Volume 109, Issue 8 p. 2897-2908
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Floral complexity can help maintain plant diversity by inducing pollinator specialization

Yael Gurevich

Yael Gurevich

School of Plant Sciences and Food Security, Tel-Aviv University, Tel-Aviv, Israel

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Lilach Hadany

Corresponding Author

Lilach Hadany

School of Plant Sciences and Food Security, Tel-Aviv University, Tel-Aviv, Israel


Lilach Hadany

Email: [email protected]

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First published: 31 May 2021
Citations: 2

Handling Editor: Shurong Zhou


  1. The global decline in plant biodiversity throughout recent human history has attracted broad scientific attention, as biodiversity plays a key role in promoting a productive ecosystem. Pollination is a major factor in plant survival but carries an additional cost for locally rare plant species: they are likely to receive high levels of incompatible pollen that does not contribute to reproduction and can even impair seed production. Therefore, floral traits that diminish the risk of incompatible pollen receipt may be favoured by natural selection.
  2. We developed a theoretical framework to explore the influence of floral morphological complexity on competition for pollinator services between self-incompatible simultaneously flowering plant species.
  3. We show that when a rare plant species is morphologically complex, it may persist in competition with a more common species.
  4. Synthesis. The results show that, through its influence on pollinator foraging behaviour, complex floral morphology can contribute to the maintenance of plant diversity.


Ecological studies have widely demonstrated that plant diversity positively affects ecosystem functioning and ability to respond to changing conditions (Hooper & Vitousek, 1997; Isbell et al., 2011). As most flowering plants are pollinated by animals, plant–pollinator interactions play a significant role in the health of terrestrial ecosystems (Klein et al., 2007; Ollerton et al., 2011). The stable coexistence of multiple species in plant communities requires explanation, as many plants compete for resources such as water, light, soil nutrients and pollinators (Barot & Gignoux, 2004; Rathcke, 1983). Various factors can contribute to plant coexistence (Wilson, 2011). Flowering plants may mitigate competition, for example, by forming spatial patches (Tilman, 1982), by temporal heterogeneity in resource consumption (Questad & Foster, 2008) or by pollination niche partitioning (Benadi, 2015; Pauw, 2013). Recent theoretical papers have integrated the foraging behaviour of pollinators with plant community dynamics and discussed factors that could allow plant coexistence: adaptive foraging behaviour of individual pollinators (Revilla & Křivan, 2016; Song & Feldman, 2014); high immigration rate of a rare plant species (Song & Feldman, 2014); pollen carryover (Montgomery, 2009; Song & Feldman, 2014); and dynamics of floral reward production and limited information of pollinators regarding reward distribution (Benadi & Gegear, 2018).

The effects of pollinators’ foraging behaviour on plant coexistence may also be mediated by floral traits, such as complex flower morphology. Morphological complexity (Figure 1) can have conflicting effects on the plant and on the pollinator during a visit: it tends to be beneficial for the plant, since it encourages longer visits and thus potentially increased pollen transfer (Harder, 1990; Manetas & Petropoulou, 2000; Thomson & Plowright, 1980) but it also inflicts a cost on the pollinator, in terms of a greater time expenditure (Chittka & Thomson, 1997; Gegear & Laverty, 1995; Laverty, 1994a; Muth et al., 2015), thus potentially affecting pollinator preferences.

Details are in the caption following the image
Three species of flowers in increasing order of morphological complexity. (a) Apocynum androsaemifolium, Dogbane. Nectar is at an exposed location, the entrance to the corolla is open and the pollinator can gain access from any position on the flower. (b) Impatiens capensis, Jewelweed. The entrance is open, but the nectar is at the base of a long corolla tube. (c) Aconitum napellus, Monkshood. The nectar is concealed at an unusual location inside the petal. The corolla does not guide the visitor's tongue directly into the nectary

We developed a theoretical model to explore the effect of flower morphology on competition for pollinator services between self-incompatible simultaneously flowering plant species. The model has the following general outline—a single species of pollinator interacts with two plant species, less frequent (‘rare’) and more frequent (‘common’). Individual pollinators are flexible in behaviour and can specialize on one or the other plant species or be generalists and visit both. Their choice depends on rewards of nectar encountered within flowers, and on the energy cost of searching for the next flower and of gaining access to its nectar.

