Quaternary range dynamics of ecologically divergent species (Edraianthus serpyllifolius and E. tenuifolius,Campanulaceae) within the Balkan refugium

Aim We investigated Quaternary range dynamics of two closely related but ecologically divergent species (cold‐tolerant Edraianthus serpyllifolius and thermophilic Edraianthus tenuifolius) with overlapping distribution ranges endemic to the western Balkan Peninsula, an important yet understudied Pleistocene refugium. Our aims were: to test predictions of the ‘refugia‐within‐refugia’ model of strong genetic subdivisions due to population isolation in separate refugia; to explore whether two ecologically divergent species reacted differently to Pleistocene climatic fluctuations; and to test predictions of the displacement refugia model of stronger differentiation among populations in the thermophilic E. tenuifolius compared with the cold‐tolerant E. serpyllifolius. Location The western Balkan Peninsula. Methods We gathered amplified fragment‐length polymorphism (AFLP) data and plastid DNA sequences from two to five individuals from 10 populations of E. serpyllifolius and 22 populations of E. tenuifolius, spanning their entire respective distribution areas. AFLP data were analysed using a Bayesian clustering approach and a distance‐based network approach. Plastid sequences were used to depict relationships among haplotypes in a statistical parsimony network, and to obtain age estimates in a Bayesian framework. Results In E. serpyllifolius, both AFLP and plastid sequence data showed clear geographic structure. Western populations showed high AFLP diversity and a high number of rare fragments. In E. tenuifolius, both markers congruently identified a major phylogeographic split along the lower Neretva valley in central Dalmatia. The most distinct and earliest diverging chloroplast DNA (cpDNA) haplotypes were found further south in the south‐easternmost populations. North‐western populations, identified as a separate cluster by Bayesian clustering, were characterized by low genetic diversity and a low number of rare AFLP markers. Main conclusions Clear evidence for multiple Pleistocene refugia is found not only in the high‐elevation E. serpyllifolius, but also in the lowland E. tenuifolius, despite the lack of obvious dispersal barriers, in line with the refugia‐within‐refugia model. Genealogical relationships and genetic diversity patterns support the hypothesis that cold‐adapted E. serpyllifolius responded to climatic oscillations mostly by elevational range shifts, whereas thermophilic E. tenuifolius did so mainly by latitudinal range shifts, with different phases (and probably extents) of range expansion. In contrast to the displacement refugia hypothesis, the two elevationally differentiated species do not differ in their genetic diversity.     

Ecological specialization promotes diversity and diversification in the Eastern Mediterranean genus Ricotia (Brassicaceae)

Despite its amazing biodiversity, the Eastern Mediterranean remains a highly understudied region when compared withthe Western Mediterranean, restricting our understanding of diversity across the entire Mediterranean. Here we use a combination of molecular markers and presence/absence data from all species of the Eastern Mediterranean genus Ricotia collected across its full geographic range to determine historical, ecological, and evolutionary factors responsible for lineage-specific diversification in the Eastern Mediterranean. Network analysis based on molecular data revealed a high genetic structure within all lineages, and phylogenetic reconstructions based on the multispecies coalescent showed that within-lineage diversification corresponded to the onset of the Mediterranean climate. Reconstruction of ancestral histories indicates that the genus originated within Anatolia and spread across the Eastern Mediterranean and Levant using the Taurus mountains. Ecological niche models suggest that local populations did not go through any major distributional shifts and have persisted in present-day habitats since the Last Glacial Maximum. Furthermore, niche differentiation tests revealed significant differences between closely related species and showed the main variables predicting species limits to be different for each species. Our results give crucial information on the patterns and processes shaping diversity in the Eastern Mediterranean and show the main factors promoting diversification to be local environmental dynamics and ecological specialization and not large-scale latitudinal movements, as often reported for southern Europe. By determining local and regional patterns of diversification in an Eastern Mediterranean genus, we further our understanding of the major trends influencing plant diversity in the Mediterranean basin as a whole.     

