Kumar Mainali
email: kpmainali@utexas.edu

Subodh Adhikari

Sushila Shrestha

Michael C Singer

Joseph White

Camille Parmesan

Charles D Canham

Reciprocal transplants reveal asymmetric local adaptation of Himalayan Rhododendron approaching elevational range limit

As plant species expand their upper limits of distribution under current warming, some retain both traditional climate space and biotic environment while others encounter novel conditions. The latter is the case for Rhododendron campanulatum, a woody shrub that grows both above and below treeline at our study site in the Eastern Himalayas where a very conspicuous, stable treeline was defined by a nearly contiguous canopy of tall Abies spectabilis trees, many of which are over a century old. Prior work showed that treeline had remained static in this region while R. campanulatum expanded its elevational range limit. We tested local adaptation of R. campanulatum by performing reciprocal transplants between the species' current elevational range limit (4023 m above sea level [asl]) and just above treeline (3876 m asl).

Contrary to expectation, the coldest temperatures of late winter and early mid-spring were experienced by plants at the lower elevation: R. campanulatum at species' limit (upper site) were covered by snow for a longer period (40 more days) and escaped the coldest temperatures suffered by conspecifics at treeline (lower site). The harsher spring conditions at treeline likely explain why leaves were smaller at treeline (15.3 cm 2 ) than at species limit (21.3 cm 2 ). Contrary to results from equivalent studies in other regions, survival was reduced more by downslope than by upslope movement, again potentially due to extreme cold temperatures observed at treeline in spring. Upslope transplantation had no effect on mortality, but mortality of species limit saplings transplanted downslope was three times higher than that of residents at both sites. A general expectation is that locals should survive better than foreign transplants, but survival of locals and immigrants at our species limit site was identical. However, those species limit saplings that survived the transplant to treeline grew faster than both locals at treeline and the transplants at species limit. Overall, we found asymmetric adaptation:

Compared with treeline saplings, those at species limit (147 m above treeline) were more tolerant of extremes in the growing season but less tolerant of extremes in

INTRODUCTION

Current climate change is shifting temperature isotherms upward in mountains [START_REF] Beniston | Climatic Change in Mountain Regions: A Review of Possible Impacts[END_REF][START_REF] Ipcc | Climate Change 2007: Impacts, Adaptation and Vulnerability[END_REF]IPCC, , 2014)), inducing responses from species in distribution and phenology [START_REF] Chen | Rapid Range Shifts of Species Associated with High Levels of Climate Warming[END_REF][START_REF] Parmesan | A Globally Coherent Fingerprint of Climate Change Impacts across Natural Systems[END_REF]. Included in the distributional responses is a general trend for population extinctions and range contractions at lower elevational boundaries [START_REF] Wiens | Climate-Related Local Extinctions Are Already Widespread among Plant and Animal Species[END_REF] and for range expansions driven by colonization at upper boundaries [START_REF] Freeman | Rapid Upslope Shifts in New Guinean Birds Illustrate Strong Distributional Responses of Tropical Montane Species to Global Warming[END_REF][START_REF] Grabherr | Climate Effects on Mountain Plants[END_REF][START_REF] Lenoir | A Significant Upward Shift in Plant Species Optimum Elevation during the 20th Century[END_REF][START_REF] Liang | Species Interactions Slow Warming-Induced Upward Shifts of Treelines on the Tibetan Plateau[END_REF][START_REF] Lustenhouwer | Rapid Evolution of Phenology during Range Expansion with Recent Climate Change[END_REF][START_REF] Parmesan | Climate and Species' Range[END_REF].

Studies of plant evolution at expanding range margins are still rare [START_REF] Lustenhouwer | Rapid Evolution of Phenology during Range Expansion with Recent Climate Change[END_REF]. However, plants typically show high spatial variation in phenology, growth, and ecophysiology, often in response to elevational gradients [START_REF] Aitken | Adaptation, Migration or Extirpation: Climate Change Outcomes for Tree Populations[END_REF][START_REF] Keller | Climate-Driven Local Adaptation of Ecophysiology and Phenology in Balsam Poplar, Populus balsamifera L.(Salicaceae)[END_REF], and there is a long history of research on phenotypic variation of plants across elevational transects. Investigations of the adaptive significance and mechanistic basis of within-species variation across elevations have typically used common garden experiments or reciprocal transplants among natural habitats [START_REF] Adhikari | Phenotypic Trait Variation in Populations of a Global Invader Mayweed Chamomile (Anthemis cotula): Implications for Weed Management[END_REF][START_REF] Clausen | Experimental Studies on the Nature of Species. IV. Genetic Structure of Ecological Races[END_REF][START_REF] Hargreaves | Are Species' Range Limits Simply Niche Limits Writ Large? A Review of Transplant Experiments beyond the Range[END_REF][START_REF] Johnson | Reciprocal Transplant Gardens as Gold Standard to Detect Local Adaptation in Grassland Species: New Opportunities Moving into the 21st Century[END_REF][START_REF] Körner | Alpine Treelines: Functional Ecology of the Global High Elevation Tree Limits[END_REF][START_REF] Lee-Yaw | A Synthesis of Transplant Experiments and Ecological Niche Models Suggests that Range Limits Are Often Niche Limits[END_REF][START_REF] Midolo | Plant Performance and Survival across Transplant Experiments Depend upon Temperature and Precipitation Change along Elevation[END_REF][START_REF] Ohsawa | Global Patterns of Genetic Variation in Plant Species along Vertical and Horizontal Gradients on Mountains[END_REF][START_REF] Turesson | The Genotypical Response of the Plant Species to the Habitat[END_REF]. Results from these studies have been diverse. Plants sampled from different elevations may not differ at all [START_REF] Fetched | Lack of Ecotypic Differentiation: Plant Response to Elevation, Population Origin, and Wind in the Luquillo Mountains, Puerto Rico[END_REF] or, when they do differ, the divergence can be mostly in heritable traits [START_REF] Clausen | Experimental Studies on the Nature of Species. IV. Genetic Structure of Ecological Races[END_REF], in plasticity [START_REF] Pfennigwerth | Trait Variation along Elevation Gradients in a Dominant Woody Shrub Is Population-Specific and Driven by Plasticity[END_REF], or in both [START_REF] Van Nuland | Intraspecific Trait Variation across Elevation Predicts a Widespread Tree Species' Climate Niche and Range Limits[END_REF].

Here, we contribute to the sparse literature on the mechanistic basis and adaptive significance of variation around expanding elevational range limits of plants by reporting results of reciprocal transplants performed on a tall woody shrub, Rhododendron campanulatum D. Don, that is currently expanding its range limit in the Himalayas [START_REF] Rana | Dendroecological Studies of Rhododendron campanulatum D. Don along the Elevational Gradient of Manaslu Conservation Area, Nepal Himalaya[END_REF][START_REF] Singh | Expansion of Rhododendron campanulatum Krummholz in the Treeline Ecotone in Tungnath, Garhwal Himalaya[END_REF]. Our study area is the vicinity of treeline in Langtang National Park, Nepal [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF], a region with negligible influence of direct anthropogenic effects such as land use changes. Although there have been hundreds of studies of reciprocal transplant performed across geographic and elevational ranges worldwide (see [START_REF] Hargreaves | Are Species' Range Limits Simply Niche Limits Writ Large? A Review of Transplant Experiments beyond the Range[END_REF][START_REF] Lee-Yaw | A Synthesis of Transplant Experiments and Ecological Niche Models Suggests that Range Limits Are Often Niche Limits[END_REF][START_REF] Midolo | Plant Performance and Survival across Transplant Experiments Depend upon Temperature and Precipitation Change along Elevation[END_REF] for review and synthesis of those studies), to the best of our knowledge, this is the first reciprocal transplant experiment conducted in the Eastern Himalayas excluding dry Tibetan plateau and one of the very few in the tropical and subtropical geographies of the world (see [START_REF] Datta | Processes Affecting Altitudinal Distribution of Invasive Ageratina adenophora in Western Himalaya: The Role of Local Adaptation and the Importance of Different Life-Cycle Stages[END_REF] for a reciprocal transplant experiment conducted in the Western Himalayas, and [START_REF] Shen | Seed-Based Treeline Seedlings Are Vulnerable to Freezing Events in the Early Growing Season under a Warmer Climate: Evidence from a Reciprocal Transplant Experiment in the Sergyemla Mountains, Southeast Tibet[END_REF][START_REF] Cui | Plastic Population Effects and Conservative Leaf Traits in a Reciprocal Transplant Experiment Simulating Climate Warming in the Himalayas[END_REF] for the reciprocal transplant experiments in Tibet).

Treeline researchers define three upper elevational boundaries. Following [START_REF] Körner | A World-Wide Study of High Altitude Treeline Temperatures[END_REF], the virtual line representing the uppermost boundary of closed forest canopy is designated as timberline. Above timberline, trees are found in clumps. The virtual line that connects the highest clumps is designated as treeline [START_REF] Körner | A World-Wide Study of High Altitude Treeline Temperatures[END_REF]. Treeline is not identical to species limit: globally, saplings of various tree species have been observed above treeline [START_REF] Gaire | Treeline Dynamics with Climate Change at the Central Nepal Himalaya[END_REF][START_REF] Körner | Alpine Treelines: Functional Ecology of the Global High Elevation Tree Limits[END_REF][START_REF] Singh | Expansion of Rhododendron campanulatum Krummholz in the Treeline Ecotone in Tungnath, Garhwal Himalaya[END_REF]. Therefore, the uppermost boundary at which any individual (of any size or class) of a tree species is found is defined as the species limit. The position of treeline depends on how a "tree" is defined; [START_REF] Körner | A World-Wide Study of High Altitude Treeline Temperatures[END_REF] defined a treeline as the virtual line connecting the uppermost patches of upright tree individuals that are at least 3 m tall.

