Positive Frequency Dependence Research Articles

Parental-effect gene-drive elements under partial selfing, or why do Caenorhabditis genomes have hyperdivergent regions?

Self-fertile Caenorhabditis nematodes carry a surprising number of Medea elements, alleles that act in heterozygous mothers and cause death or developmental delay in offspring that don't inherit them. At some loci, both alleles in a cross operate as independent Medeas, affecting all the homozygous progeny of a selfing heterozygote. The genomic coincidence of Medea elements and ancient, deeply coalescing haplotypes, which pepper the otherwise homogeneous genomes of these animals, raises questions about how these apparent gene-drive elements persist for long periods of time. Here I investigate how mating system affects the evolution of Medeas, and their paternal-effect counterparts, peels. Despite an intuition that antagonistic alleles should induce balancing selection by killing homozygotes, models show that, under partial selfing, antagonistic elements experience positive frequency dependence: the common allele drives the rare one extinct, even if the rare one is more penetrant. Analytical results for the threshold frequency required for one allele to invade a population show that a very weakly penetrant allele, one whose effects would escape laboratory detection, could nevertheless prevent a much more penetrant allele from invading under high rates of selfing. Ubiquitous weak antagonistic Medeas and peels could then act as localized barriers to gene flow between populations, generating genomic islands of deep coalescence. Analysis of gene expression data, however, suggest that this cannot be the whole story. A complementary explanation is that ordinary ecological balancing selection generates ancient haplotypes on which Medeas can evolve, while high homozygosity in these selfers minimizes the role of gene drive in their evolution.

Effects of Seed Size and Frequency on Seed Dispersal and Predation by Small Mammals.

Frequency-dependent predation is common in predator-prey interactions. Size is an important characteristic of seeds and is crucial in the regeneration stage of plant seeds. However, the frequency dependence of animal predation on seed size has not been reported. In this study, we conducted a field experiment and used different sizes of Liaodong oak (Quercus wutaishanica) seeds to test the frequency dependence of intraspecific seed size selection in rodents. We used the number ratio of large to small seeds as the frequency. The results show that the rate of small seeds being eaten in situ was significantly higher than that of large seeds (p < 0.05). The rates of different-sized seeds being eaten after removal decreased with increasing frequencies, and there was no significant difference between frequencies except for 1:9 and 9:1. The rates of large seeds being scatter-hoarded were significantly higher than those of small seeds at different frequencies (p < 0.05). The eating distances after removal of large seeds were significantly longer than those of small seeds at the same frequencies (p < 0.05). Furthermore, the scatter-hoarding distances of large seeds were significantly longer than those of small seeds at three frequencies (1:9, 3:7, and 9:1) (p < 0.05). That is, rodents consumed more small seeds in situ, dispersed and scatter-hoarded more large seeds, and dispersed large seeds over longer distances. Rodents exhibited a negative frequency dependence for small seeds and a positive frequency dependence for large seeds on being eaten in situ. Moreover, rodents exhibited a negative frequency dependence for large seeds and a positive frequency dependence for small seeds on being eaten after removal and scatter-hoarding. These results reveal the frequency dependence of rodent selection on seed size and provide new insights into animal-mediated seed dispersal and the regeneration of plant populations.

Exploring polymorphism in a palatable prey: predation risk and frequency dependence in relation to distinct levels of conspicuousness.

Camouflage and warning signals are different antipredator strategies, which offer an excellent opportunity to study the evolutionary forces acting on prey appearance. Edible prey often escape detection via camouflage, which usually leads to apostatic selection favoring rare morphs. By contrast, defended prey often display conspicuous coloration acting as warning signals to predators, which usually leads to positive frequency dependence and signal uniformity. However, when two morphs of the same species vary greatly in conspicuousness, the maintenance of both cryptic and conspicuous forms in profitable prey populations remains enigmatic. Using the white and melanic morphs of the invasive box tree moth (Cydalima perspectalis) presented at three different frequencies, we investigate (a) the palatability of caterpillars and adult moths to birds, (b) predation rates on the less conspicuous melanic morph, and (c) the role of frequency dependence in balancing morph frequencies. Our results show that caterpillars are distasteful for birds but not adult moths that are fully palatable. We found that the less conspicuous, melanic morph, benefits from reduced predation due to its lower detectability. The more conspicuous, white morph, instead, is more predated and is best off when common, suggesting positive frequency dependence. These results offer new insights into the evolution of color polymorphism and prey defenses in a polymorphic moth species. Further investigation is required to understand the role of different predation regimes on the maintenance of the polymorphism in this species and test whether additional selection pressures operate in natural populations.

