Population Trend and Distribution of Mountain (Lepus Timidus) and Brown Hares (Lepus Europaeus) in Central ALPS (N-Italy, 1980-2020)

Mountainous regions are very vulnerable to climate changes, as they experience higher temperature increases than the surrounding environments. A general movement of species towards higher altitudes, in search of suitable sites, is being observed. In the case of the Italian Alps, an expansion of the brown hare (Lepus europaeus) is possible within the zones occupied by the mountain hare (Lepus timidus), which frequents higher altitudes. The risk is an increase in the hybridization and a contraction of the mountain hare’s range. In this study we analysed the hunting bags of brown and mountain hares from the period 1980-2020, in the province of Sondrio, in northern Lombardy (N-Italy), with the aim of: i) identify the environmental variables that in�uence the distribution of the two species, ii) create suitability maps of the study area, iii) identify the changes of the ranges of the two species, iv) highlight any population trends in relation to climate change. The results indicate that the two species select different altitudes, with the exception of the altitudes between 1000-1400 and 1800 m a. s. l. Both species select pastures and coniferous forests. The brown hare also selects mixed and broad-leaved forests, while the mountain hare high-altitude grasslands. No signi�cant trends in population size, altitude, or spatial overlap of the two species were observed over the period investigated. Considering the period between 2000 and 2020, however, a moderate increase was highlighted for the brown hare. In all cases, weather variables do not seem to have in�uenced population trends.


