The Effects of Structured Variation in Nectar Standing Crop on Currency Choice and Optimal Foraging by Bumble Bees

University of Calgary PRISM: University of Calgary's Digital Repository

Graduate Studies The Vault: Electronic Theses and Dissertations

2014-01-08 The effects of structured variation in nectar standing crop on currency choice and optimal foraging by bumble bees

Simspon, Paul

Simspon, P. (2014). The effects of structured variation in nectar standing crop on currency choice and optimal foraging by bumble bees (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/28119 http://hdl.handle.net/11023/1247 master thesis

University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY

The effects of structured variation in nectar standing crop on currency choice and optimal

foraging by bumble bees

Paul A Simpson

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

BIOLOGICAL SCIENCES

CALGARY, ALBERTA

JANUARY, 2014

Foragers commonly exploit patchy habitats in which resource abundance can vary within and among patches. Studies measuring resource variation tend to consider only single sources of variation, so the extent of structured resource variation and how it impacts foraging animals are unclear. A survey of nectar abundance in five plant species revealed the spectrum from only within- to solely among-plant variation. Captive bumble bees

(Bombus impatiens) confronted with an increasing component of among-inflorescence nectar variation departed inflorescences in manners that diverged increasingly from expectations of the Marginal Value Theorem (MVT). Bees apparently assess inflorescence quality on a per-patch basis, changing their exploitation behavior in response to poor or rewarding inflorescences as expected from a speed-accuracy trade- off, rather than maximizing their overall average return rate. This quantitative test of the

MVT demonstrates the need to incorporate responses to variation within patches in models of forager behavior.

ii Acknowledgements

The experience of writing this thesis has been a learning experience unlike any I have ever had; fortunately there were many in my life who were able to advise me and educate me through their own experiences along the way.

First and foremost, I extend my utmost appreciation and thanks to Lawrence

Harder for his Orwellian economy with words; inexhaustible patience; unbounded openness to alternatives in experimentation, theory and methodology; and sagely insight into all things statistical. These qualities invoked a change in me from a mathematician with biological inclinations and Dr. Seussian prose, to an ecologist with an appreciation for mathematics and Hemingway’s ability to tell a story. Under your guidance, Lawrence,

I have learned to design studies and write in a manner that is of interest to myself, and hopefully others too. I would like to acknowledge that NSERC provided funding for this thesis through Dr. Lawrence Harder’s NSERC Discovery and Accelerator Grants.

Secondly, to those who facilitated my research, I extend my heartfelt appreciation.

Specifically I thank my advisory committee, Ralph Cartar and Robert Barclay, for their thoughtful comments on research proposals, research grants and graduate program applications; the sharing of data sets and lab space; and for serving as sound boards for all ideas noble and ignoble.

Thanks to Lisa O’Donnell my wonderful girlfriend, lab mate, con-conspirator and first set of critical eyes. Romain Richard for encouraging me to always have another explanation. To Luke J Antosz for tirelessly watching and rewatching bumble bee videos.

To field assistants: Portia Lloyd, Hazel Cameron-Inglis, and Takashi Ida for helping me to sample nectar in Kananaskis.

iii Additionally, thanks to Ralph Cartar for providing me with nectar data for

Penstemon confertus and Plectritis congesta, and also to Hiroshi Ishii for providing me with nectar data for Delphinium glaucum and D. bicolor.

Last, but not least of all, to my wonderful family. To my parents who have been incredibly supportive, except for the times when my research objective needed to be held up to the cold, cruel light of the real world. And to my brother Josh, for his help with processing nectar samples in the lab and watching the odd bee video.

iv Table of Contents

Abstract ...... ii! Acknowledgements ...... iii! Table of Contents ...... v! List of Tables ...... vii! List of Figures and Illustrations ...... viii! Epigraph ...... x!

CHAPTER ONE: STRUCTURED VARIATION AND OPTIMAL FORAGING ...... 1! 1.1 General Overview ...... 1! 1.2 Study system ...... 5! 1.3 Thesis Objectives ...... 8!

CHAPTER TWO: THE STRUCTURE OF VARIANCE IN NECTAR STANDING CROP IN NATURAL POPULATIONS ...... 10! 2.1 Introduction ...... 10! 2.2 Materials and Methods ...... 12! 2.2.1 Nectar Surveys ...... 12! 2.2.1.1 Wick-sampling procedure ...... 14! 2.2.1.2 Capillary-and-refractometer procedure ...... 14! 2.2.1.3 Corolla volume estimation procedure ...... 14! 2.2.2 Statistical Analysis ...... 15! 2.3 Results ...... 16! 2.3.1 Delphinium glaucum ...... 16! 2.3.1.1 2005 ...... 16! 2.3.1.2 2012 ...... 16! 2.3.2 Delphinium bicolor ...... 17! 2.3.3 Chamerion angustifolium ...... 17! 2.3.4 Plectritis congesta ...... 18! 2.3.4.1 1986 ...... 18! 2.3.4.2 1988 ...... 18! 2.3.5 Penstemon confertus ...... 21! 2.4 Discussion ...... 23!

CHAPTER THREE: THE EFFECT OF STRUCTURED VARIATION IN NECTAR STANDING CROP ON FORAGING BY BUMBLE BEES ...... 28! 3.1 Introduction ...... 28! 3.2 Materials and Methods ...... 34! 3.2.1 Experimental Design ...... 34! 3.2.2 Forager Training ...... 37! 3.2.3 Experimental Trials ...... 38! 3.2.4 Statistical Analysis ...... 39! 3.2.4.1 Behavioral Responses ...... 39! 3.2.4.2 Foraging Currency Maximization ...... 40! 3.3 Results ...... 42! 3.3.1 Behavioral Responses ...... 42!

v 3.3.1.1 Probing Time ...... 43! 3.3.1.2 Flight Time ...... 47! 3.3.1.3 Floral Inspections ...... 50! 3.3.1.4 Visits ...... 54! 3.3.2 Foraging Currencies ...... 56! 3.3.2.1 Rate of Net Energy Intake ...... 56! 3.3.2.2 Foraging Efficiency ...... 62! 3.4 Discussion ...... 65! 3.4.1 Behavioral Responses ...... 65! 3.4.2 Currency Maximization ...... 67! 3.4.3 Speed-accuracy Tradeoffs ...... 70! 3.5 Appendix – Determination of treatment conditions ...... 74!

CHAPTER FOUR: CONSEQUENCES AND EVOLUTIONARY SIGNIFICANCE OF STRUCTURED RESOURCE VARIATION ...... 75! 4.1 Structured Variation and Foraging ...... 75! 4.2 Towards an Optimal Stalemate ...... 77!

REFERENCES ...... 81!

vi List of Tables

Table 2.1 Sampling and nectar characteristics of 5 plant species ...... 19!