Seeds of tree species at treeline are carried upslope where abiotic and biotic elements of the habitat affect whether and how the seeds grow. Tree saplings establishing above treeline face a new set of environmental conditions including different amounts of radiation, longer snowpack duration at higher elevation, and different moisture regimes, soil types, and biotic interactions. For example, under the canopy of tall trees (e.g., Abies spectabilis) below treeline in the Himalayas, ground vegetation is close to nonexistent, except in gaps [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF]. Trees at or below treeline, with their open architecture, have little resistance to free atmospheric convection, resulting in tree canopy temperatures only slightly above ambient air temperatures [START_REF] Körner | Alpine Treelines: Functional Ecology of the Global High Elevation Tree Limits[END_REF]. Tall trees below treeline also cast dense shade with their thick canopies, further contributing to a cold microhabitat for saplings [START_REF] Körner | Alpine Treelines: Functional Ecology of the Global High Elevation Tree Limits[END_REF]; note however that krummholz and adult-sized clusters of trees can also have the opposite effect [START_REF] Mcintire | Wind Exposure and Light Exposure, More than Elevation-Related Temperature, Limit Tree Line Seedling Abundance on Three Continents[END_REF]. Conversely, the ground vegetation above treeline is dense [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF] and temperatures experienced by short vegetation, with its compact canopy, can decouple from free atmospheric convection, resulting in substantial solar heating that offers beneficial facilitation to saplings [START_REF] Körner | A World-Wide Study of High Altitude Treeline Temperatures[END_REF][START_REF] Liang | Species Interactions Slow Warming-Induced Upward Shifts of Treelines on the Tibetan Plateau[END_REF][START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF][START_REF] Shen | Causes for Treeline Stability under Climate Warming: Evidence from Seed and Seedling Transplant Experiments in Southeast Tibet[END_REF]. By studying 87 mountain summits belonging to 10 mountain ranges in Europe, the GLORIA project found that tree canopy temperature is coupled with the atmospheric temperature but ground vegetation maintains a higher temperature [START_REF] Bürli | A Common Soil Temperature Threshold for the Upper Limit of Alpine Grasslands in European Mountains[END_REF]. [START_REF] Körner | Alpine Plant Life: Functional Plant Ecology of High Mountain Ecosystems[END_REF] reported heating of alpine cushions to 20 C above air temperature and of shrubs and alpine grass to 10 C warmer. Because of these differences between environments above and below treeline in their aerodynamic properties and warmth by sunlight, saplings experience colder air below treeline than above it until they become tall enough (trees) to couple with the free atmospheric convection.

Seed dispersal upslope from treeline is likely random; however, the seedling establishment process differentially filters out the genotypes that do not tolerate local conditions [START_REF] Davis | Range Shifts and Adaptive Responses to Quaternary Climate Change[END_REF]. This selective sieving of unfit genotypes can continue for several seasons, leaving in the colonized habitat only those individuals that can tolerate year-round conditions. Therefore, natural selection on thermal traits such as cold tolerance will differ between populations above and below treeline. Response to such selection can be plastic [START_REF] Anderson | Selection Favors Adaptive Plasticity in a Long-Term Reciprocal Transplant Experiment[END_REF][START_REF] Münzbergov A | Genetic Differentiation and Plasticity Interact along Temperature and Precipitation Gradients to Determine Plant Performance under Climate Change[END_REF][START_REF] Pfennigwerth | Trait Variation along Elevation Gradients in a Dominant Woody Shrub Is Population-Specific and Driven by Plasticity[END_REF] and/or genetic [START_REF] De Villemereuil | Patterns of Phenotypic Plasticity and Local Adaptation in the Wide Elevation Range of the Alpine Plant Arabis alpina[END_REF][START_REF] Gonzalo-Turpin | Local Adaptation Occurs along Altitudinal Gradient despite the Existence of Gene Flow in the Alpine Plant Species Festuca eskia[END_REF]. In the present case, genetic response is possible, provided that appropriate genetic variation exists in the source populations below treeline. Not surprisingly, a global meta-analysis of reciprocal common garden experiments shows that the climate-regime-induced differences in trait values (survival, reproduction, biomass, and growth)-an expression of local adaptation-were more distinct and stronger (higher Hedge's d) for experiments conducted with seedlings than with seeds [START_REF] Lortie | A Synthesis of Local Adaptation to Climate through Reciprocal Common Gardens[END_REF]. Some of the aspects of genetic differentiation of the saplings, potentially resulted due to the selection pressure of local edaphoclimatic conditions, can be estimated with reciprocal transplant experiments that yield responses from plants based on their genetic adaptation, plasticity, or both. Therefore, these experiments are the standard practices used to determine the adaptive potential of plant populations from one place when grown in a different place with a different set of climatic, environmental, and biotic conditions [START_REF] Johnson | Reciprocal Transplant Gardens as Gold Standard to Detect Local Adaptation in Grassland Species: New Opportunities Moving into the 21st Century[END_REF][START_REF] Lortie | A Synthesis of Local Adaptation to Climate through Reciprocal Common Gardens[END_REF].

We aim to determine whether and how saplings of R. campanulatum, the most common tree species at the treeline ecotone of the Eastern Himalayas in Nepal [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF][START_REF] Polunin | Flowers of the Himalaya[END_REF], are adapted to living above the current treeline. We assessed this by performing a reciprocal transplant of saplings between two sites: one immediately above treeline (i.e., treeline site) and a second near the species limit (i.e., species limit site) located at an elevational distance of ~147 m above the first site. Specifically, we test the following hypotheses:

(1) Because the saplings from species limit sites are dormant during other seasons, these individuals are better adapted to growing season climate extremes than saplings from treeline site. (2) Adaptation to extreme climate conditions during the growing season may not necessarily offer year-round protection, which requires strategies to avoid, rather than tolerate, extremes, for example, by remaining dormant during unfavorable conditions because breaking dormancy could exacerbate problems.

MATERIALS AND METHODS

Study site

The study was conducted in Nepal's Langtang National Park, 50 km north of the Kathmandu Valley (treeline site: 85.36532 E, 28.07401 N, 3876 m above sea level [asl]; species limit site: 85.36738 E, 28.0717 N, 4023 m asl). The park (1710 km 2 in area) has an elevation ranging from 1000 to 7200 m [START_REF] Fox | Mapping Conflicts between Biodiversity and Human Needs in Langtang National Park, Nepal[END_REF] and has been relatively undisturbed by humans for centuries. While cattle grazing occurs at lower elevation within the park areas, our study sites, located at the treeline ecotone (at or above 3876 m asl), are distant from the nearest human settlements (>7-h walk for the locals). Little human impact is observed at the sites that are 4-5 h walk from the nearest, and least favored, tourist trail. The study was conducted on a north-facing slope of a mountaintop with a wide belt of geographic space available at and above treeline. At our study sites, a very conspicuous treeline was defined by the presence of a nearly contiguous canopy of tall and over a century old A. spectabilis trees [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF]; hence, by definition, it is also a "timberline." This space above treeline was completely covered by plants, mostly by ground vegetation dominated by Rhododendron anthopogon, with a fraction of it occupied by individuals of several tree species (Figure 1). The vertical distance between the treeline and the top of the mountain was >400 m. The uppermost part of this space above species limit site had no tree species, not even small saplings (additional details about the site are provided in [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF].

In accordance with the regional climate warming [START_REF] Ipcc | Climate Change 2007: Impacts, Adaptation and Vulnerability[END_REF](IPCC, , 2014)), gridded monthly estimates by Climate Research Unit (TS3.10, 0.5 spatial resolutions) show that the climate at our study sites has indeed been warming since ca. 1970 [START_REF] Mitchell | An Improved Method of Constructing a Database of Monthly Climate Observations and Associated High-Resolution Grids[END_REF]. This has been supported by the nearest weather station with complete long-term data in Kathmandu, ~50 km south from the field site that also indicates regional warming, whether analyzed for annual mean temperatures or separate seasonal trends [START_REF] Shrestha | Recent Treeline Dynamics Are Similar between Dry and Mesic Areas of Nepal, Central Himalaya[END_REF]. In addition, more frequent warm nights and a decline in cooler weather are predicted for the region [START_REF] Ipcc | Climate Change 2007: Impacts, Adaptation and Vulnerability[END_REF](IPCC, , 2014)). No systematic trend in precipitation has been determined in the long term [START_REF] Shrestha | Recent Treeline Dynamics Are Similar between Dry and Mesic Areas of Nepal, Central Himalaya[END_REF]. However, an increase in variability of precipitation has been predicted for the region [START_REF] Ipcc | Climate Change 2007: Impacts, Adaptation and Vulnerability[END_REF](IPCC, , 2014)).

Study species and co-occurring vegetation R. campanulatum D. Don is an evergreen broad-leaved woody shrub, sometimes classified as a tree. The plant achieves a height of 2-6 m (Figure 1) and is distributed between 3000 and 4400 m asl in the Himalayan Mountains [START_REF] Polunin | Flowers of the Himalaya[END_REF]. At our study site and in other upper distributional limits of trees in the Himalayas, R. campanulatum is a highly abundant plant species associated with another abundant tree species, A. spectabilis (D. Don) Mirbel (Himalayan silver fir; locally known as gobre salla, talis patra, or thingre salla). A. spectabilis is a tall evergreen conifer growing in a wide elevational belt of 2800 and 4000 m asl [START_REF] Polunin | Flowers of the Himalaya[END_REF]. The tree has a single main axis holding whorls of branches, each of them profusely branched and densely foliated. It is the tallest (Figure 1) and one of the most abundant tree species in the high Himalayas. At our study site, A. spectabilis presents a sharp distributional boundary of tall trees forming a conspicuous treeline. Below the treeline, R. campanulatum is found growing under the canopy of the much taller trees of A. spectabilis. Above the treeline, isolated saplings of A. spectabilis are found only occasionally with extremely rare tall trees. In the absence of the canopies of taller trees above treeline, R. campanulatum saplings can be found growing as isolated individuals or in cluster. The A. spectabilis treeline is likely to have been stable for over a century [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF], with its trees in the top 50-m elevational band being 35-170 years old (mean age 86 years) and several trees being more than a century old right at the edge of the sharp treeline (K. Mainali, unpublished data). Other associated plant species at the study site included Betula utilis, Prunus sp., Salix sp., and Sorbus microphylla.

