Reproductive traits explain occupancy of predicted distributions in a genus of eastern North American understory herbs

Abiotic, biotic and dispersal factors interact to shape species distributions. At broad geographic extents, abiotic factors are thought to exert the greatest influence on the distribution, while biotic and dispersal factors strongly influence the distribution regionally and locally. We test whether reproductive traits relating to biotic and dispersal factors explain differences between estimated potential and occupied geographic distributions for 21 species of Trillium.


| INTRODUC TI ON
For more than a century, ecologists have attempted to understand the constraints on species' distributions (Dobzhansky, 1950;Grinnell, 1917;Hutchinson, 1957Hutchinson, , 1978Lomolino et al., 2005;MacArthur, 1984;Peterson, 2001). The concept of the ecological niche, which bears a long history (Chase & Leibold, 2003;Grinnell, 1917;Pocheville, 2015), is currently viewed as a multidimensional combination of environmental conditions that permit a species to survive and reproduce (Soberón & Arroyo-Peña, 2017) and is interwoven into explanations of patterns of biodiversity and species coexistence (Pocheville, 2015). This modern usage of the ecological niche is rooted in the niche concept as described by Grinnell (1917), which emphasized the influence of the environment on the physical distribution of biological populations and their evolution.
Grinnell's niche concept encompassed abiotic factors such as temperature, precipitation and elevation, and biotic factors such as the presence of food, competitors or predators where the species in question existed (Grinnell, 1917;Pocheville, 2015). Hutchinson later advanced niche theory by introducing the concepts of the fundamental and realized niche, which respectively distinguish between the abiotic space that would permit a species to exist indefinitely in the absence of competitors, and the space actually occupied by a species (Hutchinson, 1957).
Today, biogeographers also recognize dispersal limitation as a critical factor constraining the distribution of species. Dispersal limitation, while not a formal component of the ecological niche, includes both extrinsic barriers preventing dispersal (e.g. fragmentation), as well as intrinsic dispersal limitations, which can be a function of traits that govern the ability of a species to reach areas that might otherwise be suitable (Soberón & Peterson, 2005). Dispersal limitation and differential migration have been postulated to influence current distribution and diversity patterns. This is particularly evident for forest plant species and communities in the northern hemisphere following glacial retreat (Jacquemyn et al., 2001;Svenning et al., 2008;Svenning & Skov, 2007;Verheyen & Hermy, 2001;Willner et al., 2009). To gain a better understanding of the constraints on a species' geographic distribution, the relative importance of abiotic, biotic and dispersal factors should be considered. One way to do this is by estimating the disparity between the fundamental and realized niche in geographic space.
If a species is able to track its fundamental niche on the landscape, the primary constraints on the geographic distribution are presumed to be abiotic. Conversely, if the geographic distribution of a species' fundamental niche is larger than its occupied geographic distribution (i.e. its realized niche), it can be inferred that biotic factors, dispersal limitation or a combination of these affect the distribution of the species (Munguía et al., 2008;Peterson, 2006;Soberón & Peterson, 2005;Svenning & Skov, 2004).
An estimate of the fundamental niche can be obtained through ecological niche modelling (also referred to as species distribution modelling), which has been used extensively over the past two decades to relate species' distributions to abiotic factors (Araújo et al., 2019;Elith et al., 2006Elith et al., , 2011Elith & Leathwick, 2009;Guisan & Zimmermann, 2000;Phillips et al., 2006). By combining known occurrences with a set of climate variables, ecological niche models (ENMs) predict areas potentially suitable for the species in question.
Much work has been conducted to determine whether ENMs estimate the realized or the fundamental niche; consensus suggests that ENM predictions are likely estimating an environmental space in between the two, depending on whether the species is close to or far from equilibrium with its environment (Araújo & Peterson, 2012;Guillera-Arroita et al., 2015;Peterson et al., 2011;Soberón & Nakamura, 2009). Nevertheless, the areas predicted to be suitable by climate-calibrated ENMs only take into consideration the impacts of abiotic factors, thus the expectation is that the model is more often closer to an estimate of the Hutchinsonian fundamental niche than the realized niche.