Table 3.1 Inflorescence and flower characteristic of the five treatments used to assess the effects of within- and among- inflorescence variation ( and , respectively) in nectar availability on foraging and energetics for Bombus impatiens workers...... 36!

Table 3.2 Results of generalized linear mixed models assessing the effects of variance conditions (Treat), inflorescence type (Itype), flower type (Ftype) and covariates on temporal aspects of bee behavior on artificial inflorescences...... 45!

Table 3.3 Results of generalized linear mixed models assessing the effects of variance conditions (Treat), inflorescence type (Itype), and flower type (Ftype) on the numbers of floral inspections and flower visits per inflorescence visit by 15 Bombus impatiens...... 52!

Table 3.4 Results of the generalized linear mixed models assessing the effects of variance type (Treat), inflorescence type (Itype), and the type of the last flower visited (Ftype) on the realized and residual rate of net energy intake (RNEI) and foraging efficiency (FE) per inflorescence visit for 15 B. impatiens workers...... 58!

vii List of Figures and Illustrations

Figure 2.1 Decomposition of total variance of NSC measured as sugar content (mg) for P. congesta, P. confertus, C. angustifolium, and D. glaucum (sampled in 2012) and as nectar volume (µL) for D. bicolor and D. glaucum (2005) into within- and among-inflorescence variance components (%) (± 95% CI)...... 20!

Figure 2.2 The distributions of nectar standing crop within a D. glaucum population sampled during 2005 (panels A, C and E) and 2012 (panels B, D, and F)...... 21!

Figure 2.3 The distributions of nectar standing crop within populations of C. angustifolium (panels A, C and E) and Penstemon confertus (panels B, D, and F)...... 22!

Figure 3.2 An artificial inflorescence (A) and a 2 x 3 array of artificial inflorescences arranged within the 100 cm x 120 cm x 90 cm (height) flight cage (B)...... 35!

Figure 3.3 Variation in the least-squares mean (± 95% confidence interval) proportion of visits to low-quality flowers on artificial inflorescences by 15 B. impatiens workers on low- and high-quality inflorescences in environments that differed in the relative among-inflorescence variation in nectar volume per flower...... 43!

Figure 3.4 Variation in the least-squares mean (± 95% confidence interval) duration of flower visits by 15 B. impatiens workers on A) low- and high-quality inflorescences and B) low- and high-quality flowers in environments that differed in the relative among-inflorescence variance in nectar volume per flower...... 46!

Figure 3.5 Relations of least-squares mean (± SE) duration of inter-floral flight by 15 B. impatiens workers to within- and among-inflorescence variation in nectar volume per flower and inflorescence quality...... 49!

Figure 3.6 Relation of the least-squares mean (± SE) duration of inter-floral flights by 15 B. impatiens workers to the number of flowers inspected during a flight...... 50!

Figure 3.7 Relations of least-squares mean (± SE) A) number of floral inspections at departure from inflorescences to within- and among-inflorescence variation in nectar volume per flower and inflorescence quality, and B) incidence of inspection during inflorescence visits to nectar variance and flower quality...... 53!

Figure 3.8 Relations of the least-squares mean (± SE) number of flowers visited on artificial inflorescences by 15 B. impatiens workers to within- and among- inflorescence variation in nectar volume and inflorescence quality...... 55!

viii Figure 3.9 Influence of the number of floral inspections during an inflorescence visit on the least-squares mean (± SE) number of flower visits by 15 B. impatiens workers...... 56!

Figure 3.10 Relations of the least-squares mean (± SE) A) realized and B) residual rate of net energy intake (RNEI) per inflorescence visit to within- and among- inflorescence variation in nectar volume and inflorescence quality...... 60!

Figure 3.11 Effects of inflorescence and the type of the last flower visited on an inflorescence on least-squares mean (± 95% CI) residual RNEI...... 61!

Figure 3.12 Relations of least-squares mean (± SE) foraging efficiency (FE) of 15 B. impatiens workers to within- and among-inflorescence variation in nectar volume and inflorescence quality...... 63!

Figure 3.13 Relations of least-squares mean (± 95% confidence interval) foraging efficiency (FE) of 15 B. impatiens workers to the structure of variation in nectar volume on A) high- and B) low-quality inflorescences and the quality of flower from which bees departed inflorescences...... 64!

Epigraph

You cannot create experience, you must undergo it.

Albert Camus

There must be some way out of here

Said the joker to the thief

There’s too much confusion,

I can’t get no relief

But you and I we’ve been through that

And this is not our fate

So let us not talk falsely now

The hour is getting late

‘All Along the Watchtower’ Bob Dylan (1967)

Chapter One: Structured variation and optimal foraging

1.1 General Overview

Foraging decisions can influence an individual’s fitness (Schoener 1971, Pyke et al.

1977, Burns and Thomson 2005, Cole et al. 2012). Specifically, behaviors that enable individuals to maximize their energy gains should be favored by natural selection over less rewarding behaviors (McNamara 1982, Stephens and Krebs 1986, Ydenberg et al.

1994). However, the ‘best’ foraging strategy depends on the distribution of resources within and among habitats (Tversky and Simonson 1993, Houston 1997, Bateson et al.

2003, Morgan et al. 2012), as well as an individual’s ability to assess resource quality

(Lima et al. 1985, Harder and Real 1987, Houston 1997, Nonacs 2001). For example, many animals must allocate time between foraging and other behaviors, such as finding mates, defending territory and raising their young. Consequently, individuals that can identify and exploit rich aggregations of food resources in their habitat will be able to devote more time and energy to other activities that directly influence their fitness

(Schmid-Hempel et al. 1985, Stephens and Krebs 1986, Bautista et al. 1998).

Resources can be distributed heterogeneously at different spatial scales within habitats (Murphy et al. 1988, Zimmerman 1988, Kotliar and Wiens 1990, Hodges 1993,

Boose 1997). When variation in resources is structured hierarchically, an individual’s foraging success depends on both patch-level variation, and the individual’s ability to respond to it. Foraging animals obtain information from ingested food and develop expectations about the distribution and quality of the remaining food items within the current patch (Stephens and Krebs 1986, Brown et al. 1997, Fauchald 1999). This process is counteracted by forager memory constraints, which interact with patch-level resource

variation to influence an animal’s assessment of the expected quality of unvisited patches and to realize maximal foraging success (Stephens and Krebs 1986, Brown et al. 1997,

Fauchald 1999, Henry and Stoner 2011).

