Diversification of pollination systems as a function of variation in floral abundance, community context and pollinator assemblage
I then tested if changes in species abundance associated with the colonization of new communities, as well as inter-community variation in plant species composition and pollinator assemblage can drive pollination system diversification in plant clades. Each simulation consisted of a new colonist successively invading and adapting to 20 different plant communities, representing the diversification of a plant clade extending its geographical range. Assuming that 1) there is some degree of variation in the composition of the different communities and 2) the composition of each community is likely to be most similar to the community nearest to it in space, the attributes of each new colonized community (abundance of the new colonist, abundance of the other plant species, or of the different pollinators) were randomly sampled from a normal distribution characterized by a mean equal to the average value of the attributes of the last colonized community. Different sets of 100 simulations were run with different degrees of variation of the normal distribution from a coefficient of variation of 0.01 to 1, with increments of 0.01 between sets of simulations (the coefficient of variation corresponds to the standard deviation standardized to represent a proportion of variation around the average). Distributions were truncated at minimum values of 2 (assuming that at least two individuals are necessary for species survival) to avoid sampling negative values using the ‘rtruncnorm’ function from the R package ‘truncnorm’ (Mersmann et al. 2018). The initial plant-pollinator networks used for the simulations were generated in the same way as in the previous simulations.
Three different sets of simulations were performed in which the invaded communities varied in either 1) the abundance of the new colonist, 2) the abundance of the existing plant species in the community and 3) the abundance of the different pollinator species. The subset of pollinators on which the colonist evolved toward were recorded for each simulation.

Results

The impact of pollinator abundance and pollen removal rate on plant pollination success increased with floral abundance, while the impact of pollen carryover and pollinator specialization decreased with floral abundance (fig. 1A-D). Overall, the quality component of pollination was more important for pollination success than the quantity component at low floral abundance, while the quantity component was more important for pollination success at high abundance (fig. 1E).
For simulated plant communities in which plant species varied in abundance, the different species exhibited variable degrees of specialization within the communities (average number of links ± standard deviation = 2.17± 0.29) (fig. 2A, B). In contrast, in simulated plant communities where all plant species were of low abundance, most species specialized on a limited subset of the available pollinators (average number of links ± standard deviation = 1.58 ± 0.32) (Fig. 2C, D). In plant communities composed of abundant plant species, most species generalized on a high proportion of the pollinators available (average number of links ± standard deviation = 3.41 ± 0.48) (Fig. 2E, F).
The simulated plant communities in which species varied in abundance exhibited more variation in degree of specialization among species relative to the communities with no variation in plant abundance (Fig. 3A). This effect was more pronounced in communities with high average floral abundance. The communities with variation in abundance shared fewer pollinators between plant species (Fig. 3B) and produced more nested (Fig. 3C) and less connected plant-pollinator networks (Fig. 3D). Incorporating adaptive foraging produced less connected networks while high flower constancy of the pollinators had the opposite effect (Appendix S1).
The subset of available pollinators to which a new plant colonist evolved was a function of its floral abundance. At very low floral abundance, the colonist specialized on pollinators weakly exploited by the other plant species, thereby reducing competition via interspecific pollen transfer (Fig. 4). These less-preferred pollinators were often relatively rare and had a low carryover capacity, as pollinators with high abundance and carryover were generally exploited by several plant species. From very low to relatively low abundance, there was a tendency for the new colonist to shift toward specialization on a subset of pollinators with high carryover rather than low competition. This pattern was less pronounced when all plant species were of low abundance and all pollinators were therefore weakly exploited (at average flower abundance of 100, see Appendix S1). In this case, given that competition was low for all pollinators, high carryover was favored at both very low and low abundance. From intermediate to high abundance, the new colonist favoured more abundant pollinators. Generalization increased with abundance, but only at very high abundance were the majority of the available pollinators exploited. Pollinator competition (degree of specialization of the pollinator) and carryover were opposed such that pollinators with high carryover capacity were exploited by several plant species, while pollinators with low carryover capacity were less exploited. This pattern resulted in plants evolving on pollinators with less competition in average at high plant abundance relative to low abundance. Indeed, increased generalization at high abundance resulted in the incorporation of both pollinators with high carryover and low competition (specialized pollinators) comparatively to only pollinators with high carryover (and therefore highly exploited pollinators) at low abundance.
For the simulated plant clades colonizing new communities, diversity in pollination systems increased with variation in species abundance within the clade, as well as with variation in plant community composition and pollinator assemblage (Fig. 5).