To that end, although most ENMs do not explicitly consider the effects of biotic factors and dispersal limitation on species distributions (Beale et al., 2014;Dormann et al., 2012;Elith & Leathwick, 2009;Leach et al., 2016), they can be used to address potential constraints on geographic distributions. Previous studies have used ENMs to assess the relationship between the fundamental and realized niche in a variety of ways. For example, Strubbe et al. (2013) and Villaverde et al. (2017) assessed niche conservatism in non-native bird species and niche shifts in bipolar sedges after long-distance dispersal events by estimating the overlap, equivalency, similarity, expansion and unfilling of climatic niches and potential distributions. Niche expansion in these studies was defined as a species moving into a new environment, whereas niche unfilling was defined as a species only partially filling its niche in the invaded range. Tingley et al. (2016) and Zhu et al. (2017) explored intraspecific variation in realized niche expansion and unfilling in an invasive skink and an invasive stink bug, respectively; their methods incorporated knowledge about nativerange source populations and global introduction history into niche modelling approaches to explore the effects of intraspecific niche variation and different invaded-range environments on niche lability.
Fewer studies have attempted to connect species traits that directly or indirectly relate to dispersal ability and/or species interactions to niche filling. For instance, Park et al. (2018) related mating system (self-pollinating versus outcrossing) in flowering plants to niche breadth using ENM and mixed-effects models, and determined that niche breadth was not greater for self-pollinating plant species than for their outcrossing relatives, despite larger geographic range sizes.
In this paper, we ask whether reproductive life history traits of herbaceous understory plants in the genus Trillium can explain differences in the magnitude of the mismatch between the predicted suitable distribution (geographic estimation of the fundamental niche) and the occupied distribution (geographic estimation of the realized niche). Reproductive life history traits of herbaceous understory plants are often associated with dispersal ability and biotic factors, such as competition, herbivory, mutualism or parasitism. Relating these to occupancy of suitable distributions among closely related species will elucidate whether geographic distributions are constrained primarily by abiotic factors, or whether biotic factors and dispersal limitations constrain the distribution.
Species of Trillium in eastern North America (ENA)-a Trillium biodiversity hotspot (Case & Case, 1997;Ohara, 1989)-can be divided into two floral morphological types based on the presence ("pedicellate") or absence ("sessile") of a pedicel. "Sessile" refers to the attachment of the flower directly by its base, whereas "pedicellate" refers to taller and more noticeable flowers and fruits borne on pedicels. Trillium flower type is representative of many other biotic and dispersal factors that might impact extent of occupied distribution, relative to predicted suitable distribution. For example, although all trilliums are myrmecochorous (i.e., their seeds are dispersed short distances by ants), some of the seeds of pedicellate-flowered species are also known to be dispersed intermediate distances by yellow jackets ([Vespula spp.]; Jules, 1996;Zettler et al., 2001) and much longer distances via frugivory by white-tailed deer ([Odocoileus virginianus]; Vellend et al., 2003;Myers et al., 2004;Griffin & Barrett, 2004a, Griffin & Barrett, 2004b. Importantly, long-distance dispersal (LDD) by deer has not been recorded for any members of the sessile-flowered group. Several mechanisms might explain this phenomenon. Leaf mottling is present in most sessile-flowered species, which may camouflage them in the understory and reduce the probability of browsing by deer (Givnish, 1990). It is also possible that the greater plant height and biomass of many pedicellateflowered species-in combination with the greater flower and fruit height conferred by the pedicel-might promote browsing and frugivory, and thus LDD, by deer by making pedicellate-flowered species more conspicuous in the understory. Because sessile flower positioning is a synapomorphy for the subgenus Sessilium (Farmer & Schilling, 2002), other reproductive traits that potentially impact the likelihood or efficacy of seed dispersal-such as ovule number, seed mass, seed setting rate and adult biomass-may also be linked to this phylogenetic distinction.
Given the notable differences in probability of LDD, other reproductive life history traits, and biotic interactions among pedicellateand sessile-flowered trilliums, we hypothesize that the mismatch between the predicted suitable distributions and occupied distributions of 21 native Trillium species in ENA can be explained by flower type in combination with other relevant reproductive traits. To test this hypothesis, we first estimate proportional occupancies of predicted suitable distributions (also referred to as "range filling" and "niche filling" [Estrada et al., 2015;Fordham et al., 2012]) with ENMs.
We then use a model-building framework to assess what set of reproductive life history traits (flower type, ovule number, seed setting rate, number of seeds per plant, seed weight and adult biomass) best predict proportional occupancy of predicted suitable distributions.
Our study represents a comprehensive investigation of geographic distributions of eastern North American Trillium species as a function of traits related to reproduction and seed dispersal.

