Incorporating intraspecific variation in tests of trait-based community assembly

Environmental filtering and niche differentiation are processes proposed to drive community assembly, generating nonrandom patterns in community trait distributions. Despite the substantial intraspecific trait variation present in plant communities, most previous studies of trait-based community assembly have used species mean trait values and therefore not accounted for intraspecific variation. Using a null model approach, I tested for environmental filtering and niche differentiation acting on three key functional traits??vegetative height, specific leaf area (SLA), and leaf dry matter content (LDMC)??in old-field plant communities. I also examined how accounting for intraspecific variation at the among-plot and individual levels affected the detection of nonrandom assembly patterns. Tests using fixed species mean trait values provided evidence of environmental filtering acting on height and SLA and niche differentiation acting on SLA. Including plot-level intraspecific variation increased the strength of these patterns, indicating an important role of intraspecific variation in community assembly. Tests using individual trait data indicated strong environmental filtering acting on all traits, but provided no evidence of niche differentiation, although these signals may have been obscured by the effects of dispersal limitation and spatial aggregation of conspecific individuals. There was also strong evidence of nonrandom assembly of individuals within single species, with the strength of environmental filtering varying among species. This study demonstrates that, while analyses using fixed species mean trait values can provide insights into community assembly processes, accounting for intraspecific variation provides a more complete view of communities and the processes driving their assembly.     

A trait-based approach to determining principles of plant biogeography

Lineage-specific traits determine how plants interact with their surrounding environment. Unrelated species may evolve similar phenotypic characteristics to tolerate, persist in, and invade environments with certain characteristics, resulting in some traits becoming relatively more common in certain types of habitats. Analyses of these general patterns of geographical trait distribution have led to the proposal of general principles to explain how plants diversify in space over time. Trait–environment correlation analyses quantify to what extent unrelated lineages have similar evolutionary responses to a given type of habitat. In this synthesis, I give a short historical overview on trait–environment correlation analyses, from some key observations from classic naturalists to modern approaches using trait evolution models, large phylogenies, and massive data sets of traits and distributions. I discuss some limitations of modern approaches, including the need for more realistic models, the lack of data from tropical areas, and the necessary focus on trait scoring that goes beyond macromorphology. Overcoming these limitations will allow the field to explore new questions related to trait lability and niche evolution and to better identify generalities and exceptions in how plants diversify in space over time.     

Trait-based community assembly of understory palms along a soil nutrient gradient in a lower montane tropical forest

Two opposing niche processes have been shown to shape the relationship between ecological traits and species distribution patterns: habitat filtering and competitive exclusion. Habitat filtering is expected to select for similar traits among coexisting species that share similar habitat conditions, whereas competitive exclusion is expected to limit the ecological similarity of coexisting species leading to trait differentiation. Here, we explore how functional traits vary among 19 understory palm species that differ in their distribution across a gradient of soil resource availability in lower montane forest in western Panama. We found evidence that habitat filtering influences species distribution patterns and shifts community-wide and intraspecific trait values. Differences in trait values among sites were more strongly related to soil nutrient availability than to variation in light or rainfall. Soil nutrient availability explained a significant amount of variation in site mean trait values for 4 of 15 functional traits. Site mean values of leaf nitrogen and phosphorus increased 37 and 64%, respectively, leaf carbon:nitrogen decreased 38%, and specific leaf area increased 29% with increasing soil nutrient availability. For Geonoma cuneata, the only species occurring at all sites, leaf phosphorus increased 34% and nitrogen:phosphorus decreased 42% with increasing soil nutrients. In addition to among-site variation, most morphological and leaf nutrient traits differed among coexisting species within sites, suggesting these traits may be important for niche differentiation. Hence, a combination of habitat filtering due to turnover in species composition and intraspecific variation along a soil nutrient gradient and site-specific niche differentiation among co-occurring species influences understory palm community structure in this lower montane forest.     