Our model predicts that a rare plant species can persist in competition with a more common one if the rare species has complex flowers. This can result from encouraging pollinator specialization of some of the pollinators, due to a combination of mechanisms that embody both optimal diet choice (due to higher reward offered) and foraging choice under a cognitive constraint (Waser, 1986). The results stemming from our model suggest that traits such as complex floral morphology may be key in maintaining plant diversity.


Co-evolution of plants and pollinators may be viewed as an ‘evolutionary game’, involving plants and their pollinators as players (Pyke, 2016). The outcome of the interaction between plants and pollinators affects their fitness, and the relevant plant and animal traits evolve through natural selection (Goulson, 1999; Pyke, 1978). An evolutionary stable strategy (ESS) in the pollination context would be a set of traits of plants and pollinators that cannot be invaded by rare, mutant individuals with different traits, either plant or animal.

The model presented here follows similar initial assumptions to those of the previous theoretical models of pollinator preference and plant competition (Kunin & Iwasa, 1996; Levin & Anderson, 1970): (a) a colony of two simultaneously flowering, randomly intermixed species of plants, (b) self-incompatible plants, completely dependent on the activities of the pollinators for their reproduction, (c) a single pollinator species and (d) a plant species’ ability to maintain its numbers in the next generation depends on its ability to attract pollinators. We consider the following pollination scenario (Figure 2): each plant has a single flower, and the flowers of the two species produce rewards at the same rate. Let urn:x-wiley:00220477:media:jec13690:jec13690-math-0001 and urn:x-wiley:00220477:media:jec13690:jec13690-math-0002 be the fraction of flowers of the two types so that urn:x-wiley:00220477:media:jec13690:jec13690-math-0003. The total density of plants in the field is assumed to be at carrying capacity and will be denoted by urn:x-wiley:00220477:media:jec13690:jec13690-math-0004, so the total density of plants of a given species urn:x-wiley:00220477:media:jec13690:jec13690-math-0005 is urn:x-wiley:00220477:media:jec13690:jec13690-math-0006. The pollinators are bees that have information about the plants’ reward distribution and are capable of plastic foraging strategies that maximize their fitness, choosing whether they specialize on either type of plants or behave as generalists. We assume pollinator density is fixed, determined by factors outside our model (Roulston & Goodell, 2011), such as habitat availability. The default values of most parameters have been derived from empirical studies (Table 1).

Details are in the caption following the image
Illustration of the model dynamics
TABLE 1. Main model parameters and values. For additional parameters, see Section 1 of the Supporting Information
Name Tested range Units Meaning
f1, f2 f1 > f2 Fraction of plants of the two types
D 1–100 plant/m2 Total density of plants in the field (Elliott, 2009)
ϕ 0.0001–0.1 μl/s Pollinator fitness, as foraging success
P total 0.01–1 pollinator/m2

Total pollinator density (Blaauw & Isaacs, 2014)

P1, P2, P3 -- Fraction of pollinators adopting each of the three foraging strategies
R max 0.1–100 μl Maximum value of floral reward (Stout & Goulson, 2002)
R1, R2 0.05–2 μl Mean floral reward (standing crop; Zimmerman, 1988)
V1, V2, V3 0.01–0.1 visit/s Per-capita visit rate for each pollinator (Eeraerts et al., 2020)
a 0–5 s/μl Time required to collect a unit amount of floral reward (Roubik & Buchmann, 1984)
b1, b2, b3 1–20 s Flower access time (Laverty, 1980)
S1, S2 1–100 Seed set for the common and rare plant, respectively (Waites & Ågren, 2004)
g 0.000001–0.01 μl/s Floral reward refill rate (Stout & Goulson, 2002)

We assume that selection acting on individual plants has a frequency-dependent component (Greenspoon & M’Gonigle, 2013; Kunin, 1993; Pauw, 2013) such that a rare self-incompatible plant would suffer a reproductive disadvantage due to receiving mostly heterospecific pollen, and this disadvantage increases with rarity. The purpose of this model is to find the range of conditions in which the rare species could persist in the plant community. For each total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0007 and the rare plant fraction urn:x-wiley:00220477:media:jec13690:jec13690-math-0008, we can determine the stable composition of pollinator strategies. The pollinators’ behavior sets the quantity and quality of pollination for both rare and common plant species, which, in turn, determines the reproductive success of each species (Figure 2). In the next generation of plants, the abundance of the rare plant may change, per its relative reproductive success.