Evolution of realized niche breadth diversity driven by community dynamics.

Why many herbivorous insects are host plant specialists, with non-negligible exceptions, is a conundrum of evolutionary biology, especially because the host plants are not necessarily optimal larval diets. Here, I present a novel model of host plant preference evolution of two insect species. Because habitat preference evolution is contingent upon demographic dynamics, I integrate the evolutionary framework with the modern coexistence theory. The results show that the two insect species can evolve into a habitat specialist and generalist, when they experience both negative and positive frequency-dependent community dynamics. This happens because the joint action of positive and negative frequency dependence creates multiple (up to nine) eco-evolutionary equilibria. Furthermore, initial condition dependence due to positive frequency dependence allows specialization to poor habitats. Thus, evolved habitat preferences do not necessarily correlate with the performances. The model provides explanations for counterintuitive empirical patterns and mechanistic interpretations for phenomenological models of niche breadth evolution.

Why cultural distance can promote - or impede - group-beneficial outcomes.

Quantifying the distance between cultural groups has received substantial recent interest. A key innovation, borrowed from population genetics, is the calculation of cultural FST (CFST) statistics on datasets of human culture. Measuring the variance between groups as a fraction of total variance, FST is theoretically important in additive models of cooperation. Consistent with this, recent empirical work has confirmed that high values of pairwise CFST (measuring cultural distance) strongly predict unwillingness to cooperate with strangers in coordination vignettes. As applications for CFST increase, however, there is greater need to understand its meaning in naturalistic situations beyond additive cooperation. Focusing on games with both positive and negative frequency dependence and high-diversity, mixed equilibria, we derive a simple relationship between FST and the evolution of group-beneficial traits across a broad spectrum of social interactions. Contrary to standard assumptions, this model shows why FST can have both positive and negative marginal effects on the spread of group-beneficial traits under certain realistic conditions. These results provide broader theoretical direction for empirical applications of CFST in the evolutionary study of culture.

Stage-mediated priority effects and season lengths shape long-term competition dynamics.

The relative arrival time of species can affect their interactions and thus determine which species persist in a community. Although this phenomenon, called priority effect, is widespread in natural communities, it is unclear how it depends on the length of growing season. Using a seasonal stage-structured model, we show that differences in stages of interacting species could generate priority effects by altering the strength of stabilizing and equalizing coexistence mechanisms, changing outcomes between exclusion, coexistence and positive frequency dependence. However, these priority effects are strongest in systems with just one or a few generations per season and diminish in systems where many overlapping generations per season dilute the importance of stage-specific interactions. Our model reveals a novel link between the number of generations in a season and the consequences of priority effects, suggesting that consequences of phenological shifts driven by climate change should depend on specific life histories of organisms.

Decolonizing drug-resistant E. coli with phage and probiotics: breaking the frequency-dependent dominance of residents.

Widespread antibiotic resistance in commensal bacteria creates a persistent challenge for human health. Resident drug-resistant microbes can prevent clinical interventions, colonize wounds post-surgery, pass resistance traits to pathogens or move to more harmful niches following routine interventions such as catheterization. Accelerating the removal of resistant bacteria or actively decolonizing particular lineages from hosts could therefore have a number of long-term benefits. However, removing resident bacteria via competition with probiotics, for example, poses a number of ecological challenges. Resident microbes are likely to have physiological and numerical advantages and competition based on bacteriocins or other secreted antagonists is expected to give advantages to the dominant partner, via positive frequency dependence. Since a narrow range of Escherichia coli genotypes (primarily those belonging to the clonal group ST131) cause a significant proportion of multidrug-resistant infections, this group presents a promising target for decolonization with bacteriophage, as narrow-host-range viral predation could lead to selective removal of particular genotypes. In this study we tested how a combination of an ST131-specific phage and competition from the well-known probiotic E. coli Nissle strain could displace E. coli ST131 under aerobic and anaerobic growth conditions in vitro. We showed that the addition of phage was able to break the frequency-dependent advantage of a numerically dominant ST131 isolate. Moreover, the addition of competing E. coli Nissle could improve the ability of phage to suppress ST131 by two orders of magnitude. Low-cost phage resistance evolved readily in these experiments and was not inhibited by the presence of a probiotic competitor. Nevertheless, combinations of phage and probiotic produced stable long-term suppression of ST131 over multiple transfers and under both aerobic and anaerobic growth conditions. Combinations of phage and probiotic therefore have real potential for accelerating the removal of drug-resistant commensal targets.