Patchily distributed resources influence forager behavior in two ways. First, given among-patch differences in resource quality, foragers benefit from adjusting their time in patches according to patch quality to maximize energetic returns from foraging efforts

(MacArthur 1972, Charnov 1976, Croy and Hughes 1991, Ohashi and Yahara 2002,

Cartar 2009). Second, within-patch variability creates uncertainty about overall patch quality and when a patch is no longer profitable (Emlen 1966, Krebs et al. 1974, Valone

1991, Templeton and Giraldeau 1996, Dall et al. 2005). Uncertainty in patch quality can lead to premature or delayed departure from a patch, both of which will decrease a forager’s resource intake rate due to lost foraging opportunities or excessive energetic expenditure, respectively. Resource quality and quantity can vary within and among patches due to differing rates of resource renewal and differing patterns of patch exploitation by previous and present foragers (Cruden et al. 1983, Hodges 1993, Wu and

Loucks 1995, Alonso et al. 1995, Fauchald 1999, Ishii and Harder 2006).

A forager must concurrently assess patch quality and decide whether to quit a patch based on its assessment of the current patch and the expected quality of other accessible patches (Charnov and Krebs 1974, Charnov 1976). Patch assessment and departure decisions are greatly complicated when resource variation is structured hierarchically.

The implications of resource variation for foragers are illustrated by a simple example.

Variation among, but not within, patches allows inexperienced foragers to assess patch quality immediately and determine whether the patch warrants further exploitation

(Biernaskie et al. 2009). In contrast, when resources vary only within patches, and not among patches, longer patch residence becomes necessary for a forager to assess patch quality accurately (Hodges 1985a, Valone and Brown 1989, Valone 1991). Therefore, a forager’s ability to maximize its energetic gains within a habitat should depend on the relative magnitude of within- and among-patch variation.

Animals foraging in hierarchically structured habitats must assess patch quality and make departure decisions based on the benefits and costs of exploiting a particular patch (Pyke 1978c, McNamara 1982, Hodges 1985b, Stephens and Krebs 1986 and sources therein, McNamara et al. 2006). In particular, foraging theory typically represents the economic utility of accumulated energetic benefits and costs of foraging in a particular patch to the foraging animal as a foraging currency (Pyke 1978c, Schmid-

Hempel et al. 1985, Harder and Real 1987, Charlton and Houston 2010). Further, foraging currencies are commonly used as proxies for evolutionary fitness (Stephens and

Krebs 1986), such that natural selection should favor individuals that maximize an appropriate currency (McNamara 1982, Cresswell 1990, Ydenberg et al. 1994).

Foraging currencies allow predictions of expected forager behavior with which observations can be compared to assess underlying mechanisms. Two currencies have primarily been considered: the rate of net energy intake (RNEI, the ratio of net energy gains to the time spent acquiring the gains: Emlen 1966, Charnov 1976, Pyke 1978c,

Charlton and Houston 2010) and foraging efficiency (FE, the ratio of net energy gains to energy costs incurred while foraging: Schmid-Hempel et al. 1985, Houston et al. 1988,

Ydenberg et al. 1994, Denny et al. 2001, Charlton and Houston 2010). Whereas RNEI is often regarded as the currency that underlies animal decisions about patch use and

departure (Charnov 1976, Pyke 1978c, Hodges 1985b), FE has been demonstrated, theoretically and empirically, to be an equally useful predictor of forager behavior

(Schmid-Hempel et al. 1985, Charlton and Houston 2010). Animals that quickly, but inaccurately, exploit resources within a patch should forage as rate maximizers, whereas those exploiting patches systematically, should forage as efficiency maximizers (Chittka et al. 2009, Ohashi and Thomson 2012). Whether rate or efficiency maximizing foragers are best-suited to exploit habitats with structured variation is unclear. Consequently, assessment of patch-departure rules for foragers in habitats with structured variation in food resources should consider both currencies.

When resources are distributed heterogeneously, optimal patch departure is often considered in the context of the marginal value theorem (MVT; Charnov 1976). Given a habitat comprising randomly distributed patch types in which many distinct patches are visited during a single foraging bout, the MVT states that a forager maximizes its rate of net energy intake during a foraging bout involving multiple patch visits by leaving each patch when its marginal (instantaneous) capture rate in the patch drops to the average rate among patches (Charnov 1976, Pyke 1978c, Waage 1979, Giraldeau and Kramer 1982,

Cibula and Zimmerman 1984, Pleasants 1989, Wajnberg et al. 2000). Thus, the MVT assumes that animals maximize their long-term rate of net energy intake during foraging bouts, despite foragers not necessarily possessing commensurate cognitive ability. This limits the use of the MVT in theory and practice, as the extent of the forager’s memory of resources in its habitat must be understood before utilizing the theorem.

Although the MVT has much empirical (Pyke 1978a, Hodges 1981, Giraldeau and

Kramer 1982, Cresswell 1990) and theoretical support (Oaten 1977, Green 1980,

Fauchald 1999, Dreisig 2011) when food resources are distributed deterministically or stochastically within patches or among patches in a habitat, these studies have not considered joint within- and among-patch variation. Consideration of resource variation at only a single scale may provide an incomplete perspective on forager responses in structured environments. Specifically, analyses may fail to detect explainable patterns of forager behavior (Green 1980, Pleasants 1989). If variation occurs only among patches, then foragers will not value information obtained whilst ingesting food items (McLinn and Stephens 2006) and often adopt an invariant, exploitation strategy (Krebs et al. 1974,

Alonso et al. 1995, McLinn and Stephens 2006). Within-patch variation can cause foragers to sample haphazardly within the patch before ascertaining and responding to present patch quality (Valone and Brown 1989, Valone 1991, Biernaskie and Gegear

2007). Investigation of the responses of foragers to differing components of within- and among-patch variation will reveal how foragers value information obtained from foraging, estimate expectation of patch quality, and use information about present patch quality alongside expectations of future patch quality to adjust patch residence time. This was the primary objective of my thesis.

1.2 Study system

I used experiments with nectar-foraging bumble bees to study the optimal exploitation of structured resource variation. Nectar-foraging bees are ideal subjects, because they typically encounter clearly defined and highly variable hierarchical resource distributions.

Foraging bumble bees consume nectar presented within flowers that are arranged on flowering stalks (inflorescences), and inflorescences are presented on different plants

(Best and Bierzychudek 1982, Kadmon et al. 1991, Biernaskie and Cartar 2004). Nectar volume and concentration can vary over all of these spatial scales (Cruden et al. 1983,

Kadmon et al. 1991, Biernaskie and Cartar 2004). In addition, the ability of a bumble-bee colony to produce sexually reproductive individuals depends on the efforts of nectar- and pollen-collecting workers focused primarily on provisioning their colony (Heinrich

1979a, Oster and Wilson 1979). Typically, individual workers do not reproduce, and thus those engaged in foraging allocate most of their time to this activity (Heinrich 1979a,

Oster and Wilson 1979, Plowright et al. 1993). Consequently, nectar-collecting bumble bees forage so as to maximize foraging currencies, such as RNEI (Pyke 1978c, Best and

Bierzychudek 1982, Harder and Real 1987) or FE (Schmid-Hempel et al. 1985, Cresswell et al. 2000, Charlton and Houston 2010), which should promote colony fitness.