The geography of speciation in narrow‐range endemics of the ‘Haenydra’ lineage (Coleoptera,Hydraenidae, Hydraena)

Aim We test whether species of western Mediterranean aquatic Coleoptera of the ‘Haenydra’ lineage (Hydraenidae, Hydraena) originated through: (1) successive periods of dispersal and speciation, (2) range fragmentation by random vicariance, or (3) range fragmentation by geographic isolation owing to a general reduction of population density. Location Europe. Methods To discriminate between scenarios we use contrasting predictions of the relationship between phylogenetic and geographic distance. The phylogeny was based on 3 kb of four mitochondrial and two nuclear gene fragments of about half of the known species of ‘Haenydra’, including most western Mediterranean taxa. Divergences were estimated using a molecular clock. The relationship between phylogenetic and geographic distance was tested using bivariate plots, Mantel tests and comparison of the observed phylogeny with the one minimizing geographic distances between species, as measured using Euclidean minimum spanning trees (EMSTs). Results The monophyly of ‘Haenydra’ was strongly supported, although its phylogenetic placement was not resolved. ‘Haenydra’ was estimated to be of late Miocene age, with most species originating during the Pleistocene. In two clades (Hydraena tatii and Hydraena emarginata clades) there was a significant association between geographic and phylogenetic distance, and the reconstructed phylogeny was identical to that obtained through the EMST, demonstrating a strong non‐randomness of the geographic distribution of the species. In two other clades (Hydraena iberica and Hydraena bitruncata clades) there was no association between geographic and phylogenetic distance, and the observed phylogeny was not the one minimizing geographic distances. In one of the clades this seems to be due to a secondary, recent range expansion of one species (H. iberica), which erased the geographic signal of their distributions. Main conclusions We show that it is possible to obtain strong evidence of stasis of the geographic ranges of narrow‐range endemic species through the study of their phylogenetic relationships and current distributions. In at least two of the studied clades, current species seem to have originated through the fragmentation of a more widely distributed species, without further range movements. A process of range expansion and fragmentation may have occurred repeatedly within the ‘Haenydra’ lineage, contributing to the accumulation of narrow‐range endemics in Mediterranean Pleistocene refugia.     

Evolutionary history of the scorpionfly Dicerapanorpa magna (Mecoptera,Panorpidae)

Climate changes can have fundamental impacts on the distributional patterns of montane species, and range shifts frequently lead to allopatric divergence followed by the establishment of secondary contact zones. Many European and North American organisms have retreated to southern refugia during glacial periods and colonized northward during postglacial periods, but little is known about the evolutionary response of cold‐adapted insects to Pleistocene climate changes in eastern Asia. The scorpionfly Dicerapanorpa magna (Chou), with cold temperate habitat preference and weak dispersal ability, provides a good model system to explore how climate changes have influenced the distribution and divergence of cold‐adapted insects in eastern Asia. This study reconstructed the demographic dynamics and evolutionary history of D. magna with phylogeographic approaches, and predicted the species’ suitable areas under the Last Glacial Maximum (LGM) and current scenarios with the ecological niche modelling analysis. The mitochondrial cytochrome c oxidase subunit I resolved three phylogenetic lineages in D. magna dating back to Pleistocene, corresponding well with the geographically isolated Qinling, Bashan and Minshan Mountains. The ecological niche modelling recovered the suitable habitats for D. magna were the Qinling and Bashan Mountains under LGM and current conditions. The three lineages of D. magna might be in a process of incipient speciation, and likely derived their current distribution from separate glacial origins, followed by vicariance and divergence.     

Several Pleistocene refugia detected in the high alpine plant Phyteuma globulariifolium sternb & hoppe (Campanulaceae) in the European Alps

Phyteuma globulariifolium is a high alpine plant species growing in the European Alps and the Pyrenees. In order to elucidate its glacial history, 325 individuals from 69 populations were analysed using the amplified fragment length polymorphism (AFLP) technique. A strongly hierarchical phylogeographical pattern was detected: Two major east-west vicariant groups can be separated along a gap in the distributional area. A further subdivision into at least four populational groups is in congruence with presumed peripheral glacial refugia. There is no indication for survival on unglaciated mountain tops (nunataks) in the interior of the Pleistocene ice shield covering the Alps. Our results favour glacial survival in peripheral, unglaciated or not fully glaciated areas. Populations of P. globulariifolium in the Pyrenees are the result of relatively recent long-distance dispersal. Within the Alps, there is strong differentiation among groups of populations, whereas within them the differentiation is weak. This suggests high levels of gene-flow over short to middle distances.     

