Climate Envelope Models Research Articles

Dispersal based climate change sensitivity scores for European species

Assessments of climate change impacts on species are needed for anticipating potential biodiversity losses. Climate change impacts on species are often simulated with climate envelope models, but most climate envelope models do not account for dispersal limitations. Most studies only consider two extreme (and unrealistic) dispersal options: no dispersal versus full dispersal. This study attempts to include dispersal limitation into the calculation of climate change sensitivity scores for a range of vertebrate and plant species. We calculate climate change sensitivity scores -expressed as an index- by using the 'spatial turnover' of a species under climate change, defined as the projected difference between current and future area occupied by a species within a region, and include a dispersal factor to account for dispersal limitations. We calculate climate sensitivity scores with three dispersal factors: d0 (no dispersal), d1 (full dispersal) and with an estimated value of d calculated directly from species specific dispersal data and literature estimates (de). We compared climate sensitivity scores across species groups and European bio-geographical regions in order to determine whether explicitly accounting for dispersal limitations causes significant differences in sensitivity for climate change. Our results show that the climate sensitivity scores calculated with de differ slightly from d0 (no dispersal), but differ significantly from d1 (full dispersal) for the less mobile species groups (amphibian, reptiles, plants). This indicates that assuming full dispersal significantly overestimates the future distribution in Europe under climate change for these species, whereas assuming no dispersal may slightly underestimates this. However, this conclusion could not be drawn for the more mobile birds and mammas: climate sensitivity scores calculated with de are approximately intermediate of those calculated with d0 (no dispersal) and d1 (full dispersal). This indicates that assuming either no or full dispersal results in poor estimates of the future distribution of these species in Europe under climate change, and that dispersal capacity should therefore always be considered when assessing climate change impacts on these species. Disaggregating climate sensitivity scores per European bio-geographical regions reveals that regional climate sensitivity scores are similar to the European level.

Including Fossils in Phylogenetic Climate Reconstructions: A Deep Time Perspective on the Climatic Niche Evolution and Diversification of Spiny Lizards (Sceloporus).

Fossils and other paleontological information can improve phylogenetic comparative method estimates of phenotypic evolution and generate hypotheses related to species diversification. Here, we use fossil information to calibrate ancestral reconstructions of suitable climate for Sceloporus lizards in North America. Integrating data from the fossil record, general circulation models of paleoclimate during the Miocene, climate envelope modeling, and phylogenetic comparative methods provides a geographically and temporally explicit species distribution model of Sceloporus-suitable habitat through time. We provide evidence to support the historic biogeographic hypothesis of Sceloporus diversification in warm North American deserts and suggest a relatively recent Sceloporus invasion into Mexico around 6 Ma. We use a physiological model to map extinction risk. We suggest that the number of hours of restriction to a thermal refuge limited Sceloporus from inhabiting Mexico until the climate cooled enough to provide suitable habitat at approximately 6 Ma. If the future climate returns to the hotter climates of the past, Mexico, the place of highest modern Sceloporus richness, will no longer provide suitable habitats for Sceloporus to survive and reproduce.

Prestoration: using species in restoration that will persist now and into the future

Climate change presents new challenges for selecting species for restoration. If migration fails to keep pace with climate change, as models predict, the most suitable sources for restoration may not occur locally at all. To address this issue, we propose a strategy of “prestoration”: utilizing species in restoration for which a site represents suitable habitat now and into the future. Using the Colorado Plateau, United States, as a case study, we assess the ability of grass species currently used regionally in restoration to persist into the future using projections of ecological niche models (or climate envelope models) across a suite of climate change scenarios. We then present a technique for identifying new species that best compensate for future losses of suitable habitat by current target species. We found that the current suite of species, selected by a group of experts, is predicted to perform reasonably well in the short term, but that losses of prestorable habitat by mid‐century would approach 40%. Using an algorithm to identify additional species, we found that fewer than 10 species could compensate for nearly all of the losses incurred by the current target species. This case study highlights the utility of integrating ecological niche modeling and future climate forecasts to predict the utility of species in restoring under climate change across a wide range of spatial and temporal scales.

Thermal Components of American Pika Habitat—How does a Small Lagomorph Encounter Climate?