Bumble bees contend with hierarchically structured variation through the use of both short- and long-term memory. Short-term spatial memory represents flowers that a bee has probed recently (Redmond and Plowright 1996, Chittka et al. 1997, Burns and

Thomson 2005), whereas long-term spatial memory manifests in the tendency of bees to return repeatedly to forage within the same area (Heinrich 1979a, 1979b, Thomson

1996), even revisiting highly rewarding plants (Cartar 2004). Short-and long-term memory likely determine an individual’s ability to respond productively to within-patch and among-patch variation in resource availability, respectively.

In addition to the energetic benefits of nectar foraging, bumble bees have clearly defined foraging costs. Importantly, non-rewarding forager behaviors, such as returning to a previously visited, now empty flower, and hovering in front of flowers to detect scent marks of past visits, without landing to probe (inspection), greatly increase the costs

incurred by individuals while foraging on inflorescences (Best and Bierzychudek 1982,

Ohashi and Yahara 1999, V.S.T. Amiot, H.S. Ishii and L.D. Harder unpublished manuscript). Costs from these redundant behaviors arise because flight is expensive for bumble bees (Heinrich 1979a). In spite of cognitive constraints, bumble bees avoid costly flower-revisitation when allowed by patch structure (i.e. inflorescence architecture). For example, on vertical inflorescences, bumble bees commonly commence foraging at the bottom and move upward to unvisited flowers (Pyke 1978b, Heinrich 1979a, Corbet et al.

1981, Best and Bierzychudek 1982, Kadmon 1992). As bees visit successive flowers on an inflorescence, the probability of encountering previously depleted flowers increases; thereby increasing the time spent inspecting flowers for olfactory evidence (scent marks) of prior visitation (Schmitt and Bertsch 1990, Giurfa and Núñez 1992, Goulson and Stout

2000, Saleh et al. 2006). Additionally, prolonged visits to inflorescences depress resource availability, thereby intrinsically reducing forager expectations of the quality of a given inflorescence (Kadmon and Shmida 1992, Biernaskie and Cartar 2004). Such effects can stimulate inflorescence departure before all flowers are visited, even if all flowers initially contain equivalent nectar (V.S.T. Amiot, H.S. Ishii and L.D. Harder, unpublished manuscript).

A flower’s nectar standing crop (NSC) is influenced by its nectar production schedule and recent history of visitation by nectar feeders (Cruden et al. 1983, Pleasants and Zimmerman 1983). As distributions of NSC within and among individual plants influence pollinator responses (i.e. floral visitation patterns), resulting pollinator responses may have consequences for NSC distributions (Pleasants 1981, Cruden et al.

1983, Ishii and Harder 2006). As bees tend to concentrate foraging in rich areas and

move quickly through poor areas (area restriced search: Heinrich 1979b, Morse 1980), nectar-rich inflorescences tend to have neighbors that are likely to contain nectar; similarly empty inflorescences tend to have neighbors that are also empty (Pleasants and

Zimmerman 1979).

1.3 Thesis Objectives

In this thesis, I examine the role of hierarchically structured resource variation on foraging pollinators in ecological and evolutionary contexts. The remainder of this thesis comprises three chapters that address hierarchically structured variation and its impacts, both theoretical and realized, on pollinator foraging.

• Chapter 2 reports a survey of nectar standing crop for five many-flowered,

nectar-producing species to assess the nature of resource variation

encountered naturally by bees. The total variance in nectar standing crop

for each survey is decomposed into within- and among-plant components.

I discuss the causes and consequences of partitioning total resource

variation.

• Chapter 3 reports a test of predictions of the Marginal Value Theorem

(Charnov 1976) with a manipulative experiment that assessed bumble-bee

responses to complementary gradients of within-patch and among-patch

variation. I consider the implications of these results in the context of the

observed structure of nectar variation reported in the literature and

demonstrated in Chapter 2.

• Chapter 4 considers the implications of the findings described in the

preceding chapters for the coevolution of foraging strategies in bumble

bees and the consequences for the nectar production schedules of

flowering plants.

Chapter Two: The structure of variance in nectar standing crop in natural populations

2.1 Introduction

Resource variation in habitats is influenced by a hierarchy of abiotic and biotic processes governing the accumulation of resources from habitats and the patches they contain

(Pickett et al. 1987, Wu and Loucks 1995). Whereas habitat-level constraints govern variation in mean abundance among patches, providing context for the variation observed within the habitat (Wu and Loucks 1995), processes within individual patches generate variation in abundance within patches, imposing bottom-up constraints on how resource variation is structured in a habitat. For example, local climatic conditions impose habitat- level constraints on vegetation growth as all individuals in a plant community experience the same UV, ambient humidity, and environmental disturbances (Bormann and Likens

1979, Corbet et al. 1979). In contrast, resource exploitation by foragers acts within individual patches to cause variation in resource abundance whenever animals do not remain in patches until they have been depleted (Charnov 1976, Gibson et al. 2006).

Given that foraging animals instantaneously experience patches on a shorter temporal scale, understanding the variation at any given level in a hierarchical patch system will provide insight into how foragers respond to structured variation.

Bumble bees forage for nectar in hierarchically-structured patch systems. They drink nectar that accumulates in flowers, which are arranged in inflorescences, which may be replicated on individual plants, which are distributed heterogeneously in the population (Boose 1997). Further, plant communities often include multiple coflowering plant species, such that worker bumble bees often exploit floral nectar from multiple 10

plant species that differ in the floral and inflorescence traits that influence bees’ foraging ability. Variation in nectar abundance within an inflorescence can prompt bees to depart early, with full flowers left unvisited, impacting the resulting distribution of nectar

(Hodges and Wolf 1981, Dukas and Real 1993, Biernaskie and Gegear 2007).

Conversely, variation in nectar abundance within an inflorescence can also prompt delayed departure, often resulting in bees visiting recently depleted flowers and thereby wasting time and energy (Kadmon and Shmida 1992, Redmond and Plowright 1996).

