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Supplementary Material

Study systems

We investigated how climate change and population dynamics together affect the range

limits of two lagomorphs of conservation concern: the Mexican Volcano Rabbit

5(Romerolagus diazi) and the European Mountain Hare (Lepus timidus). Romerolagus

diazi is protected by national and international legislation: listed as an endangered species

in the Mexican law (DOF 2001) and in the IUCN Red List (LSG 1996). Lepus timidus is

listed under Annex V of the EC Habitats Directive (1992), which implies that a number

of methods of capture are restricted or banned (JNCC 2007).

The current distribution of Romerolagus diazi is at its range limit (see Fig. S1

supplementary material), due to historical non-climatic drivers of range contraction.

Although the species has always been endemic to a small region of the Transvolcanic

Belt in central Mexico, between 2,800 and 4,250 meters above sea level (Romero &

15Velázquez 1999; Velázquez et al. 1999) it was previously more widespread. A total

occupancy area of about 280 km2 has been estimated in a discontinuous distribution

pattern, from which four major core areas have been identified (Velázquez et al. 1996).

Population size at the end of the 1980’s was estimated at between 2,478 and 12,120

(Velázquez 1994). Besides its natural restricted distribution, several factors threaten the

20long-term persistence of Romerolagus diazi. First, two of its core areas are located about

30 km south of Mexico City -one of the largest urban areas in the world- imposing a

strong pressure to the rabbit’s habitat, which has been quickly reducing in the last

decades due to urbanization and expansion of the grazing and cropland frontier, the ESM_Changes in range limits under climate change Page 2 of 12

increase of frequency of wildfires, illegal hunting, and introduction of domestic dogs and

25cats that prey upon the rabbits are among the most important ones (Hoth et al. 1989;

Romero & Velázquez 1999). Second, more recent climatic changes have been detected in

the distributional area of Romerolagus diazi, in particular an increase in the winter

temperature of more than 1.5 °C in the last 40 years (Domínguez 2007). It is this

combination of pressures that makes this species highly vulnerable to extinction.

Fig. S1. Distribution of Romerolagus diazi (blue) superimposed over the 2010 climate

suitability.

Lepus timidus is an arctic/subartic species with a fragmented range across Europe,

35extending across Russia in the east and to Scotland and Ireland in the west (Mitchell-

Jones et al. 1999; Thulin 2003). In Europe the northwest range limit of this species is in ESM_Changes in range limits under climate change Page 3 of 12

Scotland. It is highly fragmented and although Lepus timidus is capable of existing in a

wide range of habitats and environmental conditions, in Great Britain (England, Wales

and Scotland) it is generally associated with heather (Calluna and Erica spp., Newey et al.

402007). The current distribution of Lepus timidus populations show generally regular but

sometimes dramatic changes in density, depending on habitat suitability related to

vegetation and climate [see below] (Newey et al. 2007). The current distribution of Lepus

timidus within Britain, the geographical area of interest in the current paper, is estimated at

76 721 km2 (JNCC 2007).

Habitat suitability

Romerolagus diazi inhabits coniferous forests with a dense sub-alpine grassland cover in

the herbaceous stratum. It is highly sensitive to vegetation structure and composition,

thus perturbations to structural habitat has an important impact in its populations

50(Cervantes et al. 1990; Cervantes & Martínez 1996). The habitat map for the Volcano

Rabbit was obtained from the last land use / land cover map generated for the whole

country in 2000 (IGUNAM-INEGI 2001). Original land cover classes were reclassified in

highly suitable (1), suitable (0.5), and unsuitable (0) for the Volcano Rabbit based on

Velázquez et al. (1999).

Habitat for Lepus timidus was based on the proportion of suitable habitat in the cell using

the 1990 Land Cover Map (Fuller et al. 1994) sub categories that are largely heather,

open shrub moor (10) and shrub heath (25). In the absence of more detailed information

on the relationship between hare density and vegetation cover, we here assumed that grid ESM_Changes in range limits under climate change Page 4 of 12

60cells were potentially suitable habitat if the percentage cover of heather exceeded 70%.

After applying this vegetation mask (categorical threshold), the bioclimatic was thereafter

used to determine relative habitat suitability.

Occurrence data

Occurrence data for the Volcano Rabbit was obtained from four scientific collections

65[Colección Nacional de Mamíferos, Instituto de Biología, UNAM (CNMA); Museum of

Natural History, University of Kansas (KU); Instituto Politécnico Nacional (IPN) and

Colección de Mamíferos of Universidad Autónoma Metropolitana (Unidad Iztapalapa)

(UAMI)], scientific literature (Velázquez et al. 1996), and from fieldwork carried out

from 2004-2007 {Domínguez, 2007 #1262}.

