pollinators, herbivores, and plant neighborhood …

Volume 95, No. 1 March 2020THE QUARTERLY REVIEW OF BIOLOGY

POLLINATORS, HERBIVORES, AND PLANTNEIGHBORHOOD EFFECTS

Nora Underwood

Department of Biological Science, Florida State University

Tallahassee, Florida 32306 USA

Department of Ecology, Environment & Plant Sciences, Stockholm University

106 91 Stockholm, Sweden

e-mail: [email protected]

Peter A. Hambäck




Brian D. Inouye

Department of Biological Science, Florida State University

Tallahassee, Florida 32306 USA




keywords

neighborhood effect, plant spatial structure, insect pollination and herbivory,theory, density dependence, frequency dependence

abstract

Pollinator and herbivore interactions with individual plants can be strongly influenced by the densitiesand frequencies of other plants in local neighborhoods. The importance of these neighborhood effects is notyet clear, due in part to a profound disconnect between studies of pollinator and herbivore neighborhoodeffects. Considering these effects jointly is critical for understanding the role of plant spatial heterogeneitybecause plant fitness is often affected by pollinators, herbivores, and their interactions. We bring togetherthese two types of neighborhood effects, describing the pathways through which these insects mediate neigh-borhood effects, and comparing their implementation in mathematical models. We find that ideas from

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38 Volume 95THE QUARTERLY REVIEW OF BIOLOGY

each field can improve work in the other. For example, pollinator theory should broaden consideration ofhow pollinator traits influence responses to plant neighborhoods, while herbivore theory should consideradaptive foraging and connect herbivore neighborhood effects to plant fitness. We discuss approaches totheory that integrate pollinator and herbivore effects, particularly considering the nested spatial and tem-poral scales of these insects’ responses to neighborhoods. Ultimately, models will need to combine neighbor-hood effects from the diverse species that affect plants with direct plant interactions to determine theimportance of spatial structure for plant performance and evolution.

Introduction

T HEORETICAL and empirical work hasdemonstrated that local plant spatial

structure can influence the outcomeof plantcompetition and the evolution of plant traits(Harper 1977; Stoll and Weiner 2000) be-cause plant neighbors can strongly influenceeach other’s fitness. Both pollinators andherbivores can also influence plant popula-tion growth and evolution, and the strengthof these consumer interactions with individ-ual plants can also be influenced by plantsgrowing nearby (e.g., Waddington and Hol-den 1979;Underwoodet al. 2014). For exam-ple, neighborhood effects on pollination mayinfluence the evolution of floral traits (e.g.,Caruso 2002; Thomson et al. 2019) or neigh-borhood effects on herbivory may alter theoutcome of plant competition (e.g., Kim andUnderwood 2015), creating feedbacks be-tween current and future compositionof plantneighborhoods (Stastny and Agrawal 2014;Underwood et al. 2014). Because of the greatvariety of potential mechanisms for neighbor-hood effects, researchers have hypothesizedeverything from positive to negative effects

on plant fitness (Table 1). In contrast to plantcompetition, which occurs primarily at thescale of immediate neighbors, per capita her-bivory and pollination rates can change withplant density and frequency in neighborhoodsat spatial scales well beyond immediate neigh-bors (Antonovics and Levin 1980; Barbosaet al. 2009; Mitchell et al. 2009; Underwoodet al. 2014). Due to the logistical difficulty ofmeasuring population dynamics and evolu-tion in the field, empirical studies of neigh-borhood processes have focused mainly onper capita interaction strengths, such as pol-linator-mediated selection (e.g., Gigord et al.2001) or herbivory rates (Barbosa et al. 2009),while the population-level consequences ofherbivore and pollinator neighborhood ef-fects have primarily been addressed withmathematical models.

In this paper we compare pollinator- andherbivore-mediated neighborhood effectsas a step toward addressing the question ofwhen plant spatial structurematters for plantpopulation dynamics and evolution. Our fo-cus on pollinators and herbivores is moti-vated by the fact that these groups typically

TABLE 1Effect of neighboring plants on focal plant species or genotype

Insect type Positive (+) Negative (−)

Herbivore 1. Associational resistance (effect of heterospecificneighbors)

2. Associational susceptibility (effect of heterospecificneighbors)

3. Resource dilution (effect of conspecificneighbors)

4. Resource concentration (effect of conspecificneighbors)

Pollinator 5. Magnet plants (effect of heterospecificneighbors)

6. Interspecific pollen transfer (effect ofheterospecific neighbors

7. Pollinator facilitation (effect of heterorspecificor conspecific neighbors)

Although pollinators have positive effects on plant fitness and herbivores have negative effects on plant fitness, neighborhood ef-fects mediated by pollinators and herbivores have been hypothesized to be both positive and negative, depending on the particularmechanisms involved. Here we list some examples of named hypotheses for positive and negative effects: 1. Tahvanainen and Root(1972); 2. Letourneau (1995); 3. Cromartie (1975); 4. Root (1973); 5. Thomson (1978); 6. Levin and Anderson (1970); 7. Schemske(1981). Additionalmechanisms have been considered in the literature (see Barbosa et al. 2009,Mitchell et al. 2009, andUnderwoodet al. 2014 for reviews).

POLLINATORS, HERBIVORES, AND PLANT NEIGHBORSMarch 2020 39

have contrastingfitness effects (primarily pos-itive versus primarily negative), while at thesame time responding to and affecting plantsthrough the same basic steps: plants influ-ence pollinator or herbivore numbers or be-havior, and herbivores and pollinators mayinfluence plant-per-capita fitness. For exam-ple, the density or frequency of a neighbor-ing plant species might influence futuredensities of a focal plant species by affectinghow often herbivores find and damage thefocal plant (Barbosa et al. 2009) or how fre-quently its flowers receive appropriate pol-len (Morales and Traveset 2008). Progresstoward integrating pollinator and herbivoreneighborhood effects in models has beenlimited because studies of pollination, her-bivory, and other processes (such as plantcompetition) typically engage different re-searcher communities, resulting in separatedevelopment of theory. We argue that fur-ther theoretical and empirical work wouldbenefit from crosstalk and integration amongthe fields. In particular, we need to under-stand how differences in pollinator and herbi-vore biology, such asmobility, diet breadth, orability to learn, may translate to differences inthe strength, direction, or scale of their neigh-borhood effects.

