Heap, Culham and Osborne [17] used MAXENT [20] environmental niche models (ENMs) to predict species probability of occurrence for 4209 Euro/Mediterranean plant species at 1-km spatial resolution across the Mediterranean Basin defined by the geographical coordinates 50˚N, 26˚S, −10˚W, 40˚E and under four climate scenarios (baseline 1950-2000, 2020, 2050 & 2080). MAXENT models were computed using 22 environmental layers consisting of: 19 BIOCLIM layers [21] ; one elevation layer; one soil layer [22] ; and one land-use layer [23] . Each MAXENT species ENM weighted the environmental input layers according to their relevance to that specific species’ distribution. Given that the Iberian Peninsula covers a wide range of habitats this methodology was considered more appropriate than the selection of a smaller range of environmental layers as used by Pliscoff and colleagues in their limited study of 13 flora species in the Atacama desert [24] .

Baseline climate (1950-2000) BIOCLIM data was downloaded from WorldClim (http://www.worldclim.org). Data on near-future (2020) climatic conditions data was downloaded from Climate Change, Agriculture and Food Security (http://www.ccafsclimate.org) elaborated with methodology developed by Ramirez and Jarvis [25] . Most of the plant species occurrence data came from GBIF (http://www.data.gbif.org) with remaining data from the University of Reading Herbarium listed as RNG in Index Herbariorum [26] . These data were then cleaned removing various errors [27] , for example; extraneous records, duplications, taxonomic disambiguation, spatial coordinate imprecision and points missing environmental data using the filtering methodology described in Heap and Culham [28] . It was not possible to temporally filter as, except for more recent data, most of the data was undated. However, it is probable that much of the older data was collected in the 1950:2000 timeframe corresponding to the baseline climate period. As noted in Heap, Culham and Osborne [17] , the species occurrence data used included data from a low resolution UTM grid that skewed projected biodiversity losses for France [17] . Consequently, we removed these data and recomputed the ENMs to remove this error source (Fig- ure 1(a)). From the resulting pool of 4150 species, we extracted probability grids covering just the Iberian Peninsula and Balearics for 3267 Iberian plant species (see Appendix S1 in Supporting Information for a detailed list) under the baseline (1950-2000) and 2020 climate scenarios (Figure 1(b)). The 3267 studied species represent about 40% of the 8500 Iberian & Balearics flora estimated by Castroviejo [29] and each plant species has a known Iberian range principally established from the following sources: Castroviejo [29] , Casas [30] , Rivas-Martínez and colleagues [31] , Euro + Med [32] , The Plant List [33] , Ros and colleagues [34] , Roskov and colleagues [35] & Encyclopedia of Life [36] . We included native, non-native and crop species as they all potentially contribute to overall biodiversity. Interactions between these categories were outside the scope of this study.

A mask representing the 294 Iberian PAs was then prepared using data from the World Database on Protected Areas (http://www.wdpa.org/) and ENMs for the previously defined Iberian plant species were mined to obtain suitable habitat grid cells contained by the polygonal park borders under the baseline climate and near-future climate scenarios (Figure 1(c)). Suitable habitat was defined by grid cells with values greater or equal to 0.1 similar to the approach used by Pittman and Brown [37] . This threshold was consistently applied to all species under both climate scenarios. Morin and Thuiller [38] have observed that “at the continental scale, niche-based models have been widely used in the last 10 years to predict the potential impacts of climate change on species distributions all over the world”. The rough approximation to the fundamental niche described by these ENMs is based mainly on bioclimatic data. However, Araújo and colleagues [12] expressed their reservation that “using the full bioclimatic envelopes to assess the impacts of climate change on protected areas would amount to estimating species losses from areas where they might not occur, thus undermining the usefulness of the assessment”. The solution to this problem offered by Araújo and colleagues [12] was to only consider species presence predicted by ENMs where it was confirmed by atlas records. The leading resource for European flora is the Atlas Florae Europaeae (AFE). As of December 2013, this atlas covers just over 20% of European taxa―currently a significant limit on the number of taxa that could be considered in a biodiversity richness change study using the cross-validation approach proposed by Araújo and colleagues [12] . Consequently, our species presence cross-validation procedure was limited to plants belonging to the species pool of the Iberian Peninsula.