Priority Effects Determine How Dispersal Affects Biodiversity in Seasonal Metacommunities.

AbstractThe arrival order of species frequently determines the outcome of their interactions. This phenomenon, called the priority effect, is ubiquitous in nature and determines local community structure, but we know surprisingly little about how it influences biodiversity across different spatial scales. Here, we use a seasonal metacommunity model to show that biodiversity patterns and the homogenizing effect of high dispersal depend on the specific mechanisms underlying priority effects. When priority effects are driven only by positive frequency dependence, dispersal-diversity relationships are sensitive to initial conditions but generally show a hump-shaped relationship: biodiversity declines when dispersal rates become high and allow the dominant competitor to exclude other species across patches. When spatiotemporal variation in phenological differences alters species' interaction strengths (trait-dependent priority effects), local, regional, and temporal diversity are surprisingly insensitive to variation in dispersal, regardless of the initial numeric advantage. Thus, trait-dependent priority effects can strongly reduce the effect of dispersal on biodiversity, preventing the homogenization of metacommunities. Our results suggest an alternative mechanism that maintains local and regional diversity without environmental heterogeneity, highlighting that accounting for the mechanisms underlying priority effects is fundamental to understanding patterns of biodiversity.

The effect of non-linear competitive interactions on quantifying niche and fitness differences

The niche and fitness differences of modern coexistence theory separate mechanisms into stabilizing and equalizing components. Although this decomposition can help us predict and understand species coexistence, the extent to which mechanistic inference is sensitive to the method used to partition niche and fitness differences remains unclear. We apply two alternative methods to assess niche and fitness differences to four well-known community models. We show that because standard methods based on linear approximations do not capture the full community dynamics, they can sometimes lead to incorrect predictions of coexistence and misleading interpretations of stabilizing and equalizing mechanisms. Specifically, they fail when both species occupy the same niche or in the presence of positive frequency dependence. Conversely, a more recently developed method to decompose niche and fitness differences, which accounts for the full non-linear dynamics of competition, consistently identifies the correct contribution of stabilizing and equalizing components. This approach further reveals that when the true complexity of the system is taken into account, essentially all mechanisms comprise both stabilizing and equalizing components and that local maxima and minima of stabilizing and equalizing mechanisms exist. Amidst growing interest in the role of non-additive and higher order interactions in regulating species coexistence, we propose that the effective decomposition of niche and fitness differences will become increasingly reliant on methods that account for the inherent non-linearity of community dynamics.

Patterns of frequency and density dependence are highly variable in diverse annual flowering plant communities.

Applications of ecological theory to natural communities often assume that competitive, negative density-dependent processes are the only type of interaction important for diversity maintenance. Recent advances suggest that positive interactions within trophic levels (e.g. plant-plant) may also affect plant coexistence. Though positive plant-plant interactions theoretically might result in positive or nonmonotonic frequency or density dependence (FD/DD), less is known about how commonly these patterns occur, or which ecological processes might result in such patterns in natural plant communities. In this study we test for signals of variable frequency and density dependence in annual flowering plant communities in Western Australia, and search for evidence that interactions among plants during flowering might induce positive or nonmonotonic FD/DD in flowering plants. Using four common annual wildflower species, we ask if plant fecundity exhibits positive or nonmonotonic FD/DD, and if pollinator-mediated plant-plant interactions during flowering change patterns of FD/DD relative to pollinator-independent plant interactions. Three species exhibited nonmonotonic (hump-shaped) density dependence, and only one species experienced strictly negative density dependence. Each species exhibited a different pattern of frequency dependence (positive, negative, weakly nonmonotonic, and no detectable frequency dependence). Pollinator-mediated plant-plant interactions during flowering induced both nonmonotonic density dependence and negative frequency dependence in one species. Importantly, the extent of variation in FD/DD observed in our study brings into question the dominance of negative density and frequency dependence in theory, suggesting instead that demographic responses of plants to their communities fall along a continuum of possible density- and frequency-dependent patterns.