| Study system
Our study system is comprised of plants in the genus Trillium: perennial monocot rhizomatous herbs found in Northern Hemisphere temperate deciduous forests of eastern Asia and eastern and western North America (Freeman, 1975). Species in this genus are either pedicellate-flowered or sessile-flowered. Sessile-flowered trilliums are phylogenetically distinct, forming a monophyletic clade: subgenus Sessilium (formerly Phyllantherum; Farmer & Schilling, 2002;Case, 2002aCase, , 2002b. Within the pedicellate species, subgenus Delostylium is monophyletic; all other pedicellate species form an informal group (subgenus Trillium; Farmer & Schilling, 2002;Millam, 2006). For the purposes of this study, flower type (sessile/ pedicellate) will be used as a proxy for comparison of two groups: (i) the clade Sessilium, and (ii) an informal grouping of non-sessile species including the clade Delostylium and all other pedicellate species with currently unresolved taxonomy. Species in these two groups are characterized by reproductive differences such as the number of seeds produced per plant, seed setting rates, ovule number and seed weight (Ohara, 1989; Figure A1 in Appendix S1), as well as distinct floral scents and leaf mottling (Weakley, 2015). Pedicellate species can be further distinguished based on erect or declinate flower positioning. There are four pedicellate-declinate species which differ from pedicellate-erect species in having lower seed setting rates (Ohara, 1989).
Reproductive trilliums in ENA produce flowers from March to June, with flowering lasting 2-4 weeks, followed by the production of a single ovary containing seeds with elaiosomes (seed coat-borne appendages rich in lipids and other nutrients; Miller et al., 2020).
Ripe ovaries dehisce and drop mature diaspores (the dispersal unit of the plant; the seed-elaiosome complex) in mid-to late summer. The seeds of Trillium are dispersed by ants (i.e. myrmecochory) primarily in the Aphaenogaster fulva-rudis-texana species group (DeMarco & Cognato, 2016;Ness et al., 2009;Umphrey, 1996). However, other seed dispersers have been noted for some species of Trillium. Yellow jackets (Vespula spp.) have been observed dispersing the seeds of both pedicellate and sessile species (Bale et al., 2003;Gonzales & Hamrick, 2005;Jules, 1996;Zettler et al., 2001), and white-tailed deer (Odocoileus virginianus) have been noted dispersing the seeds of two of the most ubiquitous pedicellate species in ENA, T. grandiflorum and T. erectum (Griffin & Barrett, 2004a;Myers et al., 2004;Vellend et al., 2003). This long-distance dispersal mechanism has not, to our knowledge, been recorded or observed for any sessile species.
At least 33 species of Trillium are native to ENA (NatureServe, 2020; Weakley, 2015). Fifteen of these are ranked as high conservation priority (e.g. G1, G2 or G3; NatureServe, 2020). Both the sessile and pedicellate groups include species that are characterized by narrow endemism (e.g. they inhabit restricted geographic regions or specific habitat types), and many of these endemic species co-occur locally with geographically widespread congeners. We included 21 of the 33 native ENA species of Trillium in our study, based on taxonomic certainty and number (>20), reliability and type of records.