Accounting for species dispersal is a daunting challenge. Ideally we would handle this by grid cell but since there are hundreds of species per grid cell and several hundred thousand grid cells to consider, this becomes a monumental computing task. Consequently, we took a less intensive approach assuming unlimited dispersion within a focal PA and migration from other PAs at various distance intervals. Regarding external species immigration, there was only one species in our data north of the border between Spain and France that was sufficiently close to potentially migrate into our study region. The nearest Iberian PA to the southern Spanish border is 40 km away and we had only 21 non Iberian plant species in northern Africa within 30 km of the southern border. Consequently, we did not calculate potential species immigration to Iberia from neighbouring countries due to the paucity of proximate different species and insufficient number of proximate PAs. In determining unlimited species dispersal within a PA, where a species’ environmental niche was present under the 2020 climate scenario then this was allowed where the species’ environmental niche was also present under the baseline climate scenario in the same PA. For migration from other PAs, we considered six scenarios of annual dispersal rates; namely, zero, 0.1 km, 0.5 km, 1 km, 2 km and unlimited.

Aggregate species probability values were summed by PA grid cell for the two climate scenarios and the percentage change of biodiversity richness derived applying the formula described in Heap, Culham and Osborne [17] .

Species environmental niche directional movement represents the bearing in degrees derived from the azimuth drawn between the centre of mass of the species’ distributions under the baseline and 2020 climate scenarios. The resulting species directional data vectors were then converted to a random VonMises distribution to which a Kuiper test was applied. A VonMises distribution of circular data is the equivalent of the normal distribution for linear data and the Kuiper test determined the extent to which the distribution differed from random. The distance moved by the centre of mass between the two climate scenarios was calculated using Euclidean geometry. This methodology is similar to that described in Groom [8] .

Horizontal range limit changes for “northern” and “southern” species were computed based on the methodology described by Brommer [39] where the change in range margin was plotted against change in distribution on a log10 scale. The range margin was defined as the median latitude of the 10 most marginal grid cells. Positive values for range margin change indicated northward movement and negative values southward movement. Distribution changes were calculated as the log10 proportion of baseline climate occupied grid cells over 2020 climate occupied grid cells. “Northern” species were defined as those plant species occupying at least 10 grid cells under each climate scenario with a southern range margin within the Iberian Peninsula. “Southern” species were similarly defined though this time with a northern range margin within the Iberian Peninsula. Vertical niche movement compared mean altitude changes of occupied PA grid cells with change in distribution. In each case, the “y” intercept was then subject to a “t-test” to determine the probability P of range movement.

Figure 2(a) used zero species dispersal (from other PAs) but there were no observable changes at this scale regardless of the species dispersal scenario used.

For most Iberian PAs, the effects of species dispersal rate on mapped biodiversity richness change for the map legend ranges used is invisible. Picos de Europa National Park located near the northern Spanish coastline was a notable exception. As expected, biodiversity richness changes between the baseline and 2020 climate scenarios are positively correlated with increasing dispersal rates. There are no observable differences in biodiversity change between zero and 0.1 km per annum dispersal from other PAs (Figure 2(b)). Biodiversity change is similar for 0.5 km, 1 km and 2 km annual dispersal rates (Figure 2(c)). Figure 2(d) is included to circumscribe the maximum possible effect of species dispersal on biodiversity change but it is clearly an unrealistic scenario as it potentially would permit dispersal from a southern coastal PA to a northern coastal PA between the two climate scenarios. Figure 2(c) (at 1 km per annum) is the most realistic representation of biodiversity change for this national park where species dispersal results in slightly smaller diversity losses and slightly higher diversity gains than zero dispersal (Figure 2(b)).

The 3267 modelled species consisted of 3206 “persistent” species (i.e., computed to be present under both climate scenarios) and 61 “extirpated” species (computed to become locally extinct under the 2020 climate scenario). Persistent species were further classified in Table 1.

The 61 plant species computed to become locally extinct under the 2020 climate scenario represent a 1.87% loss in overall biodiversity. However, there are a further 38 critically endangered plant species that will see a habitat contraction of ≥ 99% (regardless of dispersal scenario) so by 2020, overall biodiversity loss may easily affect approx. 100 species or 3% of the 3267 plant species modelled.