Evolutionary mechanisms that determine which bacterial genes are carried on plasmids.

The evolutionary pressures that determine the location (chromosomal or plasmid‐borne) of bacterial genes are not fully understood. We investigate these pressures through mathematical modeling in the context of antibiotic resistance, which is often found on plasmids. Our central finding is that gene location is under positive frequency‐dependent selection: the higher the frequency of one form of resistance compared to the other, the higher its relative fitness. This can keep moderately beneficial genes on plasmids, despite occasional plasmid loss. For these genes, positive frequency dependence leads to a priority effect: whichever form is acquired first—through either mutation or horizontal gene transfer—has time to increase in frequency and thus becomes difficult to displace. Higher rates of horizontal transfer of plasmid‐borne than chromosomal genes therefore predict moderately beneficial genes will be found on plasmids. Gene flow between plasmid and chromosome allows chromosomal forms to arise, but positive frequency‐dependent selection prevents these from establishing. Further modeling shows that this effect is particularly pronounced when genes are shared across a large number of species, suggesting that antibiotic resistance genes are often found on plasmids because they are moderately beneficial across many species. We also revisit previous theoretical work—relating to the role of local adaptation in explaining gene location and to plasmid persistence—in light of our findings.

Frequency-dependent tree growth depends on climate.

Climate and competition interact to affect species' performance, such as growth and survival, and help determine species distributions and coexistence. However, it is unclear how climatic conditions modulate frequency-dependent performance, that is, how performance changes as a species becomes locally rare or common. This is critical because declines in performance as a species becomes more common (negative frequency dependence) is a signature of niche differences among species that stabilize coexistence, whereas positive frequency dependence leads to priority effects and hampers species coexistence. Here, we used dendrochronology and hierarchical models to test whether frequency-dependent growth of sugar pine (Pinus lambertiana) depends on climatic conditions. We found that growth rates were strongly dependent on annual precipitation, but no frequency dependence was evident across all years. However, there was a strong interaction between precipitation and frequency dependence, revealing stabilizing niche differences in dry years but positive frequency dependence in wet years. These differences emerged because of precipitation-driven changes in the direction and strength of both con- and heterospecific competition. Overall, these results show how stabilizing and destabilizing effects can be temporally dynamic for long-lived species and interact with climate variation.

Soliton dynamics in an all-normal-dispersion photonic crystal fiber with frequency-dependent Kerr nonlinearity

We explore high-order soliton evolution in a composite all-normal dispersion photonic crystal fiber with frequency-dependent doping nonlinearity that can vary from positive to negative and vanish at a specific wavelength, named the zero-nonlinearity wavelength (ZNW). The change in frequency dependence of doping nonlinearity dramatically adjusts the position of the ZNW and the nonlinear strength acting on the supercontinuum spectral component. As the negative (positive) frequency dependence decreases (increases), one of two generated fundamental solitons via the combined action of negative nonlinearity and normal dispersion first has a gradually boosting soliton self-frequency shift (SSFS), and then a more suppressed SSFS, but is finally limited within an increasingly small spectral range while the other has a gradually decreasing SSFS toward the ZNW and radiates a broader and stronger phase-matched dispersive wave (DW) in the nonsolitonic region. Note that the collision between two fundamental solitons plays a significant role in regulating their temporal and spectral shift as well as energy redistribution. Furthermore, the numeric sign of the frequency dependence of doping nonlinearity provides another potential tool in controlling the spectral shift direction of fundamental solitons and DWs.

Strain Background, Species Frequency, and Environmental Conditions Are Important in Determining Pseudomonas aeruginosa and Staphylococcus aureus Population Dynamics and Species Coexistence.