Discussion

Many plant lineages and communities are characterized by high floral diversity (Van der Niet & Johnson 2012). However, the causes of floral diversification and specialization remain elusive (Kay & Sargent 2009; Johnson 2010; Van der Niet & Johnson 2012; Armbruster 2017). Here I propose that a species’ relative abundance in a community determines the pollination system offering the optimal evolutionary solution (Fig. 1, 4). Given that abundance is evolutionarily and ecologically labile (Ricklefs 2010; Loza et al. 2017), shifts in abundance associated with the colonization of new habitats or geographic ranges could promote floral diversification. This model complements the Grant-Stebbins model in which flower diversification results from geographical variation in pollinator assemblages (Grant & Grant 1965; Stebbins 1970). In this more holistic view, floral diversification is the result of variability in pollinator assemblages (Fig. 5c), floral abundance (Fig. 5a), and plant-community composition (Fig. 5b). This perception considerably relaxes the conditions under which floral diversification occurs and offers an explanation for the variability in pollinator use and degree of specialization within and among communities.
Within communities, the presence of interspecific variation in species abundance increased diversity in degree of generalization and decreased niche overlap in pollinator use (Fig. 3). Such variability also contributed to producing more realistic network structures. Indeed, while networks from communities without variation in abundance were frequently less nested and more connected then empirical plant-pollinator networks, communities with variable species abundance produced networks with nestedness and connectance within the range of empirical values (Fig. 3, compared to values of nestedness of 0.59 to 0.98 from 25 plant-pollinator networks in Bascompte et al. 2003 and values of connectance of 0.02 to 0.29 from 29 networks in Olesen & Jordano 2002).
In the simulated plant communities, flower specialization was observed at low abundance while generalization was favoured at higher abundance (Fig. 2A, B, Fig. 4), a pattern consistent with the frequently observed link between abundance and degree of generalization in plant-pollinator networks (Jordano et al. 2002; Bascompte et al. 2003; Vázquez & Aizen 2003). While the cause of this pattern is debated (Dorado et al. 2011; Fort et al. 2016), the model presented here suggests that the link between abundance and generalization can originate from a selective advantage of generalization at high abundance. Furthermore, simulated plant communities composed of plant species of low abundance resulted in widespread specialization, while communities of high abundance species were associated with generalized pollination (Fig. 2). This observation is consistent with the widespread floral specialization characterizing highly diverse plant communities composed mostly of rare species, such as in Mediterranean and tropical climates (Johnson & Steiner 2000; Vamosi et al. 2006). In such communities, plants should be under stronger selective pressure for specialization in order to avoid pollen loss from inefficient carryover and interspecific pollen transfer (Feinsinger 1983, Johnson and Steiner 2000).
Interestingly, while at moderately low abundance plants specialized on a subset of pollinators with high carryover capacity, at very low abundance the species frequently specialized on pollinators of low abundance and carryover (Fig. 4). Those pollinators were less exploited by more abundant plant species, which instead evolved pollination by abundant and efficient carriers of their pollen, offering a competition-free space for very rare species. This pattern of plant community assembly can be explained by the increasing probability of interspecific visits with increasing plant rarity, exacerbating the importance of interspecific pollen loss at very low abundance. The propensity for rare plant species to fill up unexploited pollination niches has the potential to give rise to the evolution of unique pollination systems, potentially contributing to the impressive diversity in modes of pollination characterizing tropical and Mediterranean communities.
The mathematical model and the simulated plant-pollinator networks demonstrate that, from low to intermediate abundance, plants should specialize on a subset of pollinators offering the optimal combination of pollination quantity and quality components (Fig. 1, 4). However, as plant abundance increases and most pollinators are not sufficiently abundant to remove the majority of pollen grains, highly generalized pollination should be favoured. But what happens at the extreme end of the plant abundance spectrum, when the entire pollinator community cannot provide enough visits to prevent pollen limitation? In those conditions, perhaps the best strategy is for plants to relax their dependence on biotic pollen vectors. While the evolution of wind pollination from animal pollination has mostly been attributed to reduced reliability of animal pollinators, most wind-pollinated plants are characterized by large population size and high density (Culleyet al. 2002; Friedman & Barrett 2009). Indeed, it seems doubtful that any combination of pollinators could adequately pollinate the thousands of flowers per square metre characterizing the bloom of temperate deciduous trees or Poaceae grasslands. Moreover, despite wind representing a relatively inefficient system of pollen transport, the high abundance characterizing most wind-pollinated plants reduces the importance of pollen vector efficiency.
Several theoretical models emphasize the importance of fitness trade-offs in the evolution of flower specialization (Aigner 2001; Sargent & Otto 2006; Muchhala 2007). Such trade-offs are expected to occur when adaptation to a pollinator decreases the effectiveness of pollination by other pollinators. However, despite having been detected in some studies, fitness trade-offs in the effective use of different pollinators are often weak or absent (see Armbruster 2014, 2017). Hence, it seems unlikely that floral specialization is the sole result of trade-offs. Here, similar to Muchhala et al. (2010), who investigated the role of interspecific pollen transfer in flower specialization, I demonstrate that specialization can evolve without trade-offs. Rather, specialization should be advantageous when pollinator quantity is less limiting than pollinator quality.
When present, fitness trade-offs in the effective use of different pollinators should increase floral specialization. However, the model presented here is consistent with the perception that floral specialization might be governed not only by adaptation to increase pollen removal and deposition by the most effective pollinator, but also by the exclusion of less efficient ones (Thomson 2003; Castellanoset al. 2004; Muchhala et al. 2010; Armbruster 2017). Paralleling evolution toward the most effective pollinator, exclusion of less efficient pollinators through the evolution of pollinator filters could produce trade-offs if it also excludes efficient but infrequent pollinators. In other words, pollinator filters might rarely allow singling out unwanted pollinators. For instance, the evolution of long nectar spurs prevents access to pollinators with short mouthparts, even if some of those pollinators might act as occasional but efficient visitors. Plants might therefore often evolve a high degree of evolutionary specialization despite several visitors acting as effective pollinators due to the limited capacity to maintain pollination by a subset of effective pollinators while precisely excluding the ineffective ones.