Australian Tropical and Subtropical Rain Forest Community Assembly: Phylogeny,Functional Biogeography,and Environmental Gradients

To compare community assemblage patterns in tropical northeastern and subtropical central eastern Australia across selected gradients and scales, we tested the relationship of species traits with phylogenetic structure, and niche breadth. We considered phylogenetic relationships across current‐day species in assemblages in relation to rain forest species pool sizes, and trait values along gradients including elevation and latitude. Trait values were quantified across scales for seed size, leaf area, wood density and maximum height at maturity for 1137 species and 596 assemblages using trait gradient analysis (TGA). Local assemblages of subtropical species had narrower trait ranges, and higher niche breadth values than corresponding assemblages of tropical species. Leaf size and seed size increased at low latitudes, and community phylogenetic structure was most strongly correlated with seed traits in the subtropics, reflecting dispersal and re‐colonization processes. Elevation accounted for little of the variance in community phylogenetic structure or trait variation across local and regional scales. Stable moist forest areas retained many species from ancestral rain forest lineages across a range of temporally conserved habitats; species within assemblages were less related; and rain forest assemblages had higher functional diversity, but lower niche breadth. This suggests that on average, assemblages of species in stable areas had greater trait variation and narrower distributions. Historic and recent rain forest contraction and re‐expansion can result in recolonized areas that are dominated by species that are more related (phylogenetically) than by chance, have smaller, widely dispersed seeds, and greater niche breadth (broader distributions).     

Challenges in linking trait patterns to niche differentiation

Among approaches to establish the importance of niche differentiation for species coexistence, the use of functional traits is attractive for its potential to suggest specific coexistence mechanisms. Recent studies have looked for trait patterns reflective of niche differentiation, building on a line of research with a deep but somewhat neglected history. We review the field from its foundation in limiting similarity theory in the 1960s to its resurgence in 2000s, and find the theory of trait patterning still in a stage of development. Elements still to be accounted for include environmental fluctuations, multidimensional niche space, transient dynamics, immigration, intraspecific variation, evolution and spatial scales. Recent empirical methods are better than early approaches, but still focus on patterning arising in simplistic models, and should rigorously link niche space with trait space, use informative null models, and adopt new metrics of pattern as theory develops. Because tests based on overly simplistic expectations of trait pattern are of little value, we argue that progress in the field requires theory development, which should entail exploring patterns across a set of conceptual and system‐specific models of competition along trait axes. Synthesis Traits relate to ecological performance and are easy to measure. Trait patterns can thus be a practical tool for inferring community assembly processes, and have been extensively used for this purpose. Classical trait patterning theory dates back to the 1960s, and despite heavy criticism still persists in empirical studies. Here we highlight steps needed for traits to realize their potential. These include firmly linking them to niche axes, and updating pattern expectations to consider recent results from models of niche dynamics, such as the emergence of species clusters. Further theory development should reveal whether there is a common traits‐based signature across different niche mechanisms.     

Functional traits of individual trees reveal ecological constraints on community assembly in tropical rain forests

Niche differentiation and ecological filtering are primary ecological processes that shape community assembly, but their relative importance remains poorly understood. Analyses of the distributions of functional traits can provide insight into the community structure generated by these processes. We predicted the trait distributions expected under the ecological processes of niche differentiation and environmental filtering, then tested these predictions with a dataset of 4672 trees located in nine 1‐ha plots of tropical rain forest in French Guiana. Five traits related to leaf function (foliar N concentration, chlorophyll content, toughness, tissue density and specific leaf area), and three traits related to stem function (trunk sapwood density, branch sapwood density, and trunk bark thickness), as well as laminar surface area, were measured on every individual tree. There was far more evidence for environmental filtering than for niche differentiation in these forests. Furthermore, we contrasted results from species‐mean and individual‐level trait values. Analyses that took within‐species trait variation into account were far more sensitive indicators of niche differentiation and ecological filtering. Species‐mean analyses, by contrast, may underestimate the effects of ecological processes on community assembly. Environmental filtering appeared somewhat more intense on leaf traits than on stem traits, whereas niche differentiation affected neither strongly. By accounting for within‐species trait variation, we were able to more properly consider the ecological interactions among individual trees and between individual trees and their environment. In so doing, our results suggest that the ecological processes of niche differentiation and environmental filtering may be more pervasive than previously believed.     

