Allee Effects Determine Pollinator Services at Local and Geographic Scales

Climatic factors have attracted much attention in the study of species’ distributions, while little is known about the role of biotic interactions. Here, we tested for variation in pollinator service across the distribution of a plant species, and evaluated the driving mechanisms. We monitored insect pollinators using time-lapse cameras in populations of North American Arabidopsis lyrata from the southern to the northern range limit. We spotted 67 pollinating insect taxa, indicating that this plant-pollinator network is a generalist system. Pollinator service increased with latitude. Higher pollinator visitation was correlated with the richness of other owering plants and with plant census size, which was largest in northern populations. Furthermore, pollinator service reached a maximum at intermediate local ower density. Synthesis: This study indicates that pollination service underlies Allee effects on a local and species’ range scale, and that plant populations at range limits receive only marginal pollination service if they are small.


Introduction
Species' range limits, when not caused by dispersal limitation, should generally re ect the limits of the ecological niche. In many species, niches and ranges seem to be limited by climatic factors such as temperature and precipitation (Sexton et al., 2009). Species' distribution modelling (SDM) indicates that a handful of climate variables can often explain distribution limits rather well (e.g., Normand  Pollinator service is especially important for plant persistence as 80% of all temperate-zone owering plant species rely on animals for pollination (Ollerton et al., 2011). At range edges, reduced pollinator service might constrain the abundance of plants that rely on animals as pollen vectors for reproduction (Gaston, 2009). Indeed, population persistence is commonly reduced at range edges. , but pollinator services could also vary due to attractiveness and pollinator preferences. For example, as climatic conditions deteriorate toward range limits -possibly together with habitat availability or habitat quality -population census size, local ower density, ower attractiveness or the richness of owering plant species may decrease. Below we discuss in detail the mechanisms potentially reducing pollinator service and their relation with plant species' range limits.
One mechanism that may reduce pollinator service at a plant's range edge is based on the observation that across the distribution of a species, abundance tends to decline toward the edges, presumably because habitat suitability decreases toward range edges (Brown, 1984). The so-called 'abundant-center hypothesis' is broadly supported by a recent study documenting a decline of both the density of populations and the density of individuals within populations from the centre to the edges of species' distribution (Pironon et al., 2017). Lower regional and local densities of plants at range edges may also lower attractiveness to pollinators because pollinators commonly exhibit a preference for patches with a high density of owering plants (reviewed by Ohashi and Yahara, 1999;Stone and Jenkins, 2008;Elliott and Irwin, 2009). This hypothesis describes an Allee effect (Courchamp et al., 1999), namely that pollinator service is lower in plant populations of small size and low density.
A second mechanism is reduced oral attractiveness at range edges. Animal-pollinated plants can sometimes enhance attractiveness to pollinators by producing more owers per plant or larger owers ( e.g., Klinkhamer and De Jong, 1990;Grindeland et al., 2005). However, investments in the oral display may be costly and hard to achieve if the environment is marginal and provides limited resources. Finally, a fourth mechanism for reduced pollinator service at a plant's range edge is that climatic conditions may be unsuitable for pollinator activity. As conditions are expected to become harsher toward the edges, guilds of pollinators that are to some extent specialized on a community of plants may also decline in abundance. It is well known that pollinator abundance and metabolic activity are highly affected by temperature (Herrera, 1990;Hillyer and Silman, 2010;Rader et al., 2012;Knop et al., 2018). It is reasonable to propose that an environmental gradient that limits plant populations may have similar consequences for the pollinator assembly (e.g., Battisti et al., 2006).
In this study, we tested whether pollinator service decreased toward the range edges of a plant species (research question I) and explored the mechanisms at play (research question II). Our study organism was the short-lived perennial Arabidopsis lyrata subsp. lyrata in North America, which has been the subject of ongoing research focusing on the ecological and evolutionary causes of distribution limits . Time-lapse cameras take images at short intervals, capturing complete records over the entire day and allowing several patches in the same habitat to be monitored simultaneously. The cameras provide enough precision to identify and quantify ower visitors independently of the ower morphology or insect group (Edwards et al., 2015). In each population of A. lyrata, 10-12 cameras recorded separate ower patches for three 12-hour days, recording images at 3-sec intervals from 8 am to 8 pm (see Table S1 for detailed observation period and patches recorded). The 3-sec interval has been shown to detect 90% of all visits (Edwards et al., 2015). As the abundance of insect visitors is highly affected by temperature, wind, and precipitation (Cruden, 1972;Roubik, 1989), observations were carried out only when the weather was sunny and the sky was clear. If the image was blurry and the pollinator unrecognizable, the taxon was categorized as "unidenti able". Therefore, not all visits were identi ed to the same taxonomic depth. Some groups -especially in the Hymenoptera -were split into categories based on characters such as morphology, size, and colour pattern. We discarded from the analysis members of the Formicidae (ants) because their contribution to pollination is minimal (Junker et al., 2007). Curculionidae (weevils) were observed in one of the patches of a southern population, but not considered because it was di cult to see them. The genus Meligethes (Coleoptera) was considered to be a ower herbivore rather than a pollinator, so infested owers were discarded from the analysis. For each patch and day, only mature and fully opened owers in the video frame were considered.
Pollinator service was summarized with the following variables. Visitation rate was the total number of insect-ower interactions detected per day (abundance) divided by the total number of open owers visible in the video frame. Pollination rate was the number of owers visited at least once during the day divided by the total number of owers in the video frame. Pollinator richness was the total number of different taxa/morphotypes observed. We also calculated Shannon (1948) (1), latitude and its square term (2), latitude and elevation (3) and latitude, its square term and elevation (4). All covariates were mean-centered (before taking the square). Random effects were camera nested within population and year, and population. Secondary dependent variables were pollinator richness and Shannon diversity index. Mechanistic variables were also tested for a relationship with latitude, its square term and elevation by model selection. These included population census size (log 10 -transformed), local ower density (log 10 -transformed), ower size, plant species richness, and daily mean temperature. Random effects were adjusted depending on levels of replication.
The mechanistic hypotheses about pollination service were addressed by testing the effects of log 10transformed population census size, log 10 -transformed local ower density, the square of logtransformed local ower density, ower size, plant species richness, and daily mean temperature on dependent variables of daily visitation rate and pollination rate (research question II). Fixed effects were mean-centered (before squaring). Random effects were camera within population and year, and heterogeneity in slopes of local ower density, squared local ower density, and mean temperature against population.