Reconstructing the demise of Tethyan plants: climate‐driven range dynamics of Laurus since the Pliocene

Aim Climate changes are thought to be responsible for the retreat and eventual extinction of subtropical lauroid species that covered much of Europe and North Africa during the Palaeogene and early Neogene; little is known, however, of the spatial and temporal patterns of this demise. Herein we calibrate ecological niche models to assess the climatic requirements of Laurus L. (Lauraceae), an emblematic relic from the Tethyan subtropical flora, subsequently using these models to infer how the range dynamics of Laurus were affected by Plio‐Pleistocene climate changes. We also provide predictions of likely range changes resulting from future climatic scenarios. Location The Mediterranean Basin and Macaronesian islands (Canaries, Madeira, Azores). Methods We used a maximum‐entropy algorithm (Maxent) to model the relationship between climate and Laurus distribution over time. The models were fitted both to the present and to the middle Pliocene, based on fossil records. We employed climatic reconstructions for the mid‐Pliocene (3 Ma), the Last Glacial Maximum (21 ka) and a CO₂‐doubling future scenario to project putative species distribution in each period. We validated the model projections with Laurus fossil and present occurrences. Results Laurus preferentially occupied warm and moist areas with low seasonality, showing a marked stasis of its climatic niche. Models fitted to Pliocene conditions successfully predicted the current species distribution. Large suitable areas existed during the Pliocene, which were strongly reduced during the Pleistocene, but humid refugia within the Mediterranean Basin and Macaronesian islands enabled long‐term persistence. Future climate conditions are likely to re‐open areas suitable for colonization north of the current range. Main conclusions The climatic requirements of Laurus remained virtually unchanged over the last 3 Myr. This marked niche conservatism imposed largely deterministic range dynamics driven by climate conditions. This species's relatively high drought tolerance might account for the survival of Laurus in continental Europe throughout the Quaternary whilst other Lauraceae became extinct. Climatic scenarios for the end of this century would favour an expansion of the species's range towards northern latitudes, while severely limiting southern populations due to increased water stress.     

Multiple refugia and barriers explain the phylogeography of the Valais shrew,Sorex antinorii (Mammalia: Soricomorpha)

The aim of the present study was to investigate the genetic structure of the Valais shrew (Sorex antinorii) by a combined phylogeographical and landscape genetic approach, and thereby to infer the locations of glacial refugia and establish the influence of geographical barriers. We sequenced part of the mitochondrial cytochrome b (cyt b) gene of 179 individuals of S. antinorii sampled across the entire species' range. Six specimens attributed to S. arunchi were included in the analysis. The phylogeographical pattern was assessed by Bayesian molecular phylogenetic reconstruction, population genetic analyses, and a species distribution modelling (SDM)‐based hindcasting approach. We also used landscape genetics (including isolation‐by‐resistance) to infer the determinants of current intra‐specific genetic structure. The phylogeographical analysis revealed shallow divergence among haplotypes and no clear substructure within S. antinorii. The starlike structure of the median‐joining network is consistent with population expansion from a single refugium, probably located in the Apennines. Long branches observed on the same network also suggest that another refugium may have existed in the north‐eastern part of Italy. This result is consistent with SDM, which also suggests several habitable areas for S. antinorii in the Italian peninsula during the LGM. Therefore S. antinorii appears to have occupied disconnected glacial refugia in the Italian peninsula, supporting previous data for other species showing multiple refugia within southern refugial areas. By coupling genetic analyses and SDM, we were able to infer how past climatic suitability contributed to genetic divergence of populations. The genetic differentiation shown in the present study does not support the specific status of S. arunchi. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105 , 864–880.     

Persistence and diversification of the Holarctic shrew,Sorex tundrensis (Family Soricidae), in response to climate change

Environmental processes govern demography, species movements, community turnover and diversification and yet in many respects these dynamics are still poorly understood at high latitudes. We investigate the combined effects of climate change and geography through time for a widespread Holarctic shrew, Sorex tundrensis. We include a comprehensive suite of closely related outgroup taxa and three independent loci to explore phylogeographic structure and historical demography. We then explore the implications of these findings for other members of boreal communities. The tundra shrew and its sister species, the Tien Shan shrew (Sorex asper), exhibit strong geographic population structure across Siberia and into Beringia illustrating local centres of endemism that correspond to Late Pleistocene refugia. Ecological niche predictions for both current and historical distributions indicate a model of persistence through time despite dramatic climate change. Species tree estimation under a coalescent process suggests that isolation between populations has been maintained across timeframes deeper than the periodicity of Pleistocene glacial cycling. That some species such as the tundra shrew have a history of persistence largely independent of changing climate, whereas other boreal species shifted their ranges in response to climate change, highlights the dynamic processes of community assembly at high latitudes.     