Appendix S2 in Supporting Information provides a detailed list of extirpated and critically endangered species. Local extinctions (Table 2) are generally distributed in the north of the Iberian Peninsula with a mean latitude ranging from 42.0565 to 43.357 and mean longitude ranging from −6.7945 to +2.5206. We defined critically endangered species (Table 2) as those whose distribution under the baseline climate will contract by ≥ 99%. The general distribution pattern of this group is again the northern Iberian Peninsula with a range similar to that for local extinctions.

The 3206 persistent species will see an average contraction in their habitat of 13.14% with 683 (21%) of these species seeing a contraction of more than 50%. Centre of mass movement will exceed 1 km per year for 963 or

^a335 species present in the southern half of Iberia & 129 species in the northern half; ^bPresent in less than ten 1 km² grid cells.

roughly 30% of persistent species. Both these statistics were determined under the 1 km per year dispersal scenario.

For all persistent species, although the overall azimuth of niche movement is northerly, there are significant numbers of species showing westerly and easterly niche movement, especially for scenarios of low annual dispersal rates (Figure 3). The main contributors to this phenomenon are northern species (Figures 4(a)-(c)). Increasing northerly niche movement is positively correlated with faster species dispersal rates for persistent species where southern species are chiefly responsible for this movement (Figure 3 & Figures 4(d)-(f)). The effect of species dispersal rates is minor on overall movement of northern species niches (Figures 4(a)-(c)) but for southern species, there is a radical change in direction/magnitude from somewhat westerly to strong northerly (Figures 4(d)-(f)). Kuiper test scores were highly significant (P < 0.01) for all species categories at all species dispersal rates.

Under the 1 km per annum species dispersal scenario, the southerly range margin of northern species will retreat northward at a rate of 8.9 km per decade (P < 2e−16) (Figure 5(a)) between the two climate scenarios. Scenarios of higher dispersal rates from other PAs will reduce this trend to a small degree (Appendix S3: Table 1).

We did not find any statistically significant changes in the northern range margin of southern species until the dispersal rate reached at least 0.5 km per year (Appendix S3: Table 2). Assuming an average 1 km per year dispersal rate, the habitat of southern species will expand northwards at a statistically significant (P < 0.02) rate of 1.3 km per decade. Overall distribution change is balanced between southern species with some species expanding and others contracting their ranges (Figure 5(a)).

Vertical niche movement is strongest for northern species (Figure 5(b)) whose overall decadal shift of +25 m is highly significant (P < 2e−16)?see Table 3. For southern species there is a highly significant (P < 2e−16) overall vertical niche movement of +5.5 m per decade which by contrast with northern species is more influ-

enced by the migration rate (Table 4). There are more southern species than northern species exhibiting downward vertical niche movement (Figure 5(b)).

Of the 61 species calculated to become locally extinct, several have large environmental niches within Iberian PAs under the 1950:2000 climate scenario (Appendix S2). Strikingly, all 61 of these species as well as all 38 critically endangered species have a distinctly northern current range. While the azimuth of overall niche move- ment is northward, there are distinct trends within Iberia that we will discuss next.

The azimuth of movement of persistent species niches is northerly where species migration from other PAs is unlimited and north-westerly where species migration from other PAs is zero (Figure 3). However, this overall movement belies two distinct westerly and easterly trends driven by northern species (Figures 4(a)-(c)). Extreme predicted shifts of the centre of mass for northern species are likely due to massive population extirpation in remotely located parks and the west/east layout of northern Iberian PAs is driving this. However, at smaller rates of niche movement (between 0 and 10 km) Figures 4(a)-(c) reveal a similarly strong westerly/easterly trend so other factors must be at work. Two important factors will be local climate and topography. In the Iberian Peninsula winter rain is brought by north-west and westerly winds producing a strong precipitation gradient [41] as reflected by our analysis. Much of this terrain is mountainous (Figure 2(a)) and there are prominent north/ south oriented valleys particularly in the high Pyrenees. Thus, climatic niche movement is predominantly eastward or westward in search of cooler temperatures and wetter conditions, particularly so in northern Spain. Working at 1 km resolution rather than a coarser resolution enabled us to observe in detail this phenomenon.