2.1 Pollinator fitness

The plant–pollinator relationship is generally considered to be an appropriate application (Pyke, 1984, 2016) of optimal foraging theory (Emlen, 1966; MacArthur & Pianka, 1966), which assumes that animals have evolved to forage so as to maximize their fitness. Maximization of fitness, in the case of nectar feeding bees, is obtained with maximization of the net rate of energy intake (Pyke, 2016), and we hereafter use ‘foraging success’ and ‘fitness’ interchangeably. Foraging success urn:x-wiley:00220477:media:jec13690:jec13690-math-0009 is defined here as the long-term average rate of net intake (Pyke et al., 1977; Stephens & Krebs, 1986) of a forager with strategy i:
We assume, for simplicity, that energetic costs per unit time for search and for flower handling are equal. Thus, the term for the energetic cost per unit time is common to all strategies and cancels out in the equations (Supporting Information Section 3, Equation 1.7). It has been demonstrated in previous theoretical work that for realistic values, relaxing this assumption has little effect on the qualitative dynamics of the model (Kunin & Iwasa, 1996; Song & Feldman, 2014). We consider three pollinator foraging strategies. The first two are specialists, one visiting only flowers of type 1 (‘common plant specialist’, visiting only the more common flower type), the second visiting only type 2 (‘rare plant specialist’, visiting only the less common flower). The third pollinator strategy is generalist, visiting both flowers indiscriminately. While the total number of pollinators urn:x-wiley:00220477:media:jec13690:jec13690-math-0011 is an intrinsic value of the model, the number of pollinators adopting each strategy (urn:x-wiley:00220477:media:jec13690:jec13690-math-0012 is determined by the relative profitability of each strategy. Each pollinator, as a player, chooses the strategy attaining the maximum foraging success for itself, given the set of behaviours chosen by all the others. Let urn:x-wiley:00220477:media:jec13690:jec13690-math-0013 be the foraging success of the common plant specialist, rare plant specialist and generalist, respectively.

2.2 Average level of reward per visit

We consider here the flowers’ nectar rewards, although it is possible that similar assumptions could be applied to plants that release their pollen gradually over time (Thomson et al., 1989) and offer similar reward dynamics to those of nectar rewards. An essential element in this model is the depletion of floral reward level due to visiting pollinators. We assume, for simplicity, that the standing crop of floral rewards is extracted to depletion by the visiting pollinator. The reward is refilled at a constant rate until a maximum level is reached (Cruden et al., 1983; Heinrich, 1976). It is worth noting that in nature, reward refill rate may be affected by external factors, such as light conditions (Devlin, 1988), irrigation (Petanidou et al., 1999) and pollinators’ sounds (Veits et al., 2019). In our model, both flower types have the same maximum reward urn:x-wiley:00220477:media:jec13690:jec13690-math-0014 and the same rate of refill (see supplementary for relaxation of this assumption). However, the expected reward obtained per visit can still vary, as it decreases with the frequency of visits due to exploitation (Supporting Information Section 3, Equation 1.2 and 1.3). Let urn:x-wiley:00220477:media:jec13690:jec13690-math-0015 be the mean reward per visit (used in the numerator of Equation 1) for a common plant specialist, urn:x-wiley:00220477:media:jec13690:jec13690-math-0016 for a rare specialist and urn:x-wiley:00220477:media:jec13690:jec13690-math-0017 for a generalist. The full derivation can be found in Section 3 of the Supporting Information.

2.3 Rates of flower visits

Let urn:x-wiley:00220477:media:jec13690:jec13690-math-0018 be the rates of flower visits for pollinators adopting the three behavioural strategies. These rates are inversely proportional to the sum of the search time for a flower and the handling time of a flower (equal to the denominator in Equation 1).