Recognizing commonalities and differ-ences in themechanisms that create pollina-tor and herbivore neighborhood effects willhelp build a more general understanding ofthe consequences of plant spatial structure,and is of practical as well as fundamental im-portance. Agriculture and silviculture bothmanipulate plant neighborhoods as a formof pest control (Cook et al. 2007), and agri-culture uses plant neighborhoods to increasecrop pollination (e.g., Blaauw and Isaacs2014). Even though many empirical studiesfind neighborhood effects on individual-leveldamage or pollination rates for agriculturalspecies, our understanding of how and whenthese translate to increased yield at largerscales is limited. Similarly, impacts of inva-sive plants on native plants can be mediatedby pollinator or herbivore responses to localplant densities or frequencies (Brown et al.2002; Flanagan et al. 2010; Dietzsch et al.2011; Bruckman and Campbell 2016), butwe do not have a full understanding of when

these effects are likely to be positive or neg-ative (Charlebois and Sargent 2017).

In this review, we compare neighborhoodeffects mediated by insect herbivores andpollinators, while keeping inmind that othertypes of organisms (e.g., pathogens: Smith-son and Lenne 1996; soil organisms: Beveret al. 1997; mammals: Rautio et al. 2012 andChampagne et al. 2018; and birds: Nottebrocket al. 2017) can also mediate plant-plant in-teractions and should be considered in fu-ture work. To be precise, when we refer to“pollinators” we mean insects that deliverenough pollen to plants to be consideredmutualists in most situations, and by “herbi-vores” we mean insects that have primarilynegative effects on plants through consump-tion of plant tissue.Wefirst lay out the similar-ities and differences in the pathways throughwhich insect pollinators and herbivores me-diate effects of plant neighborhoods onplantfitness, drawing on the empirical literaturefor examples. We then focus on the treat-ment of these pathways inmodels of pollina-tor and herbivore neighborhood effects and,finally, consider what these differences sug-gest for future work in each field and for theultimate goal of integrating different types ofneighborhood effects.

Effects of Plant Spatial Structure

on Pollinator and Herbivore

Interactions With Plants:

Similarities and Differences

Insect herbivore andpollinator interactionswith plant neighborhoods could influenceplant populations through similar pathways(Figures 1A and 1B), where individual insectresponses to local plant density and frequencyare influenced by fixed traits, plastic traits,and features of the environment that changebased on plant neighborhood composition.Examples of relatively fixed traits that can af-fect insect movement include constitutivedefenses, floral traits such as color or archi-tecture, or insect abilities to perceive visualversus olfactory cues (e.g., Holt 1984; Pfisterand Hay 1988; Hambäck et al. 2003). Exam-ples of insect traits that change with plantneighborhoods include preference hierar-chies that change with plant frequency (e.g.,


Figure 1. Pathways For Neighborhood Effects

Potential mechanisms for plant neighborhood effects on insect and plant population processes, as estimatedthrough per capita effects mediated by herbivores (A) and by pollinators (B). Plant neighborhoods are


Smithson and Macnair 1996; Hersch and Roy2007), andmovement behaviors that changewith plant density (Morris 1993; Altizer et al.1998). Plant neighborhoods can also changeplant traits, including defenses, nutrient com-position, floral display, and reward invest-ment (e.g., Koricheva et al. 1998; Cipolliniand Bergelson 2001; Burkle and Irwin 2010),and neighbors can influence the microcli-mate on or near a plant (Kim 2017). Therecan also be feedbacks between plant-insectinteractions and plant traits, such as whendamage by herbivores induces plant resis-tance (Karban and Baldwin 1997) or whenpollinators deplete nectar or pollen and thusinfluence resources for other pollinators (e.g.,Schaffer et al. 1983). These effects of plantneighborhoods result in changes in per cap-ita interactions, such as numbers of insectsor visits per plant, damage levels, or pollina-tion rates; per capita interactions may changepopulation-level outcomes, including plantpopulation size or genetic composition andpollinator and herbivore population size (e.g.,Gigord et al. 2001).

Despite these broad similarities, there areseveral key differences in how pollinatorsand herbivores are expected to mediate ef-fects of plant neighborhoods on plant fit-ness. Most obviously, pollinators increaseplant fitness, so many flowers have traits toattract pollinators, whereas herbivores gen-erally decrease plantfitness andmany plantshave traits that reduce interactions with her-bivores. Flowers typically provide conspicu-ous visual cues, so we expect pollinators torespond strongly to them (with the caveatthat floral scents have until recently beenless widely studied than floral display). Incontrast, herbivores have long been knownto rely on volatile compounds at long rangesand other cues at short ranges (e.g., Schoon-

hoven et al. 2005). Althoughmany herbivoresalso use visual cues and pollinators also useolfactory cues (e.g., Larue et al. 2016; Lawsonet al. 2017), we expect pollinators to morecommonly rely on visual cues thanherbivores.Because of differences in how visual and olfac-tory cues are perceived at a distance, visuallyand olfactorily guided insects should differin their response to plant neighborhoods(Hambäck and Beckerman 2003; Hambäckand Englund 2005; Hambäck et al. 2014).

Traits related to diet breadth and learn-ing may also differ between pollinators andherbivores and influence their responses tolocal plant density and frequency. Althoughthere is variation in diet breadth for bothgroups, the proportion of specialists tendsto be higher among herbivores than amongpollinating insects (Fontaine et al. 2009). Thisimplies that plant neighborhoods commonlyinclude alternative resources for pollinators(although even generalists can be functionalspecialists at times), while containing mainlynonhosts for herbivores. Pollinators mighttherefore respond to the total resources pro-vided by the plant community, while herbi-vores may be more strongly influenced bythe identity of particular plants. Pollinatorsare also more likely to use learning to adjusttheir foraging (Bernays 2001; Jones and Ag-rawal 2017), resulting in a larger potentialfor change in their responses to plants withina season. For instance, pollinators often ex-hibit floral fidelity or constancy (Thomson1981a), which is the tendency of a pollinatorto make repeated visits to the same type ofplant (species or morph) within a foragingbout and thereby to be a facultative special-ist. Pollinator preferences and floral fidelitycould be influenced by plant neighborhoods,for example, if pollinators are most faithful tothe most frequent plant species (see Schmid

described in terms of the densities and frequencies of “focal” and “neighbor” plants. As the majority of empiricalstudies of insect-mediated neighborhood effects focus on interactions between plant species, “focal” plantswould most often be some plant species of particular interest, while “neighbor” plants would be species otherthan the focal species. However, it is important to bear in mind that neighborhoods could alternately be de-scribed in terms of distributions of plant phenotypes or genotypes. Densities may be best measured in termsof individuals or biomass, depending on the natural history of the species. Mechanisms may directly cause neigh-borhood effects or modify the effect of another mechanism. See the online edition for a color version of this figure.


et al. 2016 for a discussion of this phenome-non in pollinating birds). Plant constancyand learning have rarely been investigatedin herbivores, which are instead assumed inneighborhood models to have fixed prefer-ence hierarchies over short time scales (Wik-lund 1974; Thompson 1993), although thereis some evidence that larval experience withone plant may influence host plant prefer-ence in adults or across generations (referredto as Natal Habitat Preference Induction; Da-vis and Stamps 2004) or Hopkins’Host Selec-tion Principle (Hopkins 1917; e.g., Lhommeet al. 2018).