For this study, we define R. campanulatum plants that were <2 m tall as "saplings," while the taller plants are designated as "mature plants." Our transplanted plants were 10-50 cm tall. Very small plants, often <15 cm, are considered as "seedling." However, making a distinction between seedling and saplings in this size range would not add to our study. So, we used the term "sapling" to denote all the short plants we studied.

Experimental design and measurements

Two study sites were set up on a mountain slope, arranged to be very similar in slope, aspect, and soil properties (Figure 1). Each of the sites measured ~50 m along the contour of elevation and ~35 m toward the top of the mountain, spanning 15 m in elevational distance. The lower site (Figure 1), hereafter referred to as the "treeline site," was situated ~45 m (elevational distance 16 m) above the treeline at 3876 m, established at a sufficient distance from the treeline to exclude any canopy effect of trees on the site. The other site, hereafter designated as "species limit site," was set up at 147 m (elevational distance) above the treeline site. A few R. campanulatum saplings were found further upward from the species limit site. However, the species limit site was the highest location on the mountain where we could find enough healthy saplings.

In 2010, we transplanted saplings, transferring plants between species limit and treeline sites. Within each site, we randomly sampled 40 healthy saplings of 10-50 cm in height, with no easily noticeable damage. We maintained similarity in plant heights between the two sites by stratified sampling. In each site, we assigned the saplings to two groups of equal size. One group was then randomly chosen to be transplanted to the other site; we define these saplings as "treatment transplants" and the group as "foreign" at the site where they were planted. The other group of saplings was dug up and replanted at the same spot, retained in their site of origin as control; we define these saplings as "control transplant" and the group as "resident" or "home." All saplings that were dug up were excavated with the entire root system intact and ~0.03 m 3 (1 × 1 × 1 ft) of soil around them. The transplanted saplings along with the soil were placed in the emptied spots in the foreign site such that 20 saplings from one site exchanged their locations with 20 saplings from the other site. While transplanting the saplings, care was taken to physically orient the saplings in the same direction as they were in their extracted location.

In situ measurements were taken before and after transplanting the saplings, and exactly one year later. For each sapling, the following measurements were recorded: plant height, total number of healthy and unhealthy leaves if any (some plants had a few leaves with a small portion damaged or necrotic), length of newly added main axis in the current growing season, length of previous year's shoot expansion (the current topmost internode below the newly added shoot), length and width at the widest part of all the leaves produced in the current growing season, and four measurements of the spread of the crown at every 45 interval in angle. From each plot we also collected ~100 healthy leaves, at least two per plant, from a new random set of undisturbed plants of similar height to the transplants. These leaves were pressed between piles of paper, brought back to lab, and dried. A high-resolution image of each leaf was then analyzed with Adobe Photoshop CS 5.5 to determine the length, width, and area with a precision of 0.085 mm (1/300 inch). The model derived from destructive sampling of these leaves was used for estimating the area of leaves in the transplanted saplings.

We also took measurements of biotic and abiotic factors as potential covariates of the measured traits of target saplings. We set up 1-m-diameter plots, each centered on control and treatment saplings used in the experiment. In each plot, we measured the proportion of the ground surface covered with vegetation (which was almost always comprised of a congener species R. anthopogon), height of surrounding vegetation as measured at four points on the periphery of the plot, slope, aspect, and soil fertility. For soil fertility, we collected four samples of soil (100-200 g in total) from each plant after the plant was dug up with the samples and mixed to homogenize. The soil samples were provided to the lab of Nepal Agricultural Research Center, Kathmandu where the concentrations of soluble N, P, K, and organic matter in the soils of both sites were measured. Temperature measurements were collected for each plot (toward the center in a location that represents the slope and aspect of the overall plot) every hour for 9 months with a data logger (HOBO Pendant Temperature/Light Data Logger 8K, Onset Computer Corp, Bourne, MA, USA). Each data logger was securely mounted on a sturdy pole and placed 22 cm above the ground toward the middle of the study site. Although we initially installed two data loggers per site, only one in each site retrieved the temperature for a sufficiently long duration.

Of the 80 study saplings (40 saplings per site, with 20 as control/replanted and 20 as moved/transplanted to another site), 19 plants were either uprooted, damaged, or missing before their measurements in the second year. We found that the animals liked to chew the aluminum tag we used; the uprooted plants had their tag with dental marks and crumbled. These 19 plants were excluded from the analysis. Of the remaining 61 saplings, 19 were dead during the second field visit (mortality calculated from these numbers), leaving a total of 42 plants intact and available for calculation of growth rates and other variables.

A noticeable limitation of this study is the sample size. We conducted the experiment at an elevation where hypoxia (effective oxygen concentration ~12% compared with 21% at sea level) was a substantial constraint for the team to carry saplings along with ~35 kg of soil (27,000 cm 3 per sapling) between the two sites (walking distance >400 m). We exhaustively searched for healthy saplings of our criteria at species limit site on one flank of the mountain, which was suitable for conducting this experiment because of the availability of the two sites to compare. We could not find another flank in the vicinity that provided both sites on one flank. Given these constraints, we were only able to transplant a total of 80 saplings for our study.

Analysis

The experimental sapling size range of 10-50 cm height encompassed most of the existing saplings in both the species limit and the treeline sites. This design enhances the generalization of the finding of this study because of the size range in saplings. Regression analysis included plant height as a potential covariate. Repeated measurements after a year allowed a paired design in the sense that the "before" and "after" transplant measurements can be compared within a plant, removing the noise of plant-to-plant variability in height. For these variables, the measurements of the previous year were subtracted from that of the latter year, allowing a treatment-wise and site-wise difference in annual growth/change. For the variables that did not permit paired design, we used plant height as a covariate in the analysis.

Data analysis and plotting were performed in R ×64 4.0.0 (The R Project for Statistical Computing) using the following packages: e1071, fields, graphics, grDevices, grid, ineq, mvpart, plotrix, plyr, reshape, and sciplot. We applied the following statistical tests for various analyses: Welch two-sample t test, Mann-Whitney-Wilcoxon test, two-way ANOVA, and log-likelihood ratio test (G test) of independence on a contingency table, multiple linear regression, and regression trees. The choice of the test depended on model diagnostics for its assumptions of the given data. Details about the tests used are provided in the figure captions. In all tests, labels for the levels of various factors are used as below: for plant origin, "Species limit" or "Treeline," for transplant site "home/control," or "foreign/moved," and for status "dead" or "alive."

RESULTS

Leaf size, covariates, and significant explanatory variables before transplant

The measurement of saplings at the beginning of the experiment (before transplant) showed that the recently produced leaves (in the summer months before our field visit in August) had a higher average size at species limit site (21.3 cm 2 ) than at treeline site (15.3 cm 2 ) (Figure 2a). The average total area of such leaves in a plant was also higher in species limit population (75.25 cm 2 ) than in treeline plants (48.51 cm 2 ) (Figure 2b). The two sites were not significantly different for sapling height (25.38 cm in species limit and 27.47 cm in treeline; Figure 3a) or the crown size of the saplings (18.11 cm in species limit and 16.60 cm in treeline; Figure 3b). However, compared with species limit, the surrounding vegetation in 1-m-diameter plot of treeline site occupied more area (33.16% in species limit and 78.24% in treeline; Figure 3c) and was taller on average (17.28 cm in species limit and 35.19 cm in treeline; Figure 3d). The number of damaged leaves per individual (scaled by the total number of leaves) was not significantly different between the two sites (43.1% in species limit and 34.9% in treeline; Figure 3e). Regression tree analysis on aggregated data of the two sites showed that a sapling's total area of leaves produced in the current year was significantly predicted only by surrounding vegetation cover, explaining 28% of the variance in leaf area; the relationship between total area and surrounding vegetation cover was negative (Figure 4).

Growth and mortality after a year of transplant

Data collected one year after the transplant revealed the cumulative year-long response of the saplings after transplantation. A G test on the three-way contingency table showed that interaction between the three factors-plant origin (species limit or treeline), transplant site (home or foreign), and plant status (dead or alive)-was significant (p = 0.036), indicating an asymmetric response between plants of different origin at the two sites (Figure 5a). Subsequent pair-wise analyses showed that there was a significantly higher mortality for saplings moved from species limit to treeline site than for controls, that is, saplings from species limit replanted at species limit (58.8% in transplanted and 16.7% in control plants; p = 0.019; Figure 5a). When the controls on the two sites were compared, in situ mortality was not different. So, the elevation of origin did not affect mortality.

For surviving saplings, results indicated that the species limit population, when moved downhill, showed generally higher productivity than the treeline population at either site. Specifically: (1) the annual growth of saplings was significantly positively impacted by the source, in general (main effect of a two-way ANOVA, p = 0.0331) and importantly, the growth of species limit saplings in response to transplant (control vs. transplant) was significantly higher than the growth of treeline saplings in response to transplant (two-way ANOVA, origin × transplant interaction, p = 0.0334; Figure 5b); (2) compared with the previous year, the new shoot expansion in the current year was higher for species limit saplings transplanted to treeline than for controls at species limit (p = 0.045, Figure 5c); however, such effect of transplant was not observed for treeline saplings (Figure 5c); and (3) saplings transplanted from treeline to species limit lost more leaf area than did the control at treeline (p = 0.007; Figure 5d), whereas species limit saplings lost comparable leaf area whether they were retained in home or transplanted to foreign site (Figure 5d).