ABSTRACTAnticipating the response of small mammals to climate change requires knowledge of thermal conditions of their habitat during times of the day and year when individuals use them. We measured diurnal and seasonal temperatures of free air and of six habitat components for American pikas (Ochotona princeps) over five years at 37 sites in seven mountain ranges in the western Great Basin, United States. Talus matrices (subsurfaces) had low daily variances and, in the warm season, remained cool during the hottest times of the day relative to surfaces and free air. During winter, matrices were warmer than free air. Talus surfaces were warmer than free air in the warm and cold seasons, and had large daily variances. Summer forefield and dispersal environments were warmest of all habitat components. Talus surfaces in summer were highly responsive to solar radiation over the course of the day, warming quickly to high midday temperatures, and cooling rapidly in the evening. By contrast, matrices lagged the daily warm-up and remained warmer than free air at night. These differences afford diurnal and seasonal opportunities for pikas to adapt behaviorally to unfavorable temperatures and suggest that animals can accommodate a wider range of future climates than has been assumed, although warming of the dispersal environment may become limiting. Climate envelope models that use or model only surface air measures and do not include information on individual thermal components of pika habitat may lead to errant conclusions about the vulnerability of species under changing climates.

US forest response to projected climate-related stress: a tolerance perspective.

Although it is widely recognized that climate change will require a major spatial reorganization of forests, our ability to predict exactly how and where forest characteristics and distributions will change has been rather limited. Current efforts to predict future distribution of forested ecosystems as a function of climate include species distribution models (for fine-scale predictions) and potential vegetation climate envelope models (for coarse-grained, large-scale predictions). Here, we develop and apply an intermediate approach wherein we use stand-level tolerances of environmental stressors to understand forest distributions and vulnerabilities to anticipated climate change. In contrast to other existing models, this approach can be applied at a continental scale while maintaining a direct link to ecologically relevant, climate-related stressors. We first demonstrate that shade, drought, and waterlogging tolerances of forest stands are strongly correlated with climate and edaphic conditions in the conterminous United States. This discovery allows the development of a tolerance distribution model (TDM), a novel quantitative tool to assess landscape level impacts of climate change. We then focus on evaluating the implications of the drought TDM. Using an ensemble of 17 climate change models to drive this TDM, we estimate that 18% of US ecosystems are vulnerable to drought-related stress over the coming century. Vulnerable areas include mostly the Midwest United States and Northeast United States, as well as high-elevation areas of the Rocky Mountains. We also infer stress incurred by shifting climate should create an opening for the establishment of forest types not currently seen in the conterminous United States.

Where to Dig for Fossils: Combining Climate-Envelope, Taphonomy and Discovery Models.

Fossils represent invaluable data to reconstruct the past history of life, yet fossil-rich sites are often rare and difficult to find. The traditional fossil-hunting approach focuses on small areas and has not yet taken advantage of modelling techniques commonly used in ecology to account for an organism’s past distributions. We propose a new method to assist finding fossils at continental scales based on modelling the past distribution of species, the geological suitability of fossil preservation and the likelihood of fossil discovery in the field, and apply it to several genera of Australian megafauna that went extinct in the Late Quaternary. Our models predicted higher fossil potentials for independent sites than for randomly selected locations (mean Kolmogorov-Smirnov statistic = 0.66). We demonstrate the utility of accounting for the distribution history of fossil taxa when trying to find the most suitable areas to look for fossils. For some genera, the probability of finding fossils based on simple climate-envelope models was higher than the probability based on models incorporating current conditions associated with fossil preservation and discovery as predictors. However, combining the outputs from climate-envelope, preservation, and discovery models resulted in the most accurate predictions of potential fossil sites at a continental scale. We proposed potential areas to discover new fossils of Diprotodon, Zygomaturus, Protemnodon, Thylacoleo, and Genyornis, and provide guidelines on how to apply our approach to assist fossil hunting in other continents and geological settings.