The amount of nectar available at a given instant (nectar standing crop, NSC) is a function of ambient humidity (Corbet et al. 1979, Cruden et al. 1983, Zimmerman 1988,

Hodges 1993) and recent secretion and depletion (Pleasants and Zimmerman 1979,

Zimmerman 1981b, Cibula and Zimmerman 1984). Secretion depends on: habitat influences, such as ambient temperature (Cruden et al. 1983, Michaud 1990), which can influence concentration (however see Heinrich and Raven 1972); plant-specific characteristics, such as genotype (Leiss et al. 2004, Leiss and Klinkhamer 2005) and soil moisture (Carroll et al. 2001, Leiss and Klinkhamer 2005); and flower-specific characteristics of nectar production, such as flower age (Cruden et al. 1983, Torres and

Galetto 1998; although see Pleasants 1983), sex(-phase) (Devlin and Stephenson 1985,

Kadmon et al. 1991, Carlson and Harms 2006) and condition (Kadmon et al. 1991).

Depletion depends on the evaporation of water due to relatively low ambient humidity

(Corbet et al. 1979, Cruden et al. 1983), the abundance of pollinators within a community

(Wolf and Hainsworth 1990) and the rate of visitation by pollinators to an individual plant within a population (Zimmerman and Pyke 1986, Thomson 1988).

Nectar variation is dynamic, depending on processes at the level of individuals and their surrounding communities. Therefore, understanding variance in NSC in a plant population must consider how NSC can vary at these scales. Whereas many studies have quantified overall variation in nectar standing crop (Pleasants and Zimmerman 1983,

Zimmerman and Pyke 1986, Kadmon et al. 1991, Corbet 2003), few have considered the structure of this variation, despite nectar being presented hierarchically within flowers, inflorescences, and plants (Boose 1997).

Here, I characterize the structure of variation in NSC within and among plants for five species with many-flowered inflorescences. All five species are visited and pollinated regularly by bumble bees (Bombus spp.): Chamerion angustifolium L.

(Onagraceae) (Galen and Plowright 1985); Delphinium bicolor Nutall (Ranunculaceae)

(Bauer 1983, Ishii and Harder 2006); Delphinium glaucum S. Watson (Ranunculaceae)

(Ishii and Harder 2006); Penstemon confertus Douglas ex. Lindl. (Plantagenaceae)

(Tindall 2006); and Plectritis congesta (Lindl.) DC. (Valerianaceae) (Cartar 1991).

2.2 Materials and Methods

2.2.1 Nectar Surveys

As described below, I collected data for Chamerion angustifolium and Delphinium glaucum (2012), whereas the data for Delphinium bicolor, Penstemon confertus,

Plectritis congesta and a second sample of D. glaucum (2005) were collected by others as parts of other studies. For all species, inflorescences had previously been exposed to pollinators, so that measured nectar characteristics reflect the natural variation owing to differences in pollinator visitation and/or nectar secretion patterns. Thus, all data

represent a largely instantaneous snapshot of the variation in a population. For D. glaucum (2012), C. angustifolium, Penstemon confertus and Plectritis congesta, NSC was measured as total sugar content. For the remaining samples, NSC was measured as nectar volume, which will misrepresent variation in sugar content to the extent that nectar concentration differed among flowers.

For D. glaucum and C. angustifolium, I sampled four flowers per inflorescence per haphazardly selected plant, including two randomly selected, male-phase flowers and two female-phase flowers. Inflorescences of 34 individuals of D. glaucum were sampled in the meadow at Sibbald Creek Flats (51.04°N, -114.87°W) on July 22, 2012, and 41 C. angustifolium plants were sampled near a trailhead off of Sibbald Creek Trail (51.05°N, -

114.91°W) on August 10, 2012. All samples were gathered between 10:45 – 12:45.

Plectritis congesta was sampled by Ralph Cartar and Mary Reid on Mittlenatch

Island Provincial Park, BC (49.95°N, - 125.00°W: Cartar 1991). Inflorescences of 65 individuals were sampled from May 4 – 7 and 26 – 29, 1986, and of 63 individuals from

May 11 – 21, 1988. I treated measurements from all sampling days during the same year as a single sample, thereby overestimating the instantaneous variance among plants in the population. Three flowers were sampled from each of nine whorls per plant.

Nectar standing crop data for Penstemon confertus were provided by Ralph Cartar; the population was surveyed along a 116-m transect north of Crowsnest Pass, Alberta

(49.895°N, - 114.580°W) from July 9 – 11, 1999. Measurements from all sampling days were treated as a single sample. The survey included 59 individuals. Six flowers were sampled from each inflorescence, and samples were drawn equally from each whorl on an inflorescence.

Delphinium bicolor (51 plants) and a second sample of D. glaucum (36 plants) were sampled in the same meadow at Sibbald Flat sampled during 2012. Sampling occurred from 10:00 – 15:00 on June 16, 2005 (D. bicolor) and July 28, 2005 (D. glaucum) (Ishii and Harder 2006). All open D. bicolor flowers, and five open D. glaucum were sampled.

2.2.1.1 Wick-sampling procedure

Nectar standing crops for D. glaucum (2012) and C. angustifolium were quantified following the methods of McKenna and Thomson (1988). Nectar was absorbed from individual flowers with small triangular wicks of Whatman Number 1 filter paper impaled on insect pins. Sugars absorbed by the wicks were later dissolved in boiling water. Anthrone solution (0.4 g anthrone / 200 mL concentrated H2SO4) was added to an aliquot of the dissolved sugar solution in a test tube, which was then placed in a boiling water bath (97 °C). After the sample was vortexed and cooled to room temperature, its absorbance at 320 nm was measured with a spectrophotometer. Absorbances were compared to those of known sucrose standards, from which the sucrose content per sample (mg) was calculated.

2.2.1.2 Capillary-and-refractometer procedure

For Penstemon confertus, D. glaucum (2005), and D. bicolor, nectar was extracted from flowers with 2 uL micro-capillary tubes and the volume was estimated by measuring the length of the tube filled with nectar.

2.2.1.3 Corolla volume estimation procedure

For Plectritis congesta, the amount of nectar in the floral spur was measured with an eyepiece micrometer (Cartar 1991). This measurement was converted to volume based on the average volume of flowers. Given the minute amounts of nectar in P. congesta

flowers, the nectar from many flowers at the same sampling period, mostly from the same individual, was pooled to estimate sucrose concentration with a hand refractometer.

2.2.2 Statistical Analysis

Variance in NSC was partitioned into within- and among-plant components with a non- linear, mixed-effects model using PROC NLMIXED in SAS 9.3. All analyses considered a zero-augmented gamma distribution for within-plant variation, and a normal distribution for among-plant variation. For the zero-augmented gamma distribution for plant i is,

$1 − pi if x = 0 ! ai f (x) = pi b a −1 −bx # x i e if x 0 ! > " Γ(a) where x is the measure of NSC for an individual flower, pi is the proportion of flowers on plant i with x > 0, ai and φ are the shape and scale parameters, respectively, of the gamma component, and Γ() is the complete gamma function. I adopted the parameterization of

µΓ,i 2 Richards (2008), ai = , where µΓ,ι and σ ,i = µ ,iφ are the mean and variance of the φ Γ Γ gamma portion of the distribution for plant i. Accordingly, the overall mean of the zero-

2 inflated gamma distribution is µ0Γ = pµΓ and the variance is p(1− p)µΓ + pφµΓ . As a proportion, pi is bounded between 0 and 1 and is unlikely to exhibit normal variation (the only option available in SAS) among plants. Therefore, I considered normal variation in

2 the associated logit, ln(pi/[1 – pi]), with a mean of ln(p /[1− p]) and a variance of σ L .