| Occurrence data
We sought to obtain every publicly available presence record for each Trillium species in ENA, these records dated back to 1900. The half of all records we obtained consisted of descriptive localities without latitude/longitude coordinates. To assign geographic coordinates to these localities, we used the GEOLocate software (Rios & Bart, 2010; https://www.geo-locate.org/, accessed from August 2018 to September 2019). A centroid of uncertainty with an area of 3 km 2 was automatically assigned to each locality by GEOLocate.
Minimum uncertainty was adjusted manually based on specificity of record descriptions. Descriptive localities were georeferenced by one of three researchers, and all final coordinates and uncertainties were checked and confirmed by the first author.

| Study extent
We defined the study extent as ENA north of Mexico, including all U.S. states and Canadian provinces east of the western extent of the Mississippi River (−92.9 degrees longitude), because all 21 study species have known ranges that occur within the bounds of this extent and do not occur beyond this extent. We chose this extent because the Mississippi River represents the intuitive geographic boundary between eastern and western North America, and also because the Great Plains region, which begins west of the Mississippi River, is not part of the geographic range of Trillium. We used 1 km 2 spatial resolution (0.0083 decimal degrees; 30 arc-seconds) to match that of the TA B L E 1 List of Trillium species included in the study, subgenus, flower type and reproductive life history traits. Reproductive traits (biomass (g), ovule number, number of seeds per plant, seed setting rate (%) and seed mass (mg)) obtained from Ohara (1989)  climate variable layers (see Climate variables below). Occurrence records for each species were spatially rarified to include one unique record per 1 km 2 using the spatial rarefication tool in SDMtoolbox 2.0 (Brown, 2014;Brown et al., 2017)

| Climate variables
Climate variables were generated by Wang et al. (2016) Figure 1 and Appendix S4. We did not attempt to minimize correlation among the predictor variables prior to modelling, because removing correlated variables does not significantly alter model fit statistics when implementing machine learning algorithms, as these algorithms have built-in procedures to minimize multidimensionality and collinearity of predictor variables (Feng et al., 2019;Tanner et al., 2017). Instead, we relied on the modelling algorithm to rank the variables that contributed to model accuracy gain (Table 2).

| Training and testing of ecological niche models
We used the Maxent 3.4.1 program (Phillips et al., 2006)  We evaluated final model performance with three metrics: (i) the area under the curve (AUC) of the receiver operating characteristic (ROC), which reflects the ability of the model to correctly predict presences relative to the proportion of the area predicted present (Phillips et al., 2006); (ii) omission error, or the false-negative rate that calculates the proportion of presences incorrectly predicted as absences (Fielding & Bell, 1997); and (iii) the Boyce Index, an evaluation method for presence-only models that measures how much model predictions differ from a random distribution of the known presences across prediction gradients (Boyce et al., 2002;Hirzel et al., 2006).
AUC is a widely used metric for model performance, although it is known to have shortcomings. For instance, it is highly dependent on the prevalence of the species, which is generally not known (Smith, 2013 (Hirzel et al., 2006). We used the package "ecospat" in R to calculate Boyce Index values (Broennimann et al., 2021).

| Determining the relationship between predicted suitable area and occupied distribution
To calculate the proportional occupancy of the predicted suitable area (corresponding to estimated fundamental niche) for each species, we projected all rasters to Albers equal-area map projection, then overlaid the EOO and the PSA rasters in ArcMap (v.10.7) and used the Raster Calculator feature to identify the intersection. We then divided the area of the intersection (km 2 ) by the total area of the PSA to yield the proportion of occupancy of the predicted suitable area for each species, PO (Equation 1).