Pollinators are on average more mobilethan herbivores, in terms of both frequencyand distance of moves among plants, due tothe need to visit multiple flowers and plantsto gather sufficient resources (pollen or nec-tar). On the other hand, insect herbivorescan often complete development on a singleplant. Although pollinators are usually capa-ble of flight, insect herbivores often interactmost strongly with plants while in the larvalstage, with their location largely determinedby adult oviposition. Thus, we expect polli-nators to mediate neighborhood effects atlarger spatial scales than herbivores, althoughthe mobility of both insect herbivores andpollinators varies greatly among species. Asfew studies have attempted tomeasure scalesof insect-mediated neighborhood effects (e.g.,Thomson 1981b; Johnson et al. 2003; Lach-muth et al. 2018), it is not clear in generalhow neighborhood effects change with scaleor how they differ between types of insects;previous studies mostly consider only one ora few spatial scales. It might seem that neigh-borhood effects should be strongest at thesmallest possible spatial scales (i.e., immedi-ate neighbors) and decline in strength withdistance from a focal plant, but some studieshave found that neighborhood effects areactually stronger at larger scales ( Johnsonet al. 2003; N. Underwood and B. D. Inouye,unpublished data), and can even reversesign between scales (Hegland 2014; Charle-bois and Sargent 2017). Future studies shouldquantify plant communities and collect dataon interaction strengths of plants with pollina-tors and herbivores over a range of spatialscales. Spatially explicit data on responses

such as pollination rates, damage rates, andplant fitness could be used to characterizeneighborhood effects at multiple scales innatural or experimental populations, givensufficient variation in neighborhood compo-sition. To our knowledge, no study has yetcompared the scale of neighborhood effectsfor pollinators and herbivores in the samesystem.

Differences inmobility also affect howpol-linators and herbivores interact with plantresources. For pollinators, plant resources(pollen and nectar) are dynamic at the sametime scale as foraging decisions. Every visitby a pollinator depletes pollen and/or nec-tar, making individual flowers less profitablefor subsequent visits, yet nectar (and some-times pollen) can also replenish. Althoughherbivores can also influence the quantityand quality of their resource (Morris 1997),for example, through induced resistance, thisseldom happens at the time scale of foragingdecisions. As a result of experiences withmul-tiple flowers in a short time, or repeated visitsalonga trapline (Ohashi andThomson2009),pollinators canhavedynamic foraging choices,either increasing or decreasing constancyand preference for particular flower typesand thus the strength of frequency depen-dence in plant performance. Herbivores areless likely to be able to use familiarity with in-dividual plants in their foraging as they moveamong plants less often.Many herbivores re-spond to the plant neighborhood when ovi-positing, but then larvaemove little or not atall among plants, making their feeding be-havior less responsive to rapid changes inneighborhood properties. Some generalistand highly mobile herbivores (e.g., grass-hoppers andwhiteflies) could be exceptionsto this pattern (Bernays et al. 1994).

Finally, a major difference between her-bivory and pollination is that for plants thatrequire outcrossed pollen, the value of a pol-linator visit depends critically onwhichplantsthe pollinator has visited recently, whereasthe order of visits to plants is largely irrele-vant for thefitness impacts of herbivoredam-age. Pollen from a conspecific can lead toseed production, but heterospecific pollenmay be of no value or can have a negativeeffect through stigma clogging (Waser and


Fugate 1986; Galen et al. 1989), allelopathy(Morales and Traveset 2008), or pollen dis-counting (Holsinger et al. 1984). The averagevalue of pollen arriving at a particular flowercan thus depend on the frequency of differ-ent plant species or morphs in the popula-tion. As a plant type becomes more frequentin its neighborhood, even random pollinatormovements aremore likely to confer effectivepollination, causing positive frequency de-pendence in plant fitness (indicated by thearrow inFigure1Bdirectly linkingplantneigh-borhood characteristics to pollendeposition,bypassing pollinator behavior; Levin and An-derson 1970).

There are potentially important pathwaysthat are not included in Figure 1 becausethey have so far received little attention inmodels of neighborhood effects; they shouldbe considered in future work. Feedbacks be-tween current densities and frequencies ofplants and the composition of future plantneighborhoods have not yet been fully dem-onstrated, but there is evidence that they arelikely (Stastny and Agrawal 2014). It has alsooften been suggested that neighborhoodeffects can be mediated by predators (the“enemies” hypothesis) when predator abun-dance or effectiveness change with plant den-sity or frequency (Elton 1958; Stiling et al.2003). Pollinators and herbivores can also re-spond to plant diversity rather than the pres-ence or frequency of particular plants (e.g.,Bernays 1999; Hegland and Boeke 2006). Fi-nally, insect population densities could in-fluence how individual insects respond toplant neighborhoods (e.g., Thomson et al.1987; Brosi and Briggs 2013); although somemodels of pollinator neighborhood effectsconsider the influenceof variation in totalpol-linator density (e.g., Kunin and Iwasa 1996;Hanoteaux et al. 2013), studies of herbivoreneighborhood effects have generally not con-sidered the potential effect of average herbi-vore density on herbivore behavior (but seeMerwin et al. 2017 for an empirical example).For herbivores with rapid generations andthat move among nearby plants (i.e., aphids),herbivore loads on individual plants can beinfluenced by plant neighborhood effectson herbivore population dynamics (Under-wood 2004, 2009).