Bacterial communities in the environment and in infections are typically diverse, yet we know little about the factors that determine interspecies interactions. Here, we apply concepts from ecological theory to understand how biotic and abiotic factors affect interaction patterns between the two opportunistic human pathogens Pseudomonas aeruginosa and Staphylococcus aureus, which often cooccur in polymicrobial infections. Specifically, we conducted a series of short- and long-term competition experiments between P. aeruginosa PAO1 (as our reference strain) and three different S. aureus strains (Cowan I, 6850, and JE2) at three starting frequencies and under three environmental (culturing) conditions. We found that the competitive ability of P. aeruginosa strongly depended on the strain background of S. aureus, whereby P. aeruginosa dominated against Cowan I and 6850 but not against JE2. In the latter case, both species could end up as winners depending on conditions. Specifically, we observed strong frequency-dependent fitness patterns, including positive frequency dependence, where P. aeruginosa could dominate JE2 only when common (not when rare). Finally, changes in environmental (culturing) conditions fundamentally altered the competitive balance between the two species in a way that P. aeruginosa dominance increased when moving from shaken to static environments. Altogether, our results highlight that ecological details can have profound effects on the competitive dynamics between coinfecting pathogens and determine whether two species can coexist or invade each others' populations from a state of rare frequency. Moreover, our findings might parallel certain dynamics observed in chronic polymicrobial infections.IMPORTANCE Bacterial infections are frequently caused by more than one species, and such polymicrobial infections are often considered more virulent and more difficult to treat than the respective monospecies infections. Pseudomonas aeruginosa and Staphylococcus aureus are among the most important pathogens in polymicrobial infections, and their cooccurrence is linked to worse disease outcome. There is great interest in understanding how these two species interact and what the consequences for the host are. While previous studies have mainly looked at molecular mechanisms implicated in interactions between P. aeruginosa and S. aureus, here we show that ecological factors, such as strain background, species frequency, and environmental conditions, are important elements determining population dynamics and species coexistence patterns. We propose that the uncovered principles also play major roles in infections and, therefore, proclaim that an integrative approach combining molecular and ecological aspects is required to fully understand polymicrobial infections.

When rarity has costs: coexistence under positive frequency-dependence and environmental stochasticity.

Stable coexistence relies on negative frequency-dependence, in which rarer species invading a patch benefit from a lack of conspecific competition experienced by residents. In nature, however, rarity can have costs, resulting in positive frequency-dependence (PFD) particularly when species are rare. Many processes can cause positive frequency-dependence, including a lack of mates, mutualist interactions, and reproductive interference from heterospecifics. When species become rare in the community, positive frequency-dependence creates vulnerability to extinction, if frequencies drop below certain thresholds. For example, environmental fluctuations can drive species to low frequencies where they are then vulnerable to PFD. Here, we analyze deterministic and stochastic mathematical models of two species interacting through both PFD and resource competition in a Chessonian framework. Reproductive success of individuals in these models is reduced by a product of two terms: the reduction in fecundity due to PFD, and the reduction in fecundity due to competition. Consistent with classical coexistence theory, the effect of competition on individual reproductive success exhibits negative frequency-dependence when individuals experience greater intraspecific competition than interspecific competition, i.e., niche overlap is less than one. In the absence of environmental fluctuations, our analysis reveals that (1) a synergistic effect of PFD and niche overlap that hastens exclusion, (2) trade-offs between susceptibility to PFD and maximal fecundity can mediate coexistence, and (3) coexistence, when it occurs, requires that neither species is initially rare. Analysis of the stochastic model highlights that environmental fluctuations, unless perfectly correlated, coupled with PFD ultimately drive one species extinct. Over any given time frame, this extinction risk decreases with the correlation of the demographic responses of the two species to the environmental fluctuations, and increases with the temporal autocorrelation of these fluctuations. For species with overlapping generations, these trends in extinction risk persist despite the strength of the storage effect decreasing with correlated demographic responses and increasing with temporal autocorrelations. These results highlight how the presence of PFD may alter the outcomes predicted by modern coexistence mechanisms.

Within-Host Priority Effects Systematically Alter Pathogen Coexistence.

Coinfection of host populations alters pathogen prevalence, host mortality, and pathogen evolution. Because pathogens compete for limiting resources, whether multiple pathogens can coexist in a host population can depend on their within-host interactions, which, in turn, can depend on the order in which pathogens infect hosts (within-host priority effects). However, the consequences of within-host priority effects for pathogen coexistence have not been tested. Using laboratory studies with a coinfected zooplankton system, we found that pathogens had increased fitness in coinfected hosts when they were the second pathogen to infect a host, compared to when they were the first pathogen to infect a host. With these results, we parameterized a pathogen coexistence model with priority effects, finding that pathogen coexistence (1) decreased when priority effects increased the fitness of the first pathogen to arrive in coinfected hosts and (2) increased when priority effects increased the fitness of the second pathogen to arrive in coinfected hosts. We also identified the natural conditions under which we expect within-host priority effects to foster coexistence in our system. These outcomes were the result of positive or negative frequency dependence created by feedback loops between pathogen prevalence and infection order in coinfected hosts. This suggests that priority effects can systematically alter conditions for pathogen coexistence in host populations, thereby changing pathogen community structure and potentially altering host mortality and pathogen evolution via emergent processes.

