survival (Surv.),

fecundity (Fecund.), environmental variation (Env. Var.), carrying capacity (K), probability

of an outbreak of Feline Leukemia Virus (FeLV) (Catast. prob.), severity of a FeLV outbreak

(Catast. mult.) and dispersal.






Table S2: CORINE land cover categories used to define breeding habitat (suitable/unsuitable) and friction values for Iberian lynx dispersal. Friction values represent the difficulty of movement through different land-cover types: very good for dispersal (Friction value = 1); appropriate for dispersal (5); unsuitable for dispersal (10); highly unsuitable for dispersal (50)

Broad class Category Breeding Friction Artificial surface Continuous urban fabric Unsuitable 50 Artificial surface Discontinuous urban fabric Unsuitable 50 Artificial surface Industrial or commercial units Unsuitable 50 Artificial surface Road and rail networks and associated land Unsuitable 50 Artificial surface Port areas Unsuitable 50 Artificial surface Airports Unsuitable 50 Artificial surface Mineral extraction sites Unsuitable 50 Artificial surface Dump sites Unsuitable 50 Artificial surface Construction sites Unsuitable 50 Artificial surface Green urban areas Unsuitable 50 Artificial surface Sport and leisure facilities Unsuitable 50 Agricultural areas Non-irrigated arable land Unsuitable 50 Agricultural areas Permanently irrigated land Unsuitable 50 Agricultural areas Rice yields Unsuitable 50 Agricultural areas Vineyards Unsuitable 10 Agricultural areas Fruit trees and berry plantations Unsuitable 50 Agricultural areas Olive groves Unsuitable 10 Agricultural areas Pastures Unsuitable 10 Agricultural areas Annual crops associated with permanent

crops Unsuitable 50

Agricultural areas Complex cultivation patterns Unsuitable 10 Agricultural areas Land principally occupied by agriculture

with significant areas of natural vegetation Unsuitable 1

Agricultural areas Agro-forestry areas Unsuitable 5 Forests and semi-natural areas

Broad-leaved forests Unsuitable 1

Forests and semi-natural areas

Coniferous forests Unsuitable 1


Mixed forests Unsuitable 1


Natural grasslands Unsuitable 5


Moors and heathland Unsuitable 1


Sclerophyllous vegetation Suitable 1


Transitional woodland-shrub Suitable 1


Beaches, dunes, sands Unsuitable 50


Bare rocks Unsuitable 50


Sparsely vegetated areas Unsuitable 5

Forests and semi- Burnt areas Unsuitable 1 NATURE CLIMATE CHANGE | www.nature.com/natureclimatechange 37





natural areas Forests and semi-natural areas

Glaciers and perpetual snow Unsuitable 50

Wetlands Inland marshes Unsuitable 50 Wetlands Peat bogs Unsuitable 50 Wetlands Salt marshes Unsuitable 50 Wetlands Salines Unsuitable 50 Wetlands Intertidal flats Unsuitable 50 Water bodies Water courses Unsuitable 50 Water bodies Water bodies Unsuitable 50 Water bodies Coastal lagoons Unsuitable 50 Water bodies Estuaries Unsuitable 50 Water bodies Sea and ocean Unsuitable 50






Table S3: CORINE land cover categories used to define rabbit habitat as unsuitable, habitable or highly productive.

Broad class Category Habitat Artificial surface Continuous urban fabric unsuitable Artificial surface Discontinuous urban fabric unsuitable Artificial surface Industrial or commercial units unsuitable Artificial surface Road and rail networks and associated

land unsuitable

Artificial surface Port areas unsuitable Artificial surface Airports unsuitable Artificial surface Mineral extraction sites unsuitable Artificial surface Dump sites unsuitable Artificial surface Construction sites unsuitable Artificial surface Green urban areas habitable Artificial surface Sport and leisure facilities unsuitable Agricultural areas Non-irrigated arable land habitable Agricultural areas Permanently irrigated land unsuitable Agricultural areas Rice yields unsuitable Agricultural areas Vineyards habitable Agricultural areas Fruit trees and berry plantations habitable Agricultural areas Olive groves habitable Agricultural areas Pastures highly