INTRODUCTION
Climate change has many effects on animals because temperature directly affects both their basal metabolic rate and development.Many phenomena (e. g. migratory behaviour) are regulated by the seasonality of climatic conditions; in particular, during the last century, the typical spring activities (for example the stop of dormancy or the beginning of reproductive activity) tend to be anticipated.The interactions between species within ecological communities are changing, in some cases favouring one species over another, changing the nature of the relationships between competitors or between predators and prey (Scheffers et al. 2016).Furthermore, climate change is causing a shift in the ranges of animals towards the poles and towards higher altitudes.In addition, many species risk to be unable to disperse rapidly enough to remain in suitable conditions of temperature and rainfall (Jackson et al. 2009; Post et al. 2009).Furthermore, habitat fragmentation, caused by human activities, often slows down or prevents migration to new sites suitable for their survival (Cardinale et al. 2021).In this way, only species with wide distribution and greater dispersal ability will adapt more easily to changes (Laurance et al. 2011).
Mountainous regions are more vulnerable to climate change, as there are generally higher temperature increases than surrounding areas (Fischlin et al. 2007).In particular, in the Alps the temperature is increasing at about twice the global average observed over the last century (Auer et al. 2007).
Another phenomenon due to climate change is the mismatch (or mistiming) between previously synchronous activities in two or more species, which has been observed in many taxonomic groups (e.g. in birds, between births of migratory insectivorous species and the presence of caterpillars; Pape Møller et al. 2010).For instance, a study conducted in the central Apennines, in Italy, demonstrated how the signi cant increase in spring temperatures can affect the population dynamics of Apennine chamois (Rupicapra pyrenaica ornata) (Lovari et al. 2020).In recent years, in fact, the onset of green-up in the grasslands has been anticipated by about one month.In these places the species feeds during the period of suckling and weaning of the young.However, the birth period of the chamois has not changed in recent decades (Lovari 1984;Lovari and Locati 1991), causing a reduction in the period of availability of high-quality forage, with a subsequent negative effect on the quantity and quality of milk produced by the mothers and the availability of food resources for juveniles.This has therefore led to a reduction in body growth and to an increase in winter mortality (Festa-Bianchet 1988; Coté and Festa-Bianchet 2001; Douhard et al. 2018).
In some cases, the adaptive response to climate change can be hindered by the presence of other species.For example, a study carried out on a population of Northern chamois (Rupicapra rupicapra) in the Gran Paradiso National Park, in Italy, has shown that the diurnal altitudinal migration of this species is in uenced by temperature, but it can be strongly disturbed by the presence of other species (Mason et al. 2014).If in the future the effects observed following the introduction of a competing species (in this case the domestic sheep, Ovis aries) and climate change were to act simultaneously, an upward shift of the chamois would occur which could lead to a reduction in 55% of the foraging habitat in the species' range in the Alps.
In this context, therefore, some species will have the opportunity to colonize new areas, due to the expansion of suitable environmental conditions, while others could have negative consequences due to the reduction of the habitat.In some cases, this process can lead to a greater overlap of the ranges of previously allopatric species, increasing the probability of hybridization, if it is possible between the two species (Garroway et al. 2009).An example concerns mountain hare (Lepus timidus) and brown hare (Lepus europaeus), two species present in the Alps, with the rst located at higher altitudes than the second.
The brown hare has a large range, extending over almost all of Europe up to the Middle East and central Asia.The species has also been successfully introduced in many parts of the world (including America, Australia, New Zealand) (Hacklander and Schai-Braun 2019).In Italy it is now present in all the peninsular regions, while it is absent in Sicily and Sardinia where it was introduced in the years 1920-1930.The IUCN (International Union for Conservation of Nature) considers the brown hare to be of Least Concern (LC) worldwide and in Italy (Hacklander and Schai-Braun 2019;Rondinini et al. 2022).Despite this, there has been a generalized decline in population size in almost all European countries, including Italy, starting around 1960.Probably the main factor that contributed to this decline was a qualitative-quantitative reduction of the habitats suitable for this species, due to the intensi cation and mechanisation of the agriculture (Amori et al. 2008).The high hunting pressure, and the restocking operations connected to them, represent a further factor in uencing the population density of the species.The brown hare is included among the species that can be hunted in Italy from the third Sunday of September to 31 December (Law 11 February 1992, n. 157).
The mountain hare is an arctic-alpine species, characterized by a fragmented distribution in Europe (Smith and Johnston 2019).In Italy the subspecies L. t. varronis is present, whose range is quite uniform and continuous along the Alpine chain (Amori et al. 2008).The IUCN considers the species at Least Concern (LC), worldwide and in Italy (Smith and Johnston 2019; Rondinini et al 2022).It has been included in Annex V of Directive 92/43/EEC (Habitats).The mountain hare is included among the species that can be hunted in Italy from 1 October to 30 November (Law 11 February 1992, n. 157).The size of mountain hare populations appears to be slowly declining in many areas.The causes are mainly of anthropic origin, including the change in agricultural practices, the abandonment of mountains and the spontaneous reforestation of meadows and pastures.Winter warming has been identi ed as a signi cant threat to mountain hare populations.In fact, it facilitates the spread of the brown hare at high altitudes, increasing the probability of competition and hybridization events (Jansson and Pehrson 2007;Reid 2011;Bisi et al. 2015).In addition, climate changes may cause a mismatch in seasonal coat color due to decreased snow cover duration and low phenotypic plasticity of the species (Pedersen et al. 2017).
This study aimed to evaluate any changes in the population size and distribution of the mountain hare and the brown hare in the province of Sondrio (N-Italy, Central Alps) in the last decades.In particular, the analyses aimed to i) identify the environmental variables that in uence the distribution of the two species, ii) create suitability maps in the study area, iii) identify the variations of the distribution areas of the two species over the years, iv) highlight any population trends in relation to climate change.We used hunting bag data for this purpose.These offer a good monitoring strategy, as they can be used as a general index of long-term trends and they can give indications regarding changes in population size and distribution (Cattadori et al. 2003;Kitson 2004;Carlsson et al. 2010).
We predicted that the brown hare would be more present in open areas (e. g. pastoral areas) and in traditional agricultural ecosystems, but also within broad-leaved forests (Amori et al. 2008).The brown hare is found up to 2000-2100 m a. s. l. in the Alps, and above 1500 m a. s. l. it can live in sympatry with the mountain hare.The latter is present from the coniferous and deciduous forest belt up to the nival zone, mainly frequenting woodlands, heaths, high pastures and alpine tundra (Amori et al. 2008).
Following climate change we expected an expansion of the brown hare towards higher altitudes, within the areas occupied by the mountain hare, thus increasing the spatial overlap between the two species.This would also lead to a contraction of the range of the mountain hare and a reduction in the size of its population (Thulin 2003;La Morgia et al. 2008).

