Introduction
A defining feature of the angiosperms is their remarkable floral
diversity. (Armbruster 2014; Hernández-Hernández & Wiens 2020). Darwin
first recognized that the diversity of floral shape, size, colour and
scent could be attributable to selection by pollinators (Darwin 1877).
This realization has resulted in a large modern research program,
spawning ecological, evolutionary and genetic studies, investigating how
interactions between plants and pollinators drive floral evolution
(Harder & Johnson 2009; Van der Niet & Johnson 2012). While we are now
heading toward a strong mechanistic understanding of how flowers evolve
(Moyroud & Glover 2017; Shan et al. 2019; Fattorini & Glover
2020), the ecological processes involved in flower diversification
remain poorly understood (Kay & Sargent 2009; Johnson 2010; Van der
Niet & Johnson 2012; Armbruster 2017).
Most of our understanding of how flowers diversify derives from two
principles, which were combined into the Grant-Stebbins model (Johnson
2006, 2010). First, flowering plants should adapt to the most effective
pollinator in a given environment (Stebbins 1970); that is, the
pollinator that visits most frequently (number of visits) and
efficiently (per-visit pollen transport efficiency) (Armbruster 2014).
Second, since pollinator assemblages are geographically variable, plants
should be under divergent selection in different environments, resulting
in adaptation to different pollinators (Grant & Grant 1965).
Shifts in floral characteristics and pollination systems, however,
frequently occur without associated geographical shifts in pollinator
assemblages, suggesting that other factors drive flower diversification
(Herrera et al. 2006; Van Der Niet et al. 2014; Ferreiroet al. 2017). In the last few decades, several studies have
emphasized the importance of community context in understanding the
ecology and evolution of plant pollination (Caruso 2000; Sargent &
Ackerly 2008; Mitchell et al. 2009; Muchhala et al. 2010).
Competition and facilitation among plant species for access to
pollinator visitation, and interspecific pollen transfer play important
roles in determining the outcome of pollination (Geber & Moeller 2006;
Morales & Traveset 2008; Sargent & Ackerly 2008; Mitchell et
al. 2009; Pauw 2013). Furthermore, competition via interspecific pollen
transfer offers a potential mechanism promoting divergence in pollinator
use by favoring reduced pollinator sharing (Muchhala et al. 2010;
Moreira-Hernández & Muchhala 2019). However, despite now having a more
comprehensive understanding of pollination ecology and several
hypotheses having been proposed to explain either variability in
pollinator use or degree of specialization (Waser et al. 1996;
Johnson & Steiner 2000; Aigner 2001; Gómez & Regino 2006; Sargent &
Otto 2006; Muchhala et al. 2010; Moreira-Hernández & Muchhala
2019), we still lack a theory explaining the broad patterns of floral
diversity within and among communities.
A general mechanism promoting floral diversity in both pollinator use
and degree of specialization might derive from the consideration that
several processes governing pollination success (e.g. intraspecific
competition for access to pollinator visitation, interspecific pollen
transfer and pollen carryover) are modulated by floral abundance, which
intrinsically varies among species within communities. It is therefore
possible that different plant species of different floral abundances
face divergent selective pressures from a same pollinator assemblage.
For example, interspecific pollen transfer is expected to have a
stronger impact on populations of low abundance, as the proportion of
interspecific pollinator visits increases with the proportion of
heterospecific individuals in plant communities (Rathcke 1983;
Feinsinger et al. 1991; Caruso 2002; Palmer et al. 2003;
Sargent & Otto 2006; Mitchell et al. 2009; Runquist & Stanton
2013). Likewise, opportunities for pollen loss, whether passively or due
to pollinator grooming, should be greater for rare plant species because
pollinators visiting rare plants spend more time between conspecific
visits (Minnaar et al. 2019). Therefore, pollen carryover— the
proportion of the removed pollen carried to the next conspecific
flower—is expected to increase with floral abundance. Conversely,
intraspecific competition for pollinator visitation should be stronger
at high floral abundance, as more flowers compete for visitation by the
same pollinator community (Rathcke 1983; Geber & Moeller 2006; Duffy &
Stout 2008; Pauw 2013; Benadi & Pauw 2018). While studies carried out
at limited spatial scales often find increased per flower pollinator
visitation with increasing floral density (due to greater attractiveness
of larger flowering patches) (see Ghazoul 2005), at the landscape
scale—the scale that ultimately matters for floral evolution—the
opposite trend is observed: the number of visits received per flower
decreases with a species abundance (see Pauw 2013 and references
therein; Hegland 2014; Benadi & Pauw 2018; Bergamo et al. 2020).