Theory For Pollinator and Herbivore

Neighborhood Effects

General ecological theory describes howvariation in plant density and frequency caninfluence population dynamics and speciespersistence; negative density dependence af-fects equilibrium population size and thecoexistence of competing species, negativefrequency dependence (i.e., per capita per-formance declining with frequency) contrib-utes to the coexistence of competing species(Barabás et al. 2018) or genotypes (Livelyand Howard 1994), and positive frequencydependence destabilizes systems and contrib-utes to exclusion of rare species unless thereis persistent spatial patterning in a landscape(Molofsky et al. 2001).Models specifically ad-dressing the contribution of insect-mediatedneighborhood effects to plant populationdynamics and evolution build upon generaltheory by including some reference to spatialstructure, specifying how plant composition(density and/or frequency) in physical neigh-borhoods interacts with insect traits to influ-ence interaction intensities with plants. Inthis section, we describe general ecologicaltheory that has contributed important ideasto neighborhood models, outline the basiccomponents of neighborhood models, andreview key papers in the historical develop-ment of neighborhood models for plant-her-bivore and plant-pollinator systems. Thesemodels have addressed a variety of questions,collectively providing a growing library ofapproaches. In Table 2 we summarize thebasic features (structure, response variables,and mechanisms of neighborhood effects)of all insect-mediated neighborhood mod-els of which we are aware. Network modelswere not included in this review primarilybecause none have yet addressed insect-me-diated neighborhood effects, but also be-cause network models are not the best toolfor connecting individual-level traits or fit-ness with population-level consequences.

foundational ideas from

nonneighborhood models

Several studies have provided crucial in-sights and mathematical building blocks for


TABLE 2A summary of the key features of mathematical and simulation models

of insect-mediated neighborhood effects

Model StructurePrimaryresponsevariables

Mechanisms generatingneighborhood effects

Mechanismsmodifying

neighborhoodeffects

1 2 3 4 5 6 7 8 9 10Con

sumer

type

Neigh

borhoo

dstructure

Primaryrespon

sevariab

les

Req

uiremen

tfor

intraspe

cificpo

llen

Resou

rcedy

namics

Ada

ptiveforaging

Unspe

cified

beha

vioral

respon

seto

neighb

orho

od

Con

stan

cy

Preferenc

e

Pollencarryover

Levin and Anderson (1970) P Well mixed Plant frequency ● ● ● ●Straw (1972) P Well mixed Plant frequency ● ● ●Bobisud and Neuhaus (1975) P Well mixed Per capita effects ● ● ●Waser (1978) P Explicit Plant density ● ● ●Fowler and Levin (1984) P Well mixed Plant density ● ●Goulson (1994) P Well mixed Per capita effects ● ● ● ● ●Kunin and Iwasa (1996) P Well mixed Plant frequency ● ● ●Ishii and Higashi (2001) P Well mixed Plant density ● ●Feldman et al. (2004) P Implicit Plant density ● ● ●Sargent and Otto (2006) P Well mixed Genotype

frequency●

Rodriguez-Gironés andSantamaría (2007)

P Explicit Plant frequency ● ● ●

Montgomery (2009) P Well mixed Per capita effects ● ● ●Tachiki et al. (2010) P Implicit Per capita effects ● ●Hanoteaux et al. (2013) P Explicit Plant density ● ● ● ● ●Song and Feldman (2014) P Well mixed Plant density ● ● ●Mesgaran et al. (2017) P Implicit Plant density ● ● ●Qu et al. (2017) P Explicit Plant density ● ● ● ●Benadi and Gegear (2018) P Explicit Per capita effects ● ● ● ● ●Turchin (1991) H Explicit Per capita effects ●Tuomi and Augner (1993) H Well mixed Genotype

frequency● ●

Tuomi et al. (1994) H Well mixed Genotypefrequency

● ●

Leimar and Tuomi (1998) H Well mixed Genotypefrequency

● ●

Orrock et al. (2010b) H Implicit Plant density ● ● ●Orrock et al. (2010a) H Explicit Plant density ● ● ●Hambäck et al. (2014) H Implicit Per capita effects ● ●

Models address either herbivores (Consumer type = H) or pollinators (Consumer type = P), are spatially explicit, spatially implicit,or represent single well-mixed populations, and target effects on a range of plant variables. The key mechanisms included inmodels are separated between those that directly cause neighborhood effects and those that modify those effects. See the text foradditional column heading explanations.


constructingmodels of neighborhoodeffects.The general insight that density and fre-quency dependence are important for pop-ulation dynamics and evolution comes froma large body of theory that has no definedspatial structure; it assumes that all individu-als interact with all others (“well-mixed”pop-ulations) and population regulation occursat the same spatial scale for all species. Mod-els of apparent competition or facilitation,which describe how consumer populationgrowthmediates indirect interactions betweentwo resource species (Holt 1977; Kuang andChesson 2010), clearly resemble insect-me-diated neighborhood effects betweenplants.However, these are poor matches for neigh-borhood effects via most insect herbivoresand pollinators because of the assumptionsthat consumers and resources have popu-lation dynamics at the same temporal andspatial scales, that interactions are random(species are well mixed), and that plant pop-ulations are limited by only a single consumerspecies. Due to their mobility, insects (partic-ularly pollinators) will often have populationdynamics regulated at a spatial scale well be-yond a local plant neighborhood, and fewplant populations rely on a single pollinatorspecies for reproduction, or are only dam-aged by a single herbivore species.

Nonneighborhood models have contrib-utedmathematicalmachinery for represent-ing the consumer movement that allows forinsect-mediated neighborhood effects. Opti-mal foraging models introduced the ideathat consumers change behavior based onresource abundances when foraging withinpatches ofheterogeneous resources (e.g.,Holtand Kotler 1987), a framework that may beappropriate for insects such as bees thatcan have good spatial memories. For otherinsects, amoreappropriatebehavioral frame-work is area-restricted search. Kareiva (1982)and Turchin (1991) showed that plants canaffect insect movement parameters such asstep length and turning angles, thus influ-encing herbivore distributions. Area-restrictedsearch models do not specify a neighbor-hood structure, yet they describe how hostplantdensityaffectsherbivoredensitieswhenwithin-patch processes dominate distribu-tions. Hambäck andEnglund (2005) initiated

a set of models where the emphasis was onthe probability of finding resource patches inrelation to patch properties (size and geom-etry), instead of on responses after enteringa patch. These models focused on the effectof density of a single plant type, and theirmain innovation was to model insect densi-ties as resource-dependent scaling of patchfinding and leaving. This led to the insightthat responses to plant cues will depend onthe searchmode of the insect (visual or olfac-tory; see also Capman et al. 1990).

neighborhood models:

basic components

The spatial structure necessary to modellocal neighborhood effects can be includedin models of interactions between insectsand plants in three general ways (Table 2,column 2). At one extreme are models ofwell-mixed plant populations that imply a lo-cal neighborhood by explicitly modeling onlyplant population dynamics or evolution,mak-ing insect population regulation occur out-side the scale of the plant population. Thesemodels differ from apparent competition byassuming that individual pollinators or herbi-vores arrive from an external pool and thenmove among all plants. This assumption im-plies a relatively small spatial scale for theplant populations, i.e., a single type of plantneighborhood that is the same for all plants.Neighborhood effects can be included phe-nomenologically in this type of model, with-out specifying their spatial extent.