Study area
The study area coincides with the province of Sondrio, in northern Lombardy (N-Italy, Fig. 3).It is a predominantly mountainous land of 3200 km 2 .There are valleys with a latitudinal trend, such as Valtellina, crossed by the Adda River, or longitudinal, like Valchiavenna, crossed by the Mera River.The province is characterized by a very wide altitudinal range, extending from less than 200 up to about 4000 m a. s. l.To the north and west it borders with Switzerland, to the west with the province of Como and the province of Lecco, to the south with the province of Bergamo and to the east with the province of Brescia and with Trentino-Alto Adige.
The climate changes with the altitude: at the valley bottoms the climate has been de ned as Dfb, according to the Köppen classi cation.Dfb includes cold climates with wet winters, average temperature of the warmest month below 22°C and at least 4 months with temperatures above 10°C.The average annual temperature is 5.1°C.Precipitation occurs in all seasons, with a greater concentration in the summer period.The average annual rainfall is generally higher than 1200 mm.At higher altitudes, the climate is classi ed as ET, which indicates the tundra climate.The average annual temperature is below zero (-1.7°C) and the average rainfall is around 1066 mm.Finally, above 3000 m a. s. l. climate H is present, which indicates the high mountain climate, with the average temperature of the hottest month below 10°C and scarce rainfall.
21.0% of the study area is covered by coniferous forests and 37.7% by open spaces with little or no vegetation.High-altitude grasslands are 9.0% of the study area, mixed forests 7.9%, broad-leaved forests 7.0%, pastures 5.8% and heathlands 5.0%.Urban areas and infrastructures are 2.8%; inland waters and transitional woodlands are present with a coverage of less than 3%.

Data collection
We analysed the bags of brown and mountain hares, provided by the Wildlife service of the Province of Sondrio for the period 1980-2020.We also considered the number of active hunters in the study area.In recent years bags data has been supplemented with more information on the location of individual kills (2010-2019 and 2012-2019 for brown and mountain hare, respectively).
To the aims of this research, we analysed altitude, land cover and meteorological data.We determined the altitude of the study area using the Digital Terrain Model with a spatial resolution of 20 m (https://www.geoportale.regione.lombardia.it/).We analysed the effects of 13 land use types, obtained by the regional land use map (DUSAF, Destinazione d'Uso dei Suoli Agricoli e Forestali; scale 1:10,000), freely available online from the Regional Geoportal.DUSAF maps are available approximately every two years; therefore, considering the hunting bags' data, we used those of the years 2009, 2012, 2015 and 2018.Since the data relating to kills are annual, the DUSAF relating to the year closest to that considered was used (e.g., DUSAF 2009 for data of 2010, DUSAF 2012 for data of 2011, 2012 and 2013, and so on).
We downloaded the meteorological data relating to temperatures and precipitation from the Regional Environmental Agency (ARPA Lombardia) website (https://www.arpalombardia.it/).They concern one meteorological station located near the city of Sondrio during the entire period examined (from 1980 to 2020).For temperature data, the months between November and March were considered.We obtained the snow cover data from satellite images and the Normalized Difference Snow Index (NDSI), an index that is related to the presence of snow (Hall et al. 2001).It is calculated from satellite imageries in as much snow typically has very high visible (VIS) re ectance and very low re ectance in the shortwave infrared (SWIR), a characteristic used to detect snow by distinguishing between snow and most cloud types.We obtained NDSI data from the MOD10A2 product of the MODIS sensor (Moderate Resolution Imaging Spectroradiometer) from the TERRA satellite of NASA (Hall and Riggs 2021) accessible from the Earth Explorer website of the United States Geological Survey (USGS; https://earthexplorer.usgs.gov,accessed on 11 May 2022).We used 956 scenes of MODIS from 2000 to 2020, with a temporal resolution of 8 days and a spatial resolution of 500 m.For the analyses, we used the average snow cover for each winter since the winter 2000-2001 to the winter 2020-2021.All the spatial analyses were carried out by the software Quantum GIS (QGIS) v. 3.4.13.

Data analysis 2.3.1. Population trends
We analysed the trends of hare populations considering the bags weighted on the number of active hunters in each year, from 1980 to 2020.We performed the analyses with the software TRIM 3.54 (Trend analysis and Indices for Monitoring data; Pannekoek and van Strien 2005).The software calculates an index as the ratio between the value of each year and that of the rst year of the series and uses Loglinear models and Generalized Estimating Equations (GEE) to calculate the slope of the line representing the data.The t of the resulting model was veri ed by the chi-square test, the Likelihood Ratio (LR) and the Akaike Information Criterion (AIC).The program also allows you to consider the site, de ne a weight for each site (e.g., based on the extent) and check the effect of categorical covariates (e.g., habitat).It is also possible to verify the change in the slope of the trend in de ned subsequent periods, specifying the years in which it is believed that the change may have occurred (change points).The signi cance of the effects of covariates are veri ed using the Wald test.We used as covariates minimum and maximum temperatures, precipitation, and snow cover for each year.