Forecasting fine‐scale changes in the food‐web structure of coastal marine communities under climate change

Climate change is inducing deep modifications in local communities worldwide as a consequence of individualistic species range shifts. Understanding how complex interaction networks will be reorganized under climate change represents a major challenge in the fields of ecology and biogeography. However, forecasting the potential effects of climate change on local communities, and more particularly on food‐web structure, requires the consideration of highly structuring processes, such as trophic interactions. A major breakthrough is therefore expected by combining predictive models integrating habitat selection processes, the physiological limits of marine species and their trophic interactions. In this study, we forecasted the potential impacts of climate change on the local food‐web structure of the highly threatened Gulf of Gabes ecosystem located in the south of the Mediterranean Sea. We coupled the climatic envelope and habitat models to an allometric niche food web model, hence taking into account the different processes acting at regional (climate) and local scales (habitat selection and trophic interactions). Our projections under the A2 climate change scenario showed that future food webs would be composed of smaller species with fewer links, resulting in a decrease of connectance, generality, vulnerability and mean trophic level of communities and an increase of the average path length, which may have large consequences on ecosystem functioning. The unified framework presented here, by connecting food‐web ecology, biogeography and seascape ecology, allows the exploration of spatial aspects of interspecific interactions under climate change and improves our current understanding of climate change impacts on local marine food webs.

Forward Planning for Scottish Gardens in the Face of Climate Change

The impact of climate change and its effects on gardens has so far received limited academic attention. This paper offers a partial correction of this imbalance by investigating the potential impact of climate change on a selection of common Scottish garden plants. A climate envelope modelling approach was taken, whereby wild species distribution data were used to build climate ‘envelopes’ or descriptions of the native climates of selected species. The envelope models were projected onto future climate scenarios for Scotland, allowing observations to be made regarding the climatic suitability of Scotland, both currently and into the future, for each of the plants studied. The models and predictions for four species are described here along with strengths and limitations of the methodology. It is suggested that this approach, or variations of it, could become a useful tool in forward planning for gardens in assisting efforts to mitigate the effect of climate change.

Forward Planning for Scottish Gardens in the Face of Climate Change

The impact of climate change and its effects on gardens has so far received limited academic attention. This paper offers a partial correction of this imbalance by investigating the potential impact of climate change on a selection of common Scottish garden plants. A climate envelope modelling approach was taken, whereby wild species distribution data were used to build climate ‘envelopes’ or descriptions of the native climates of selected species. The envelope models were projected onto future climate scenarios for Scotland, allowing observations to be made regarding the climatic suitability of Scotland, both currently and into the future, for each of the plants studied. The models and predictions for four species are described here along with strengths and limitations of the methodology. It is suggested that this approach, or variations of it, could become a useful tool in forward planning for gardens in assisting efforts to mitigate the effect of climate change.

Predicting Future European Breeding Distributions of British Seabird Species under Climate Change and Unlimited/No Dispersal Scenarios

Understanding which traits make species vulnerable to climatic change and predicting future distributions permits conservation efforts to be focused on the most vulnerable species and the most appropriate sites. Here, we combine climate envelope models with predicted bioclimatic data from two emission scenarios leading up to 2100, to predict European breeding distributions of 23 seabird species that currently breed in the British Isles. Assuming unlimited dispersal, some species would be “winners” (increase the size of their range), but over 65% would lose range, some by up to 80%. These “losers” have a high vulnerability to low prey availability, and a northerly distribution meaning they would lack space to move into. Under the worst-case scenario of no dispersal, species are predicted to lose between 25% and 100% of their range, so dispersal ability is a key constraint on future range sizes. More globally, the results indicate, based on foraging ecology, which seabird species are likely to be most affected by climatic change. Neither of the emissions scenarios used in this study is extreme, yet they generate very different predictions for some species, illustrating that even small decreases in emissions could yield large benefits for conservation.

Selecting Populations for Non-Analogous Climate Conditions Using Universal Response Functions: The Case of Douglas-Fir in Central Europe.

Identifying populations within tree species potentially adapted to future climatic conditions is an important requirement for reforestation and assisted migration programmes. Such populations can be identified either by empirical response functions based on correlations of quantitative traits with climate variables or by climate envelope models that compare the climate of seed sources and potential growing areas. In the present study, we analyzed the intraspecific variation in climate growth response of Douglas-fir planted within the non-analogous climate conditions of Central and continental Europe. With data from 50 common garden trials, we developed Universal Response Functions (URF) for tree height and mean basal area and compared the growth performance of the selected best performing populations with that of populations identified through a climate envelope approach. Climate variables of the trial location were found to be stronger predictors of growth performance than climate variables of the population origin. Although the precipitation regime of the population sources varied strongly none of the precipitation related climate variables of population origin was found to be significant within the models. Overall, the URFs explained more than 88% of variation in growth performance. Populations identified by the URF models originate from western Cascades and coastal areas of Washington and Oregon and show significantly higher growth performance than populations identified by the climate envelope approach under both current and climate change scenarios. The URFs predict decreasing growth performance at low and middle elevations of the case study area, but increasing growth performance on high elevation sites. Our analysis suggests that population recommendations based on empirical approaches should be preferred and population selections by climate envelope models without considering climatic constrains of growth performance should be carefully appraised before transferring populations to planting locations with novel or dissimilar climate.