Presences for the Mountain Hare (Lepus timidus) were based on records held at the

Biological Records Centre (BRC) for Great Britain (www.nbn.org.uk/). Squares (10km

x 10km) within Great Britain with no record at or below 10km resolution were

considered an absence. For simplicity, all 1km squares within a 10km square were

75considered a potential occupancy, provided the total habitat suitability threshold

(vegetation + climate – see below) was >0.2.

Historic distribution of Romerolagus diazi

Occurrence data for the Romerolagus diazi were obtained from four scientific collections

80(see above). Historical distribution map was generated using species distribution

modelling techniques and GIS analysis. A potential distribution map of the species was

created using a maximum entropy approach implemented in the MaxEnt software 5ESM_Changes in range limits under climate change Page 5 of 12

(Phillips et al. 2006). For the purpose of this study, we used all available occurrences of

the species and a suite of 19 bioclimatic variables produced specifically for Mexico with

85the ANUSPLIN software (Hutchinson 1997) and kindly provided by O. Tellez-Valdes.

Automatic settings were used in Maxent for all tuning parameters following Phillips and

Dudik (2008) and we selected the new logistic output format to obtain a map that is

interpreted as an estimate of the probability of presence. The probabilistic map was

converted into a binary map (presence/absent) selecting as threshold the minimum

90probability value in which all occurrences were predicted. Finally, those climatically

suitable areas which have never been inhabited by the species due to dispersal limitation

or historical reasons were trimmed based on distributional range limits described in

Cervantes et al. (1990) and Velázquez et al. (1996).

Climate suitability methods

95Generalized Additive Models (GAMs) with binomial errors, a logit link and a smoothed

function (3 nodes) were used to build the bioclimatic models (mgcv (1.4-1) library in R,

Wood 2008). GAMs are semi-parametric models with data-driven response curves

(Hastie 1992). We took an ensemble modelling approach using a multi-model inference

framework (Burnham & Anderson 2002; Araujo & New 2007; Thuiller et al. 2007) based

100on all-subsets selection of the GAMs using the AIC measure. The ten ‘best’ models

(lowest AIC) were conserved and the final projections were a weighted average of these.

Romerolagus diazi

The Mexican volcano rabbit model was built and projected on a 0.01° x 0.01° (~1km2)

grid. This is a very range-restricted species and the number of presences was small

105compared to the number of absences. Rather than using all the absences in the ESM_Changes in range limits under climate change Page 6 of 12

surrounding area (>180 000 points) we chose a random set of absences. Bioclimate

modelling was the same as for the mountain hare except that due to the smaller number of

presences only three bioclimatic variables were used to build the models; Annual Mean

Temperature, Temperature Seasonality (standard deviation *100), Annual Precipitation.

110These three variables were highly correlated (r >0.6) with a larger set of variables

including those used in the mountain hare modelling. All 7 possible models (i.e., one

model for each unique combination of the three bioclimate variables) were used and were

weighted as in the mountain hare modelling (see below).

Lepus timidus

115The mountain hare (Lepus timidus) bioclimatic model was built on the ~50 x 50km Atlas

Flora Europea (AFE) grid, using presence absence distribution data from the European

Mammals Atlas (Mitchell-Jones et al. 1999) as the response variable. We used four

bioclimatic variables that have been previously been shown to correspond well to species

range limits: mean temperature of the warmest month and coldest month, annual

120precipitation, and the ratio of actual to potential evapotranspiration (Thuiller et al. 2005;

Levinsky I. et al. 2007). Climate data used to build the model was based on the 10’

European grid for the last recognized climate normal period (1961-1990) generated by

the FP5 ATEAM project (New et al. 2002; Schroter et al. 2005). These data were

aggregated to 50 x 50 km Universal Transverse Mercator (UTM) in ArcGIS/ArcInfo 9.2

125(ESRI, Redlands, California, USA) to match the species data grid. The model was then

projected onto the 10 x 10km British National Grid (BNG) using climate data for the

same variables for both the recent past and future (1961-2100). ESM_Changes in range limits under climate change Page 7 of 12

Future projections

Future projections for the climate variables were derived using climate model outputs

130from the HadCM3 global climate model made available through the Intergovernmental

Panel on Climate Change (IPCC) Data Distribution Centre (ipcc-ddc.cru.uea.ac.uk).

Modelled climate anomalies were scaled based on the A2 storyline (Special Report on

Emissions Scenarios: http://www.grida.no/climate/ipcc/emission/); this scenario describes

a heterogeneous future world focused on self-reliance, preservation of local identities and

135slower and more regional economic development (Nakicenovic & Swart 2000). This

scenario is more conservative than the A1FI scenario, which we are currently tracking

well above (Rahmstorf et al. 2007), but A2 better reflects emissions scenarios now

gaining favour among mitigation policy researchers, encompassing a later shortage of

fossil fuels and more active mitigation policies which come into force by mid century

140(www.ipcc.ch). Given the likelihood of currently unmodelled slow feedbacks in the

climate system (Hansen et al. 2007), it is plausible that future climate change will be

more extreme than that used here, so we consider our simulations to be a mid-range

projection.