Hare distribution
We evaluated the ranges of hare populations by Kernel Analysis (KA; Worton, 1989).We de ned for each species the isopleths at 95% and 50% using the kill points; the former identi es the ranges occupied by the species in the province of Sondrio while the latter identi es the core area of the range, i. e. the area with the highest density of observations.The smoothing parameter (h) used coincides with the average value of the distances between the hare kill points.
To highlight the range shifts for both species we performed the Kernel Analyses annually from 2012 to 2019 for brown hare and from 2010 to 2019 for mountain hare, based on data availability.
To evaluate any signi cant variations in the distribution of the two species over the years, we performed linear regression analyses applied to the time series (Cowpertwait and Metcalfe 2009).We tested the variance explained by the regression by the coe cient of determination R 2 .For both species, we considered the variables relating to the size of the occupied area and the mean, minimum and maximum altitude of the 95% kernels.
We used the Mann-Whitney U test to test for signi cant differences in the size and in the mean, minimum and maximum altitude of the ranges between the two species (Legendre and Legendre 1998).This test was applied by comparing the data relating to the kernels of the two species and using the altitude of the single kill points.Moreover, we used the Kruskal-Wallis non-parametric analysis of variance to test for signi cant differences between the altitude of the kill points over the years for both species.
Finally, the spatial overlap between species was evaluated by calculating the common land area between the 95% kernels of the brown hare and the mountain hare for each year.Subsequently, a linear regression analysis applied to the time series was used to highlight any changes over time.

Habitat selection
We analysed the selection of both altitude and land use types by brown and mountain hares; speci cally, we divided the altitudinal range of the Sondrio province into 200-m belts.We carried out the selection analyses for the altitudinal belts and for the land use classes at three levels, based on the comparison between usage and availability proportions (Johnson 1980;Manly et al. 2002): i) comparing the proportions of the surfaces included in the 95% kernels (use) with those of the province of Sondrio (availability), ii) comparing the proportions of the surfaces included in the core areas (use) with those of the province of Sondrio (availability), iii) comparing the proportions of the kill points in the altitudinal belts and in the types of land use (use), with those of the distribution area at 95% (availability).
The rst two levels allow to highlight the selection for the surfaces of the altitudinal bands and habitats by the two species, in the range and in the core area, and therefore they concern the need at a spatial level.The third level provides information on punctual selection and, therefore, is more concerned with the attendance of altitudinal bands and habitats.
The habitat selection was analysed by means of the permutation-based combination of sign tests (Fattorini et al. 2014), that is a non-parametric method that evaluates the overall selection considering the proportions of use.In our case, the sign test is applied for each altitudinal band and land use type.The partial null hypothesis is that the species uses the altitudinal bands or the types of habitats proportionally to its availability.The overall null hypothesis, on the other hand, is that the species uses altitudes or habitats overall based on their availability and, to evaluate it, the partial P values are combined by applying the permutation procedure proposed by Pesarin (2001).If the null hypothesis of the overall test is rejected, the P values of each partial hypothesis are taken into consideration to understand which altitudinal bands or habitats are used as well as their availability (P > 0.05) and which, instead, are selected or avoided (P < 0.05).These analyses were carried out by cumulating all the years for which data were available, using the "phuassess" R package (Fattorini et al. 2017).