Results
The total observation period for all populations, cameras and days was 4522 hours. During this recording time, 7310 owers were monitored, and 17508 insects visited A. lyrata owers. Visitors fell into 67 morphotypes, and 88% were identi ed to the taxonomic level of order (see Table S4 for the full list). About 49% of insects were Hymenoptera of the Apocrita group, followed by 48% Diptera (Table S2). Lepidoptera represented 3.2% of the visits and Coleoptera 0.1%. The fraction of each insect order varied among populations, but there was no trend with latitude ( Fig. 2A). Within the Diptera, Syrphidae and Bombyliidae were the most frequent visitors (46% and 32%, respectively), followed by Muscoidea and Empididae ( Fig  2B; Table S3). While southern A. lyrata populations were visited more often by bombyliids; centre and northern populations were visited more frequently by syrphids (Fig 2B). Some taxa were observed in more than one population, particularly the hover y Toxomerus marginatus, which was a common visitor in all populations. Although several other insects occurred across the entire latitudinal gradient, there were also unique pollinators in each population. Some of the pollinator service variables were correlated (Fig. S1A): visitation rate and pollination rate (r = 0.51) and richness and diversity (r = 0.93).
The mechanistic variables hypothesized to be associated with pollinator service varied greatly. Population census size ranged from 600 to 378000 plants, and local ower density varied from 23 to 255 per m 2 (Tables S5, S6). Flower size was largest in a self-compatible population in Virginia (VA2, see Table  S6). The richness of owering plant species ranged from 0 to 7 species (Tables S5, S7). Several of the mechanistic factors were signi cantly correlated (Fig. S1B).
I. Does pollinator service decline from the centre toward range edges?
Model selection for pollinator service and mechanistic variables indicated that the model with latitude alone was best supported by the data (Tables 1, S8). An exception was plant species richness, for which the model with latitude and its square term received the highest support.
Both visitation rate and pollination rate were positively correlated with latitude, with fewer pollinator interactions in southern populations (Fig. 3). Southern populations such as NC2 and VA2 received less than one visit per day, on average, and 60% of owers were visited (Table S9). Meanwhile, in centre and northern populations such as WV1 and NY4, 3-5 pollinators per day were observed and over 80% of owers were visited. Of the ve mechanistic environmental variables, only population census size was associated (positively) with latitude (Fig. 3B).
II. What are the mechanisms for reduced pollinator service?
To address research question II, we tested for an association between pollinator service and potential mechanistic variables independent of the range position (Table 2). Visitation rate -as a trend -and pollination rate were positively related with population census size. The result is illustrated in Figure 4 on a map, with the large northern and centre populations having higher visitation and pollination rates. There was also an increase in visitation rate with the richness of owering plant species (Fig. 3C). At the same time, high local ower density was associated with a lower visitation and pollination rate, indicating that pollinators did not visit patches proportional to local ower density but under-visited dense patches. This pattern was indicated by a signi cant negative linear term of local ower density for visitation rate and a signi cant negative quadratic term of local ower density for pollination rate (Table 2, Fig. 3D). The quadratic term further implied that also at low patch density of owers, the chance of a ower being visited on a day was proportionally lower. The shape of curves depicting the relationship between pollination rate and local ower density within patches differed among populations, together within the position along the gradient of local ower density (Fig. 3D).
Analyses on further variables such as pollinator richness and Shannon diversity index revealed some role of local ower density ( Table 2). A higher local ower density was associated with a higher pollinator richness and Shannon diversity index. Furthermore, larger owers attracted a more diverse community of pollinators; the pattern was signi cant for pollinator richness and a trend for Shannon diversity index.