The niche, biogeography and species interactions

In this paper, I review the relevance of the niche to biogeography, and what biogeography may tell us about the niche. The niche is defined as the combination of abiotic and biotic conditions where a species can persist. I argue that most biogeographic patterns are created by niche differences over space, and that even ‘geographic barriers’ must have an ecological basis. However, we know little about specific ecological factors underlying most biogeographic patterns. Some evidence supports the importance of abiotic factors, whereas few examples exist of large-scale patterns created by biotic interactions. I also show how incorporating biogeography may offer new perspectives on resource-related niches and species interactions. Several examples demonstrate that even after a major evolutionary radiation within a region, the region can still be invaded by ecologically similar species from another clade, countering the long-standing idea that communities and regions are generally ‘saturated’ with species. I also describe the somewhat paradoxical situation where competition seems to limit trait evolution in a group, but does not prevent co-occurrence of species with similar values for that trait (called here the ‘competition–divergence–co-occurrence conundrum’). In general, the interface of biogeography and ecology could be a major area for research in both fields.     

Towards a trait-based quantification of species niche

Aims Although the niche concept is of prime importance in ecology, the quantification of plant species' niches remains difficult. Here we propose that plant functional traits, as determinants of species performance, may be useful tools for quantifying species niche parameters over environmental gradients.Important findings Under this framework, the mean trait values of a species determine its niche position along gradients, and intraspecific trait variability determines its niche breadth. This trait-based approach can provide an operational assessment of niche for a potentially large number of species, making it possible to understand and predict species niche shifts under environmental changes. We further advocate a promising method that recently appeared in the literature, which partitions trait diversity into among- and within-community components as a way to quantify the species niche in units of traits instead of environmental parameters. This approach allows the switch of the focus from ecological niches to trait niches, facilitating the examination of species coexistence along undefined environmental gradients. Altogether, the trait-based approach provides a promising toolkit for quantifying the species ecological niche and for understanding the evolution of species niche and traits.     

Trait adaptation promotes species coexistence in diverse predator and prey communities

Species can adjust their traits in response to selection which may strongly influence species coexistence. Nevertheless, current theory mainly assumes distinct and time‐invariant trait values. We examined the combined effects of the range and the speed of trait adaptation on species coexistence using an innovative multispecies predator–prey model. It allows for temporal trait changes of all predator and prey species and thus simultaneous coadaptation within and among trophic levels. We show that very small or slow trait adaptation did not facilitate coexistence because the stabilizing niche differences were not sufficient to offset the fitness differences. In contrast, sufficiently large and fast trait adaptation jointly promoted stable or neutrally stable species coexistence. Continuous trait adjustments in response to selection enabled a temporally variable convergence and divergence of species traits; that is, species became temporally more similar (neutral theory) or dissimilar (niche theory) depending on the selection pressure, resulting over time in a balance between niche differences stabilizing coexistence and fitness differences promoting competitive exclusion. Furthermore, coadaptation allowed prey and predator species to cluster into different functional groups. This equalized the fitness of similar species while maintaining sufficient niche differences among functionally different species delaying or preventing competitive exclusion. In contrast to previous studies, the emergent feedback between biomass and trait dynamics enabled supersaturated coexistence for a broad range of potential trait adaptation and parameters. We conclude that accounting for trait adaptation may explain stable and supersaturated species coexistence for a broad range of environmental conditions in natural systems when the absence of such adaptive changes would preclude it. Small trait changes, coincident with those that may occur within many natural populations, greatly enlarged the number of coexisting species.     

Contrasting Effects of Intraspecific Trait Variation on Trait-Based Niches and Performance of Legumes in Plant Mixtures

Niche differentiation, assumed to be a key mechanism of species coexistence, requires that species differ in their functional traits. So far it remains unclear to which extent trait plasticity leads to niche shifts of species at higher plant diversity, thereby increasing or decreasing niche overlap between species. To analyse this question it is convenient to measure niches indirectly via the variation in resource-uptake traits rather than directly via the resources used. We provisionally call these indirectly measured niches trait-based niches. We studied shoot- and leaf-morphological characteristics in seven legume species in monoculture and multi-species mixture in experimental grassland. Legume species varied in the extent of trait variation in response to plant diversity. Trait plasticity led to significant shifts in species niches in multiple dimensions. Single-species niches in several traits associated with height growth and filling of canopy space were expanded, while other niche dimensions were compressed or did not change with plant diversity. Niche separation among legumes decreased in dimensions related to height growth and space filling, but increased in dimensions related to leaf size and morphology. The total extent of occupied niche space was larger in mixture than in the combined monocultures for dimensions related to leaf morphology and smaller for dimensions related to whole-plant architecture. Taller growth, greater space filling and greater plasticity in shoot height were positively, while larger values and greater plasticity in specific leaf area were negatively related with increased performance of species in mixture. Our study shows that trait variation in response to plant diversity shifts species niches along trait axes. Plastically increased niche differentiation is restricted to niche dimensions that are apparently not related to size-dependent differences between species, but functional equivalence (convergence in height growth) rather than complementarity (divergence in traits associated with light acquisition) explains increased performance of legumes in mixture.     