Species distribution models
We formulated the distribution models of the two species by the Ecological Niche Factor Analysis (hereafter ENFA: Hirzel et al. 2002).This method compares the distribution of environmental variables between the presence sites and the study area.ENFA summarizes all environmental variables into a few, uncorrelated factors retaining most of the information.With this method we obtained two simple measures of the species niche: the marginality and the specialization; the former measures how much the mean of the environmental variables in the sites of presence differs from the mean of the same variables in the whole study area, and the latter how much their variance in the presence sites is different from the variance of the variables in the study area.
The rst factor concerns the marginality; the marginality coe cients range from − 1 to + 1 for each environmental variable (Hirzel et al. 2004;Hirzel et al. 2006).The higher the absolute value of a coe cient, the further the species departs from the mean available habitat regarding the corresponding variable.Negative coe cients indicate that the species select values lower than the average of the study area, while positive coe cients indicate a selection for values higher than the average (Hirzel et al. 2002;Santos et al. 2006).
The other factors concern the specialization and re ect the niche breadth.They are calculated by the ratio between the variance of the global distribution and the variance of the distribution of the species considered (Hirzel et al. 2004).The specialization coe cients range from − 1 to + 1 and only their absolute value matters.The higher the absolute value, the narrower the range of variability of the species with respect to the availability of the corresponding variable.
Furthermore, to provide general information on the species niche, the global marginality, specialization and tolerance coe cients can also be determined.The tolerance is de ned as the inverse of specialization and ranges from 0 to 1; low tolerance values (close to 0) indicate that the species has a narrow niche with respect to the conditions in the study area.
We performed ENFA with Biomapper 4 (Hirzel et al. 2004(Hirzel et al. , 2005(Hirzel et al. , 2007)).We measured the environmental variables using a grid superimposed on the study area, with cells of 585 × 585 m for the brown hare and 663 × 663 m for the mountain hare.We have chosen the size of the cells considering the average home range for the two species found in the literature, equal to 34.2 ha for the brown hare and 44 ha for the mountain hare (

Distribution of hares
The hunting bags showed that 2252 brown hares (from 2012 to 2019) and 596 mountain hares (from 2010 to 2019) were harvested and geolocated by hunters.The average surface (± SD) of the brown hare range was 361.3 ± 49.9 km 2 while that of the mountain hare was 945.3 ± 156.48 km 2 ; the mean altitude of the range was 1247.3 ± 10.80 m a. s. l. for brown hares and 1877.3 ± 57.35 for the mountain hare.The average minimum altitude was 208.9 ± 16.62 for brown hares and 265.3 ± 37.52 for mountain hare while the maximum altitude was respectively 2579.3 ± 73.65 and 3530.1 ± 170.78.The differences between the two species were signi cant both for range size and for altitudes (Mann Whitney U test P < 0.01 in all cases).Also, the mean altitudes of kill points showed signi cant differences between the two species (U = 105188, d.f.= 2846, P < 0.001).
The size and altitudes of the ranges of the two species did not show any signi cant trend in the period considered.No signi cant differences resulted between the altitude of the kill points over the years, both for the brown hare (Kruskal-Wallis test: χ 2 = 3.277, d.f.= 7, P = 0.858) and for the mountain hare (χ 2 = 13.399,d.f.= 9, P = 0.145).The spatial overlap between the two species in the considered period did not change signi cantly (β = 6.521 ± 3.996, P = 0.154, R 2 = 0.307).

Altitude and habitat selection
The use of altitude belts by the two hare species was non-random for the core area, range and considering the kill locations (Table 1).Within the core areas, brown hares selected the altitudes between 600 and 1800 m a. s. l. and mountain hares those between 1400 and 2200 m a. s. l.Within the range, brown hares selected the altitudes between 400 and 1800 m a. s. l. and mountain hares those between 1000 and 2400 m a. s. l.Using the kill locations, brown hares selected the altitudes between 1000 and 1600 m a. s. l. and mountain hares those between 1600 and 2000 m a. s. l.
Habitat selection was more marked for mountain hare than for brown hare; instead, overall signi cances of the differences from a random use were higher for the former species than for the latter both considering core areas, ranges, or kill sites (Table 2).Brown hare selected pastures and, in the range and core area, broad leaved, coniferous, and mixed forests; considering the kill sites, a selection for the highaltitude grasslands was observed.The mountain hare, on the other hand, selected pastures, coniferous forests, and high-altitude grasslands, within the core area, while within the range only coniferous forests were selected.Considering the kill sites, a selection by the mountain hare for pastures and coniferous forests resulted.3).The suitability map for the brown hare showed an average suitability within the study area of 17.09 (SD = 25.77,min = 0, max = 100) (Fig. 3).The areas characterized by high altitudes are considered unsuitable, while the most suitable areas are located along the slopes near the valley oor.Pastures, high-altitude grasslands and heathlands also had relatively high positive coe cients, while open spaces and broad-leaved forests had negative ones.The specialization was linked to the average altitude, inland waters and broad-leaved forests (Table 4).
The suitability map for the mountain hare showed an average suitability within the study area of 25.58 (SD = 28.26,min = 0, max = 100) (Fig. 4).The most suitable areas are located along the slopes, at higher altitudes than those suitable for the brown hares.The least suitable areas are all along the valley oor and on the mountain peaks.