productive Agricultural areas Annual crops associated with permanent

crops habitable

Agricultural areas Complex cultivation patterns habitable Agricultural areas Land principally occupied by

agriculture with significant areas of natural vegetation

habitable

Agricultural areas Agro-forestry areas habitable Forests and semi-natural areas

Broad-leaved forests unsuitable


Coniferous forests unsuitable


Mixed forests habitable


Natural grasslands highly productive


Moors and heathland habitable


Sclerophyllous vegetation habitable


Transitional woodland-shrub highly productive


Beaches, dunes, sands habitable


Bare rocks unsuitable







Sparsely vegetated areas highly productive


Burnt areas habitable


Glaciers and perpetual snow unsuitable

Wetlands Inland marshes unsuitable Wetlands Peat bogs unsuitable Wetlands Salt marshes unsuitable Wetlands Salines unsuitable Wetlands Intertidal flats unsuitable Water bodies Water courses unsuitable Water bodies Water bodies unsuitable Water bodies Coastal lagoons unsuitable Water bodies Estuaries unsuitable Water bodies Sea and ocean unsuitable






Table S4: Results of the Latin-hypercube-sampling sensitivity analysis for expected mean

final abundance in 2090 (for persistent iterations of the stochastic demographic model only)

of Rabbits under a Policy climate scenario that assumes strong mitigation of greenhouse gas

emissions.

Dependent variable SRC Coeff Lower CI Upper CIRmax 0.56 20292.10 20140.68 21046.70

Env. var. 0.24 -10042.60 -10400.52 -9481.97Catast. prob. 0.16 5745.20 5501.87 6428.11Catast. mult. 0.03 -1094.90 -1499.04 -800.03

Carrying capacity 0.01 403.40 49.41 772.25

Standardized regression coefficients (SRC), actual model coefficients (Coeff) and their upper and

lower confidence intervals (0.025 and 0.975 bootstrap percentiles) for final mean population size of

non-terminal runs according to the saturated generalized linear model, with the independent variables:

maximum annual finite rate of population increase (Rmax), year-to-year variation in Rmax (Env. var.),

probability of a RHD outbreak (Catast. prob.), severity of an RHD outbreak (Catast. mult.) and

carrying capacity.






Fig. S1: Forecast lynx abundance and number of populations in Iberia between 2015 and

2090 according to three possible management options and a high-CO2 concentration

stabilising Reference scenario (WRE750). The interventions are: (i) present-day conservation

practices, including increasing prey (lagomorph) densities, habitat alteration, preventing

disease and non-natural mortality (Present); (ii) reintroducing captive-bred lynx to

unoccupied habitat according to a geopolitical scheme that favours establishing lynx





populations in every autonomous region in Spain, plus Portugal as an additional ‘region’,

within its recent historical range (Geopolitical); and (iii) a peninsula-wide strategy, focused

on releasing animals into the best quality habitat regardless of region (Peninsula-wide). The

solid lines show mean estimates for each scenario. Band widths represent 5th and 95th

percentiles.






Fig. S2: Reintroduction areas for Iberian lynx on the Iberian Peninsula according to a

Geopolitical scenario that aims to establish viable breeding populations in five autonomous

Spanish regions, plus Portugal, within its recent historical range. The Spanish regions are:

Andalucía, Castilla-La Mancha, Comunidad Valenciana, Extremadura and Murcia. In

Portugal, suitable habitat currently exists south of the black-dashed line.






Fig. S3: Location of lynx populations in Iberia in 2050 under the Peninsula-wide and

Geopolitical reintroduction scenarios for two climate change scenarios: a high-CO2

concentration stabilising Reference scenario (WRE750) and an alternative Policy scenario

that assumes strong mitigation (LEV1). Maps capture lynx demographic responses to spatial

patterns of rabbit abundance (conditioned by disease, climate and environmental variation)

and changes in climate suitability and landscape modification. Only grid cells where lynx

were present in 75% of runs were treated as populated. See Methods for further details.






Fig. S4: Variation in CORINE land cover categories across the Iberian Peninsula: CORINE land cover types are shown for artificial surfaces (A), forests and semi-natural areas (B), agricultural areas (C) and water bodies. See Table S2 and S3 for CORINE land cover types that make up artificial surfaces and wetlands and water bodies.





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