Integrating selection,niche, and diversification into a hierarchical conceptual framework

Recently, new phylogenetic comparative methods have been proposed to test for the association of biological traits with diversification patterns, with species ecological “niche” being one of the most studied traits. In general, these methods implicitly assume natural selection acting at the species level, thus implying the mechanism of species selection. However, natural selection acting at the organismal level could also influence diversification patterns (i.e., effect macroevolution). Owing to our scarce knowledge on multi-level selection regarding niche as a trait, we propose a conceptual model to discuss and guide the test between species selection and effect macroevolution within a hierarchical framework. We first assume niche as an organismal as well as a species’ trait that interacts with the environment and results in species-level differential fitness. Then, we argue that niche heritability, a requirement for natural selection, can be assessed by its phylogenetic signal. Finally, we propose several predictions that can be tested in the future by disentangling both types of evolutionary processes (species selection or effect macroevolution). Our framework can have important implications for guiding analyses that aim to understand the hierarchical perspective of evolution.     

Spatial effects favour the evolution of niche construction

We present an individual-based, spatial implementation of an existing two-locus population genetic model of niche construction. Our analysis reveals that, across a broad range of conditions, niche-construction traits can drive themselves to fixation by simultaneously generating selection that favours 'recipient' trait alleles and linkage disequilibrium between niche-construction and recipient trait alleles. The effect of spatiality is key, since it is the local, resource-mediated interaction between recipient and niche-constructing loci which gives rise to gene linkage. Spatial clustering effects point to a possible mechanism by which an initially rare recipient trait whose selection depends on niche construction could establish in an otherwise hostile environment. The same mechanism could also lead to the spread of an established niche-constructing colony. Similar phenomena are observed in the spatial modelling of two species 'engineering webs'. Here, the activities of two niche-constructing species can combine to drive a particular recipient trait to fixation, or in certain circumstances, maintain the presence of polymorphisms through the preservation of otherwise deleterious alleles. This may have some relevance to ecosystem stability and the maintenance of genetic variation, where the frequencies of key resources are affected by the niche-constructing activities of more than one species. Our model suggests that the stability of multi-species webs in natural populations may increase as the complexity of species-environment interactions increases.     

Spatial effects favour the evolution of niche construction

We present an individual-based, spatial implementation of an existing two-locus population genetic model of niche construction. Our analysis reveals that, across a broad range of conditions, niche-construction traits can drive themselves to fixation by simultaneously generating selection that favours ‘recipient’ trait alleles and linkage disequilibrium between niche-construction and recipient trait alleles. The effect of spatiality is key, since it is the local, resource-mediated interaction between recipient and niche-constructing loci which gives rise to gene linkage. Spatial clustering effects point to a possible mechanism by which an initially rare recipient trait whose selection depends on niche construction could establish in an otherwise hostile environment. The same mechanism could also lead to the spread of an established niche-constructing colony. Similar phenomena are observed in the spatial modelling of two species ‘engineering webs’. Here, the activities of two niche-constructing species can combine to drive a particular recipient trait to fixation, or in certain circumstances, maintain the presence of polymorphisms through the preservation of otherwise deleterious alleles. This may have some relevance to ecosystem stability and the maintenance of genetic variation, where the frequencies of key resources are affected by the niche-constructing activities of more than one species. Our model suggests that the stability of multi-species webs in natural populations may increase as the complexity of species–environment interactions increases.     