DISCUSSION
The distributions of the brown and mountain hare within the province of Sondrio were different.In fact, the brown hare has been found at lower altitudes, between 381 m a. s. l. and 2288 m a. s. l., while the mountain hare is present at higher altitudes, between 1100 m a. s. l. and 2744 m a. s. l., in agreement with their ecology (Amori et al. 2008).For both species, no statistically signi cant variation was found in the altitude of the single kill points over the years; furthermore, the spatial overlap between the two species did not change signi cantly.
Considering the period between 1980 and 2020, no signi cant trends in population size were observed for either the brown or the mountain hares.On the other hand, between 2000 and 2020 a moderate increase was highlighted for the brown hare.In all cases, climatic variables do not seem to have in uenced population trends.
Considering the size and altitudes of the 95% kernels of the two hares in the investigated period, no signi cant trends were highlighted.Looking at the data, however, it is possible to notice a slightly positive trend of the maximum altitude of the ranges of both species, a slight expansion of the range size of the brown hare and a slight contraction of the range size of the mountain hare, albeit not signi cant.These trends could be con rmed by observing the distribution of species in the coming years and they could be correlated with climate change.In fact, due to the increase in temperatures, a general movement of species towards higher altitudes, in search of suitable sites for their survival is being observed in the Alps (Primack and Boitani 2013; Bisi et al. 2015).In the case of hares, an expansion of the brown hare within the areas occupied by the mountain hare is probable, with the risk of an increase in the hybridization between the two species and a contraction of the range occupied by the mountain hare, potentially leading the species to a threatened state in the Alps (Thulin 2003;La Morgia et al. 2008).
Hybridization between brown hare and mountain hare is widely documented in many European countries, with male brown hares able to mate with female mountain hares and produce fertile offspring A recent study conducted in the Italian Alps has shown that it is possible, with the current climatic conditions, to maintain a stable balance between brown hare, mountain hare and hybrids (La Morgia and Venturino 2017).However, by modelling the future effects of climate change, the study predicted an increase in brown hare and hybrid hare populations and a reduction in mountain hare.The conditions allowing for the three populations coexistence became more restricted and a total collapse of the mountain hare populations was predicted.
Both the brown hare and the mountain hare seem to select some altitude bands.The results show, in fact, that the two species use altitude in a signi cantly different way to its availability.The two species select substantially different altitude ranges, with the exception of altitudes between 1400 and 1800 m a. s. l., considering the core areas, and the range between 1000 and 1800 m a. s. l. considering the range.From the point selection analysis, however, there seems to be no overlap.Furthermore, both species selected for some land-use variables and the selection seems to have been more marked for mountain hare than for brown hare.Both the selection analysis and the ENFA showed that the brown hare selects pastures and forests, while the mountain hare selects coniferous forests, pastures and high-altitude grasslands.Thus, it appears that the two species used pastures and coniferous forests in a similar way and that there is overlap in the selection of them.Additionally, the brown hare avoided arable land.In fact, modern cultivation criteria make these areas unsuitable for the species (Smith et al. 2005).The brown hare also avoided the high-altitude grasslands (except for punctual analysis), heathlands and open spaces with little or no vegetation, which are generally present at high altitudes, while the mountain hare avoided the broad-leaved forests and arable land, which characterize low slopes.
ENFA's results show that higher global marginality values were obtained for the brown hare compared to the mountain hare.This indicates a greater deviation of the environmental variables used compared to the mean values of the study area.
From the comparison of the suitability maps, it can be observed that the areas suitable for the two species tend not to overlap, but, on the contrary, they seem complementary.The areas suitable for the brown hare, in fact, are located near the valley oor and they are not suitable for the mountain hare.
Conversely, the areas suitable for the mountain hare are at higher altitudes and appear to be avoided by the brown hare.
Some studies demonstrated that the mountain hare may have a relatively narrow distribution due to competitive exclusion by the brown hare, rather than very speci c habitat selection (Wolfe et al. 1996).In Ireland, for example, the introduced brown hare and the endemic Irish hare (Lepus timidus hibernicus) occupy very similar habitats within their sympatric ranges and they exhibit almost complete ecological niche overlap (Reid and Montgomery 2007).Furthermore, in Finland, the brown hare arrived naturally from the south-east as early as the nineteenth century (Pohjoismäki et al. 2021); Lind (1963) studied where the two species had their forms in sympatry and allopatry and he found that in sympatry the mountain hares tended to have their forms in denser forests and further away from open elds than if they were allopatric.In southern Sweden, the beginning of the contraction of the mountain hare's range coincided with the establishment and expansion of the brown hare in these areas (Thulin 2000).These studies show that the two species potentially occupy very similar ecological niches, but, due to competitive exclusion, their distribution areas rarely overlap, and their co-presence tends to be a transitory phenomenon (Flux 1981).