Human population dynamics in Europe over the Last Glacial Maximum.

The severe cooling and the expansion of the ice sheets during the Last Glacial Maximum (LGM), 27,000-19,000 y ago (27-19 ky ago) had a major impact on plant and animal populations, including humans. Changes in human population size and range have affected our genetic evolution, and recent modeling efforts have reaffirmed the importance of population dynamics in cultural and linguistic evolution, as well. However, in the absence of historical records, estimating past population levels has remained difficult. Here we show that it is possible to model spatially explicit human population dynamics from the pre-LGM at 30 ky ago through the LGM to the Late Glacial in Europe by using climate envelope modeling tools and modern ethnographic datasets to construct a population calibration model. The simulated range and size of the human population correspond significantly with spatiotemporal patterns in the archaeological data, suggesting that climate was a major driver of population dynamics 30-13 ky ago. The simulated population size declined from about 330,000 people at 30 ky ago to a minimum of 130,000 people at 23 ky ago. The Late Glacial population growth was fastest during Greenland interstadial 1, and by 13 ky ago, there were almost 410,000 people in Europe. Even during the coldest part of the LGM, the climatically suitable area for human habitation remained unfragmented and covered 36% of Europe.

Climate change and Ixodes tick-borne diseases of humans.

The evidence that climate warming is changing the distribution of Ixodes ticks and the pathogens they transmit is reviewed and evaluated. The primary approaches are either phenomenological, which typically assume that climate alone limits current and future distributions, or mechanistic, asking which tick-demographic parameters are affected by specific abiotic conditions. Both approaches have promise but are severely limited when applied separately. For instance, phenomenological approaches (e.g. climate envelope models) often select abiotic variables arbitrarily and produce results that can be hard to interpret biologically. On the other hand, although laboratory studies demonstrate strict temperature and humidity thresholds for tick survival, these limits rarely apply to field situations. Similarly, no studies address the influence of abiotic conditions on more than a few life stages, transitions or demographic processes, preventing comprehensive assessments. Nevertheless, despite their divergent approaches, both mechanistic and phenomenological models suggest dramatic range expansions of Ixodes ticks and tick-borne disease as the climate warms. The predicted distributions, however, vary strongly with the models' assumptions, which are rarely tested against reasonable alternatives. These inconsistencies, limited data about key tick-demographic and climatic processes and only limited incorporation of non-climatic processes have weakened the application of this rich area of research to public health policy or actions. We urge further investigation of the influence of climate on vertebrate hosts and tick-borne pathogen dynamics. In addition, testing model assumptions and mechanisms in a range of natural contexts and comparing their relative importance as competing models in a rigorous statistical framework will significantly advance our understanding of how climate change will alter the distribution, dynamics and risk of tick-borne disease.

Climate envelope modeling and dispersal simulations show little risk of range extension of the Shipworm, Teredo navalis (L.), in the Baltic sea.

The shipworm, Teredo navalis, is absent from most of the Baltic Sea. In the last 20 years, increased frequency of T. navalis has been reported along the southern Baltic Sea coasts of Denmark, Germany, and Sweden, indicating possible range-extensions into previously unoccupied areas. We evaluated the effects of historical and projected near-future changes in salinity, temperature, and oxygen on the risk of spread of T. navalis in the Baltic. Specifically, we developed a simple, GIS-based, mechanistic climate envelope model to predict the spatial distribution of favourable conditions for adult reproduction and larval metamorphosis of T. navalis, based on published environmental tolerances to these factors. In addition, we used a high-resolution three-dimensional hydrographic model to simulate the probability of spread of T. navalis larvae within the study area. Climate envelope modeling showed that projected near-future climate change is not likely to change the overall distribution of T. navalis in the region, but will prolong the breeding season and increase the risk of shipworm establishment at the margins of the current range. Dispersal simulations indicated that the majority of larvae were philopatric, but those that spread over a wider area typically spread to areas unfavourable for their survival. Overall, therefore, we found no substantive evidence for climate-change related shifts in the distribution of T. navalis in the Baltic Sea, and no evidence for increased risk of spread in the near-future.