Correlated development, organism‐wide asymmetry and patterns of asymmetry in two moth species

Understanding the mechanisms that determine the development of a bilaterally symmetrical trait is crucial to the interpretation of patterns of fluctuating asymmetry (FA). Experimental and theoretical studies have indicated that feedback mechanisms both within and between developing traits, may participate in the developmental control of asymmetry. This study provides evidence that naturally occurring patterns of FA are affected by interactions between different traits. We found positive between‐trait correlations in signed FA values for tibia lengths on different legs, but not between wing and tibia FA in two moth species. Further research should investigate if trait functionality is related to this presumed correlated development. An extension of the Rashevsky–Turing model of morphogenesis further showed that correlations between the signed FA values can be generated by feedback mechanisms that regulate growth patterns between traits. We argue that such feedback mechanisms can be expected to be widespread and show that between‐trait correlations in the unsigned FA then become confounded with correlations in the signed FA. In addition, correlated development appeared to invalidate the use of the hypothetical repeatability to translate correlations between the unsigned FA values into correlations in the presumed underlying developmental instability. In conclusion, the presence of an organism‐wide asymmetry, which are most frequently found in morphologically integrated traits, may be even less common than previously thought. This revised version was published online in July 2006 with corrections to the Cover Date.     

Functional traits reveal the expansion and packing of ecological niche space underlying an elevational diversity gradient in passerine birds

Variation in species richness across environmental gradients may be associated with an expanded volume or increased packing of ecological niche space. However, the relative importance of these alternative scenarios remains unknown, largely because standardized information on functional traits and their ecological relevance is lacking for major diversity gradients. Here, we combine data on morphological and ecological traits for 523 species of passerine birds distributed across an Andes-to-Amazon elevation gradient. We show that morphological traits capture substantial variation in species dietary (75%) and foraging niches (60%) when multiple independent trait dimensions are considered. Having established these relationships, we show that the 14-fold increase in species richness towards the lowlands is associated with both an increased volume and density of functional trait space. However, we find that increases in volume contribute little to changes in richness, with most (78%) lowland species occurring within the range of trait space occupied at high elevations. Taken together, our results suggest that high species richness is mainly associated with a denser occupation of functional trait space, implying an increased specialization or overlap of ecological niches, and supporting the view that niche packing is the dominant trend underlying gradients of increasing biodiversity towards the lowland tropics.     

Antagonistic coevolution between multiple quantitative traits: Matching dynamics can arise from difference interactions

Coevolution is one of the major drivers of complex dynamics in population ecology. Historically, antagonistic coevolution in victim-exploiter systems has been a topic of special interest, and involves traits with various genetic architectures (e.g., the number of genes involved) and effects on interactions. For example, exploiters may need to have traits that “match” those of victims for successful exploitation (i.e., a matching interaction), or traits that exceed those of victims (i.e., a difference interaction). Different models exist which are appropriate for different types of traits, including Mendelian (discrete) and quantitative (continuous) traits. For models with multiple Mendelian traits, recent studies have shown that antagonistic coevolutionary patterns that appear as matching interactions can arise due to multiple difference interactions with costs of having large trait values. Here we generalize their findings to quantitative traits and show, analogously, that the multidimensional difference interactions with costs sometimes behave qualitatively the same as matching interactions. While previous studies in quantitative genetics have used the dichotomy between matching and difference frameworks to explore coevolutionary dynamics, we suggest that exploring multidimensional trait space is important to examine the generality of results obtained from one-dimensional traits.     

Climatic niche breadth determines the response of bumblebees (<Emphasis Type="Italic">Bombus</Emphasis> spp.) to climate warming in mountain areas of the Northern Iberian Peninsula

Studies examining species range shifts in the face of climate change have consistently found that response patterns are complex and varied, suggesting that ecological traits might be affecting species response. However, knowledge of how the traits of a species determine its response to climate change is still poorly understood. Here we investigate the role of species-specific climate niche breadth in forecasting bumblebee (Bombus spp.) responses to regional climate warming in the Cantabrian Range (north-western Iberian Peninsula). Climate niche breadth was defined using known data for occurrences of specific species at their continental (i.e., European) scale of distribution. For each bumblebee species, climate niche breadth was found to be related to (1) the elevational range shifts of species between their historical (1988–1989) and recent (2007–2009) distribution and (2) the variation in the climatic conditions of the localities they inhabited (i.e., the local climate space) between both study periods. Our results show a strong relationship between climate niche breadth, particularly thermal niche breadth, and the response of bumblebee species to climate warming, but only when this response was determined as variations in local climate space. The main conclusions of our work are thus twofold. First, variations in the climatic conditions underlying range shifts are useful in making accurate assessments of the impact of climate change on species distributions. Second, climate niche breadth is a particularly informative ecological trait for forecasting variations in species responses to climate change.     