Conservatism of ecological niche characteristics in North American plant species over the Pleistocene-to-Recent transition

Aim  To provide a test of the conservatism of a species' niche over the last 20,000 years by tracking the distribution of eight pollen taxa relative to climate type as they migrated across eastern North America following the Last Glacial Maximum (LGM).
Location  North America.
Methods  We drew taxon occurrence data from the North American pollen records in the Global Pollen Database, representing eight pollen types – all taxa for which ≥5 distinct geographic occurrences were available in both the present day and at the LGM (21,000 years ago ± 3000 years). These data were incorporated into ecological niche models based on present-day and LGM climatological summaries available from the Palaeoclimate Modelling Intercomparison Project to produce predicted potential geographic distributions for each species at present and at the LGM. The output for each time period was projected onto the 'other' time period, and tested using independent known occurrence information from that period.
Results  The result of our analyses was that all species tested showed general conservatism in ecological characteristics over the climate changes associated with the Pleistocene-to-Recent transition.
Main conclusions  This analysis constitutes a further demonstration of general and pervasive conservatism in ecological niche characteristics over moderate periods of time despite profound changes in climate and environmental conditions. As such, our results reinforce the application of ecological niche modelling techniques to the reconstruction of Pleistocene biodiversity distribution patterns, and to project the future potential distribution range of species in the face of global-scale climatic changes.     

Phylogeography and palaeodistribution modelling of Nassauvia subgenus Strongyloma (Asteraceae): exploring phylogeographical scenarios in the Patagonian steppe

The Patagonian steppe is an immense, cold, arid region, yet phylogeographically understudied. Nassauvia subgen. Strongyloma is a characteristic element of the steppe, exhibiting a continuum of morphological variation. This taxon provides a relevant phylogeographical model not only to understand how past environmental changes shaped the genetic structure of its populations, but also to explore phylogeographical scenarios at the large geographical scale of the Patagonian steppe. Here, we (1) assess demographic processes and historical events that shaped current geographic patterns of haplotypic diversity; (2) analyze hypotheses of isolation in refugia, fragmentation of populations, and/or colonization of available areas during Pleistocene glaciations; and (3) model extant and palaeoclimatic distributions to support inferred phylogeographical patterns. Chloroplast intergenic spacers, rpl32–trnL and trnQ–5′rps16, were sequenced for 372 individuals from 63 populations. Nested clade analysis, analyses of molecular variance, and neutrality tests were performed to assess genetic structure and range expansion. The present potential distribution was modelled and projected onto a last glacial maximum (LGM) model. Of 41 haplotypes observed, ten were shared among populations associated with different morphological variants. Populations with highest haplotype diversity and private haplotypes were found in central‐western and south‐eastern Patagonia, consistent with long‐term persistence in refugia during Pleistocene. Palaeomodelling suggested a shift toward the palaeoseashore during LGM; new available areas over the exposed Atlantic submarine platform were colonized during glaciations with postglacial retraction of populations. A scenario of fragmentation and posterior range expansion may explain the observed patterns in the center of the steppe, which is supported by palaeomodelling. Northern Patagonian populations were isolated from southern populations by the Chubut and the Deseado river basins during glaciations. Pleistocene glaciations indirectly impacted the distribution, demography, and diversification of subgen. Strongyloma through decreased winter temperatures and water availability in different areas of its range.     