Soil fertility and air temperature

We found no site-wise differences in the concentrations of soluble N, P, K, and organic matter in the soils (not shown in figure). However, the air temperature measurement shows that the data logger (placed 22 cm above ground) was buried under snowpack on January 19 at species limit but on February 5 at treeline (Figure 6). In spring, the data logger was exposed to the air starting on May 1 at species limit but on April 8 at treeline. This collectively gives the species limit site (at 22 cm height) an extra 17 days in winter and 23 days in spring to be protected under the snowpack when the treeline site is still exposed to air. We have adopted the convention that

DISCUSSION

Due to climate change, treeline species are shifting upward, but there are limited studies regarding how these newly migrated populations experiencing new set of abiotic and biotic conditions perform as compared with the treeline populations. In our reciprocal transplant experiment conducted in Nepal Himalayas, R. campanulatum plants from the treeline and species limit sites along an elevational gradient of ~150 m performed differently, showing asymmetric local adaptations of these two populations. Specifically, species limit saplings suffered significantly higher mortality when moved down to the treeline site compared with their home. However, those saplings at the species limit that survived the transplant at treeline grew faster than the locals (at treeline) and the transplants at species limit.

If extremes of cold are judged as harsh conditions, then plants at the treeline suffered harsher conditions than those at even higher elevations at the species limit. This was because species limit plants were protected by snowpack both during the coldest January ambient conditions and during cold days in April, when treeline plants were exposed to air for 23 days before those at the species limit (Figure 6; see Appendix S1: Figure S2 for an alternate version of Figure 6 showing hourly data point). During spring thaw, the earlier exposure of saplings at treeline experienced a strong diurnal temperature variation associated with the early season when saplings at higher elevations were protected from these temperature extremes for longer period being buried under snowpack. The exposure of treeline saplings to freezing conditions of spring can cause frost damage to plant tissues (leaf necrosis was a routine observation in our field site), and the plants without adequate mechanisms to protect themselves from freezing can have higher mortality [START_REF] Sakai | Frost Survival of Plants: Responses and Adaptation to Freezing Stress[END_REF]. The freezing conditions of early spring can also create transpirational challenges for plants if the soil remains frozen, which severely limits the water uptake during spring when the plants actually may experience increased transpiration rates due to cold, dry air [START_REF] Larcher | Physiological Plant Ecology: Ecophysiology and Stress Physiology of Functional Groups[END_REF].

On the contrary, the beneficial effects of snowpack in winter (observed more at species limit site) have ) yes no

F I G U R E 4
Regression tree analysis of sapling's total area of current year's leaves with its potential explanatory variables, measured before transplantation. Fully grown regression tree model was pruned with cross validation to save the minimum error tree. Slope, aspect, elevation, sapling height, surrounding vegetation cover, and surrounding vegetation height were entered into the model as potential predictors. The only significant predictor retained in the pruned tree was surrounding vegetation cover, explaining 28% of the variation in leaf area. The surrounding vegetation cover of 27.5% splits the regression tree (see "Vegetation_cover <27.5" at the top of the split) into two groups of mean total leaf area of 99.89 and 57.96 cm 2 (indicated at the leaf nodes or at the end of the two splits).

previously been demonstrated by [START_REF] Saarinen | Overwintering of Vaccinium vitis-idaea in Two Sub-Arctic Microhabitats: A Reciprocal Transplantation Experiment[END_REF], who measured winter damage to plants (electrolyte leakage in leaves) and found that plants under a moderate snowcap had less damage than exposed plants.

A lack of early-season freezing condition has been previously shown to benefit seedling survival in treeline forest [START_REF] Shen | Causes for Treeline Stability under Climate Warming: Evidence from Seed and Seedling Transplant Experiments in Southeast Tibet[END_REF], further confirming the role of snowpack in offering protection to our species limit populations during early spring.

Given the aforementioned strong differences between the two sites in our study, it is not surprising that plants from the two sites performed differently, though we cannot know to what extent those differences were based in plasticity and genetic differentiation. The treeline plants are selected to tolerate more extreme weather during late winter and spring compared with the species limit population. This precisely explains why the species limit population suffered a higher mortality when moved down to treeline. A log-likelihood ratio test (G test) of independence on a three-way contingency table to evaluate the joint independence of plant origin, transplant site, and status (live or dead) shows a significant interaction of plant origin and transplant operation on mortality; G = 8.542, χ 2 df = 3, p = 0.036. Within the species limit population, G test on a two-way contingency table: G = 5.488, χ 2 df = 1, p = 0.019, whereas within treeline, G test on a two-way contingency table: G = 0.31369, χ 2 df = 1, p = 0.575. (b) A two-way ANOVA shows significant main effects of origin (p = 0.0331) and of the origin × transplant operation interaction (p = 0.0334) on annual plant growth (plant height increase in 1 year). (c) The ratio of current year's new shoot growth to that of last year's (2011:2010 new shoot length) was significantly different for control versus moved populations of the species limit site (Mann-Whitney-Wilcoxon test, W = 34, p = 0.045) but not for the treeline populations (W = 70.5, p = 0.255). (d) Change in total leaf area in 2011 minus in 2010 (2011-2010 total leaf area). The species limit population lost similar amount of leaf area for control versus moved plants (Mann-Whitney-Wilcoxon test, W = 14, p = 0.366), whereas the treeline population lost more leaf area when moved (Mann-Whitney-Wilcoxon test, W = 11, p = 0.007).

Our findings are mostly echoed (for the response of species limit population) by a recent meta-analysis aggregating data of 49 vascular plant species from 38 transplant studies: plants transplanted downwards showed higher mortality than the local individuals, but produced higher biomass and height compared with their site of origin, whereas the plants transplanted upwards had reduced plant growth and survival than the local individuals [START_REF] Midolo | Plant Performance and Survival across Transplant Experiments Depend upon Temperature and Precipitation Change along Elevation[END_REF]. Another transplant experiment conducted in the Tibetan plateau observed decreased survival and increased productivity of the plant community when transplanted to warmer sites [START_REF] Cui | Plastic Population Effects and Conservative Leaf Traits in a Reciprocal Transplant Experiment Simulating Climate Warming in the Himalayas[END_REF]. The transplanted species limit saplings in our study that did survive at lower elevation grew faster than the residents surrounding them, suggesting a trade-off between growth and survival. We lack enough information to combine survival and growth into a single fitness measure, so we cannot say whether species limit plants had overall higher or lower fitness when transplanted downhill: they had improved performance in growth but reduced performance in survival.

Experiments conducted across elevational gradients in various mountain ranges showed that plant mortality was very often influenced by local adaptation [START_REF] Byars | Local Adaptation and Cogradient Selection in the Alpine Plant, Poa hiemata, along a Narrow Altitudinal Gradient[END_REF][START_REF] Giménez-Benavides | Local Adaptation Enhances Seedling Recruitment along an Altitudinal Gradient in a High Mountain Mediterranean Plant[END_REF][START_REF] Lortie | A Synthesis of Local Adaptation to Climate through Reciprocal Common Gardens[END_REF]. In previous common garden experiments, plants from higher elevations grew more slowly than those from lower elevations [START_REF] Burger | Untersuchungen über das Höhenwachstum verschiedener Holzarten[END_REF][START_REF] Byars | Local Adaptation and Cogradient Selection in the Alpine Plant, Poa hiemata, along a Narrow Altitudinal Gradient[END_REF][START_REF] Gonzalo-Turpin | Local Adaptation Occurs along Altitudinal Gradient despite the Existence of Gene Flow in the Alpine Plant Species Festuca eskia[END_REF]. This genetic differentiation of plant growth across elevational gradients is generally attributed to local adaptation of certain traits, for example, growth, height, morphotype [START_REF] De Villemereuil | Patterns of Phenotypic Plasticity and Local Adaptation in the Wide Elevation Range of the Alpine Plant Arabis alpina[END_REF], or trade-off between vigor and environmental stress resistance. Trade-off between growth rate and freezing tolerance has been shown to exist at latitudinal limits of tree species both in North America [START_REF] Loehle | Height Growth Rate Tradeoffs Determine Northern and Southern Range Limits for Trees[END_REF] and in Europe [START_REF] Larsen | Die geographische variation der weißtanne (Abies alba Mill.) wachstumsentwicklung und frostresistenz[END_REF]. Following the logic of this trade-off, our results suggest that during the spring, species limit saplings use less resources in freezing resistance than treeline saplings. This, along with more favorable growing season conditions at treeline site, could explain the faster growth of transplanted species limit saplings compared with the residents at the treeline site.

Leaf sizes in natural settings were significantly different across the short elevational gradient of ~150 m between the two study sites. These results differ from those in the literature (many species in other mountains) in both magnitude and direction. Previous reports found that leaf size decreased with increasing elevation and the clines were much less steep than in the present study [START_REF] Körner | Alpine Treelines: Functional Ecology of the Global High Elevation Tree Limits[END_REF][START_REF] Körner | Altitudinal Variation in Stomatal Conductance, Nitrogen Content and Leaf Anatomy in Different Plant Life Forms in New Zealand[END_REF][START_REF] Körner | Stomatal Responses and Water Relations of Eucalyptus pauciflora in Summer along an Elevational Gradient[END_REF]. Similarly, surrounding vegetation cover was significantly lower at species limit site than at treeline. Although elevation was entered as a potential predictor of leaf area, the regression tree model retained only surrounding vegetation cover as the significant predictor of leaf area, exhibiting a negative relationship: larger leaves where cover was less. Other studies using neighbor removal experiments have demonstrated that surrounding vegetation provides facilitation to plants above treeline [START_REF] Choler | Facilitation and Competition on Gradients in Alpine Plant Communities[END_REF] or in other stressful environments [START_REF] Grassein | The Importance of Biotic Interactions and Local Adaptation for Plant Response to Environmental Changes: Field Evidence along an Elevational Gradient[END_REF]. Still, other studies show that surrounding vegetation might offer climatic amelioration to seedlings, although the competition slows tree recruitment in the long run [START_REF] Liang | Species Interactions Slow Warming-Induced Upward Shifts of Treelines on the Tibetan Plateau[END_REF]. F I G U R E 6 Hourly temperature recorded at the two sites at the height of 22 cm. Daily cycle of temperature is depicted by the swing of line until data logger is buried under the snow, yielding a flat line. In late winter, the temperature of snow is below zero but it remains at zero for many weeks as spring approaches. The plants were buried under snowpack from January 19 to May 1 at the species limit site, but from February 5 to April 8 at the treeline site. This protected the plants at the species limit site under the snowpack for an extra 17 days in winter and 23 days in spring when the treeline site was still exposed to much colder air temperatures and harsher conditions daily.