2.4 Handling time

Handling times are assumed to be the sum of two components: access time and ingestion time (Harder, 1983). Access time, urn:x-wiley:00220477:media:jec13690:jec13690-math-0019, is measured from the initial contact with the flower until the bee ceases moving with its tongue inserted into the corolla tube (Gegear & Laverty, 1995; Woodward & Laverty, 1992) and is independent of the nectar standing crop. We assume that the plants in question have different floral morphologies, and the access time for the two species can vary. We focus here on the case that the rare plant is the more complex one urn:x-wiley:00220477:media:jec13690:jec13690-math-0020 (Chittka & Thomson, 1997; Gegear & Laverty, 1995; Laverty, 1994a; Muth et al., 2015) and relax this assumption later (see Supporting Information). Ingestion time, urn:x-wiley:00220477:media:jec13690:jec13690-math-0021, is the time required for collecting a unit amount of reward. Total reward collection times are urn:x-wiley:00220477:media:jec13690:jec13690-math-0022 and urn:x-wiley:00220477:media:jec13690:jec13690-math-0023 for the two specialist pollinator types and for the generalist, respectively. Due to frequent switching between the two plant species, the generalist incurs a cost of reduced efficiency (Chittka et al., 1999; Grüter & Ratnieks, 2011; Laverty, 1994a; Waser, 1986), thus taking longer to handle both plant species than their specialist pollinators. ‘Flower constancy’ is defined as a specialization that rises due to intrinsic limitations of the pollinator's nervous system (Bennett, 1883; Waser, 1986). One of the most commonly discussed hypotheses regarding the physiological constraints on pollinators’ cognitive abilities (Grüter & Ratnieks, 2011) is the ‘learning investment hypothesis’. It argues that learning to extract reward from a new flower species involves a learning phase of reduced efficiency (Chittka et al., 1999; Grüter & Ratnieks, 2011; Laverty, 1994a; Waser, 1986), and that the time needed in order to achieve maximum handling efficiency increases with the morphological complexity of the flower (Chittka & Thomson, 1997; Gegear & Laverty, 1995; Laverty, 1994a; Muth et al., 2015). We assume the generalist handling time increases with the rarity and complexity of the flower (Supporting Information Section 3, Equation 1.4). The generalist handling time for each of the plant species has a fixed component, determined by the inherent complexity of the flowers. In addition, the generalists face a cost of switching, a variable component determined by the plant's rarity.

2.5 The foraging success of pollinators

Using the previously defined components, mean rewards urn:x-wiley:00220477:media:jec13690:jec13690-math-0024 and mean rates of visit urn:x-wiley:00220477:media:jec13690:jec13690-math-0025, we can assemble the pollinator fitness, defined by the foraging success of the three pollinator strategies:

2.6 Behavioural equilibrium

The stable behavioural mixture of pollinators will be determined by the relative profitability of the various strategies. A basic assumption of this game-theoretic model is that the mixture of pollinators will shift from less profitable strategies to more profitable ones, either by differential recruitment or through a change of preferences. The profitability of each strategy tends to decrease as it gains an increasing number of adherents, since the nectar standing crop of plants decreases with visitation rate. Thus, the relative profitability of the various strategies may change as the mixture changes. Under such circumstances, two (or even three) strategies may come to coexist in a stable mixture at the point where they are equally profitable (Maynard Smith, 1982). Stable mixtures of pollinator strategies can be found by solving for those combinations, if any, where alternative strategies are equally profitable.

Seven hypothetical stable mixtures (1; 2; 3; 1 + 2; 1 + 3; 2 + 3; 1 + 2 + 3) exist. However, if a stable mixture includes rare plant specialists, then common plant specialists must also exist in the mixture (Kunin & Iwasa, 1996); thus, only five combinations may occur in our model.

2.7 Plant reproductive success

We define the plants' reproductive success as the female fitness (seed set). The rare plant fraction in the subsequent generation, urn:x-wiley:00220477:media:jec13690:jec13690-math-0028, is a function of urn:x-wiley:00220477:media:jec13690:jec13690-math-0029 and urn:x-wiley:00220477:media:jec13690:jec13690-math-0030 the seed sets for the common plant and the rare plant, respectively.
Each plant may be visited by specialist pollinators and generalist pollinators. Visits from specialist pollinators present `exclusively conspecific pollen while generalist pollinators deposit conspecific and heterospecific pollen, proportionally to the plant frequencies. We modelled seed set as a quantitative outcome of both conspecific and heterospecific pollen received by a flower (details in Section 4 of Supporting Information). It has been shown that if pollinators are either pure specialists or unbiased generalists, as are the strategies in our model, rates of pollen carryover (i.e. the deposition of pollen on flowers beyond the first flower visited after the pollen is picked up) do not affect pollen receipt: specialists carry only one type of pollen, and the expected proportion of conspecific pollen load deposited by generalists is equal to the proportional abundance of conspecifics in the pollinators’ diet (Montgomery, 2009). The amount of pollen deposited on a flower is a function of the duration of the pollinator visit, but is limited by the pollen collected at the previous visit (Thøstesen et al., 1996). Similarly to Levin and Anderson (1970) and as opposed to others (e.g. Bobisud & Neuhaus, 1975; Montgomery, 2009), we explicitly model that the receipt of heterospecific pollen reduces the plant reproductive success (Briggs et al., 2016; Morales & Traveset, 2008; Waser, 1978a, 1978b). In our model, we assumed that each heterospecific pollen grain reduces the effective number of conspecific pollen grains by some factor. Finally, effective conspecific pollen amounts were related to seed set via a nonlinear dose–response function (Cane & Schiffhauer, 2003; Niesenbaum, 1999; Silander & Primack, 1978), with an asymptote that reflects the finite number of ovules per flower or other limitations (Waser & Fugate, 1986; Waser & Price, 1991). Numerical parameters for this function were derived from empirical data (Waites & Ågren, 2004).