At the other extreme are spatially explicitmodels where individual plants and insectshave specific locations and only interact withnearby individuals, thus individual plantscan have unique neighborhoods (e.g., Or-rock et al. 2010a; Benadi and Gegear 2018).This approach is more akin to work on plantcompetition and facilitation that has acknowl-edged the importance of local neighbor-hoods for decades (Harper 1977), and hasfocused on spatially explicit plant neighbor-hoods (reviewed in Stoll and Weiner 2000).In between well-mixed and spatially explicitmodels are spatially implicit models that con-sider interactions at the scale of neighbor-hoods, but allow neighborhoods within a


larger population to contain different densi-ties or frequencies of species and/or modelmovement of insects among neighborhoods(e.g., Feldman et al. 2004; Tachiki et al. 2010).

The typeof spatial structure influences thescalesof interactionthatamodelcanaddress.Models lacking spatial structure (implyingthe existence of the neighborhood only byleavingout insectpopulationdynamics) con-sider the behavior of consumers within theneighborhood,butcannotincludeneighbor-hood effects on the number of consumersarriving to the neighborhood. Models withspatial structure (implicit or explicit) mayconsider how the plant neighborhood influ-ences the rates at which consumers find andremain within neighborhoods (immigrationand emigration), thus affecting the density ofinteracting consumers. Models that addressinsect immigration and emigration often usethe terminology “patch,” referring to somevisible area of higher density of a focal plantor set of plants; a patch could contain multi-ple scales of neighborhoods.

Models have so far included seven basictypes of mechanisms for insect-mediatedneighborhood effects (in italics below): fourthat generate (Table 2, columns 4–7) andthree that modify (Table 2, columns 8–10)neighborhood effects. The requirement forintraspecific pollen transfer creates positive fre-quency dependence for plant fitness (Levinand Anderson 1970) because random polli-nator movements are more likely to be be-tween individuals of the same species whena species is more common. This frequencydependence contributes to the exclusion ofrare species. Dynamic changes in resources pro-vided by a plant, such as pollen or nectar,can also generate neighborhood effects thatare not observed in models with fixed re-source availabilities (e.g., Waser 1978). Adap-tive foraging can create nonlinear densitydependence (Goulson 1994) or other typesof neighborhood effects (Leimar and Toumi1998). Somemodels assume unspecified behav-ioral responses to plant neighborhoods by simplyincluding a mathematical function relatingper capita interactions and plant density orfrequency; these relationships can have arange of functional forms (e.g., Hanoteauxet al. 2013; Hambäck et al. 2014). Pollinator

constancy alleviates the positive frequency de-pendence created by a need for intraspecificpollen transfer by increasing the proportionof consecutive visits to the same plant typeeven when a plant type is rare. Constancycan also weaken density dependence if polli-nators continue to visit a single plant typeeven when it is rare (e.g., Hanoteaux et al.2013).Preference can similarly alter the strengthof neighborhood effects by changing the “ef-fective frequency” of plant types; preferredplants are visited at a higher rate, effectivelyacting as if they were more frequent in aneighborhood.When assumed to have a con-stant value, the effect of consumer prefer-ence is a simple linear modification of thestrength of other mechanisms that gener-ate neighborhood effects, whereas constancycreates a nonlinear modification of neigh-borhood effects because it concerns pairs ofconsecutive visits to plant types (compare Fig-ures 1 and 2 in Levin and Anderson 1970).Like constancy, pollen carryover reduces thestrength of positive frequency dependencegenerated by the need for intraspecific pol-len because nonconsecutive visits can stillresult in pollination (e.g., Waser 1978; Feld-man et al. 2004).

the development of neighborhood

models for pollinators and herbivores

Pollination biologists have noted for over100 years that competition for pollen be-tween nearby plants should influence plantabundances and evolution (reviewed inMitchell et al. 2009; Charlebois and Sargent2017), but formal mathematical models ofpollinator-mediated neighborhood effectsbegan with the key work by Levin and An-derson (1970). They analyzed effects of pol-linators on plant coexistence and includednot only the odds of intraspecific pollen trans-fer, but also the idea of pollinator constancy.Levin and Anderson (1970) established apattern for subsequent models of pollinatorneighborhood effects by introducing theconnectionbetweenintraspecificpollentrans-fer and positive frequency dependence, andasking whether additional mechanisms canprevent the exclusion of rare species or affectfloral trait evolution. Levin and Anderson


(1970) also explored the effects of prefer-ence for one plant over another, a type of be-havior that occurs for both pollinators andherbivores.

Levin and Anderson’s analytical model ofpollinator effects was transferred into a spa-tially explicit simulation context by Waser(1978). Waser’s model repeated prior re-sults that positive frequency dependence dueto interspecific pollen transfer can rapidlycause exclusion of rare plant species. Waserdid not include preference or constancy,but introduced another pollinator-specificmechanism: pollen carryover beyond con-secutive visits. Waser (1978) was also the firstto add dynamic effects of pollinator visits onthe resources they collect. In this model pol-len can be depleted and stigma surfaces canbe filled, so that resource dynamics amplifythe negative effects of interspecific pollentransfer on plant fitness. Kunin and Iwasa(1996) considered the dynamics of pollina-tor visits and nectar resources, which (unlikestigma surfaces) can be replenished on a fasttime scale (see alsoGoulson1994). By includ-ing adaptive foraging responses to nectarquantity, Kunin and Iwasa (1996) found den-sity and frequency dependence in pollinatorpreference for different plant types, whichcaused complex forms of density and fre-quency dependence in plant fitness. Theyalso found, not surprisingly, that the risk ofinterspecific pollen transfer, and thus thestrength of frequency dependence in plantfitness, is reducedwhenpollinators specializeon a rarer plant.Models drawing on the samefour basic types of neighborhood effects havealso considered how neighborhood effectsinfluence the evolution of floral traits; thesemodels suggest that pollinator neighborhoodeffects should influence the evolution of flo-ral specialization through both floral traitsand flowering phenology (e.g., Sargent andOtto2006;Rodríguez-Gironés andSantamaría2007). Although most pollination models fo-cus on interactions between two rewardingplant species, Qu et al. (2017) considered ef-fects of rewarding species on the pollinationof a nonrewarding (deceptive) species.