The exact nature of the effect of surrounding vegetation on the plants in our sites cannot be determined with our current design. A comprehensive analysis [START_REF] Heynen | Air Temperature Variability in a High-Elevation Himalayan Catchment[END_REF] of temperature lapse rate in the same general area (Langtang) a year after the completion of our experiment shows that the temperature drops at the rate of 0.0060 C/m in pre-monsoon (March 1-June 14), and 0.0050 C/m in post-monsoon (October 1-November 30); these two windows of times very closely match the temperature record availability in our data in the season when surrounding vegetation may have ecological roles (so, we excluded deep winter). With these lapse rates, the two sites (147-m elevational gradient) are expected to have a temperature difference of 0.88 C in pre-monsoon and 0.74 C in post-monsoon. However, our observed temperature differences indicate that the treeline site was 2.1 C warmer than species limit site (4.86 vs. 2.76 C) in pre-monsoon and 2.13 C warmer (4.33 vs. 2.2 C) in post-monsoon. Hence, we have a plot-level warming of treeline site (2.1-0.88 = 1.22 C in pre-monsoon and 2.13-0.74 = 1.39 C in post-monsoon) not explained by adiabatic cooling. This observation of warming effect of surrounding vegetation has been observed in several other studies. Facilitation, alone, however, cannot explain the growth responses in our experiment; saplings from two sources had different growth rates when grown together in the treeline site. Nor can the differences in leaf size and growth rate be attributed to soil fertility, as the concentrations of soluble N, P, K, and organic matter in the soils from the two sites were similar.

Among the plants that were able to survive after a year, species limit population did not lose more total leaf area when moved down (Figure 5d, left panel) but treeline population lost more total leaf area when moved up (Figure 5d, right panel). We cannot provide a specific reason for these asymmetric responses. However, we do not believe that this was a result of transplantation shock because we followed the same transplantation procedure in the entire experiment. The effect of digging up and replanting of plants is expected to affect all plants similarly (both controls and transplanted at both sites). It is unknown whether transplantation shock interacts with some aspects of plant traits or climatic conditions, resulting in larger loss of total leaf area in some groups.

Eco-evolutionary implications

A recent decade-long observation of Tibetan mountains reported that early-season freezing events were generally more frequent, more intense, and long-lasting in the warmer years within a slope [START_REF] Shen | Causes for the Increase of Early-Season Freezing Events under a Warmer Climate at Alpine Treelines in Southeast Tibet[END_REF]. Further exploring the mechanism of this paradoxical observation, this study found that air humidity and soil moisture in pre-monsoon season are reduced by high solar radiation and air temperature in daytime, which effectively lowers the nighttime temperatures to extreme values [START_REF] Shen | Causes for the Increase of Early-Season Freezing Events under a Warmer Climate at Alpine Treelines in Southeast Tibet[END_REF]. If this holds true for the Himalayas, then an increase in early-season freezing events is likely with climate warming, further distancing the two populations at our study sites in their ability to tolerate harsh spring and late winter conditions.

While climate warming can have its implications to asymmetric adaptations, it can also affect the overall process of colonization of new habitat at range boundaries, which is a slow process that involves dispersal, establishment, population growth, and reproduction [START_REF] Jackson | Responses of Plant Populations and Communities to Environmental Changes of the Late Quaternary[END_REF]. In the present study, seed dispersal to both the treeline site (immediately above the edge of treeline) and the species limit site (150 m above treeline site) could have come either from the same mother plants below treeline and/or from the scattered mature, reproductive trees that existed above treeline. An elevational gradient of 150 m on a gentle slope presents no geographic barrier to seed dispersal of R. campanulatum, whose seeds are small, light, and scaly, and so easily carried by wind. Seed dispersal is followed by seedling establishment, which differentially removes the genotypes that do not tolerate local conditions [START_REF] Davis | Range Shifts and Adaptive Responses to Quaternary Climate Change[END_REF].

Climate-change-induced range expansions at the upper boundaries driven by colonization is a general trend observed globally [START_REF] Freeman | Rapid Upslope Shifts in New Guinean Birds Illustrate Strong Distributional Responses of Tropical Montane Species to Global Warming[END_REF][START_REF] Grabherr | Climate Effects on Mountain Plants[END_REF][START_REF] Lenoir | A Significant Upward Shift in Plant Species Optimum Elevation during the 20th Century[END_REF][START_REF] Liang | Species Interactions Slow Warming-Induced Upward Shifts of Treelines on the Tibetan Plateau[END_REF][START_REF] Lustenhouwer | Rapid Evolution of Phenology during Range Expansion with Recent Climate Change[END_REF][START_REF] Parmesan | Climate and Species' Range[END_REF]. Such expansions to new habitats likely present a novel set of environment and climate where the populations with evolutionary potential go through an adaptation. A species range with heterogeneous genetic variation can inflate the genetic variance of marginal population with migration if drift is not strong [START_REF] Connallon | In Search of a General Theory of species' Range Evolution[END_REF], which thereby increases the evolutionary potential and so expansion of species range [START_REF] Barton | Adaptation at the Edge of a Species' Range[END_REF]. On the contrary, declining population densities at the margin means genetic drift is more likely to substantially reduce genetic variation, effectively limiting the range expansion (Polechov a & [START_REF] Polechov A | Limits to Adaptation along Environmental Gradients[END_REF]. Multiple empirical and experimental studies show that marginal populations often have lower genetic variation [START_REF] Eckert | Genetic Variation across Species' Geographical Ranges: The Central-Marginal Hypothesis and Beyond[END_REF], and a combination of low genetic variation and high gene flow can diminish adaptation at species range [START_REF] Bridle | Testing Limits to Adaptation along Altitudinal Gradients in Rainforest Drosophila[END_REF][START_REF] Hendry | How Much of the Variation in Adaptive Divergence Can Be Explained by Gene Flow? An Evaluation Using Lake-Stream Stickleback Pairs[END_REF], limiting the range expansion. Without additional data, not much can be said about the adaptation of R. campanulatum at our species limit site. However, R. campanulatum, which is smaller in size compared with other tree species such as A. spectabilis, has high density at the treeline and above it, potentially facilitating adaptive evolution.

Potential impact of sample size

Sample size issue has been widely discussed in ecological research, but not all studies can be treated similarly. We began the experiment with 80 saplings. Of these, we lost 19 in a year for reasons other than natural death (mostly due to animal eating). There is no reason to believe that these lost saplings had a different growth rate than the rest at each site. After a year, we had 61 saplings available for analysis at two sites. This sample size is less than desired, especially for two-way ANOVA. So, the question is: how does a relatively small sample size impact the analysis and ecological inference? A small sample size is still a representative of the population if it is selected without bias, as is the case with our study. In that situation, there are two aspects of the analysis with obvious undesirable consequences: significance of the hypothesis testing and precision of parameter estimates. With a relatively wider CI, a small sample size has a low statistical power inflating the risk of type II error, that is, failure to reject a null hypothesis when it is false or failure to detect a true effect that actually exists [START_REF] Kutner | Applied Linear Statistical Models[END_REF][START_REF] Lemoine | Underappreciated Problems of Low Replication in Ecological Field Studies[END_REF]. In such situations, it would be incorrect to conclude the effect does not exist [START_REF] Steel | Applied Statistics in Ecology: Common Pitfalls and Simple Solutions[END_REF]. We presented a series of statistically significant relationships, making the aforementioned challenge of small sample size irrelevant to our study.

Small sample sizes are appropriate for genuinely large true effects where the sample size is large enough for a reliable detection of the effects [START_REF] Button | Power Failure: Why Small Sample Size Undermines the Reliability of Neuroscience[END_REF]. However, small studies often have a characteristic of inflated effect size estimates [START_REF] Ioannidis | Clarifications on the Application and Interpretation of the Test for Excess Significance and Its Extensions[END_REF]. When the true effect size is small, a low-powered study has a large probability of reversing the direction of the effect [START_REF] Button | Power Failure: Why Small Sample Size Undermines the Reliability of Neuroscience[END_REF][START_REF] Young | Why Current Publication Practices May Distort Science[END_REF]. It is impossible to know how much the aforementioned problems affected our analysis. However, we believe that the qualitative conclusions of our study were not hampered by these problems because (1) growth and mortality we studied had a noticeably large difference in the magnitude of site effect (Figure 2) or site-by-transplant effect (Figure 5), (2) the ecological and evolutionary inference we drew relied on the direction of the effect and not on its magnitude or effect size, and (3) the directionality of asymmetric adaptation perfectly aligns with the additional temperature data collected in the field (Figure 6).