The reason for such scale dependency is simple: large floral patches are
more attractive to pollinators, but a population composed of multiple
large floral patches will saturate the pollinators available, leading to
stronger intraspecific competition.
In this article, I propose that the pollination system offering the
optimal evolutionary solution for a plant species is a function of the
plant’s relative abundance in a community. In this view, different
pollinators and degrees of specialization are favoured at different
floral abundances. Floral diversification can result from shifts in
relative species abundance associated with the colonization of new
habitats or geographical ranges, creating new conditions under which
floral diversification can occur. Abundance has been previously
identified as a potential driver of floral specialization (Feinsinger
1983; Sargent & Otto 2006). However, the potential for variability in
species abundance to drive adaptation to different types of pollinators
has never been considered before. To demonstrate the potential of
variability in species abundance to foster floral diversity, I develop a
simple mathematical model of pollen transfer considering the interaction
of several pollination processes—pollen carryover, pollen removal,
intra- and interspecific competition for pollinator visits, and
interspecific pollen transfer. By tracking pollen fate, the model
explicitly measures male reproductive success. Female reproductive
success should be affected similarly to male reproductive success as
long as increased conspecific pollen deposition to stigmas increases
seed production. I use the model to assemble plant-pollinator networks
from simulated plant and pollinator communities. In a community context,
the interactions between plants and their pollinators are generally
investigated in terms of networks of interactions. Using this approach,
I assess if and how interspecific variation in floral abundance
generates diversity in pollinator use and degree of specialization. In
addition to supporting the conceptual model, the mathematical model is
consistent with, and suggests explanations for, several patterns
governing the evolution, diversification and community assembly of
flowers.
How floral abundance drives flower diversification: a
conceptual
model
Since plants produce a finite number of gametes, optimizing reproductive
success requires maximizing the number of ovules fertilized by a finite
amount of pollen. When limited by pollinator quantity, plants should
benefit from being less restrictive in their flower accessibility. Any
visitor, regardless of its quality (pollen carryover efficiency and
specialization), is likely to increase the number of pollen grains
deposited on conspecific stigmas (Thomson et al. 2000; Thomson
2003; Muchhala et al. 2010). However, pollen grains have a higher
probability of reaching conspecific stigmas when carried by more
efficient pollinators. When enough pollinators are available to remove
most pollen grains, pollinator quality becomes more limiting to plant
reproductive success than pollinator quantity, and plants should
specialize on the most efficient pollinator (Thomson et al. 2000;
Thomson 2003).
Here I propose that the selective importance of pollinator quantity and
quality is modulated by floral abundance. At high floral abundance, as
more pollinators are required for sufficient pollination, plant
reproduction is more strongly limited by pollinator quantity.
Conversely, pollen loss to inefficient carryover and interspecific
visits is reduced as floral density increases. Therefore, increased
floral abundance should increase the selective importance of pollinator
quantity while reducing the selective importance of pollinator quality.
Under these conditions, plants should benefit from generalized
pollination where more pollinators, but perhaps more wasteful ones, have
access to flowers. At low abundance, the dynamic is reversed and plants
should benefit from specializing on efficient carriers of their pollen.
While I have so far considered a dichotomy between low and high
abundance, plant populations can exist in any state from extremely rare
to abundant. Likewise, pollinators vary in their abundance (quantity
component) and efficiency (quality component). As each pollinator offers
a unique combination of quantity and quality components of pollination,
changes in a plant species’ relative abundance in a community will shift
the identity of the pollinator representing the most effective
pollinator, and therefore, the pollination system resulting in a fitness
optimum. In this view, floral abundance shapes the plant selective
landscape. Variations in plant abundance move the fitness peak of the
selective landscape toward different pollination systems, fostering
floral diversification.
Model of pollen transfer
Here I develop a mathematical model which determines how the optimal
pollinator or set of pollinators for a plant population changes as a
function of floral abundance. The model measures the proportion of
pollen grains produced by a single flower of the focal species
(hereafter ‘focal flower’) that reaches conspecific stigmas. This value
is influenced by the interaction of several pollination processes that
are linked to floral abundance (described above): pollen removal and
carryover, intra- and interspecific competition for pollinator
visitation, and interspecific pollen transfer. By tracking pollen fate,
the mathematical model explicitly determines the pollination system
maximizing male reproductive success. However, selection through either
male and female function is expected to reach the same solution in terms
of optimal pollination system as long as pollen receipt and export are
limiting and are governed by the same variables for each sex (i.e.
pollinator identity and abundance).