Silicon nitride and silica quarter-wave stacks for low-thermal-noise mirror coatings

This study investigates a multilayer high reflector with new coating materials for next-generation laser interferometer gravitational wave detectors operated at cryogenic temperatures. We use the plasma-enhanced chemical vapor deposition method to deposit amorphous silicon nitride and silica quarter-wave high-reflector stacks and studied the properties pertinent to the coating thermal noise. Room- and cryogenic-temperature mechanical loss angles of the silicon nitride and silica quarter-wave bilayers are measured using the cantilever ring-down method. We show, for the first time, that the bulk and shear loss angles of the coatings can be obtained from the cantilever ring-down measurement, and we use the bulk and shear losses to calculate the coating thermal noise of silicon nitride and silica high-reflector coatings. The mechanical loss angle of the silicon nitride and silica bilayer is dispersive with a linear weakly positive frequency dependence, and, hence, the coating thermal noise of the high reflectors show a weakly positive frequency dependence in addition to the normal $1/\sqrt{f}$ dependence. The coating thermal noise of the silicon nitride and silica high-reflector stack is compared to the lower limit of the coating thermal noise of the end test mirrors of ET-LF, KAGRA, LIGO Voyager, and the directly measured coating thermal noise of the current coatings of Advanced LIGO. The optical absorption of the silicon nitride and silica high reflector at 1550 nm is 45.9 ppm. Using a multimaterial system composed of seven pairs of ion-beam-sputter deposited $\mathrm{Ti}:{\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ and silica and nine pairs of silicon nitride and silica on a silicon substrate, the optical absorption can be reduced to 2 ppm, which meets the specification of LIGO Voyager.

Coexistence theory and the frequency-dependence of priority effects.

Priority effects are commonly used to describe a broad suite of phenomena capturing the influence of species arrival order on the diversity, composition and function of ecological communities. Several studies have suggested reframing priority effects around the stabilizing and equalizing concepts of coexistence theory. We show that the only compatible priority effects are those characterized by positive frequency-dependence, irrespective of whether they emerge in equilibrium or non-equilibrium systems.

Decoupled maternal and zygotic genetic effects shape the evolution of development.

Evolutionary transitions from indirect to direct development involve changes in both maternal and zygotic genetic factors, with distinctive population-genetic implications, but empirical data on the genetics of such transitions are lacking. The polychaete Streblospio benedicti provides an opportunity to dissect a major transition in developmental mode using forward genetics. Females in this species produce either small eggs that develop into planktonic larvae or large eggs that develop into benthic juveniles. We identify large-effect loci that act maternally to influence larval size and independent, unlinked large-effect loci that act zygotically to affect discrete aspects of larval morphology. The likely fitness of zygotic alleles depends on their maternal background, creating a positive frequency-dependence that may homogenize local populations. Developmental and population genetics interact to shape larval evolution.

Adaptive Foraging of Pollinators Can Promote Pollination of a Rare Plant Species.

Most pollinators have the foraging flexibility to visit a wide variety of plant species. Yet few studies of pollinator-mediated processes in plants have considered the effects of variation in individual foraging patterns on plant reproductive success. In this study, we use an individual-based model of pollinator foraging economics to predict how visitation rates and pollination success of two coflowering plant species change with their frequency (relative abundance). Whereas previous studies suggested that adaptive foraging of pollinators always favors pollination of abundant plant species (positive frequency dependence), here we show that under certain conditions the per capita pollination success of a rare plant species can exceed that of a more abundant species. Specifically, when the overall flower density is sufficiently high and pollinators' perception ranges are sufficiently large, animals with limited memory of previously encountered rewards forage in a way that favors pollination of the rarer plant species. Moreover, even with perfectly informed foragers, a rare plant species benefits more from offering a higher floral reward than a more abundant species. Our results show that adaptive foraging of individual pollinators can have important implications for plant community dynamics and the persistence of rare plant species.