CONCLUSION

Our transplant experiment yields results that are markedly different from those of other experiments conducted around elevational range limits. Reciprocal transplants failed to meet the expectation of simple local adaptation that would result in individuals doing better at "home" than at the "foreign" site. Individuals from the species limit site, if survived, performed better when moved downhill than they did at home, and also outperformed the locals. Whether the differences and asymmetries that we found stem from genetic differences, epigenetic factors, and/or plastic responses during early life (e.g., acclimation) cannot be addressed with this experimental design. However, regardless of the root nature, the asymmetric responses suggest that populations of R. campanulatum at species limit locations have undergone an adaptive response to living at the extremes of the species' boundary that result in higher growth when moved to more interior (and presumably more favorable) environments. The upper elevational boundary of R. campanulatum is rapidly shifting upward [START_REF] Mainali | Contrasting Responses to Climate Change at Himalayan Treelines Revealed by Population Demographics of Two Dominant Species[END_REF]. However, the present study indicates that strong differences still exist between individuals across a short elevational gradient, with saplings at the uppermost limit of the species range being more tolerant to extreme climate conditions of growing season but less tolerant to climatic extremes of winter and early spring compared with saplings only 150 m lower in elevation at the treeline. How these asymmetric responses of populations to seasonal climatic extremes shape the future species growth at the boundary of species range will largely depend on the nature of the future climate change in the area, complicating an inference about upward shift of the species.

F

  I G U R E 1 Treeline site right above the virtual treeline is comprised of a sharp boundary of tall Abies spectabilis in downhill. Rhododendron campanulatum (uphill) is seen both in isolation and in cluster above treeline. A thick surrounding vegetation of R. anthopogon likely offers warm microenvironment to the seedlings of R. campanulatum. Image credit: K. Mainali.

  Area of leaves that were recently produced in the growing season of summer preceding the first field visit, as measured before transplant in the first week of August 2010; mean ± 1 SE. (a) Average area of an individual leaf; Welch two-sample t test; t = 3.287, df = 76.323, p = 0.0015. (b) Total area of leaves in a plant; Welch two-sample t test; t = 3.6157, df = 74.479, p = 0.00054. Leaf area was estimated with length and width. A linear regression model developed with a sample of leaves from both sites to predict area with length and width of leaf explained ~98% of the variation in leaf area in both sites (see Appendix S1: FigureS1).

  Covariates and potential explanatory variables for the observed differences among saplings in Figure2, as measured before transplant; mean ± 1 SE. (a) Plant height

  Various parameters of plant growth and mortality measured a year after reciprocal transplantation; mean ± 1 SE. (a) Mortality (ratio of the number of dead plants to that of all plants) based on plant origin and transplant operation (control vs. moved).

  ; Welch two-sample t test; t = -1.188, df = 76.622, p = 0.238. (b) Crown spread (diameter of crown measured four times at the widest part at an angular interval of 45 ); Welch two-sample t test; t = 1.137, df = 75.412, p = 0.259.

(c) Surrounding vegetation (veg.) cover (fraction of the area covered by vegetation); Welch two-sample t test; t = -8.834, df = 33.850, p ≤ 0.001. (d) Surrounding veg. height; Welch two-sample t test; t = -6.314, df = 20.899, p ≤ 0.001. (e) Fraction of damaged leaves (ratio of the number of damaged leaves to that of total leaves); Mann-Whitney-Wilcoxon test, W = 960.500, p = 0.123. the term "spring" refers to the months of March through May at our sites, consistent with its definition elsewhere for Langtang (e.g., https://www.weather-atlas.com/en/ nepal/langtang-climate).

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ACKNOWLEDGMENTS

Many graduate and undergraduate students in Nepal assisted in the field project: Ravi Sharma, Ravindra Pandeya, Raju Bista, Manoj Raut, Niroj Basnet, Saroj Neupane, and Lokendra Karki. Nima Sherpa and Layul Tamag provided assistance with logistics in field sites. The research was funded by the following grants to Kumar Mainali: National Science Foundation Doctoral Dissertation Improvement Grant (DEB-1210767), and University of Texas at Austin Graduate Program in Ecology, Evolution and Behavior grant. This work was also supported by the following grants to Camille Parmesan: grant 1049208 from the National Science Foundation, grant 09-NICCR-1077 from

Funding information

Department of Energy, Grant/Award Number: 09-NICCR-1077; Laboratoires d'Excellences(LABEX)TULIP,Grant/Award Number: ANR-10-LABX-41; Make Our Planet Great Again, Grant/Award Number: ANR-17-MPGA-0007; National Science Foundation, Grant/Award Number: 1049208; University of Texas at Austin, Grant/Award Number: DEB-1210767; University of Texas at Austin Graduate Program in Ecology, Evolution and Behavior grant

DATA AVAILABILITY STATEMENT Data and scripts for analysis and plotting [START_REF] Mainali | Data From: Reciprocal Transplants Reveal Asymmetric Local Adaptation of Himalayan Rhododendron Approaching Elevational Range Limit[END_REF] are available from Dryad: https://doi.org/10. 5061/dryad.sqv9s4n7s.

the Department of Energy, a French Make Our Planet Great Again award (ANR-17-MPGA-0007), and the Laboratoires d'Excellences (LABEX) TULIP (ANR-10-LABX-41). An earlier version of the manuscript was reviewed by Shishir Paudel, whose insightful and helpful comments are appreciated.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.


François Dubois

Charles Frankel

Interception of a bolide ?

Keywords: asteroids, comets, collision, physics, astro-ph.EP

Interception of a bolide ?

1) Introduction

Our question is prompted by three events. First, the majority of the scientific community now agrees that the extinction of the dinosaurs and many other living species 65 million years ago was caused by an asteroid or comet, ten kilometers in diameter, which collided with the Earth [START_REF] Koeberl | Response of the Earth System to Impact Processes[END_REF]. Secondly, at the beginning of this century, a 50-meter object hit the Earth in Tunguska, Siberia, with dramatic effects on the local vegetation [START_REF] Chyba | The 1908 Tunguska Explosion: Atmospheric Disruption of a Stony Asteroid[END_REF]. A third such event occurred on Jupiter three years ago, when the two-kilometer Shoemaker-Levy comet crashed into the Jovian atmosphere [START_REF] Dufour | La fin d'une étoile[END_REF].

Three questions naturally arise: (i) What probability is there for such a catastrophe to occur on Earth in the future? (ii) What is the level of a disaster that is "acceptable" for mankind? (iii) What can be done to prevent such an event?

We stress that a global methodology is required to consider such a problem and refer the reader to previous work done at Aerospatiale [START_REF] Darquey | Hermes space plane. Design assessment report for meteorites and orbital debris environment[END_REF] to prevent damage to a space plane by micrometeroids. First, a good knowledge of the threat is required. Second, the effects of collision of an asteroid or comet with the Earth on biological and economic equilibrium must be considered. Third, the ideal type of space protection suitable for preventing such a catastrophe must be calculated.

2) Space threat

It was recently established that the collision of a meteorite with the Earth could have major global effects for living species on our planet. We need only to consider the sudden disappearance of dinosaurs 65 million years ago. In 1980, L. and W. Alvarez, F. Asaro and H. Michel [START_REF] Alvarez | Extraterrestrial Cause for the Cretaceous-Tertiary Extinction[END_REF] suggested that a correlation between this event and the unusual concentration of iridium in the Cretaceous-Tertiary K/T geological stratum could correspond to the impact of an asteroid on Earth. The asteroid was estimated to have a diameter of 10 kilometers (the same order of thickness as the troposphere). Assuming a density of 3 metric tons per cubic meter and a relative velocity of 30 kilometers per second on impact, the kinetic energy transmitted to the atmosphere by such a meteorite is around 10 24 joules. Such an asteroid would produce a crater whose diameter, by initial estimate, would be around 20 times that of the object. And a crater with a diameter of 150-250 kilometers was effectively (re)-discovered in 1991 by A. Hildebrand [START_REF] Hildebrand | Chicxulub crater : a possible cretaneous-tertiary boundary impact crater on the Yucatan peninsula, Mexico[END_REF] at Chicxulub in Yucatan, Mexico, with difficulty due to a layer of post-impact sediment around, 1 km thick. The correlation between this major biological extinction and the Chicxulub crater now seems well established. See, for example, the review article of C. Chapman and D. Morisson [START_REF] Chapman | Impacts on the Earth by Asteroids and Comets : Assessing the hazard[END_REF], the synthesis made by C. Frankel [START_REF] Frankel | La mort des dinosaures : l'hypothèse cosmique. Chronique d'une découverte scientifique[END_REF] and the scientific proposal of C. Koeberl et al. [START_REF] Koeberl | Response of the Earth System to Impact Processes[END_REF].

Moreover, geological observations suggest that four other similar catastrophic events occurred during the last 500 million years [START_REF] Chapman | Impacts on the Earth by Asteroids and Comets : Assessing the hazard[END_REF].

The 1908 event in Tunguska, Siberia, is more mysterious. An area of 2000 square kilometers of forest was destroyed by a meteorite that exploded in the atmosphere without causing any  human victims. The atmosphere was very perturbed, "night lights" were observed in Europe and Asia [START_REF] Whipple | The great Siberian meteor and the waves, seismic and aerial, which it produced[END_REF] and, according to C. Sagan [START_REF] Sagan | Cosmos[END_REF], the resulting shock wave traveled twice around the Earth. Scientific studies of this event did not begin until 20 years later with the mission of the geologist L. Kulik [START_REF] Kulik | To the question about a place of the Tunguska meteorite fall[END_REF]. The energy transmitted to the atmosphere was estimated at 5 10 16 joules. But the origin of this meteorite does not seem to have been fully established. According to Sagan [Sag80], the Earth's orbit intersected the orbit of Enke's comet on June 30, 1908, and the meteorite could be a piece of this comet. It should be noted that a kinetic energy of 5 10 16 joules is compatible with a 100-meter object with a density of 0.1 metric ton/m 3 (typical for comets [START_REF] Wyckoff | Ground-based obser-vations of Halley's comet[END_REF]) and a relative velocity of 30 km per second. The models proposed by C. Chyba, P. Thomas and K. Zahne [START_REF] Chyba | The 1908 Tunguska Explosion: Atmospheric Disruption of a Stony Asteroid[END_REF] exclude dense asteroids and light comets but show that the Tunguska meteorite could be a stony asteroid. The energy data are consistent with a 50-meter object with a specific gravity of 4 relative to liquid water and an incoming velocity of 15 km/s. It is interesting to note that this relatively "small" impacting energy is equivalent to that obtained with 10 megatons of TNT, i.e. 1000 times more than that of the atomic bombs which destroyed Hiroshima and Nagasaki in August 1945.