In the model, I treat pollinators as functional groups of pollinator
species with similar attributes (morphology, behaviour) that produce
similar selection on flowers (e.g. different species of hummingbirds,
large-bodied bees) (Fenster et al. 2004). The model assumes that
flowers are distributed homogeneously in space (i.e., flowers of the
same species are not more likely to be near one another). Variation in
floral abundance in the model is therefore the result of variation in
the abundance of the focal plant species rather than variation in the
number of flowers produced per individual of the focal species. By
assuming homogeneous spatial distribution, the model does not consider
the potential for facilitation among species sharing the same
pollinators, although facilitation is expected to benefit rarer species
(Rathcke 1983; Steven et al. 2003; Essenberg 2012), contributing to the
predicted increase in quantity limitation with abundance—i.e.
facilitation should reinforce the predictions from the conceptual model.
For a given plant species a , the total number of pollen grains
produced per flower is represented by Pt . The
proportion of grains removed with each pollinator visit to a focal
flower is represented by Ri , and depends on both
the attributes of the pollinator i and of the focal plant
species. While adaptation toward a pollination system could,
theoretically, increase R , I am more interested in the causes of
shifts between pollination systems rather the mechanisms leading to a
subsequent better fit to the system, so the model does not consider
evolution of Ri . With each new visit to a focal
flower, the amount of pollen remaining on the anthers diminishes, and
the amount of pollen picked up
with each new pollinator visit diminishes proportionally to the number
of visits already received, resulting in an exponential decline of
pollen removed with each new visit (Young & Stanton 1990; Robertson &
Lloyd 1993). Considering that pollinator i is the only visitor
(floral generalization is considered in equation 5), the total amount of
pollen removed, Pr , from the
focal flower by a given pollinator i is therefore
\({P_{r}=P}_{t}\left[1-\left(1-R_{i}\right)^{V_{\text{ij}}}\right]\)(1)
where Vij represents the number of visits by
pollinator i to flower j , which is a subset ofVi , the total number of visits made by the
pollinator in the plant community. Assuming that the visits made by the
pollinator i , Vi , are equally distributed
among all the flowers visited by the pollinator, the number of visits to
the focal flower by pollinator i is
\(V_{\text{ij}}=\frac{V_{i}}{A_{a}+\sum A_{i}}\) (2)
where Aa represents the abundance of the focal
species and ΣA i represents the total abundance of
flowers for each plant species visited by the pollinator iexcluding the focal species. In this model I treat all plant species as
being equally attractive to each pollinator (variable attractiveness
could be considered by weighting Aa by the
relative attractiveness of the focal species).
Considering the role of floral abundance and competition for a limited
number of pollinator visits, the number of pollen grains removed from a
focal flower by a given pollinator can be expressed as
\(P_{r}=P_{t}\left[1-\left(1-R_{i}\right)^{\frac{V_{i}}{A_{a}+\sum A_{i}}}\right]\)(3)
The proportion of pollen grains removed by the pollinator i that
reach a conspecific stigma depends on the pollen carryover capacity of
the pollinator, Ci — the proportion of pollen
carried over to each subsequent visit. Pollen carryover only accounts
for the proportion of pollen that is still in circulation for potential
pollination. Pollen groomed and accumulated on the scopae or corbiculae
of bees is therefore not considered in pollen carryover as this pollen
very rarely contributes to pollination (Thorp 2000). For a given
individual of the pollinator i , as with each new visit the amount
of pollen remaining on the pollinator body declines at a rateCi , the proportion of grains remaining on the
individual pollinator follows an exponential decay (Lertzman & Gass
1983; Campbell 1985; Robertson 1992) (although longer or shorter than
exponential tails have been observed; Morris et al. , 1994;
Holmquist et al. , 2012). From the pollen grains deposited on the
individual pollinator body, as pollen is lost with each visit, the
amount that will reach a conspecific stigma is a function of the number
of interspecific visits made by the pollinator before reaching a
conspecific flower, which is a function of the reciprocal of the
proportional floral abundance of the focal species in the community of
flowers visited by pollinator i : (Aa +
ΣAi ) / Aa . Therefore,
assuming that the pollinator does not exhibit floral constancy (floral
constancy is considered in Appendix S1 by weighting
ΣAi by the reciprocal of the degree of floral
constancy exhibited by the pollinator), the proportion of the removed
pollen grains by individuals of pollinator “\(i\)” that reach
conspecific stigmas is equivalent to
\begin{equation}
{C_{i}}^{\frac{A_{a}+\sum A_{i}}{A_{a}}}\nonumber \\
\end{equation}Floral constancy can be considered as temporal specialization (Waser
1986; Amaya-Márque 2009), and therefore has a similar impact on pollen
transport as fixed specialization (not behaviourally flexible), which is
represented in the model by Aa +
ΣAi . Considering both the amount of pollen
removed by the pollinator i and the proportion of this pollen
that is deposited on conspecific stigmas, the total number of pollen
grains deposited on conspecific stigmas, Pd , is
expressed as
\(P_{d}=P_{t}\left[1-\left(1-R_{i}\right)^{\frac{V_{i}}{A_{a}+\sum A_{i}}}\right]\bullet{C_{i}}^{\frac{A_{a}+\sum A_{i}}{A_{a}}}\)(4)
Equation (4) determines the effect of specialization on a given
pollinator on the pollination success of the focal plant species. The
effect of specialization on different pollinators can be evaluated by
comparing the value of Pd for exclusive
pollination by different pollinators.