Among-plant variation in µΓ,ι was represented by a normal distribution with mean µΓ and

2 2 2 variance σ Γ . I used maximum-likelihood to estimate p , µΓ, φ, σ L and σ Γ . For the species subject to wick sampling and P. congesta and P. confertus, nectar sugar content

(mg) was the response variable, whereas analyses of D. bicolor and D. glaucum (2005) considered nectar volume (µL) as the response variable.

Within-plant differences in NSC attributed to flower sex-phase, position in the inflorescence, or nectary (for D. glaucum 2012) were estimated using generalized linear mixed-effects models (PROC GLIMMIX in SAS 9.3). These analyses considered random

(normal-distributed) variation among plants. Within-plant variation was represented by a gamma distribution.

2.3 Results

2.3.1 Delphinium glaucum

2.3.1.1 2005

In the D. glaucum population sampled during 2005, within- and among-inflorescence variation each contributed significantly to the total variance in nectar volume of the flowers sampled (F2,17 = 17.94, P<0.05). Among-inflorescence variance contributed

65.18% (95% CI: 48.29-82.06%) of the total variance in nectar standing crop among the flowers sampled (t17=8.15, P<0.05; Figs 2.1, 2.2D and 2.2F). The remaining 34.82%

(95% CI: 17.94-57.71%) of the total variance was significantly attributed to variation within individuals (t17=4.35, P<0.05; Figs 2.1, and 2.3B)

2.3.1.2 2012

In the population of D. glaucum sampled in 2012, within- and among-inflorescence variation significantly contributed to the total variance exhibited by the flowers sampled

in the population (F2,32 = 14.22, P<0.05). When the total variance in NSC was decomposed into within- and among-individual components, 89.73% (95% CI: 81.76-

97.71%) was significantly attributed to variation in NSC within individuals (t32=22.93,

P<0.05; Figs 2.1 and 2.2A) and 10.27% (95% CI: 2.30-18.24%) was significantly attributed to variation in NSC among individuals (t32=2.62, P<0.05; Fig 2.1, 2.2C and

2.2E).

Sugar content significantly varied among flowers of different sex-phases (F2,32 =

103.52, P<0.05). On average, male-phase flowers contained 2.80 mg (95% CI: 2.39-3.22 mg) of sugar and female-phase flowers contained 2.65 mg (95% CI: 2.12-3.20 mg) of sugar.

2.3.2 Delphinium bicolor

Of the total variance in NSC for D. bicolor, 80.60% (95% CI: 59.33-101.87%) could be significantly attributed to variation within individuals (t24=7.82, P<0.05), but the large confidence interval suggests that all variation could have existed among individual. In support of this, variation among individuals did not significantly contribute to the total variation in nectar standing crop among the flowers sampled (t24=1.88, P>0.05; Fig 2.1).

2.3.3 Chamerion angustifolium

In C. angustifolium, only within-inflorescence variation significantly contributed to the total variance of the flowers sampled in the population (t162 = 2.57, P<0.05; Figs 2.1 and

2.3). Sugar content did not significantly vary with floral sex-phase (F1,103.9 = 2.30, P>0.1), nor did sugar content vary with the relative position of flowers on an inflorescence

(F1,41.24 = 0.14, P>0.7).

2.3.4 Plectritis congesta

2.3.4.1 1986

Of the total variance in NSC of P. congesta during 1986, 14.53% (95% CI: 8.31-20.76%l

Fig 2.1) could be attributed to variation among individuals in the population (t64=4.66,

P<0.05), whereas 85.47% (95% CI: 79.24-91.24%; Fig 2.1) was attributed to variation in

NSC within individuals (t64=27.43, P<0.05; Fig 2.1).

2.3.4.2 1988

Relative to 1986, NSC varied more, despite a decrease in the mean NSC (as reflected in the coefficient of variation in table 1). Total variance in the sugar content of

NSC could be significantly decomposed 35.96% (95% CI: 26.66-45.25%; Fig 2.1) attributed to variation among individuals (t62=7.73, P<0.05) and 64.04% (95% CI: 54.75-

73.34%; Fig 2.1) to variation within individuals (t62=13.77, P<0.05; Fig 2.1).

Table 2.1 Sampling and nectar characteristics of 5 plant species

Mean Total Variation Coefficient % Empty Flowers Species Sample Method (95% CI) (95% CI) of Variation (95% CI) D. glaucum Capillary 2005 0.36 (0.24-0.48) b 0.067 0.72 0 n = 36 (0.043-0.091) b

Wick 2012 2.69 (2.16-3.22)a 5.43 (3.35- 0.87 6.74 (3.14-10.34) n = 34 7.51)a

D. bicolor Capillary 0.15 (0.10-0.19) b 0.022 (0.011- 1.03 0 n = 51 0.034)b

C. angustifolium Wick 1.94 3.43 0.95 20.37 n = 41 (1.65-2.23)a (2.40-4.46)a (14.12-26.62)

P. congesta Corolla 1986 0.036 (0.032- 0.0001 0.88 14.87 (10.85-18.89) Volume n = 65 0.041)a (0.00008- Estimation 0.0013)a 1988 0.027 (0.019- 0.0014 1.39 34.33 (28.72-43.95) n = 63 0.034)a (0.0008- 0.0019)a P. confertus Capillary 0.15 (0.13-0.17)a 0.04 (0.03- 1.40 35.17 (30.82-39.53) n = 60 0.05)a a – Response variable was nectar sugar content measured in mg b – Response variable was nectar volume measured in µL

Figure 2.2 The distributions of nectar standing crop within a D. glaucum population sampled during 2005 (panels A, C and E) and 2012 (panels B, D, and F). Panels A and B present examples of variation in NSC among flowers within inflorescences, whereas panels C and D depict variation in mean nectar standing crop among individuals. Panels E and F illustrate the overall distributions of NSC standing crops among all flowers sampled within each population, fitted with a zero- augmented gamma distribution.