Here we wish to focus on very recent "non-events" concerning interactions between Earth and small asteroids. The asteroid Toutatis (1989AC) discovered by a French team of astronomers (A. Maury et al. [START_REF] Heudier | AC[END_REF]) is a dual object composed of two stones, 4 and 2 kilometers in diameter, that approaches the Earth every four years. The minimum distance between Earth and Toutatis was equal to 3.6 million kilometers on December 8, 1992 and will be only 1.5 million kilometers on September 29, 2004 (see e.g. [START_REF] Augereau | Le retour de Toutatis[END_REF]).

Recently, a small 9-meter object (1991 BA) intersected the Earth's orbit at only 170,000 kilometers (half the distance between Earth and Moon!) [START_REF] Scotti | Near miss of the Earth by a small asteroid[END_REF]. Object 1989FC with a diameter of 300 meters, which crossed the Earth's orbit at only 700,000 kilometers on March 23, 1989, was more of a hazard (see e.g. [START_REF] Frankel | La mort des dinosaures : l'hypothèse cosmique. Chronique d'une découverte scientifique[END_REF]).

Currently, no systematic effort is being made to catalog such small asteroids with diameters of, for instance, 100 meters to 10 kilometers, orbiting the Sun and in a position to intersect the Earth's orbit, causing a major catastrophe. Certain families of asteroids are known (e.g. Apollo, Amor, Atens) and some 250 objects have been identified [START_REF] Frankel | La mort des dinosaures : l'hypothèse cosmique. Chronique d'une découverte scientifique[END_REF]. But there are an estimated 3000 asteroids in the 1-10 km class [START_REF] Shoemaker | Asteroids and comet flux in the neighborhood of the Earth[END_REF].

Detection of small asteroids is not a trivial problem. For instance, to be compatible with the diffraction of an electromagnetic wave with a wavelength λ = 0.5 10 -6 meters, the telescope required to detect a meteoroid with a diameter α of 1 km located at a distance L of 1 astronomical unit (150 10 6 kilometers) would have to have a diameter D calculated by the following equation:

tan θ = α L ≤ 1.22 λ D
 which means that the diameter would have to be more than 100 meters! This unrealistic instrument could be replaced by a sequence of interferometers using CCD cameras, but this technology is still in development, e.g. at Kitt Peak Observatory (see [START_REF] Spacecast | Preparing for Planetary Defense. Detection and Interception of Asteroids on Collision Course with Earth[END_REF]).

It should also be noted that long-range prediction of the orbits of such small objects is not obvious because of their complex interactions with the Sun and Earth. The trajectory of an object such as Toutatis exhibits a strong resonance correlation with the Earth and this regular transfer of energy could be potentially hazardous in the future. We feel that a special effort should be made to obtain accurate ephemeris data on these very small objects.

A general effort should also be made to develop a system for studying the Earth's environment to be able to determine the real risk of collision of an asteroid with Earth in the future.

Comets are a second family of meteorites that can collide with the Earth. The risk appears small for periodic comets (e.g. Halley's comet) but the most interesting comets are irregular.

The problem is to determine the probability of collision of such an irregular comet with the Earth over a typical period of 10 6 years.

We can imagine a stochastic model based on the hypotheses of Oort's cloud (see [START_REF] Oort | Empirical data on the origin of comets[END_REF]) located 50,000 astronomical units = 7.5 10 12 kilometers from the Sun. A comet with mass M (what is the mathematical probability of this random variable?) has an initial position (what is the probability of this random variable?) with a velocity V (same question) and enters the solar system (what is the probability for the date of injection?). When the positions of the planets are known at time zero (what is the law of this random vector?), it is sufficient (but is it possible?) to compute the irregular comet's trajectory to determine the probability of collision with the Earth and the possible impact parameters (for instance, a relative velocity of such a comet is conventionally estimated at 50-60 km per second).

To our knowledge, this modeling problem has not yet been solved. A major difficulty probably resides in determining the appropriate approximate model that can take into account the mean values of the main planets in the solar system and the filtering effect of Jupiter and Saturn on telluric planets. Such a theoretical development combined with knowledge of comets with an irregular or long period for calibration of the parameters appears important for determining this risk based on irregular comets.

The risk of a collision between the Earth and a meteorite in the future is related to two separate threats: near-Earth asteroids and long-period comets. The first threat is not known, because no systematic program of observations has been developed to detail all the 100 m-10 km objects approaching the Earth. The second threat is structurally uncertain. In both cases, our knowledge could be improved by modeling to accurately predict the future possible collision of objects with complicated trajectories such as the asteroid Toutatis or determine the probability of collision with an irregular comet.

3) Global effects of a single collision

We begin again with the remark that our knowledge of previous global catastrophes remains limited. The Cretaceous/Tertiary transition 65 million years ago has been correlated with a meteorite's impact. But the exact cause of the disappearance of 70 percent of living species on Earth is still an open question. Recent studies (R. Schultz and S. d'Hondt [START_REF] Schultz | Cretaceous-Tertiary (Chicxulub) impact angle and its consequences[END_REF], N. Bhandari, V. Courtillot and R. Rocchia [START_REF] Bhandari | European Congress of Geosciences[END_REF]) show that coupling between asteroid impacts and volcanic eruptions is considerable. In particular, the amount of collision energy transferred to the atmosphere and biosphere is a very crucial parameter.

The energy levels of such collisions must be studied. A Chicxulub-like impact is associated with the transfer of 10 24 joules from the meteorite to the Earth, whereas the 1980 eruption of Mount Saint Helen's volcano caused an input of (only!) 10 16 joules, very comparable to the (small?) Tungunska event of 1908. It should also be noted that the total energy released annually by the Earth (heat flow, volcanoes, earthquakes, etc.) is estimated at 10 21 joules [START_REF] Koeberl | Response of the Earth System to Impact Processes[END_REF].

If 10 24 joules were transferred to the Earth's system, the amount of energy to be dissipated would amount to 10 14 joules i.e. the energy of 10 6 100-watt light bulbs per person during one year considering a world population of 10 10 people.

An event comparable to the Chicxulub impact occurred in July 1994, when the Shoemaker-Levy comet entered Jupiter's atmosphere. This comet was discovered in 1993 [START_REF] Shoemaker | Comet Shoemaker-Levy (1993e)[END_REF] and probably broke up into 20 pieces one year before discovery, when this long-period comet first entered Jupiter's gravitational field. The impact of several objects was predicted theoretically [START_REF] Shoemaker | The crash of Shoemaher-Levy 9 into Jupiter and its implications for comet bombardment on Earth[END_REF] and the effects caused a spot 1900 kilometers in diameter comparable to a giant red spot with light emission due to excitation of very hot gases. The total energy transferred by the nine impacts between July 16 and 22, 1994 is estimated at 4 10 21 joules and the total diameter of the initial object was around 2 km.

This interaction between the incoming meteorite and the Jovian atmosphere is now being modeled (see e.g. [START_REF] Takata | Three-dimensional analysis of impact processes on planets[END_REF]). Its effects on Jupiter's meteorology are still large several years after the collision. It should be noted that another collision of this type between a meteor and Jupiter was probably observed by J.D. Cassini in December 1690 (see e.g. [START_REF] Hir | Le choc probable d'une comète et de Jupiter "observé" 300 ans après[END_REF]).

Is it possible to mathematically describe the effects of rapid interactions such as the above?

We assume that a mathematical model of the atmosphere and biosphere can be obtained by a dynamical system using differential equations, i.e. the search for a vector X(t) with a finite number of real components (or parameters) as a function of time, satisfying a nonlinear equation of the type:

d dt X(t) = f X(t) + g(t)
where f (•) describes all the physical-chemical-biological models coupling the internal variables of system X and g(•) describes the external force, typically a function containing at least two periods, the 24-hour "day forcing" and the 365-day "year forcing". An event such as Chicxulub corresponds to adding an enormous Dirac delta function to term g(•) in the right-hand side of the above model. After integration over a short period, the initial conditions are suddenly changed at t = 0 when the catastrophic event occurs. It seems very reasonable mathematically that different equilibria can be found by the system as the time approaches infinity after such a large perturbation (see e.g. [START_REF] Hirsch | Differential Equations, Dynamical Systems, and Linear Algebra[END_REF] for the mathematical foundations of this type of dynamical phenomenology). In sum, the impact effects are hazardous if they create ruptures in the global equilibria of the Earth's ecological system.

The community of Earth sciences has developped a Global Change program (see e.g. [START_REF]International Geosphere-Biosphere Programme : A Study of Global Change of the International Council of Scientific Unions[END_REF]) whose objective is the development of a good understanding of global modifications on biosphere, atmospheric chemistry, terrestrial ecosystems, etc. that are induced by human activities on the planet. This research program is extraordinarily complex and ambitious but mathematically speaking, it corresponds to regular modifications of function g(•). On the contrary, the project of new program of Response of the Earth System to Impact Cratering [START_REF] Koeberl | Response of the Earth System to Impact Processes[END_REF] is much more adapted to these abrupt modifications. We think that this programme is scientifically essential and could be incorporated in a much more complex one. In fact, actual studies concerning risks induced by impact on the Earth by asteroids are at our knowledge based on a life-death binary option [START_REF] Chapman | Impacts on the Earth by Asteroids and Comets : Assessing the hazard[END_REF]. Our intuition is that reality of a global catastrophe is much more complex to describe. The important fact is to consider the relations between human beings and a global catastrophe can occur whereas few persons are killed by the initial cause like the impact of an asteroid but if the induced effects destroy the essential links that makes economical activity (agriculture, industry, treatment of information).