Photoperiod and Nitrogen Supply Limit the Scope of Northward Migration and Seed Transfer of Black Spruce in a Future Climate Associated with Doubled Atmospheric CO2 Concentration

The predicated changes in precipitation and temperature associated with the continued elevation of atmospheric CO2 concentration will trigger the northward shift of the Climate Envelopes for 130 North America tree species by as much as 10 degrees. However, climate envelope models do not take into account changes in other factors that may also influence the survival and growth of plants at the predicted new locations, such as photoperiod and nutrient regimes. This study investigated how photoperiod and nitrogen supply would affect the ecophysiological traits of black spruce (Picea mariana (Mill) B. S. P.) that are critical for survival and growth at new locations predicted by climate envelope models. We exposed black spruce seedlings to the photoperiod regime at the seed origin (PS) and that 10° north of the seed origin (PNM) as predicted by climate envelope models under the current and doubled atmospheric CO2 concentration and different levels of N supply (30 vs. 300 μmol·mol-1 N). We found that the PNM and the 30 μmol·mol-1 N supply both had negative impact on the development of seedling cold hardiness in the fall, and led to earlier burst of the terminal bud and greater rate of mortality in the following growing season. While the PNM stimulated seedling growth in the first growing season, the effect was not sustained in the second growing season. Our results suggest that the photoperiod regimes and poor nutrient conditions at higher latitudes will likely constrain the scope of the northward migration or seed transfer of black spruce.

Climate change and land management impact rangeland condition and sage-grouse habitat in southeastern Oregon

Contemporary pressures on sagebrush steppe from climate change, exotic species, wildfire, and land use change threaten rangeland species such as the greater sage-grouse ( Centrocercus urophasianus ). To effectively manage sagebrush steppe landscapes for long-term goals, managers need information about the potential impacts of climate change, disturbances, and management activities. We integrated information from a dynamic global vegetation model, a sage-grouse habitat climate envelope model, and a state-and-transition simulation model to project broad-scale vegetation dynamics and potential sage-grouse habitat across 23.5 million acres in southeastern Oregon. We evaluated four climate scenarios, including continuing current climate and three scenarios of global climate change, and three management scenarios, including no management, current management and a sage-grouse habitat restoration scenario. All climate change scenarios projected expansion of moist shrub steppe and contraction of dry shrub steppe, but climate scenarios varied widely in the projected extent of xeric shrub steppe, where hot, dry summer conditions are unfavorable for sage-grouse. Wildfire increased by 26% over the century under current climate due to exotic grass encroachment, and by two- to four-fold across all climate change scenarios as extreme fire years became more frequent. Exotic grasses rapidly expanded in all scenarios as large areas of the landscape initially in semi-degraded condition converted to exotic-dominated systems. Due to the combination of exotic grass invasion, juniper encroachment, and climatic unsuitability for sage-grouse, projected sage-grouse habitat declined in the first several decades, but increased in area under the three climate change scenarios later in the century, as moist shrub steppe increased and rangeland condition improved. Management activities in the model were generally unsuccessful in controlling exotic grass invasion but were effective in slowing woodland expansion. Current levels of restoration treatments were insufficient to prevent some juniper expansion, but increased treatment rates under the restoration scenario maintained juniper near initial levels in priority treatment areas. Our simulations indicate that climate change may have both positive and negative implications for maintaining sage-grouse habitat.