2.8 Model dynamics

The goal of our model is to explore the evolutionary trajectory of a rare plant in a community and identify the range of conditions allowing its persistence. We consider the individual-level reproductive success of both plants and pollinators and incorporate time-scale separation into the model. We assume that the phase of the game in which the pollinators choose their optimal foraging behaviour resolves much faster than the phase of plant generation. Thus, we can assume the distribution of pollinator strategies reaches a steady state within each plant generation. For a certain set of parameters of interest (such as total plant density, abundance of pollinators, initial rare plant frequency), we numerically evaluate the steady state for the distribution of pollinator strategies for varying environment settings. The abundance of pollinators adopting each strategy determines the rates of conspecific and heterospecific pollen deposition, this in turn determines the seed set of each plant species. The fraction of the rare plant in the next generation is determined by its fraction in the seed set. For the new value of rare plant fraction, we find the new distribution of pollinator strategies and so forth. This flow is repeated until the difference between urn:x-wiley:00220477:media:jec13690:jec13690-math-0032 in the next generation and urn:x-wiley:00220477:media:jec13690:jec13690-math-0033 in the current generation is smaller than a predefined threshold delta urn:x-wiley:00220477:media:jec13690:jec13690-math-0034. The critical frequency urn:x-wiley:00220477:media:jec13690:jec13690-math-0035 can be extinction urn:x-wiley:00220477:media:jec13690:jec13690-math-0036 equal frequencies urn:x-wiley:00220477:media:jec13690:jec13690-math-0037 or any intermediate value urn:x-wiley:00220477:media:jec13690:jec13690-math-0038. Figure 2 shows the outline of the model dynamics. A more detailed algorithm flow is shown in Section 2 of the Supporting Information.


3.1 Pollinator perspective

A stable mixture of pollinator strategies can be achieved only when pollinators adopting strategies retained in the mixture obtain equal fitness and adopting an alternative strategy would result in lower fitness. In our model, pollinator fitness is defined as the product of visitation rate and mean reward. When pollinating a plant that belongs to the rare and more complex species, pollinators endure longer search times and longer handling times (depending on the model values of urn:x-wiley:00220477:media:jec13690:jec13690-math-0039). Thus, rare plant specialists experience reduced mean visitation rate relative to common plant specialists. However, due to the lower degree of exploitation of rare plants in the presence of specialists, they offer a higher mean nectar standing crop. Under certain conditions, this would allow rare plants to provide fitness benefits equal to those of the common plants and acquire specialists.

Figure 3a demonstrates the pollinator behavioural equilibrium in an ecosystem where the rare plant is more complex. In broad outline, the results of the model are as follows: where floral resources are rare, all pollinators behave as generalists (region A), where resources are superabundant, pollinators specialize on the most profitable flower type which, all else is equal, is the common one (region C); and in between, regions exist where more than one strategy is retained in the behavioural mixture (regions B, D). In region D, pollinator specialization should prevail, if the rare flower remains reasonably common. Below some threshold density of plants, however, specialists on the rare species are replaced by generalists (regions B). This general pattern is robust to many variations of the model (Kunin & Iwasa, 1996), and reproduces across a wide range of parameters. As floral complexity increases, the areas in which generalist pollinators persist in the mixture (areas A and B) narrow while the area of full pollinator specialization (area D) broadens. As complexity increases, the cost of being a generalist increases as well. This is due to the association between the complexity of the rare plant and the cost of being a generalist visiting two different plant species. However, rare plant specialists may still obtain sufficient reward rate due to the trade-off described previously, between visitation rate and nectar standing crop. Yet, when overall plant density is high enough, the rare species cannot provide an equal overall benefit; thus, the area of exclusively common plant specialists (area C) widens.