| Incorporating reproductive life history traits
We We ran beta regression models with several life history predictor variables and used Akaike's Information Criterion (AICc; calculated using AICcmodavg [Mazerolle, 2019]) to determine best-fit models. The following continuous reproductive life history traits were considered as predictors: biomass (e.g. fruiting plants were separated into component organs and dried in an oven for 48 hr [Ohara, 1989]), number of ovules per flower, seed setting rate (%), number of seeds per plant and seed weight (mg). The nominal predictor "flower type" (three categories: pedicellate-erect,  (Table A1 in Appendix S2), we modelled PO using beta regressions with these four predictors individually and in combination.
We created multi-factor mean beta regression models by sequentially adding the best-fit factors and comparing model fit with single-factor models, and we generated mean models that considered interaction effects by sequentially adding best-fit factors as pairwise interactions. We also assessed the effects of different link functions (probit, loglog and cloglog, as compared to the default logit) on model fit for the best combination of factors, and explored the effects of specifying factors for the precision TA B L E 3 Beta regression model formulas, k (number of estimated parameters including intercept and Φ, the coefficient for the precision model), AICc scores, changes in AICc scores in relation to the lowest AICc score (∆AICc), loglikelihood and pseudo R 2 values associated with 30 candidate models testing the effects of reproductive life history traits ("FT"-flower type [three categories], "ovule"-ovule number, biomass and seed mass) on the proportional occupancy of the fundamental niche for 21 species of Trillium The table is sorted by ∆AICc, which places the most likely models at the top. Bold indicates models for which change in AICc score <5. All models without specified link functions employed the default logit link.
model. To assess overall model fit, we noted loglikelihood values (generated via maximum likelihood estimation) and calculated AICc scores. We considered a total of 30 models (Table 3). To evaluate significant differences among categories of the nominal factor "flower type" in the best-fit model, we performed a pairwise contrasts post hoc test in the R package multcomp (Hothorn et al., 2008).

| Ecological niche models
Overall, ENMs had reliable performance metrics. Testing AUC was ≥0.7 for 17 species and ranged from 0.62 to 0.69 for 4 species.
Testing omission error was low for most ENMs, ranging from zero (T. discolor) to 0.31 (T. ludovicianum), with an average of 0.17 (Table 4).
Boyce Index Spearman rank correlation coefficients were all positive and close to 1 (Table 4), indicating that our models generated predictions consistent with the distribution of presences in the test datasets.
The climate variable most frequently used was CMD (Hargreave's climatic moisture index), in the models of 17 species.

| Relationship between the predicted suitable area and occupied distribution
There was considerable variation in PO across the 21 species of Trillium. PO ranged from 1.1% (T. discolor) to 96% (T. grandiflorum), with an average of 51% (Figure 2). Sessile-flowered species comprised the majority of species with PO <60% (11/13), and only one sessile species (T. sessile) had PO >60%. Pedicellate-flowered species as a group showed broad variation in PO, ranging from 29% to 96%; however, 7 of 8 species with PO >60% were pedicellate ( Figure 2).

| Incorporating life history traits
The best-fit beta regression model included the non-interactive effects of flower type, ovule number, and seed mass for the mean model and employed a logit link (AICc = −4.83; Loglik =11.92, df =6, pseudo R 2 = 0.70; X 2 = 23.65, p <.001; Table 3). The mean model  Table 3). None of the interaction effects in any of the models considered were significant.
Simple linear models, evaluated using ANOVA, found significant differences in seed mass and seed setting rate among flower types for the 19 species included in the Ohara (1989) Figure A1 in Appendix S1).