Transboundary ecological networks as an adaptation strategy to climate change: The example of the Dutch – German border

Establishing ecological networks across national boundaries is essential for species to adapt to shifts in future suitable climate zones. This paper presents a method to assess whether the existing ecological network in the Dutch – German border region is “climate proof”. Using distribution data and climate envelope models for 846 species in Europe (mammals, birds, reptiles, amphibians and butterflies) we identified 216 species with climate-induced range shifts in the border region. A range expansion is predicted for 99 species and the ranges of 117 species are predicted to contract. The spatial cohesion of the ecological network was analysed for selected species that vary in habitat requirements and colonisation ability (forest species: Brenthis daphne, Dendrocopos medius; wetland species: Maculinea teleius, Lutra lutra). The assessment shows that optimising transboundary networks and developing corridors seems a suitable adaptation strategy for the forest species and for L. lutra. For the immobile butterfly M. teleius, the present habitat network is too weak and translocation into future suitable climate space seems to be a more appropriate adaptation measure. Our results underline that due to climate change landscape planning and management should not only focus on areas where target species occur today. The presented method can identify strongholds and bottlenecks in transboundary ecological networks and incorporate demands of climate adaptation into spatial planning which forms the basis for taking measures at a more detailed level.

Precipitation and winter temperature predict long-term range-scale abundance changes in Western North American birds.

Predicting biodiversity responses to climate change remains a difficult challenge, especially in climatically complex regions where precipitation is a limiting factor. Though statistical climatic envelope models are frequently used to project future scenarios for species distributions under climate change, these models are rarely tested using empirical data. We used long-term data on bird distributions and abundance covering five states in the western US and in the Canadian province of British Columbia to test the capacity of statistical models to predict temporal changes in bird populations over a 32-year period. Using boosted regression trees, we built presence-absence and abundance models that related the presence and abundance of 132 bird species to spatial variation in climatic conditions. Presence/absence models built using 1970-1974 data forecast the distributions of the majority of species in the later time period, 1998-2002 (mean AUC=0.79±0.01). Hindcast models performed equivalently (mean AUC=0.82±0.01). Correlations between observed and predicted abundances were also statistically significant for most species (forecast mean Spearman's ρ=0.34±0.02, hindcast=0.39±0.02). The most stringent test is to test predicted changes in geographic patterns through time. Observed changes in abundance patterns were significantly positively correlated with those predicted for 59% of species (mean Spearman's ρ=0.28±0.02, across all species). Three precipitation variables (for the wettest month, breeding season, and driest month) and minimum temperature of the coldest month were the most important predictors of bird distributions and abundances in this region, and hence of abundance changes through time. Our results suggest that models describing associations between climatic variables and abundance patterns can predict changes through time for some species, and that changes in precipitation and winter temperature appear to have already driven shifts in the geographic patterns of abundance of bird populations in western North America.

Phenotypic correlates of potential range size and range filling in European trees

Understanding the biological correlates of range sizes in plant species is important to predict the response of species to climate change. We used climate envelope models to estimate species’ potential range size and range filling for 48 European tree species. We hypothesized that potential range size relates to the climatic tolerances of plant species, and that the degree of range filling is influenced by species dispersal. We tested these hypotheses using, for each species, estimates for tolerance to cold and drought, type of dispersal, fruit size and seed size. Consistent with previous observations, we found that both the size of potential ranges and range filling increase from south to north. Species tolerance to temperature and water stress, as well as their dispersal-related traits also showed marked spatial patterns. There was, moreover, a significant positive partial correlation between cold tolerance and potential range size, when drought tolerance was partialed out, and a non-significant partial correlation between drought tolerance and potential range size, with cold tolerance partialed out. Range filling was not significantly larger in species dispersed by wind than in those dispersed by animals. There was a negative correlation between seed mass and range filling, but its statistical significance varied across different subsets of species and climate envelope algorithms; the correlation between fruit length and range filling was not significant. We conclude that climatic tolerances and dispersal traits influence species range size and range filling, and thus affect the range dynamics of species in response to global change. Using traits will therefore help to predict future distribution of species under climate change.

Arctic-Alpine Plants Decline over Two Decades in Glacier National Park, Montana, U.S.A.

Climate-based models predict global warming will cause mountain plants to migrate upward with local extirpation of species currently restricted to the highest elevations. Alpine monitoring studies have generally documented changes in alpine plant distributions consistent with these predictions; however, relatively few such studies have been reported from North America. I estimated canopy cover in 71 permanent microplots at two alpine moist-turf sites in Glacier National Park, Montana, U.S.A., three times between 1988 and 2011. Mean annual and summer temperatures were approximately 0.6 and 0.7 °C higher than the previous four decades, respectively. Plants more restricted to high elevations declined more than species with a broader elevational amplitude during this time. Dicots were more likely to have declined than monocots. These data support predictions and provide information that may help refine climate-envelope models.