Details are in the caption following the image
Increased floral complexity of the rare plant can broaden the range of plant diversity. (a) Pollinator equilibrium. Regions of stable behavioural mixture of pollinators, as a function of rare plant fraction and total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0040. Different values of rare plant morphological complexity urn:x-wiley:00220477:media:jec13690:jec13690-math-0041 are presented by the different lines, from low complexity (solid line) to high complexity (dotted line). (b) Plant–plant competition. Critical value of the rare plant frequency urn:x-wiley:00220477:media:jec13690:jec13690-math-0042, above which the two plants can coexist, plotted as a function of total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0043. Different values of rare plant morphological complexity urn:x-wiley:00220477:media:jec13690:jec13690-math-0044 are presented by the different lines as in (a). The region above the line is the region in which the two plant species can coexist. Other parameters: urn:x-wiley:00220477:media:jec13690:jec13690-math-0045 (common plant handling time), urn:x-wiley:00220477:media:jec13690:jec13690-math-0046 (floral reward refill rate)

In addition, we explored the effect of nectar replenishment rate, a significant parameter affecting the nectar standing crop. Figure 4 shows the effect of (a) lower and (b) higher nectar replenishment rate. In our model, for simplicity, we use equal replenishment rates for both plant species (we examine the effect of this assumption in Figure S1). Slower nectar refill for both species would result in decreased nectar standing crop, but more so for the more frequently visited species. Hence, since the rare plant species requires longer visit duration, a slower refill rate facilitates its competition with the common plant species. In contrast, when the refill rate is high enough, the common plant offers a substantial reward almost regardless of its exploitation, thus making it harder for the rare plant species to compete.

Details are in the caption following the image
Floral complexity, nectar refill rate and the range of plant diversity. Lower nectar refill rate allows for wider range of conditions where pollinators assume floral specialization and the rare plant species persists. (a, c) Pollinator equilibrium. Regions of stable behavioural mixture of pollinators, as a function of rare plant fraction and total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0047. Different values of rare plant morphological complexity urn:x-wiley:00220477:media:jec13690:jec13690-math-0048 are presented by the different lines, from low complexity (solid line) to high complexity (dotted line). (b, d) Plant–plant competition. Critical value of plant frequency urn:x-wiley:00220477:media:jec13690:jec13690-math-0049, above which the two plant species can coexist, plotted as a function of total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0050. Different values of rare plant morphological complexity urn:x-wiley:00220477:media:jec13690:jec13690-math-0051 are presented by the different lines as in (a, c). The region above the line is the region in which the two plant species can coexist. The parameters are similar to Figure 3 apart from nectar refill rates: (a, b) low rate of nectar refill, urn:x-wiley:00220477:media:jec13690:jec13690-math-0052. (c, d) high rate of nectar refill, urn:x-wiley:00220477:media:jec13690:jec13690-math-0053

3.2 Plant perspective

The results presented so far suggest that any floral trait that increases the length of a pollination visit may induce pollinator specialization. Interestingly, pollinator specialization on its own does not ensure the maintenance of a rare plant species. Although in this situation the rare plant species provides equal reward to that of the common species and could recruit its own specialists, it still obtains lower reproductive fitness than the common plant species. Everything else being equal, and without additional assumptions regarding the pollination ‘quality’ (defined here to be the fraction of conspecific pollen), at an initial frequency urn:x-wiley:00220477:media:jec13690:jec13690-math-0054 the rare plant would eventually go extinct (Kunin & Iwasa, 1996; Levin & Anderson, 1970; Waser, 1978b).