Spatially implicit andexplicitmodels of pol-linator neighborhood effects became morecommon in the 2000s. Feldman et al. (2004)

used a spatially implicit patch model to con-sider what happens when pollinator abun-dance responds to total flower density in apatch. In addition to the established positivefrequency dependence of intraspecific pollenreceipt, Feldman et al. found that sigmoidalresponses of pollinator abundance to totalflowers increased pollination of rare species,makingplant coexistencemore likely becauseother flowers can facilitate pollination of raretypes. Tachiki et al. (2010) similarly foundthat plant facilitation was possible when pol-linators respond to total flower density, orwhen pollinator density is an acceleratingfunction of total patch attractiveness. Thisidea that pollinator responses to neighbor-hood flower density could result in facilita-tion between plants was further exploredby Mesgaran et al. (2017), again in a modelwith implicit spatial structure. The main in-novation in Mesgaran et al. (2017) was toseparate the effects of plant competition forabiotic resources from competition for polli-nators, by including a plant’s attractivenessto pollinators separately from its density. Thisis an important step toward integrating com-petition and neighborhood effects to deter-mine net positive or negative effect on plantperformance. Hanoteaux et al. (2013) useda spatially explicit individual-based simula-tion model to point out that the distributionof neighborhood types can also affect re-gional population dynamics. In this model,intraspecific spatial aggregation of a less at-tractive plant (i.e., when present it is overrep-resented) can facilitate its own pollination,particularly if pollinators make short movesbetween plants and have small fields of per-ception and thus fail tonoticemore attractiveplants outside an aggregation of less attrac-tive plants.

Two final factors considered in models ofpollinator neighborhood effects are interac-tions among multiple pollinator types andpollinator density. For example, foraging be-havior by generalist pollinators may be al-tered by the presence of specialists becausethis changes the expected rewards from dif-ferent flower types (Kunin and Iwasa 1996;Valdovinos et al. 2013). A generalist pollina-tormight effectively have constancy for a sin-gle flower type by avoiding flowers heavily


visited by specialist pollinators (Song andFeldman 2014). This type of competition-in-duced niche shift, which can affect pollina-tion success, has been observed in bumblebees (Inouye 1978; Brosi and Briggs 2013).Several models also show that regional polli-nator density should modify neighborhoodeffects on pollination or plant fitness (e.g.,Kunin and Iwasa 1996; Feldman et al. 2004;Tachiki et al. 2010).

The development of theory for herbivoreneighborhood effects has taken a differentpath. Early influential verbal theory for plantneighborhood effects came fromRoot’s workon plant patches, where he coined the terms“associational resistance” (Tahvanainen andRoot 1972) and the “resource concentrationhypothesis” (Root 1973). Although there is along history of empirical work on herbivoreneighborhood effects, motivated by observa-tions of lower herbivore density and damagein mixed plant communities or larger plantpatches, and by interest in using plant mix-tures to reduce damage by crop pests (e.g.,Andow 1991; Smithson and Lenne 1996), thedevelopment of formal mathematical struc-tures lagged. Because of the positive fre-quency dependence created by intraspecificpollen receipt, many researchers modelingpollinator neighborhood effects have focusedon the conundrum presented by the long-termpersistence of rare plant species. Ratherthan long-term persistence, most studies ofherbivore neighborhood effects have em-phasized the short-term effects of plant den-sity on damage or herbivore loads. This isdespite the fact that insect herbivores can af-fect plant population dynamics (e.g., Kimet al. 2013; Schultz et al. 2017).

Becauseworkonherbivore-mediatedneigh-borhood effects has emphasized the role ofshort-term behavioral responses, a logicalstarting point for models was area-restrictedsearch (summarized above in the sectiontitled Foundational Ideas From Nonneigh-borhoodModels). Hambäck et al. (2014) ex-tended this approach to directly involve theneighborhood effects that arise from mixedplant communities containing different totalplant densities and frequencies, where patchfinding, host switching within patches, andpatch leaving depend on the scaling of plant

cues and on consumer preferences. Thismodel and Hambäck and Englund (2005)both indicate that the strength and even thesign of the effects of plant density and fre-quency in a neighborhood depend on howinsects perceive plants and plant patches;to our knowledge these are the only modelsto consider how insect perception influencesneighborhood effects. In addition to mod-els describing how neighborhood effects onherbivores per plant arise from insect searchbehavior, models have addressed the evo-lutionary and ecological consequences ofherbivore neighborhood effects for plant pop-ulations. Models by Tuomi and colleagues(Tuomi and Augner 1993; Tuomi et al. 1994)showed that frequency dependence in her-bivore attack rates on plants with differentlevels of resistance influences the evolutionof plant resistance. Among the few studiesof herbivore neighborhood effects that con-sider population dynamics, two by Orrocket al. (2010a,b) used spatially implicit mod-els to show that the spatial scale of consumerbehavior relative to the spatial areaoverwhichplants compete can affect the outcome ofplant competition.

Future Directions

Given the broad similarities between pol-linator- and herbivore-mediated neighbor-hood effects, it is striking how little contactthere has been between these fields, eitherempirically or theoretically. Models of polli-nator and herbivore neighborhood effectsessentially never reference each other; onlyonemodel (Feldman et al. 2004) cites theorydeveloped for the other type of consumer.Similarly, although many empirical studiesdocument neighborhood effects on pollina-tors or herbivores, almost no studies havemeasured these two effects together (but seeAndersson et al. 2016), even though herbi-vores and pollinators can jointly affect plantfitness (e.g., Strauss 1997; McCall and Irwin2006). Theory for both types of neighbor-hood effects would be improved by drawingon the differing strengths of both fields. Arange of theoretical approaches have beenused, including game theory, adaptive dyna-mics models, coupled differential equations,


and spatially explicit simulations. In gen-eral, models of neighbor effects suggest thatlocal density and frequency dependence inconsumer–resource interactions should becommon and influence population and evo-lutionary dynamics, but models so far havenot addressed nonlinear and spatially explicitfrequency dependence in neighborhood ef-fects. Ultimately, integrating pollinator andherbivore effects (as well as those of other or-ganisms that affect plant fitness) into moregeneral models of neighborhood effects willbenecessary for amore completeunderstand-ing of the function of spatial structure in plantcommunities.

extending models for herbivores

and pollinators

Connecting neighborhood effects to plantfitness is a logical starting point for the ex-tension of herbivore neighborhood models.Although it is often suggested that herbivoreneighborhood effects should influence plantpopulations (e.g., Atsatt and O’Dowd 1976;Thomas 1986; Pfister and Hay 1988; Russelland Louda 2005), most herbivore modelsstop at per capita interactions (Figure 1A;Table 2). The focus of pollination neighbor-hood models on population outcomes is areminder thatherbivoreneighborhoodmod-els could be extended to include effects onplant fitness, plant population size, and plantgenetic or community structure.