Southern isolation and northern long‐distance dispersal shaped the phylogeography of the widespread,but highly disjunct,European high mountain plant Artemisia eriantha (Asteraceae)

We investigated the range dynamics of Artemisia eriantha, a widespread, but rare, mountain plant with a highly disjunct distribution in the European Alpine System. We focused on testing the roles of vicariance and long‐distance dispersal in shaping the current distribution of the species. To this end, we collected AFLP and plastid DNA sequence data for 17 populations covering the entire distributional range of the species. Strong phylogeographical structure was found in both datasets. AFLP data suggested that almost all populations were genetically strongly differentiated, with 58% of the overall genetic variation partitioned among populations. Bayesian clustering identified five groups of populations: Balkans, Pyrenees, Central Apennines, one southwestern Alpine population and a Widespread cluster (eastern Pyrenees, Alps, Carpathians). Major groups were supported by neighbor‐joining and NeighbourNet analyses. Fourteen plastid haplotypes were found constituting five strongly distinct lineages: Alps plus Pyrenees, Apennines, Balkans, southern Carpathians, and a Widespread group (eastern Pyrenees, northern Carpathians, Mt. Olympus). Plastid DNA data suggested that A. eriantha colonized the European Alpine System in a westward direction. Although, in southern Europe, vicariant differentiation among the Iberian, Italian and Balkan Peninsulas predominated, thus highlighting their importance as glacial refugia for alpine species, in temperate mountain ranges, long‐distance dispersal prevailed. This study emphasizes that currently highly disjunct distributions can be shaped by both vicariance and long‐distance dispersal, although their relative importance may be geographically structured along, for instance, latitude, as in A. eriantha. © 2013 The Linnean Society of London, Botanical Journal of the Linnean Society, 2014, 174 , 214–226.     

Refugia of Potentilla matsumurae (Rosaceae) located at high mountains in the Japanese archipelago

Molecular phylogeographic studies have revealed the genetic patterns and glacial-interglacial history of many plant and animal species. To infer the Quaternary history of alpine plants in the Japanese archipelago, which is poorly known, we investigated 203 individuals of Potentilla matsumurae and its varieties from 22 populations. We found 11 haplotypes based on approximately 1400 bp of two intergenetic spacers in chloroplast DNA (trnT-L and rpl20-rps20). The distribution of these haplotypes was geographically structured, which was supported by haplotype composition, principal component analysis, and unweighted pair group method with arithmetic mean (UPGMA), and N(ST) (0.71) was significantly greater than G(ST) (0.68). In addition to the positive correlation between genetic and geographic distance (Mantel test, r = 0.497, P < 0.001), an abrupt genetic change was detected between mountains in central Honshu and the Tohoku region. This genetic boundary was further supported by analysis of molecular variance (AMOVA), and high variation (54.0%) was explained by differences on either side of this boundary. Moreover, haplotypes in central Honshu were thought to have diverged, based on an outgroup comparison. These results suggest that mountains in central Honshu served as refugia during the Quaternary climatic oscillation, although the results could not reveal the history of most mountains in the Tohoku region and Hokkaido. Nevertheless, following floristic studies, our results indicate that alpine plants in Japan experienced a history different from that in Europe; i.e. they retreated into refugia during warm periods to avoid forest development, rather than glaciers.     

Patterns of cytotype distribution and genome size variation in the genus Sesleria Scop. (Poaceae)

Polyploidization has played an important role in the diversification of the genus Sesleria (Poaceae), which comprises c. 48 species and subspecies mostly distributed in Europe. The genus' centre of diversity clearly is the Balkan Peninsula, harbouring about 80% of the species, half of which are endemic to this area. We employed chromosome counts, measurements of absolute genome size and determination of relative DNA‐content for 460 populations belonging to 43 species of Sesleria. Our main aim was to provide essential baseline data for future molecular genetic reconstructions of the genus' evolutionary history. Relative genome size allowed for a mostly clear separation of four ploidy levels. The most frequent and widespread cytotypes are tetraploids followed by octoploids, while di‐ and dodecaploids were only found in a few species. We present first chromosome numbers for the tetraploid species S. doerfleri, S. phleoides, S. skipetarum and S. tuzsonii as well as for diploid S. ovata. Based on relative and partly also on absolute genome size measurements, ploidy level was determined in tetraploid S. rhodopaea and S. voronovii for the first time, and new cytotypes were identified in S. interrupta, S. kalnikensis and S. wettsteinii (tetraploids), S. caerulea, S. klasterskyi, S. latifolia, S. tenerrima, S. ujhelyii and S. vaginalis (octoploids), and S. albanica and S. vaginalis (dodecaploids). While most Sesleria species are ploidy‐uniform, several comprise two or even, in the case of S. vaginalis, three ploidy levels. Genome downsizing after polyploidization was confirmed by significant negative correlation between ploidy level and monoploid genome size. Finally, we found a significant increase in monoploid relative genome size towards the margin of the genus' distribution area, which may be triggered by increased activity of transposable element in populations exposed to environmental or genomic stress. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179 , 126–143.     