We focused on the trait of floral morphological complexity. This trait is particularly intriguing since although it inflicts a time cost on the pollinators for extracting nectar rewards, it also benefits the plants in two ways: the cost of switching endured by generalist pollinators results in an advantage for the specialist pollinators, which are more effective pollinators (Figure 3a); and prolonging the duration of pollinator visits allows for an increase in the amount of collected and deposited pollen in each visit. Figure 3b shows the parameter range allowing the maintenance of plant diversity: the isoclines show the critical fraction of the rare plant species, urn:x-wiley:00220477:media:jec13690:jec13690-math-0055, as a function of total plant density urn:x-wiley:00220477:media:jec13690:jec13690-math-0056 (see Figure S2 for a wider range of urn:x-wiley:00220477:media:jec13690:jec13690-math-0057), for different values of rare plant floral complexity, b2. On the isoclines, the relative reproductive success of the rare plant is equal to that of the common plant, and the coloured areas above the lines represent the regions in which the rare plant can persist in the population in the long run. We note that our results show the minimal frequency that allows the coexistence of the plant species. An extremely rare complex plant (urn:x-wiley:00220477:media:jec13690:jec13690-math-0058) would be selected against.

Two scenarios emerge that allow the maintenance of a rare plant species—(a) ‘beggars cannot be choosers’ (when pollinator/plant ratio is high, generalist pollinators succeed, regions A and B in Figure 3a) or (b) full pollinator specialization, where all pollinators are specialists (region D in Figure 3a). In the first scenario, when plant density is low, search time may become a relatively more significant component of the visit cycle time. Generalist pollinators have the shortest search time, while rare plant specialists have the longest, thus suffering most from reduced plant density. Under these circumstances, either all pollinators forage as generalists (region A) or some as common plant specialists (region B). In the second scenario, of full specialization, the two specialist pollinator strategies dominate.

Figure 3b shows the effect of rare plant floral complexity on the range of conditions that allows maintenance of plant diversity. Diversity can be maintained only in the areas where pollinators visit the rare plants—either as generalists or as specialists. Increased complexity of the rare plant (equivalent to increasing urn:x-wiley:00220477:media:jec13690:jec13690-math-0059 values) can widen the parameter range allowing maintenance of plant diversity (compare lines in Figure 3b). In scenario (a) (Figure 3b left), the rare plant species receives conspecific pollen only from generalists (areas A and B in Figure 3a), and generalists more often carry pollen of common flowers than of rare ones. However, mean visit duration is shorter for the common plant: it has both a lower standing crop of nectar due to more frequent visits, and a shorter handling time, due to lower complexity. Thus, the amount of pollen deposited (and collected) per visit is smaller. Overall, at low plant densities (when pollen limitation is not a constraint), the rare plant may persist even without specialist pollinators. In scenario (b) (Figure 3b right), specialist pollinators can be maintained on the rare plant (area D in Figure 3a). However, the rare plant does not always persist even with specialist pollinators (compare area D in Figure 3a,b right). When overall plant density is too high (corresponding to low pollinator/plant ratio), the fraction of rare plant specialists decreases (Figure S3)—and the common plants have an advantage. Finally, if we consider the case where the rare plant has simpler morphology, we find that such a rare plant could persist under very limited conditions (Figure S4).

We also examined the effect of nectar replenishment rate on the plant reproductive success. When nectar replenishment rate is low (Figure 4a,b), the rare plant can be maintained under a wide range of conditions (Figure 4b, reddish areas). In contrast, when nectar replenishment rate is high (Figure 4c,d), the rare plant can only be maintained through generalists (Figure 4c). Under high nectar replenishment, both plant species would often offer significant standing crops, limiting the advantage of the rare plant. Since existence of the rare plant is based only on the recruitment of generalist pollinators in this range, generalist cost, and thus floral complexity, may sometimes hinder its reproductive success (compare dotted and dashed line in Figure 4d).


In this work, we studied the role of floral traits in maintaining plant diversity by inducing pollinator specialization. We examined the effect of floral morphological complexity on the foraging behaviour of pollinators and on the reproductive success of rare plants. We show that floral complexity can increase pollination quality, by providing high nectar standing crops to exclusive specialist pollinators, in addition to extending visit duration. When rare plants are pollinated only by generalists, they can still benefit from longer visits, allowing higher pollen deposition. However, when the rare plant is able to maintain specialist pollinators, increasing pollinator specialization becomes a significant component of its reproductive success as well.