Discussion
Studies on range limits and species' distribution models have focused mainly on abiotic factors to understand the edges of geographic distributions. Here we showed that biotic interactions can contribute to or at least stabilize range limits. Pollinator service in A. lyrata was signi cantly lower in the south, and this could help establish the southern range limit. The mechanistic analyses indicated that low population census size was important: there were fewer owering A. lyrata plants in the south and small population size was related with low visitation rate (as a trend) and lower probability of visitation. We discuss these and other results in the context of species' range limits and pollination biology in general.
I. Does pollinator service decline from the centre toward range edges?
Ecological niche modelling using recent climate data has shown that range limits in the south and north re ect niche limits for A. lyrata (Lee-Yaw et al., 2018). A similar conclusion was supported by a transplant experiment to sites beyond the species' range in the south and north -southern range limits, but apparently not northern limits, re ect niche limits, and the main causes of performance decline were climatic (Sánchez-Castro et al., 2021 unpublished data). The results found here indicate that pollinator services are also not favourable for A. lyrata populations at the southern range limit (Fig. 3). In southern populations, owers had an approximately 60% chance of receiving no visiting pollinators each day compared with 20% in northern populations (Fig. 3B). To evaluate the likely biological impact of this result, several factors should be considered. On the one hand, owers are generally receptive to pollinators for two days, which increases the chance of being visited at least once by a pollinator. On the other hand, our eld observations were done only during optimal conditions, when the weather was ideal for insect pollinators. Therefore, we think that across an entire blooming season many owers in small southern populations may suffer from reduced insect visitation. Even if pollinators are not a primary source causing range limits, chronically low pollinator service may nevertheless contribute to reduced reproduction and small population size (Groom, 1998). In contrast to the south, northern range-edge populations did not receive reduced pollinator service. These results, in combination with the transplant experiment described earlier, suggest that northern edge populations are limited by neither climate nor a lack of pollinator service.
Previous studies have indicated that pollinators may enforce range limits. For example, populations of Witheringia solanacea in Costa Rica had greater visitation and fruit set in a lower montane site than at the upper elevational limit (Stone and Jenkins, 2008). Similar results were found for Embothrium coccineum in northwestern Patagonia, where lower pollinator service occurred in populations at the eastern range limit and climatic variables such as precipitation were not more important than biotic interactions (Chalcoff et al., 2012). For Clarkia xantiana in the Sierra Nevada, the abundance and visitation rates of pollinators decreased and pollen limitation increased at the range limits compared to centre populations (Moeller et al., 2012). However, Hargreaves et al., (2015) found no evidence that pollination activity decreased at the upper range limit for Rhinanthus minor in the Rocky Mountains. These mixed results motivated our examination of mechanisms that may affect pollinator service and whether they vary across the latitudinal gradient.
II. What are the mechanisms for reduced pollinator service?
One of the four hypothesized mechanisms for reduced pollinator service at the southern edge of the distribution was supported. Southern A. lyrata populations were smaller, and small populations attracted fewer insect pollinators. The positive relationships among the three variables of latitudinal position, census size and pollination rate (Fig. 3B) offer a plausible mechanism by which Allee effects operate in plants. In a now classic study performed by Groom (1998), she showed in experimental populations of Clarkia concinna that owers of small and isolated populations were visited less frequently by pollinators than those of large populations -based on pollen counts. As a consequence, plants in small and isolated populations had a lower seed set and might therefore be more limited in spatial spread.
Our study found also evidence for an Allee effect independent of range position, on the scale of the local patch within populations. The relationship between pollinator visitation rate per ower and the density of owers in the patch was hump-shaped, with low visitation rates at the lowest and highest ower densities (Fig. 4D). In other words, there was positive density dependence in visitation rate at low densities and negative density dependence at high densities. The relationship was similar across all populations, although the position of maximum visitation rate was shifted slightly downward along the gradient of local ower density. For average pollination, only negative density dependence was upheld. Previous studies have found mixed evidence for density dependence. While some studies revealed positive density dependence (Kunin, 1993;Delmas et al., 2016;Nielsen and Ims, 2000), there were also some showing a negative correlation (Hendrickson et al., 2018;Grindeland et al., 2005;) or no relationship (Kirchner et al., 2005). Our study con rmed that there was considerable variation in density dependence for pollination among the populations, but that the pattern of an Allee effect was nevertheless applicable across the species.