Herbivore neighborhoodmodels can alsobe improved by including twomechanisms forneighborhood effects that pollinator modelshave found tobe important: dynamic foragingbehaviors/learning and effects of consumerdensity. Pollinator neighborhood modelsshow that adaptive foraging, constancy, andvariable preference hierarchies can generateor modify neighborhood effects in a way thatshould also be relevant for herbivores. In-deed, generalist herbivores, some of whichhave strongeffects in natural and agriculturalcommunities, can show flexible foraging be-haviors similar to those of pollinators. For ex-ample, grasshoppers can shift plant choicesto obtain a nutritionally balanced diet (Ber-nays et al. 1994), implying plant neighbor-hoods may influence their preferences and

thus patterns of damage to plants. Pollinatorneighborhood models have also shown thatpollinator density can have both evolutionaryand ecological consequences, for example,the evolution of mixed foraging strategies inpollinators and specialization in plant visita-tion are more likely with higher pollinatordensity (Kunin and Iwasa 1996; Muchhalaet al. 2010), and pollinator density can altereffects of floral resource dynamics (e.g., Wa-ser 1978; Hanoteaux et al. 2013). Herbivoreneighborhood models have not yet consid-ered the influence of insect density, despitethe fact that herbivore densities can varygreatly among seasons or years in the fieldand have been shown empirically to affectneighborhood effects (Merwin et al. 2017).

New pollinator neighborhoodmodels cansimilarly be informedby theherbivoreneigh-borhood models that focus on how move-ments in and out of neighborhoods (orpatches) determine herbivore densities. Polli-nator models mostly focus on the movementof pollinators or pollen within a neighbor-hood, althoughpollination rates are functionsof both the number of pollinators arrivingin an area and how they move after arrival.Mathematical expressions for herbivore im-migration to a patch and distribution amongplants within a patch (Hambäck et al. 2014)could be expanded to include pollinator be-havior and pollen transfer.Moreover, empir-ical work and verbal theory for herbivoresoften focuses on negative effects of neigh-boring plants on the ability of an herbivoreto locate its host (i.e., “masking” or “repel-lency”; e.g., Hay 1986; Hambäck et al. 2000),but similar negative effects of plant neigh-bors have not yet been examined for pollina-tors, although odors from multiple plantscanmake flower finding difficult for pollina-tors (e.g., Riffell et al. 2014). Finally, pollina-tionmodels havenot yet consideredhow traitssuch as body size, mobility, tongue length, orheight of foraging flights may alter neighbor-hood effects, although these traits are knownto affect flower visitation patterns.

Surprisingly few studies, whether for polli-nators or herbivores, have considered howbroad differences in consumer traits or nat-ural history predict the functional forms (i.e.,shape of frequency or density-dependence)


and scales of neighborhood effects (but seeHambäck et al. 2014). Most neighborhoodmodels assume a single suite of consumertraits and explore the neighborhood effectsentailed by that one set of assumptions. Sim-ilarly, few studies determine the consequencesof alternative model assumptions about theform of neighborhood effects for populationoutcomes. Feldman et al. (2004) comparedtwo pollinator responses to plant density (sig-moid versus saturating); only sigmoid re-sponses led to facilitation of one plant speciesby the other. Tachiki et al. (2010) comparedlinear, sigmoid, and saturating functions forthe number of pollinator visits as a functionof plant density, likewisefinding that pollina-tor visits must be an accelerating function oftotal plant density (over at least some rangeof densities) in order for plants to facilitateeach other. Increasing our ability to predictthe influence of both pollinator and herbi-vore neighborhood effects will requiremodelsthat compare alternative assumptions aboutspecies’ traits and the type of neighborhoodeffects, as opposed to varying parameter val-ues for a single functional form.

Finally, we suggest that researchers con-sider how pollinators and herbivores respondto continuous distributions of phenotypic di-versity rather discrete types. Pollinator andherbivore neighborhood models have gen-erally treated neighborhoods as containingdistinct species or genotypes, and field stud-ies of diversity effects often focus onnumbersof species or genotypes, although pollinatorsand herbivores must in fact respond to thedistribution of plant phenotypes (Hugheset al. 2008). Outside of agricultural systems,plant communities are typically diverse; bothpollinators andherbivores can respond to thediversity of a neighborhood (Bernays 1999;Hegland and Boeke 2006), at the genotypelevel as well as among species (reviewed inHughes et al. 2008). One herbivore model(Leimar and Tuomi 1998) showed that usinga continuous distribution of resistance val-ues could lead to different predictions aboutherbivore neighborhood effects than similarmodels that treated herbivore resistance as abinary trait (Tuomi andAugner 1993).Workon pathogens has also shown that consider-ing a distribution of trait variation can lead

to different dynamics than treating resistanceand virulence as binary traits (Dwyer et al.1997), and has addressed effects of multi-host communities on interaction patterns(Truitt et al. 2019). These pathogen modelsmay be good starting points for models thatexplore effects of plant diversity on neighbor-hood effects.

integrating across scales and types

of neighborhood effects

A first step toward embracing the full di-versity of neighborhood effects would be tomodel joint neighborhood effects mediatedby insect pollinators and herbivores. We seethree potentially fruitful approaches to build-ing such integrative models. For any of theseapproaches the logical response variablewouldbe plant fitness, which integrates per capitaeffects of different consumers, although onewould have to make assumptions about therelative effects of herbivore damage and pol-lination on fitness. It may seem that pollina-tion would always have larger effects, but forsome plants vegetative growth and spreadwill have large effects on fitness, and for oth-ers there may not be pollen limitation. Afirst approach would be to start with an “her-bivore-style”model, which focuses on how in-sects arrive at local neighborhoods (patches)with differing composition. One could in-clude both visual (presumably pollinator) andolfactory (presumably herbivores) searchers,with visual searchers having positive fitnesseffects and olfactory searchers having nega-tiveeffects.This approachwouldallowaskingif pollinator and herbivore effects on fitnessmight vary simply based on their perceptualdifferences, and what their net effects on fit-ness would be. A second approach would beto start with amore “pollination-style”modelof insects moving within a patch, but allowsome insects to be pollinators (with positivefrequency-dependent fitness effects) andsome to be herbivores (with negative fitnesseffects). This would allow asking about theinteraction of frequency-dependent and in-dependentconsumers.Finally,onecouldtakeamore general approach and have insects re-sponding to plants at nested spatial scales,with some responding at larger scales and


others at smaller scales. Both consumerscould be allowed density and frequency de-pendence, and one could ask what happenswhen negative neighborhood effects happenat a smaller spatial scale than positive ones (asmay occur for pollinators; Charlebois andSargent 2017).