| D ISCUSS I ON
Our results support the hypothesis that variation in proportional occupancies (POs) of Trillium species' predicted suitable areas (based on models of fundamental niches) can be explained by flower type-a component of trillium life history that relates to animal-mediated seed dispersal ability (Griffin & Barrett, 2004a;Jules, 1996;Myers et al., 2004;Vellend et al., 2003;Zettler et al., 2001., b.) and conservation status (NatureServe, 2020; Figure A2 in Appendix S1). Flower type was a significant predictor of PO, with sessile-flowered species  Total occ. is the total number of occurrences used per species. In total, 10,068 occurrences were used in this study. Training occ. is the number of occurrences used for training the model. Testing occ.
is the number of occurrences used to test the model. % Training and % Testing indicate the percentage of the total number of occurrences used for training and testing the model, respectively. Asterisks indicate species for which the first method of data splitting was used (i.e. georeferenced occurrences with ≤3 km 2 uncertainty were used as training data; all other occurrences were used as testing data).
Plus signs indicate species (2) for which crossvalidation with 5 replicates was used and the best replicate (highest AUC and lowest test omission error) was retained for analysis. Boyce Index (Spearman correlation coefficient), sensitivity/specificity for training data (AUC), sensitivity/specificity for testing data (AUC), and 10 per. training presence test omission rate are all model fit statistics. PSA (i.e. estimate of the fundamental niche) is the predicted suitable area (km 2 ) produced by ENM. EOO is an estimate of the area (km 2 ) of the known range. EOO ∩ PSA is the area of intersection between the PSA and EOO. PO is the proportional occupancy of the fundamental niche, calculated as in Equation 1. having significantly lower proportional occupancy of their predicted suitable areas than pedicellate-erect species. This finding may be explained by a variety of factors associated with flower type, including vegetative and reproductive differences, microhabitat preferences and resulting demographic consequences, or differences in the likelihood and frequency of short-and long-distance seed dispersal. Furthermore, because sessile flowers are a synapomorphy for subgenus Sessilium, variation in PO may be linked to phylogenetic differences between this clade and other species in genus Trillium.
Ovule number and seed mass were also significant predictors of PO, although the coefficient estimates for both of these factors were small. This suggests that species with higher ovule numbers and larger seed masses tended to have larger PO. The pseudo R 2 values for the five most likely beta regression models (those with ∆AICc <5) were all greater than 0.5 ( Within the pedicellate species, subgenus Delostylium (the "delostylis group") is a monophyletic clade endemic to the southeastern U.S. (Farmer, 2007). The remaining pedicellate species are informally grouped into the subgenus Trillium, which spans North America and Asia (Farmer & Schilling, 2002;Millam, 2006). The conservation status of trilliums in ENA differs as a function of flower type.
The set of 21 study species was represented by ranks G3, G4 and G5. Twenty-five percent of sessile study species comprised the highest conservation risk category (G3), compared to only 11% of pedicellate study species. Likewise, only 16% of sessile study species were ranked as lowest concern (G5), compared to 55% of pedicellate study species ( Figure A2 in Appendix S1). That more sessile trilliums are of greater conservation concern than pedicellate species in ENA may be a reflection of the higher prevalence of range-restriction and narrow endemism in sessile species. We note a few caveats to this assertion. First, while most pedicellate species in ENA are geographically widespread and of low conservation concern, there are two range-restricted pedicellate species in ENA ranked as "Critically Imperiled" (e.g. T. georgianum and T. Second, range size and habitat specificity are not the only factors considered by NatureServe when assigning conservation ranks (Master et al., 2003;Regan et al., 2004), so range size is not wholly synonymous with conservation status. Finally, we acknowledge that it is possible that a species could persist in the environmental space outside of the region represented by the training data in our models; therefore, our estimates of potential occupancy could be negatively biased (i.e. estimates could be smaller than they are in reality.) Despite these caveats, a connection can be drawn between higher frequency of narrow endemism and greater conservation threat associated with sessile trilliums, and our finding that species in this group have significantly lower PO than pedicellate species. Thus, at-risk, endemic species may be less likely to occupy their entire predicted suitable areas (based on models of fundamental niches) than geographically widespread species. This is consistent with the notion that range-restricted, endemic plant species are constrained to a greater extent by biotic factors, dispersal limitations or a combination of these non-abiotic factors compared to geographically widespread species. There is evidence for this trend in endemic flora in Australia (Rossetto & Kooyman, 2005;Rossetto et al., 2008), central Europe (Essl et al., 2011) and the Mediterranean region (Youssef et al., 2011).