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Finally, and also independent of range position, we found that average visitation rate of owers increased with plant species richness. This result is well in line with research that showed that the diversity of oral resources increases the visitation rate (Ghazoul, 2006;Hegland and Boeke, 2006) and that it attracts a greater number of pollinator species (Lázaro and Totland, 2010).

III. Pollination biology of A. lyrata
A recent study on one A. lyrata population in Isle Royale pointed to Syrphids as main ower visitors, in particular the genus Toxomerus (Edwards et al., 2019). By extending the geographical range of the study, we found that both Hymenoptera and Diptera were equally important as main pollinators, while Lepidoptera represented a small proportion of the visits (Fig. 2A). Within the Diptera, hover ies were the most frequent family in the centre and northern populations, supporting the previous results of Edwards et al. (2019), while Bombyliidae predominated at lower latitudes (Fig. 2B). Even though we found some common pollinators in all populations such as Toxomerus, most owers were visited by multiple insect taxa. Findings support that many pollinators of the temperate zone are opportunists with labile preferences of pollen and nectar. Results also demonstrate that the pollination network is a generalist system that provides ecological exibility in terms of reproduction for the plant, and a diversity of food resources for the pollinators (Waser et al., 1996;Fenster et al., 2004).
Furthermore, our research provided some noteworthy results on the distribution of pollinator diversity. First, we did not nd that pollinator diversity was increased at southern compared to northern latitudes, as e.g., suggested by Schemske et al. (2009). However, despite plant census size of A. lyrata being lower in the south, and visitation and pollination rates declining accordingly, pollinator diversity was not lower. Pollinator diversity was higher in populations that had larger owers. Finally, pollinator diversity was also higher on patches with a higher density of owers, which to some extent could be a sampling effect.

Conclusion
Pollinator service varied across the distribution of A. lyrata. Southern range edge populations had lower visitation rates by pollinators, and this was linked with their smaller census size. The result points to limited pollination service as an important stabilizer of range limits. Apart from this Allee effect on the level of the population, we also found evidence for an Allee effect on the level of local patches within populations. In patches of low density, the chance of a ower being visited at least once a day was lower compared to owers of mid-density patches; at higher densities, density dependence changed to negative. The two levels of positive density dependence under small size or density support a very important role of Allee effects in pollination.

Declarations
. Willi Y, Fracassetti M, Bachmann O, Van Buskirk J (2020) Demographic processes linked to genetic diversity and positive selection across a species' range.