Most neighborhoodmodels have not dealtdirectly with the issue of spatial scale (butsee Orrock et al. 2010a,b), a gap also foundin empirical work (reviewed in Braun andLortie 2019). Scale is critical for understand-ing the role of neighborhood effects becauseplant-insect systems vary widely in patternsand scales of plant aggregation, and neigh-borhood effects through plant competition,herbivory, and pollination likely occur at arange of spatial scales simultaneously (plantcompetition with immediate neighbors andinsect-mediated effects at a range of scales).Pollination models that have allowed an ag-gregated plant spatial structure (Levin andAnderson 1970; Waser 1978; Hanoteauxet al. 2013) are a first step toward grapplingwith spatial scale, but positive effects of intra-specific aggregation on pollination successmay be offset by negative effects of aggrega-tion on intraspecific competition or by her-bivore responses to plant aggregations. Theseanalyses are also restricted to considering pro-cesses either in or outside of aggregations, yetreal variation in plant neighborhood composi-tion is likely to be continuous. Amajor step forfuture work would be to develop models in-cluding neighborhood effects at multiple spa-tial scales, as dictated by the mobilities andbehaviors of different groups of insects. Onepromising approach to incorporating multi-ple scales is to use agent-basedmodels. Othercomputationally intensivemethods are beingdevelopedby researchersworking onproteininteractions within and among cells; thesemethodsmay also be adapted to represent in-teracting populations of species within andamong patches (e.g., Yu and Bagheri 2016).

Future work should also take into accountthe variety of temporal scales of neighbor-hood effects, as the plant resources for polli-nators and herbivores vary over a range oftime scales. The availability of host plant spe-cies for an herbivore may be relatively con-stant over a season compared to the floral

neighborhood for pollinators, which couldchange rapidly as different plants come inand out of bloom. Although both leaf tissueand floral resources (nectar and pollen) canbe rapidly depleted, floral resources typicallyrenew faster than leaves can regrow. Plant-induced defenses, which are known to influ-ence herbivore distributions across plants(Underwood et al. 2005), may change on theorder of days (Underwood 1998) or acrossyears (Haukioja 1991). Thus, neighborhoodeffects can occur at multiple temporal scales,just as they can occur at multiple spatial scales.Because of the spatialmemory of bees, neigh-borhoods at one time can even influenceplant-pollinator interactions days later (e.g.,Ogilvie andThompson 2016), suggesting thatconsidering only immediate neighbors at asingle time will underestimate total neighbor-hood effects. Even though empirical workshould take temporal variation into account,models representing temperate systems witha single reproductive season per year mightignore within-season changes in effectiveneighborhood composition by focusing onneighborhood effects on annualfitness com-ponents (growth, survival, reproduction). Forsystems with more continuous reproduction,modelers will likely need to use numerical ap-proaches that allow interactions to respondto temporal variation at multiple time scales(i.e., Holt and Barfield 2003; Yu and Bagheri2016).

Finally, it is important to acknowledge thatinsect pollinators and herbivores are not theonly guilds that interact with plant neigh-borhoods and affect plantfitness. Describingnet effects of spatial neighborhoods will re-quire accounting for multiple taxa that mayreact to neighborhoods differently andoccupydifferent trophic levels. Seed predators andflorivores are particularly interesting casesbecause they affect plant sexual reproduc-tion and are likely to respond to both floraland vegetative neighborhoods. Pathogens,some of which are vectored by insect polli-nators and herbivores, can also clearly affectplant populations andhave transmission ratesthat depend on local plant density and diver-sity (e.g., Biere andHonders 1998). Althoughthere are many spatial models of host-path-ogen dynamics, we are not aware of any that


have been used to explore effects of localneighborhood structure. Soil microbial com-munities can also potentially mediate neigh-borhood effects, although the spatial scaleof these effects is perhaps more similar tothe spatial scale of plant competitive interac-tions. Local density- and frequency-dependenteffects of plant-soil feedbacks have beenmod-eled before (e.g., Molofsky 1994; Molofskyet al. 2001); the cellular automaton frame-work applied in these models may be usefulfor future work on other types of neighbor-hood effects. Mammalian herbivores areknown to be affected by plant neighbor-hoods (e.g., Champagne et al. 2018) and, incontrast to models for insect herbivores, atleast one model of mammalian herbivoreneighborhood effects does take into accounteffects of herbivore density and flexible for-aging behavior (Ishii and Crawley 2011).Vertebrate herbivores may have behavioralflexibility in common with insect pollinators,but models for more behaviorally flexiblevertebrate predators will need to take into ac-count not just additional flexibility but alsothe very different spatial scale at which ver-tebrates forage relative to insect herbivores.For example, due to an assumption that mul-tiple plant types are eaten in a single “bite,”the Ishii and Crawley (2011) model cannoteasily be adapted to insect herbivores. Finally,predators and parasitoids can use cues fromplant neighborhoods when searching for in-sect prey (Vet and Dicke 1992) andmay alterneighborhood effects generated by insectpollinators, herbivores, or seed predators.

Conclusions

Taken together, models of pollinator andherbivore neighborhood effects have con-sideredmany paths throughwhich local plantdensity and frequency can influence per cap-ita interactions of insects with plants. Thesemodels demonstrate that a variety of mech-anisms potentially generate density- and fre-

quency-dependence in plant fitness at theneighborhood scale, which should scale upto influence population processes such astrait evolution and population dynamics. Al-though studies of herbivore and pollinatorneighborhood effects can each benefit frombeing aware of work in the other field, themost important goal for future work wouldbe to integrate multiple types of neighbor-hood effects. This is consistent with recentcalls for better integration of work on polli-nation and herbivory in other contexts suchas network theory (Sauve et al. 2016) and theevolution of plant defenses (Lucas-Barbosa2016). Future models should consider thenet neighborhood effects from pollinatorsand herbivores together, since both typesof insects affect plant fitness but in differentways (Andersson et al. 2016), and because in-sects affect each other through interactionswith plants (e.g., Brody 1992; Strauss 1997;Herrera 2000; Sletvold et al. 2015). Empiri-cal studies have foundboth additive (Sletvoldet al. 2015) and nonadditive effects (Herrera2000) of pollination and herbivory, but welack both empirical and theoretical under-standing of whether neighborhood effectsmediated by these two types of consumersmight be additive or not. With our growingknowledgeofplant-mediated interactionsbe-tweenpollination andherbivory, and expand-ing methods for analysis for spatially implicitand explicit mathematical models, we havethe resources to build amore synthetic under-standing of when and how neighborhood ef-fects are important factors in plant ecologyand evolution.

acknowledgments

The development of these ideas was supported by aWenner-Gren Stiftelserna Gästforskarstipendier to NoraUnderwood and in part by NSF DEB-1354104 to Under-wood and Brian D. Inouye. Underwood and Inouyethank Stockholm University and the faculty of DEEPfor hosting them during work on this paper.

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