Here we wish to focus on the necessity of studying the global effects of collision of a meteorite with the Earth using coupled methods that take into account, not only physically, spectacular phenomena such as those observed with the Shoemaker-Levy comet's impact on Jupiter, but also the biological and economic consequences. In particular, to be "acceptable", a collision must not damage either the essential links between human beings (energy fluxes, hydrology) or the more complex ones related to communication, such as education, economy and state organization. The availability of detailed coupled knowledge could be used to determine the cost of an intervention system.

4) Ideas for Human Action

First, it should be remembered that the collision energy of a meteorite with the Earth is basically kinetic, with relative velocities of 10 to 70 kilometers per second. Below, we consider two typical meteorites, modeling a stony asteroid and a long-period comet.

The first object is a cube with length L = 100 meters, density ρ = 3 metric tons/m 3 and relative velocity V 1 = 20 km/second. These parameters induce a mass M 1 = ρ L 3 = 3 10 6 metric tons and a kinetic energy on impact

W 1 = 1 2 M 1 V 2 1 = 6 10 17 joules.
The second object is Halley's comet, for which the data were synthesized by S. Wyckoff [START_REF] Wyckoff | Ground-based obser-vations of Halley's comet[END_REF]: a sphere with a half-surface area of 100 km 2 (i.e. a diameter of 8 km) and a  density ρ = 0.1 metric tons/m 3 consistent with the icy conglomerate model for comet nucleus proposed by F. Whipple in 1950 (see [START_REF] Whipple | On the origin of the cometary nucleous[END_REF]). The mass of Halley's comet can then be approximated at M 2 = 3 10 10 metric tons, and the typical relative velocity for long-period comets is around V 2 = 50 km/second [START_REF] Chapman | Impacts on the Earth by Asteroids and Comets : Assessing the hazard[END_REF]. The kinetic energy W 2 = 1 2 M 2 V 2 2 is then equal to 4 10 22 joules, i.e. 10 times that of Shoemaker-Levy's comet and only 1/25th that of Chicxulub.

The first idea that comes to mind is to destroy the asteroid before impact by an explosion. But although such an action would transfer some of the energy by changing the structure of the incoming asteroid, it is not at all clear whether this would change the total impulse. For instance, for a 10-metric-ton projectile with a velocity of 40 km/s, the momentum is i = 4 10 8 kg.m/s, which is negligible compared to the momentum of the small cube I 1 = M 1 V 1 = 6 10 13 kg.m/s or the momentum I 2 = M 2 V 2 = 1.5 10 18 kg.meters/second of Halley's comet. The center of gravity then continues its initial trajectory and a huge collision is replaced by a series of smaller ones (see e.g. J. Ahrens and A. Harris [START_REF] Ahrens | Deflection and Fragmentation of Near-Earth Asteroids[END_REF]). The energy transferred to the atmosphere would be considerably decreased by dispersion, but the remaining collisions are still very hazardous. According to [START_REF] Ahrens | Deflection and Fragmentation of Near-Earth Asteroids[END_REF], fragmentation is a satisfactory option only if the maximum fragment size is less than 10 meters so that the fragments burn up in the atmosphere. In sum, we feel that fragmentation can only be considered as a "degraded mode" of action, when deflection is not possible.

We now show that deflection of the stony cube is possible using conventional propulsion technologies. First, if it occurs sufficiently before the predicted time of collision, e.g. one year, a deflection ∆v = 1 cm/s will produce a much larger displacement due to gravitational amplification (e.g. by a factor of 20) than the ∆x = 310 kilometers produced by the simple hypothesis of a straight trajectory. Being optimistic about gravitational amplification, we keep this hypothesis of 1 cm/s as initial velocity deflection.

It should be noted here that the kinetic energy associated with this displacement is E 1 = 1 2 M 1 ∆v 2 = 1.5 10 5 joules. Let us consider the above small asteroid as a space rocket with a propellant mass m and a specific impulse Isp associated with a gas ejection velocity g 0 Isp = 3 km/s. The conventional relation (see e.g. [START_REF] Duret | Conception générale des systèmes spatiaux ; conception des fusées porteuses[END_REF]):

∆v = g 0 Isp log M 1 + m M 1 simplifies since m ≪ M 1 yielding m = M 1 ∆v g 0 Isp , i.e.
for a cubic asteroid and the above data, m = 10 metric tons of propellant. It is then necessary to apply such a push to the asteroid after a complex space rendez-vous somewhere in solar system relatively close to the Earth's orbit. This is of course not an easy mission, but it is a priori compatible with today's technology. However, detailed design of such a system remains to be done.

We now consider the problem of giving a similar tap to Halley's comet. First, it should be noted that the kinetic energy associated with this deflection of 1 cm/s is E 1 = 1 2 M 2 ∆v 2 = 1.5 10 9 joules [a thousand megajoules!]. This is an enormous amount of energy from the  standpoint of today's capabilities. It should be noted that although this energy is huge, it is nothing compared with W 2 = 4 10 22 joules that would be transferred to the Earth's system by a direct collision. The problem is to create an impulse J 2 = M 2 ∆v = 3 10 11 kg.meters by second somewhere around Jupiter, because there is a good probability that such a space threat would interact first with Jupiter, which is a good place in the solar system for playing with gravity.

Aside from the fact that the associated propellant mass (m = 10 5 tons) is unrealistic, the solution suggested above for a small asteroid is obviously unfeasible because a comet-like object with low density (ρ = 0.1) is somewhat like cotton wool and is a very fragile object.

A brutal method was suggested in [START_REF] Ahrens | Deflection and Fragmentation of Near-Earth Asteroids[END_REF]. It consists of using explosive nuclear radiations causing the sublimation of matter and therefore transverse impulses. Our experience at Aerospatiale shows that the explosion of a few megaton burst at a distance of few kilometers causes a velocity increment given by the equation ∆v = 3 π 8 I 0 ρ R where ρ = 0.1 ton/m 3 is the typical density of a comet, R is its radius of 4 kms and I 0 is the impulse induced by the physical processes described above. The typical value of I 0 is around 3000 pascals.second, giving ∆v = 9 10 -3 m/s, i.e. what is desired. It should be noted that the distance of some kilometers considered here is quite unrealistic and other effects such as material shock waves inside the comet may destroy the internal structure. Moreover, a large amount of energy is lost in space in the other directions by γ-ray emissions and we have not considered here the ethical problem of using nuclear charges in the space environment.

We conclude this section with a straightforward idea concerning impulse conservation. Let us assume that it is possible to sublimate a quantity of ice from the comet's nucleus. This water vapor would then expand in a vacuum with a rarefaction wave. The ejection velocity from the comet's nucleus is exactly equal to the speed of sound in the gas (see e.g. the classic book by R. Courant and K. Friedrichs [START_REF] Courant | Supersonic Flow and Shock Waves[END_REF]). Under these rarefied conditions of low external pressure and temperature, it is difficult to estimate the speed of sound; we suggest a speed c = 100 meters per second. Then, the momentum conservation equation M 2 ∆v = m c establishes that the sublimation of m = 3 10 6 tons of Halley's comet will deflect it by ∆v = 1 cm/s. The advantage of this approach is that no propellant is required. The drawback is that the ejection velocity is relatively low and the energy cost of such a propulsion system is very high.

From conventional thermodynamic data (e.g. [START_REF] Pérez | Thermodynamique ; fondements et applications[END_REF]), the latent energy of fusion is equal to 330 kjoules/kg and the evaporation energy is around 2300 kjoules/kg. As a first approach, we can estimate that the energy required for water sublimation is equal to around 3 10 6 joules/kilogram. This means that the energy required to create the appropriate impulse is S 2 = 10 16 joules, to be compared with E 2 = 10 9 joules and W 2 = 4 10 22 joules. If such  an energy is communicated by a laser source, we could also take into account the radiation pressure associated with the optical reflection of the ice off the comet, creating an additional impulse.

In this section, we have shown that human action is possible on a small asteroid using today's technology one year before impact, with the help of gravity, which would typically amplify the effect by a factor of 20. The deposit of a mass of 10 metric tons of propellant is sufficient to deflect a 100 m stony asteroid. With the same assumptions concerning kinetics, an energy of some megatons on a Halley-type comet would probably create a sufficient impulse by sublimation. This system design could be an alternative to the explosion of a large nuclear charge at a short distance from the meteor and should be studied in greater detail.

5) Conclusion

We have studied the problem of possible bolide interception from three aspects: space threat, global effects and human action. The space threat is due to predictable asteroids which are not sufficiently well known and to irregular comets whose possible long term impact prediction remains generically uncertain. The effects on Earth must be considered globally using, for instance, methodologies developed by the Global Change science community, taking into account the fact that the energy transfer induced in the system by the impact of a large object is of the same order of magnitude as the total energy dissipated each year by geophysical phenomena. Finally, possible human action remains modest in terms of velocity transfers (1 cm/s) when using early detection, interception a long time before the predicted date of the catastrophe and deflection with the help of the gravitational field. Action using a conventional propulsion system is possible for deflecting small asteroids, whereas a very large source of energy would be necessary to change the trajectory of a Halley-type comet by sublimation of a large quantity of solid ice of the comet's nucleus.

Acknowledgments

The author thanks Jean Jouzel of the Commissariat à l'Energie Atomique (Saclay) for providing reference [Koe96], Max Calabro, André Cariou, Robert Clerc, Philippe Couillard, Jean Dupont and Jean-Bernard Renard of Aerospatiale Espace & Defense (Les Mureaux) for encouragements, stimulating discussions and active participation on the subject presented herein.