CONCLUSION
This research has shown that the ranges of brown hare and mountain hare are substantially separated in the province of Sondrio in recent years and the spatial overlap between the ranges of the two species remained unchanged in the period considered.Potentially, the two species would occupy a very similar ecological niche.Due to the competitive exclusion, however, the mountain hare tends to modify its habits, when the two species are in sympatry, resulting in a contraction of the range of the mountain hare.In this study, no signi cant trends in altitude or spatial overlap of the two species were observed over the period investigated, indicating that these phenomena are not occurring immediately.However, even if not signi cant, a slight increase in the maximum altitude of the ranges of both species, a slight expansion of the size of the distribution area of the brown hare and a slight contraction of the size of the range of the mountain hare were observed.To verify that these trends do not become more pronounced over time, it would be useful to activate a long-term monitoring plan; in this way it would be possible to intervene in time in case of problems for the mountain hare.Some interventions may concern restocking within the populations most at risk, reintroductions in suitable sites where the species is no longer present, or the establishment of protected areas in correspondence with the most suitable areas.It would also be useful to monitor the presence of hybrids with morphological and genetic analyses and to avoid any new Reitz and Léonard 1994; Rühe and Hohmann 2004; Gamboni et al 2008; Masseroni et al 2008; Bisi et al 2011; Schai-Braun and Hackländer 2014).The environmental variables considered correspond to the percentage of land use coverage, using the DUSAF of the year 2015 (central year with respect to the data), and to the average altitude of each cell.The number of factors included in the model was chosen from an eigenvalue comparison based on the MacArthur broken-stick distribution (Jackson 1993; Hirzel et al. 2002).The Box-Cox transformation was used for variable normalisation, as suggested by Hirzel et al. (2002).Moreover, the suitability maps were generated using the geometric mean based on the factors retained (Hirzel and Arlettaz 2003).Finally, the Boyce index (Boyce et al. 2002) was calculated to evaluate the robustness of the model.This provides a more continuous assessment of a model predictive power and varies from − 1 to 1, with 0 indicating a random model and values > 0.70 indicating a good model (Hirzel et al. 2006).

4 .
Species distribution modelsFor the brown hare, environmental variables in 635 presence sites were analysed.The global marginality was 1.15, indicating that the habitat of the brown hare differed from the average environmental conditions of the study area.Global specialization (1.57) and tolerance (0.64) indexes highlight a habitat specialization.The Boyce index was 0.78 ± 0.209 (SD), indicating a good model.Eight factors were included in the model, explaining 94.7% of the information and 89.5% of the specialization.Marginality was positively related to pastures and mixed forests, and negatively to open spaces with little or no vegetation.The specialization was linked to the average altitude, inland waters, arable lands, pastures, high-altitude grasslands, heathlands, and open spaces (Table

(
Fraguglione 1959;Gustavsson and Sundt 1965;Gustavsson 1971;Schröder et al 1987;Thulin and Tegelström 2002).It is considered a threat to the mountain hare in the Italian Alps, but it is also one of the main problems for the conservation of the endemic Irish hare (Lepus timidus hibernicus) (Reid 2011; Smith and Johnston 2019), and a factor that may increase the decline of mountain hare populations in Sweden(Thulin and Tegelström 2002).

Table 3
ENFA for the brown hare in the Sondrio province.The rst factor explained 100% of the marginality; the explained specialization of each factor is shown in the table.In bold are the most important variables.

Table 4
ENFA for the mountain hare in the Italian Alps.The rst factor explained 100% of the marginality; the explained specialization of each factor is shown in the table.In bold are the most important variables.