The importance (or lack thereof) of niche divergence to the maintenance of a northern species complex: the case of the long‐toed salamander (Ambystoma macrodactylum Baird)

The relative importance of ecological vs. nonecological factors for the origin and maintenance of species is an open question in evolutionary biology. Young lineages – such as the distinct genetic groups that make up the ranges of many northern species – represent an opportunity to study the importance of ecological divergence during the early stages of diversification. Yet, few studies have examined the extent of niche divergence between lineages in previously glaciated regions and the role of ecology in maintaining the contact zones between them. In this study, we used tests of niche overlap in combination with ecological niche models to explore the extent of niche divergence between lineages of the long‐toed salamander (Ambystoma macrodactylum Baird) species complex and to determine whether contact zones correspond to (divergent) niche limits. We found limited evidence for niche divergence between the different long‐toed salamander lineages, substantial overlap in the predicted distribution of suitable climatic space for all lineages and range limits that are independent of niche limits. These results raise questions as to the importance of ecological divergence to the development of this widespread species complex and highlight the potential for non‐ecological factors to play a more important role in the maintenance of northern taxa.     

Lags in the response of mountain plant communities to climate change

Rapid climatic changes and increasing human influence at high elevations around the world will have profound impacts on mountain biodiversity. However, forecasts from statistical models (e.g. species distribution models) rarely consider that plant community changes could substantially lag behind climatic changes, hindering our ability to make temporally realistic projections for the coming century. Indeed, the magnitudes of lags, and the relative importance of the different factors giving rise to them, remain poorly understood. We review evidence for three types of lag: “dispersal lags” affecting plant species’ spread along elevational gradients, “establishment lags” following their arrival in recipient communities, and “extinction lags” of resident species. Variation in lags is explained by variation among species in physiological and demographic responses, by effects of altered biotic interactions, and by aspects of the physical environment. Of these, altered biotic interactions could contribute substantially to establishment and extinction lags, yet impacts of biotic interactions on range dynamics are poorly understood. We develop a mechanistic community model to illustrate how species turnover in future communities might lag behind simple expectations based on species’ range shifts with unlimited dispersal. The model shows a combined contribution of altered biotic interactions and dispersal lags to plant community turnover along an elevational gradient following climate warming. Our review and simulation support the view that accounting for disequilibrium range dynamics will be essential for realistic forecasts of patterns of biodiversity under climate change, with implications for the conservation of mountain species and the ecosystem functions they provide.     

Across the highest mountain on earth: discordant phylogeographic patterns and recent dispersal of Tibetan stone loaches (Triplophysa) in the Himalayas

Phylogeographic congruence among co-distributed taxa is regarded as an inherent inference to vicariance events. Nonetheless, incongruent patterns of contemporary lineage divergence among taxa indicated that species differ in their response to common past events. To investigate the role of past events, ecological traits and lineage diversification time in shaping the contemporary phylogeographic patterns, comparative analyses were conducted for Tibetan stone loaches in the Himalayas using three gene markers and two ecological traits (depth of caudal peduncle in their length and presence/absence of posterior chamber of the air bladder). By a thorough sampling in two flanks of the Himalayas, the authors detected that phylogenetic breaks were spatially discordant and divergences of populations were also temporally asynchronous in co-distributed loaches. Estimated divergence time using fossil-calibrated node dating indicated that the Tibetan stone loaches colonised into the south flank of the Himalayas until the Pleistocene. The demographic expansions were also disconcerted between populations in north and south flanks, or east and west Himalayas. Ongoing gene flows between populations in north and south sides implied that the Himalayas do not strictly impede dispersal of cold-adapted species. The results highlight that the quaternary climatic oscillation, in conjunction with ecological traits and lineage diversification time, shaped contemporary phylogenetic patterns of stone loaches in the Himalayas and provide new insights into the biodiversity and composition of species in the Himalayas and surrounding region.