Our map of relative Iberian floristic diversity (Figure 6) shows many similarities with that of Fernández- González and colleagues: Figure 5.2 [11] . Apart from the north Atlantic Portugal/Spain coastline, there are strong correlations both for high and low biodiversity areas. We also agree with their observation that climatic displacement will exceed dispersal rates for many species.

As noted in the introduction, most Iberian PAs are in mountainous areas containing higher than average plant diversity (Figure 6). Except for the Pyrenees and central Spain, major Iberian PAs are generally in areas of biodiversity gain or low projected biodiversity loss (Figure 2(a)).

Many of the species predicted to be locally extinct or critically endangered under the near-future climate scenario are currently widely distributed in Europe and Asia. These species generally find, in the northern part of the Iberian Peninsula, their southern range limits so we are detecting contractions of their distribution range. In contrast with Fernández-González and colleagues [11] , who predicted a higher influence of warming in northern Spain and lower water availability in the south, our results suggest that most of the taxa close to extinction or critically endangered are from northern areas such as the Pyrenees or Cantabrian range where they are linked to humid habitats. Hence, we expect not only warming but also lower rainfall to cause near-future biodiversity loss in northern Spain due to consequent increased soil moisture deficit, albeit remnant populations of plant species may still persist locally in enclaves of benign environmental conditions created by rough terrains [42] . The most vulnerable habitats to immediate species loss are those related to the presence of water and at altitudes between 650 m and 1700 m (Table 2).

The Pyrenees is the main area of high biodiversity facing the greatest threat from near-term climate warming. Centrally located protected areas like Ordesa y Monte Perdido National Park, Posests-Maladeta Park & Aigüestortes i Estany de Sant Maurici National Park will generally fair better than elsewhere. Relocating species at higher altitudes within these PAs should allow for their survival in the wild given the pronounced westerly and easterly movement of climatic envelopes for many northern species (Figures 4(a)-(c)). However, this does assume that steps are taken to mitigate the impact that translocated species could have on the locally native flora [43] .

Projected biodiversity loss for central Catalonia exceeds 40% (Figure 2(a)). The Catalonian protected areas of Can Simo, Massís del Montseny & Sant Llorenç del Munt i l’Obac will be particularly hard hit but Font Gro-

ga Collserola Park (Barcelona) shows a net counter-tendency. Therefore, Font Groga could become a refuge for Catalonian flora.

Floristic diversity is largely projected to increase in the Los Alcornocales and Sierra de Grazalema Natural Parks of Andalusia and these projected biodiversity gains will be influenced by dynamic species able to conquer new spaces, pioneer species like ruderals or species belonging to seral communities (shrublands, etc.). Additionally, we note that these projected biodiversity gains might be illusive simply because we assumed a fixed 100% rate of establishment success at newly available sites which is not likely to happen for all species. Indeed, recipient communities might resist and limit the establishment success of new colonizers at newly suitable sites. In southeast Spain, the Sierra Nevada National Park will also become a high-biodiversity refuge (Figure 2(a)) except for biodiversity loss from summits [44] . However, here thermophilization is likely to play a role in the decline of cold-adapted species and increase in warm-adapted species [45] .

There are 15 Spanish national parks administratively managed by the Spanish Institution for National Parks (an autonomous agency). Every year this institution finances different research projects to improve the scientific knowledge of biodiversity with a budget for the present year of ?26,855. The nine National Parks in the Iberian Peninsula are identified in Figure 2(a), there are others, principally in the Canary Islands, that are not included in the present study. Additional sources of scientific knowledge funding for PAs but not specifically for the National Park net are: universities; central regional or local Spanish governments; and private foundations. Considering the limited financial resources available in recent years, Alagador, Cerdeira and Araújo [46] propose a detailed species-based methodology for identifying under-performing PAs with a dire biodiversity loss forecast so that they can be released and conservation efforts concentrated elsewhere. This study aids this goal by broadly identifying PAs with significant projected floristic diversity gains and losses under near-future climate change.