F I G U R E 4
Scatterplots with trendlines illustrating the relationships between (a) ovule number and PO and (b) seed mass (mg) and PO, which, in combination with flower type, were both significant predictors of PO according to the best-fit beta regression (Table 3). Shape of points denotes flower type (circles = pedicellate-erect; triangles = pedicellate-declinate; squares = sessile). The trendlines and scatter of the points in each panel depict the isolated relationships between ovule number and PO, and seed mass and PO, respectively, and are included for illustrative purposes; these trendlines do not reflect the pseudo R 2 value for the overall best-fit model In his comprehensive study of life history evolution in the genus Trillium, Ohara (1989) compared life history characteristics for 27 species of Trillium across Japan and North America. He noted "remarkable differences" in traits among sessile and pedicellate species, finding that pedicellate species had higher individual adult biomass, larger reproductive outputs and smaller seeds than sessile-flowered species (Ohara, 1989). Among our investigated species, seed mass and seed setting rate differed significantly among flower types, but biomass and ovule number did not differ among flower types.
Somewhat paradoxically, seed mass, which we found to be significantly larger for sessile study species, had a significant, positive effect on PO; this apparent contradiction to our finding that sessile study species had significantly lower PO than pedicellate study species may be explained by the small value of the positive coefficient estimate for seed mass. Alternatively, pedicellate-declinate species, which did not have significantly different values of PO from either pedicellate-erect or sessile species (Figure 3), may explain this result; pedicellate-declinate species may have larger seed masses than pedicellate-erect species as a whole. Ovule number, which was not significantly different among pedicellate and sessile species, had a very weak positive effect on PO in combination with the effects of flower type and seed mass; as the sole factor in a beta regression model, ovule number was not a significant predictor of PO. As such, we will focus the remainder of our discussion on the stronger effects of flower type on the proportional occupancy of the predicted suitable area.
In ENA, Ohara (1989) observed that pedicellate species tended to occupy the northeast, whereas most sessile species were found in the southeast. This is generally consistent with our estimates of the known ranges of sessile and pedicellate species. Ohara also noted habitat differences, wherein pedicellate species occupied beech and sugar maple forests, and sessile species occupied alluvial flood plain terraces, river bottoms and river bluffs (Ohara, 1989). Patrick (1984) and Millam (2006) confirmed this observation, reporting that pedicellate and sessile species are characterized by microhabitat differences such as elevation and edaphic factors. The results of these studies suggest that microhabitat preferences, habitat specificity and resulting demographic effects may also contribute to our finding that pedicellate species are more likely to occupy their entire predicted suitable areas than sessile species. Given that sessile species are generally of greater conservation concern than pedicellate species, future studies should focus on risks to sessile trilliums associated with microhabitat preferences and habitat specificity.
To our knowledge, the only other study that connected life history traits with the proportional occupancy of predicted suitable area using our same methods found that dispersal mechanism was a significant predictor of PO for 89 Mexican mammal species (Munguía et al., 2008). In our study, all trillium species share a primary dispersal mechanism: myrmecochory. However, differences in seed dispersal rates and probabilities may nevertheless explain our finding that flower type and other seed-related traits are related to PO. There is empirical evidence that the rate of ant-mediated seed dispersal is significantly lower for the sessile species T. discolor than its sympatric, pedicellate congener T.
catesbaei in the southern Appalachians (Miller & Kwit, 2018). In a follow-up study, Miller et al. (2020) found that, of five southeastern Trillium species, T. catesbaei (the only pedicellate species in the group) had elaiosomes with greater concentrations of important signalling compounds and nutrients; this species also had the highest probability of seed dispersal by ants in the field. Although these studies only considered one pedicellate species in comparison with several sessile species, they provide evidence that pedicellate trilliums may produce seeds that are more attractive to ant dispersers and suggest that when sympatric, pedicellate trilliums may outcompete their sessile congeners for dispersal services.