Population trends influence species ability to track climate change

Shifts of distributions have been attributed to species tracking their fundamental climate niches through space. However, several studies have now demonstrated that niche tracking is imperfect, that species’ climate niches may vary with population trends, and that geographic distributions may lag behind rapid climate change. These reports of imperfect niche tracking imply shifts in species’ realized climate niches. We argue that quantifying climate niche shifts and analyzing them for a suite of species reveal general patterns of niche shifts and the factors affecting species’ ability to track climate change. We analyzed changes in realized climate niche between 1984 and 2012 for 46 species of North American birds in relation to population trends in an effort to determine whether species differ in the ability to track climate change and whether differences in niche tracking are related to population trends. We found that increasingly abundant species tended to show greater levels of niche expansion (climate space occupied in 2012 but not in 1980) compared to declining species. Declining species had significantly greater niche unfilling (climate space occupied in 1980 but not in 2012) compared to increasing species due to an inability to colonize new sites beyond their range peripheries after climate had changed at sites of occurrence. Increasing species, conversely, were better able to colonize new sites and therefore showed very little niche unfilling. Our results indicate that species with increasing trends are better able to geographically track climate change compared to declining species, which exhibited lags relative to changes in climate. These findings have important implications for understanding past changes in distribution, as well as modeling dynamic species distributions in the face of climate change.     

The interplay among intraspecific leaf trait variation,niche breadth and species abundance along light and soil nutrient gradients

It is assumed that widespread, generalist species have high phenotypic variation, but we know little about how intraspecific trait variation (ITV) relates to species abundance and niche breadth. In the temperate rainforest of southern Chile, we hypothesized that species with wide niche breadth would exhibit 1) high among‐plot ITV, 2) a strong relationship between trait values and the environment, and 3) a close fit between traits and local environment trait optima. We measured leaf functional traits (leaf area, LMA, leaf N and P concentrations) of saplings in woody species, and compared the relative abundance of each species with its niche breadth, measured as the range of light, soil N and P availability. We used the slope of the linear regression of species’ trait–environment relationships to assess the strength and direction of these relationships, and measured the degree to which species’ trait values track the environmental optimum across plots. In some cases, species having wide niche breadth had high ITV in leaf N and also matched traits (LMA and leaf P) to local optima along the light gradient; they also had high ITV in general and matched leaf P to local optima along the soil P gradient. The relationship between species with wide niche breadth and the strength of intraspecific trait–environment relationships was generally weak and varied depending on the niche dimension and trait in question. Species varied considerably in the strength of trait–environment relationships and total magnitude of ITV, and this variation was not generally strongly related to species abundances or niche breadth patterns. In conclusion, trait variation at the community level is not driven by a few abundant, widely distributed species, but depends on the aggregate trait responses of both abundant and rare species. This makes it difficult to scale individual species trait responses up to the community level.     

Joint effect of phylogenetic relatedness and trait selection on the elevational distribution of Rhododendron species

Congeneric species may coexist at fine spatial scales through niche differentiation, however, the magnitude to which the effects of functional traits and phylogenetic relatedness contribute to their distribution along elevational gradients remains understudied. To test the hypothesis that trait and elevational range overlap can affect local speciesʼ coexistence, we first compared phylogenetic relatedness and trait (including morphological traits and leaf elements) divergence among closely related species of Rhododendron L. on Yulong Mountain, China. We then assessed relationships between the overlap of multiple functional traits and the degree of elevational range overlap among species pairs in a phylogenetic context. We found that phylogeny was a good predictor for most functional traits, where closely related species showed higher trait similarity and occupied different elevational niches at our study site. Species pairs of R. subgen. Hymenanthes (Blume) K. Koch showed low elevational range overlap and some species pairs of R. subgen. Rhododendron showed obvious niche differentiation. Trait divergence is greater for species in R. subgen. Rhododendron, and it plays an important role between species pairs with low elevational range overlap. Trait convergent selection takes place between co-occurring closely related species that have high elevational range overlap, which share more functional trait space due to environmental filtering or ecological adaptation in more extreme habitats. Our results highlight the importance of evolutionary history and trait selection for species coexistence at fine ecological scales along environmental gradients.