145Future projections for Romerolagus diazi were calculated as an averaged projection

surface for each of three future 30year means provided by the IPCC (2010-2039, 2040-

2069, and 2070-2099). For interpolation purposes these were labelled for the first year

and the interpolation extended 30 years to 2100. For the dynamic climate maps these

values were then interpolated to annual time slices using (“gi_beta_r44.exe” Ersts & R. ESM_Changes in range limits under climate change Page 8 of 12

1502008). Grid interpolator applies a linear interpolation between two grids on a cell by cell

basis.

InterpolationIncrementi,j = EndYeari,j - StartYeari,j / ( EndYeari,j - StartYeari,j )

For each year between the StartYear and EndYear

CurrentYeari,j = StartYeari,j + ( InterpolationIncrementi,j * ( CurrentYear - StartYear ).

Future climate envelope projections for Lepus timidus were produced in the same way

(using 30-year means 1991-2020, 2021-50, 2051-80). These were then converted to a

1 x 1 km grid to match the habitat and occurrence layer for Great Britain, but with all

squares within the HadCM3-modelled 10 km having the same climate value. The annual

160interpolation was extended by 49 years to 2100.

Stochastic Population Models

Romerolagus diazi and Lepus timidus population models comprised 3 stage classes -

leveret; one year old; and those two years or greater. Demographic rates (survival, age of

165maturity and fecundity rates) were based directly on published estimates or taken from

similar species (Flux & Angerman 1990; Hewson & Hinge 1990; Marboutin et al. 2003;

Newey et al. 2004; Dahl 2005; Jennings et al. 2006; Mahony & Montgomery 2006).

Leveret survival was estimated at 30-50% and adult survival at 45-70%. Age of maturity

was modelled at 1 year (Iason 1989) and fecundity was related to age, with an average

170litter size of 5 for 2-year olds and 6 for 3-year olds. We estimated variability in vital rates

by trialling values until the fluctuations in the simulated populations matched those of the

time series. ESM_Changes in range limits under climate change Page 9 of 12

Density Dependence

Density dependence (DD) was implemented using a Scramble model (Logistic or Ricker

175type of DD), which determined the population growth rate at each time step (by

modifying fecundity and leveret survival) as a function of the population size at that time

step. Maximum rate of population growth (Rmax) was calculated by fitting exponential

and logistic models to time series of abundances from the Global Population Dynamics

Database (http://www3.imperial.ac.uk/cpb/research/patternsandprocesses/gpdd). AIC

180model averaging was used to provide a weighted estimate of maximum/intrinsic

population growth rate for 17 population time series. This procedure resulted in an Rmax

estimate of 1.34 which was used for both R. diaza and L. timidus.

Dispersal

The rate of dispersal between patches of suitable habitat during each time step was

185modelled with an exponential function, P = exp(Db), where D is the distance between

patch centroids and b is a constant. When D exceeds a specified maximum distance

(Dmax; set arbitrarily at a high value of 20 km), P is set to zero. The best estimate of b

was set at 2 based on observed mean and maximum dispersal distances (Hewson & Hinge

1990; Dahl & Willebrand 2005) and a sensitivity analysis examined alternative values of

1901 (less dispersal) and 3 (greater).

Stochasticity

Demographic stochasticity was implemented by sampling the number of survivors from

binomial distributions, and the number of young produced from a Poisson distribution

(Akçakaya & Root 2005). Environmental stochasticity was sampled from lognormal

195distributions. Environmental variability was correlated between populations depending on 10ESM_Changes in range limits under climate change Page 10 of 12

their spatial separation. Pairwise correlations were calculated using an exponential

function, P = exp(Db), where D is the distance between centroids of habitat patches and b

is a constant. This function was parameterised b=300, which was based on correlation-

distance relationship in annual mean temperature variation among 20 weather stations in

200the UK. Annual environmental variability for vital rates was estimated based on

variability of population sizes from time series data. ESM_Changes in range limits under climate change Page 11 of 12

Romerolagus diazi patches

Historic

0 ESM_Changes in range limits under climate change Page 12 of 12

205Fig. S2. Volcano rabbit habitat changes, showing size and location of habitat patches

predicted by climatic and land-use variables, with climate changing in time according to

the A2 SRES scenario. For years 2010 through 2080, the colour of grid cells indicates

habitat suitability (brighter colour more suitable), and the white outlines delineate patches

or discrete populations of the metapopulation. From 2010 to 2050, two smaller

210(northern) patches disappear, one large (western) patch splits into three smaller patches,

and two medium-sized (eastern) patches become slightly smaller. From 2050 to 2080,

two of the three western patches disappear, and the two eastern patches become

substantially smaller.

215References