2.3.5 Penstemon confertus

The total variance in NSC in the sampled population of P. confertus was significantly decomposed into within- and among-individual components (F2,178 = 45.03, P<0.05). Of the total variation in the population, 84.25% (95% CI: 79.30-89.21%; Fig 2.1) was

attributed to variation within individuals (t178=33.56, P<0.05; Fig 2.1, 2.3D and 2.3F), compared to 15.74% (95% CI: 10.79-20.70%) among individuals (t178=6.27, P<0.05; Fig

2.3B).

Figure 2.3 The distributions of nectar standing crop within populations of C. angustifolium (panels A, C and E) and Penstemon confertus (panels B, D, and F).

Panels A and B present examples of variation in NSC among flowers within inflorescences, whereas panels C and D depict variation in mean nectar standing crop among individuals. Panels E and F illustrate the distributions of NSC among all flowers sampled within each population, fitted with a zero-augmented gamma distribution.

2.4 Discussion

The composition of NSC variance ranged from solely variation among flowers within plants to most variation being associated with differences in average NSC among plants

(Table 2.1, Figure 2.1). Among the species sampled, among-plant variation generally contributed less to the total variation in NSC for each population, so that processes acting at the flower level had greater influence than plant-level characteristics and processes.

Nevertheless, the strongly contrasting patterns observed in the same D. glaucum population during different years (Fig 2.2F, Fig. 2.3F) illustrates that the structure of variation in NSC also depends strongly on prevailing conditions at the habitat level.

Extensive variation among flowers within inflorescences probably arises in part from contrasting histories of pollinator visitation and nectar depletion. Such differing histories should arise because pollinators start visiting an inflorescence on different flowers (Heinrich 1979b, Chittka et al. 1997), follow different paths within the inflorescence, and depart after visiting different numbers of flowers. Nectar-collecting bees generally forage to minimize visits to unrewarding flowers on an inflorescence

(Pyke 1978, Pleasants 1981, 1989, Charlton and Houston 2010, Chapter 3). Consequently bees tend to depart inflorescences before visiting all nectar-bearing flowers, leaving unvisited flowers in their wake (Pyke 1978c, Pleasants 1989, Charlton and Houston

2010). In the case of late-flowering C. angustifolium, all variation in sugar standing crop results from variation within individuals. This species flowers late during the growing season in association with both peak bumble-bee abundance and a general decline in flowering by other plants. Because of the high ratio of bees to flowers, inflorescences probably realize high visitation rates (Dreisig 1995, Cartar 2009), likely resulting in the frequent depletion of nectar of many flowers on each individual. Consequently, depleted 23

flowers probably had little time to replenish their NSC before they were revisited and thus presented little nectar to visiting pollinators. As I sampled destructively, the extent to which variation in nectar secretion among individual flowers contributed to the variation observed within the population could not be assessed. Nevertheless, variation in nectar secretion rates likely contribute little to the variation in NSC for populations of C. angustifolium, as depletion likely dominated the variance generating processes within plants.

Further along the spectrum of variance partitioning, D. glaucum (2005) and

Plectritis congesta (1988) exhibited moderate variation in NSC both within and among inflorescences. For D. glaucum this pattern may partially reflect the relatively infrequent visitation of inflorescences (median of 0.8 visits h-1 per inflorescence; Ishii and Harder

2006), allowing time for moderate replenishment. Relative flower position probably contributed to differences in NSC within individuals, as flowers lower on inflorescences contained more nectar than those higher on inflorescences (Ishii and Harder 2006).

Plectritis congesta individuals exhibited less variation and offered smaller nectar rewards, on average, relative to coflowering Vaccinium caespitosum, which bees visited preferentially as mean nectar load size was greater in spite of the greater variability in nectar standing crop (Cartar 1991).

Similar patterns of among-inflorescence variation in NSC in D. nelsonii, have been described using the analogy of hot- and cold-spots (Pleasants and Zimmerman 1979,

1983). Inflorescences with a high mean NSC tend to be surrounded by inflorescences with similar mean NSC in hot-spots, owing to the area-restricted search patterns of nectarivores (Pleasants and Zimmerman 1979, 1983). In contrast, inflorescences with a

small mean NSC tend to be surrounded by inflorescences that also have a small mean

NSC, forming cold-spots. The nectar rewards presented by D. glaucum are sufficiently large to condition area-restricted search in foraging bumble bees both within (Dukas and

Real 1993), and among neighboring inflorescences (Zimmerman 1981b, Burns and

Thomson 2005). Within-inflorescence variation resulting from bees assessing a plant’s mean NSC from the first few flowers visited (Hodges 1985a, 1985b) could result in variation in the resulting nectar distribution in the population. This explanation could not be assessed, as spatial data were not collected. Moreover the extent to which within- inflorescence variation can prevent homogenization of nectar distributions arising from area restricted search is unclear (Pleasants and Zimmerman 1983, Ott et al. 1985).

Alternatively, genetic relatedness, specifically with regard to nectar producing traits

(Price and Waser 1979, Boose 1997, Leiss and Klinkhamer 2005), could contribute to patterns of variation among-inflorescences.

Delphinium glaucum exhibited much more within-inflorescence variation during

2012 than during 2005. Although this difference may have arisen due to the different methods used to measure NSC, pollinator abundance differed during sampling in each year. Sampling during 2012 occurred immediately before a period of high bee activity in the season (H. Cameron-Inglis, unpublished data), whereas during 2005 there appears to have been more pollinator activity within the study site (Ishii and Harder 2006). This pattern indicates greater influence of flower-level processes, such as differential nectar secretion among flowers of an inflorescence, than of flower visitation rates by pollinators.

Habitat-level processes such as pollinator abundance (Pleasants and Zimmerman 1979,

Zimmerman 1981b), and weather conditions, which can influence plant phenology (Hirao

and Kudo 2004), probably have less influence on the structure of resource variation later in the season. However, if bees were undermatched with floral resources in 2005, then plants would experience less depletion and exhibit less variation within inflorescences

(Cartar 2009). Pollinators likely responded to perceived among-plant variation by staying longer on rewarding inflorescences than on poor-quality inflorescences, giving rise to more variation within plants (Pleasants and Zimmerman 1979, 1983; Chapter 3). Within- plant variation accounts for considerably more of the total variation in the population sampled in 2012, suggesting that those pollinators exhibited a limited ability to distinguish highly rewarding from less rewarding plants (Chittka et al. 2003, Ohashi and

Thomson 2012) or that the population simply encountered low bee density.