In this work, we model the effects of floral morphological complexity on plant–pollinator dynamics. The findings of previous papers (Kunin & Iwasa, 1996; Levin & Anderson, 1970; Waser, 1978b) were that due to competition for pollination, the reproductive success of a plant species depends on its relative frequency such that the minority species will likely be eliminated. However, our results show that a rare plant species may persist in competition with a more common one if the rare plant has more complex flowers. Our results are in agreement with previous empirical research (reviewed in Krishna & Keasar, 2018), suggesting that foragers displayed stronger specialization when visiting plant species with more complex flowers (Heinrich, 1976, 1979; Laverty, 1994a, 1994b; Stout et al., 1998) and that among self-incompatible species, rare flowers have more restricted floral access (or higher complexity) than their common counterparts (Kunin & Shmida, 1997). While the parameters explored in our model are quantifiable and derived from ecologically realistic data (Table 1), we made a few simplifying assumptions. We assumed that both plant species have equal reward replenishment rate and maximum reward capacity, while in nature these vary among co-flowering plants. On an evolutionary level, complex flowers could be selected for higher nectar and pollen production (Krishna & Keasar, 2018). However, if increased reward involves increased cost, reward evolution may be more complicated (Fishman & Hadany, 2015). Relaxing these assumptions such that the complex plant would benefit from increased nectar production could further widen the range of conditions that allow the persistence of the rare plant, even for high realistic values (Pleasants & Chaplin, 1983; Southwick, 1984) of nectar cost (Figure S1).

While we assumed plant self-incompatibility (Castric & Vekemans, 2004) and strictly biotic pollination, relaxing these assumptions would reduce the dependency of both plant species on pollinators for reproduction. This could allow the rare plant species to persist even when inefficiently pollinated by animals and would decrease the benefits of floral complexity. Rare plants may also be selected for other floral traits that encourage pollinator specialization, such as shifting of the blooming time (Heinrich, 1975; Murray et al., 2002; Pleasants, 1980) or different chemical composition of the reward (Blüthgen & Fiedler, 2004; Wright et al., 2013). It has also been suggested that morphologically complex flowers allow for a more precise placement of pollen on the bodies of pollinators such that the likelihood of conspecific pollination is increased (Krishna & Keasar, 2018; Orians, 1997). Distinct pollen placement would reduce the heterospecific pollen transfer for both plant species; however, the rare species would likely benefit more.

Future work may consider the influence of spatial patchiness on the reproductive success of a rare plant (Hanoteaux et al., 2013; Kunin, 1992, 1993; Levin & Anderson, 1970; Waser, 1978b). A species of plants can disperse its seeds locally, resulting in a patchy population structure, or disperse its seeds further apart, resulting in a more mixed population (Levine & Murrell, 2003). Travelling between patches of plants occurs less often than within-patch travel. From the specialist rare plant pollinator perspective, the penalty of higher travel times that comes with foraging on a rare plant diminishes. For a generalist pollinator, the costs of switching between varied species of plants are paid less frequently. From the plants' perspective, a generalist pollinator foraging within a patch deposits mostly conspecific pollen, inherently behaving as a specialist pollinator. So, patchiness would likely lessen the effects of population-level plant species frequency and perhaps obviate the evolution of distinctive floral traits (Bergamo et al., 2020).

It has previously been shown that diverse ecosystems tend to higher productivity in terms of biomass production and are more resistant to environmental changes (Cardinale et al., 2007; Dybzinski et al., 2008; Hector, 1999; Isbell et al., 2011; Tilman et al., 1996). Three-quarters of the global food crops depend at least partly on pollination by animals, with the economic value measuring 9.5% of the world agricultural production (Ollerton et al., 2011). Due to the importance of pollination services to global food security, recent evidence of declines in native pollinator abundance and diversity, as well as in plant–pollinator interactions (Rafferty et al., 2013) has generated widespread concern (Biesmeijer, 2006; Colla & Packer, 2008; Grixti et al., 2009; Holden, 2006; Kosior et al., 2007; Ollerton et al., 2011; Tylianakis, 2013). Considering the pollination crisis, it is of high significance to understand the mechanisms through which different plant species compete for pollination services. Our results suggest that through its effect on pollinator specialization, complex floral traits may serve important roles in maintaining plant diversity.


This project was supported by the Israeli Science Foundation 2064/18 (L.H.), by the Minerva Center on Lab Evolution (L.H.) and by the Manna Center for Food Safety & Security.


    Y.G. and L.H. designed the study, formulated the model, analysed the results and wrote the manuscript.


    The peer review history for this article is available at https://publons.com/publon/10.1111/1365-2745.13690.


    Data sharing is not applicable to this article as no new data were created or analysed in this study. The code is available at: http://doi.org/10.5281/zenodo.4742046.