When multiple pollinators visit the focal plant species (generalization
on a subset of the available pollinators), considering that the number
of pollen grains removed from a flower diminishes with each new visit,
the number of pollen grains removed by a given pollinator idepends on visitations by other pollinators. Pollinator itherefore removes a subset of the total amount of pollen removed by all
the pollinators visiting the focal flower. Assuming random visitation
order between individuals of the different pollinators, the total
proportion of pollen grains removed from the focal flower,Pr, can be expressed as the product of the
proportion of pollen removed by each pollinator alone.
\begin{equation}
\prod_{i=1}^{n}\left(1-R_{i}\right)^{\frac{V_{i}}{A_{a}+\sum A_{i}}}\nonumber \\
\end{equation}From the total number of pollen grains removed from the focal flower,
the contribution of pollinator i to the number of removed pollen
grains is relative to the proportion of visits to the focal flower made
by the pollinator i
\begin{equation}
\frac{\left(\frac{V_{i}}{A_{a}+\sum A_{i}}\right)}{\left(\sum_{i=1}^{n}\frac{V_{\text{ij}}}{A_{a}+\sum A}\right)}\nonumber \\
\end{equation}and its pollen removal rate relative to the removal rate of the other
pollinators visiting the focal flower.
\begin{equation}
\frac{R_{i}}{\left(\frac{\sum_{i=1}^{n}R_{i}}{n}\right)}\nonumber \\
\end{equation}The number of pollen grains removed by the pollinator i can
therefore be expressed as
\begin{equation}
\left[\prod_{i=1}^{n}\left(1-R_{i}\right)^{\frac{V_{i}}{A_{a}+\sum A_{i}}}\right]\bullet\frac{\left(\frac{V_{i}}{A_{a}+\sum A_{i}}\right)}{\left(\sum_{i=1}^{n}\frac{V_{\text{ij}}}{A_{a}+\sum A}\right)}\bullet\frac{R_{i}}{\left(\frac{\sum_{i=1}^{n}R_{i}}{n}\right)}\nonumber \\
\end{equation}The proportion of the removed pollen grains that reaches conspecific
stigmas is measured in the same way as for equation (4). The individual
contribution of each pollinator to Pd is summed
and the total amount of pollen deposited on conspecific stigmas
corresponds to
\begin{equation}
P_{t}=\sum_{i=1}^{n}P_{t}\left\{\left[1-\prod_{i=1}^{n}\left(1-R_{i}\right)^{\frac{V_{i}}{A_{a}+\sum A_{i}}}\right]\bullet\frac{\left(\frac{V_{i}}{A_{a}+\sum A_{i}}\right)}{\left(\sum_{i=1}^{n}\frac{V_{\text{ij}}}{A_{a}+\sum A}\right)}\bullet\frac{R_{i}}{\left(\frac{\sum_{i=1}^{n}R_{i}}{n}\right)}\right\}\bullet{C_{i}}^{\frac{A_{a}+\sum A_{i}}{A_{a}}}\ \ \ (5)\nonumber \\
\end{equation}Equation (5) is a generalization of equation (4) and determines the
effect of pollination by a combination of pollinators on the pollination
success of the focal plant species.