Consistently lower rates of seed dispersal by ants could contribute to the increased instances of range-restricted endemism observed in sessile trilliums.
It is also likely that differences in the probability of long-distance dispersal (LDD) events among flower types explain the observed variation in PO. In addition to myrmecochory, two geographically widespread pedicellate species in ENA, T. grandiflorum and T. erectum, are prone to frugivory and seed dispersal via herbivorous whitetailed deer (Griffin & Barrett, 2004a;Myers et al., 2004;Vellend et al., 2003). Whether other species of Trillium similarly obtain LDD from white-tailed deer is unknown. Notably, we are not aware of any evidence that sessile species of Trillium are adapted to dispersal by deer. Empirically calibrated diffusion models have illustrated that, given the relationship between current distributions of North American ant-dispersed woodland herbs and the extent of the glaciers at the Last Glacial Maximum (LGM), the migration of plants such as those in the genus Trillium must rely on occasional, unknown form(s) of LDD (Cain et al., 1998). Few comprehensive phytogeographical studies have been conducted for trilliums in ENA, but an interesting comparison can be drawn between two studies that used similar methods to reconstruct the glacial history and postglacial colonization of two trillium species. Gonzales et al. (2008) found that T. Program], 2015)-also survived the LGM in two southern refugia, but its dispersal was not subsequently impeded by the Appalachian Mountains. Griffin and Barrett (2004a) concluded that occasional LDD events, such as those provided by white-tailed deer, must be responsible for the post-glacial recolonization of northern areas by T. grandiflorum. By that same logic, it is possible that the lack of postglacial recolonization of northern areas by T. cuneatum may be due to the lack of LDD.
These studies, in conjunction with our findings here, provide compelling support for the notion that sessile-flowered trilliums in ENA may be characterized by higher frequencies of narrow endemism, ranges restricted to the southeastern United States, and lower occupancy of predicted suitable areas because they do not achieve LDD to the same extent as pedicellate-flowered species. As such, we posit that variation in dispersal potential in plants of the genus Trillium stemming from all sources, including ants as primary dispersers and any potential LDD vectors, is strongly related to both range size and a species' ability to occupy its suitable area (as predicted by models of fundamental niche). These insights, gained from studying the relationship between proportion of occupancy and reproductive life history traits in species with sample sizes large enough to calibrate models, might be extrapolatable to the rarest and most-threatened members of the genus.
For instance, one attribute typically associated with the pedicellate flower type-relatively tall plant stature-is lacking for the G1 pedicellate species T. georgianum, known commonly as the Georgia Dwarf Trillium (Schilling et al., 2017). The short stature of this extremely range-restricted species may preclude it from obtaining LDD by white-tailed deer. However, we stress the need for caution in extrapolating insights drawn from more common species to species with extremely small distributions, given that the latter could be range-restricted due to fine-scale parameters such as habitat specificity and/or local adaptation that would not be detected via coarse-scale distributional comparisons. In this study, we exemplify a scenario in which reproductive life history traits may shed light on why some species are geographically range-restricted when their close relatives are geographically widespread. Our methodology, particularly if combined with estimates of niche breadth, overlap, equivalency, similarity and expansion, constitutes a powerful comparative framework that can be widely applied to diverse biological systems around the globe to yield important insights into the conservation of rare species.

ACK N OWLED G EM ENTS
We thank J. Clark and J. Fordyce for their input and suggestions throughout the project. We thank J. Fordyce for help with statistical analyses. Thanks to A. Floden and to the late T. Patrick for feedback on known ranges for these species and other expert advice throughout the project. This project was made possible by funds provided through the L. R. Hesler Herbarium Support Fund at the University of Tennessee, Knoxville. We also thank the anonymous reviewers for their time and feedback, which resulted in a much-improved final product.

PE E R R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13297.

DATA AVA I L A B I L I T Y S TAT E M E N T
All data generated for use in this manuscript are archived in the