Total variation in nectar standing crop in a population is dynamic, and determined by the relative contributions of floral, plant and habitat influences. If individual plants differentially produce nectar (Pleasants and Zimmerman 1979, Zimmerman 1981b,

Carlson and Harms 2006), then pollinator visitation patterns can be expected to reflect among-plant differences, owing to the matching of pollinators to nectar resources

(Dreisig 1995, 2011, Cartar 2009). If the magnitude of variation in nectar production among flowers is great, then pollinator visitation to individual plants will initially reflect differences in NSC among the first few flowers visited among all plants in a population

(Best and Bierzychudek 1982, Kadmon et al. 1991). These differences will be confounded by the differential visitation histories of plants and flowers in the population, creating homogeneity in mean NSC among individuals, but considerable variation within individuals (Kadmon et al. 1991, Chittka et al. 1997). Given the range of variance partitions exhibited by hierarchically structured populations, it is important to understand

how NSC jointly varies at adjacent higher and lower hierarchical levels to account adequately for the processes affecting variation in NSC in plant populations.

Chapter Three: The effect of structured variation in nectar standing crop on foraging by bumble bees

3.1 Introduction

Animals that encounter variation in food quality within a patch and variation in patch quality within a habitat, confront problems of which patches to exploit (Goulson 1999,

Richards and de Roos 2001) and how thoroughly they should be exploited (Charnov

1976, Charnov et al. 1976, McNamara et al. 2011). Variation on these different spatial scales affects how foragers perceive and exploit the resources distributed throughout their habitats. Among-patch variation should confound a forager’s ability to make expectations of foraging gains elsewhere in its habitat (Winter and Stich 2005, Gibson et al. 2006), whereas within-patch variation impedes a forager’s capacity to evaluate the quality of its current patch (Best and Bierzychudek 1982, Kadmon et al. 1991, Kadmon and Shmida

1992). These sources of variation jointly contribute to lost foraging opportunities – either from staying after, or departing before a patch has been depleted (Bateson and Kacelnik

1996, Houston 1997, Bateson et al. 2003). Animals capable of using hierarchical resource variation to make inferences about patch quality will be able to forage optimally in such a stochastic resource environment, although limited cognition probably restricts an animal’s ability to track resources in its habitat (Valone 1991, Brown et al. 1997, Henry and Stoner 2011). Nevertheless, how the widespread resource variation on different spatial scales influences patch departure by foragers remains poorly understood.

The marginal value theorem (MVT; Charnov 1976) describes the optimal residence time in patches for omniscient foragers that maximize their long-term (multi-patch) rate of net energy intake (RNEI) in environments comprising many, randomly distributed,

patch types. According to the MVT, foragers should leave one patch for another unvisited patch in the environment when their instantaneous (marginal) intake rate in the patch falls to the average intake rate for the environment (Fig. 3.1, open symbols). Although the

MVT explicitly addresses the impact of among-patch variation, it and subsequent tests of the MVT are silent about the consequences of within-patch variation. Thus, the general applicability of the MVT is unclear, as most foraging environments include resource variation within patches and among patches (Pickett et al. 1987, Kotliar and Wiens 1990,

Wu and Loucks 1995; Chapter 2).

Animal foraging is commonly described using currencies, which link energetic rewards from foraging to the utility an animal derives from those rewards (Stephens and

Krebs 1986). RNEI is commonly assumed to be the relevant foraging currency in theoretical models of patch use (Charnov 1976, Dreisig 2011) and there is empirical support for this assumption (Cresswell 1990, Bautista et al. 1998, Biernaskie et al. 2002).

Additionally, foraging efficiency (FE: net benefits/costs) has been shown to be maximized by honey bees (Schmid-Hempel et al. 1985, Schmid-Hempel and Wolf 1988), chickadees (Lima 1985) and ground squirrels (Lima et al. 1985). If foraging time is limiting, animals should maximize RNEI to minimize the potential for lost foraging opportunities (Stephens and Krebs 1986, Bautista et al. 1998), whereas if effort associated with energy turnover is limiting, animals should maximize FE, as doing so makes better use of the energy an animal can allocate to foraging as opposed to other activities (Stephens and Krebs 1986, Ydenberg et al. 1994, Houston 1995). Maximization of both RNEI and FE has been demonstrated as being equally good at predicting patch departure in some animals, including bumble bees (McNamara and Houston 1997,

Charlton and Houston 2010).

Whether the assumption of the MVT, that animals maximize their RNEI in the long-term, over many patch visits (Charnov 1976), is appropriate is uncertain (Templeton and Lawlor 1981, Gilliam et al. 1982, Turelli et al. 1982). A previous study of bumble bee foraging concluded that bees tend to avoid variance in nectar volume in flowers, proportionate to the magnitude of variation in the environment (Real 1981). However, a reanalysis showed that in spite of risk-sensitivity, bees’ responses to variation were consistent with rate maximization per flower, rather than habitat-wide (Harder and Real

1987, Real et al. 1990), which was attributed to memory limitation (Real et al. 1990).

Compared to predictions of the MVT, rate maximization per patch should cause foragers to depart high-quality resource patches sooner and remain longer in low-quality resource patches (Fig. 3.1, closed symbols). The marginal value theorem implicitly assumes that foragers spend the same amount of time foraging in a patch of a certain quality, independent of the condition of the overall environment (Ollason 1980). When variation arises among- and within-patches, trading speed for accuracy, in response to patch quality, may be an optimal resolution of the problem of exploiting resources when the distribution of resources is structured over different spatial scales. Short-term rate maximization could be beneficial to animals that forage in environments where resources vary within resource patches, especially when animals assess patch quality after encountering a relatively small sample of foraging experiences (Turelli et al. 1982,

Possingham and Houston 1990). Modifying visit duration in the short-term allows animals to respond to variation in patch-quality as it is encountered, potentially staying longer when patches are rewarding, or shorter when they are of poor quality. When

resources vary mainly within, but not among, patches, animals may not readily trade speed for accuracy due to its uncertainty in the quality of the current patch. However, when resources vary primarily among patches, the trade-off between speed and accuracy should become clear when comparing the behavioral responses of foragers on high- and low-quality patches (Burns and Thomson 2005).

Figure 3.1 Expected search times in two patches of differing quality under short- term, per-patch (closed points) and long-term, among-patch (open points) maximization of rate of net energy intake (RNEI). The green and purple lines depict the change in net energy gain with increasing search time in high- and low- quality patches, respectively. The slopes of the solid gray lines represent the maximum RNEI that can be achieved in the respective patch, and the slope of the dashed gray line represents the average maximum RNEI in the habitat if low- and

high-quality patches are equally abundant. With short-term (per patch) maximization, the optimal search time occurs when the first derivative of the gain curve (marginal value) equals the slope of the respective solid gray line. With long- term (habitat wide) maximization, the optimal search time occurs when the marginal value equals the slope of the dashed gray line, as represented by the short black lines.

Bumble bees foraging for nectar encounter a highly dynamic, hierarchical distribution of resources. The amount of nectar that accumulates in a flower reflects secretion and depletion processes, each depending on variable biotic (e.g. pollinator abundance) (Zimmerman 1981b, Cibula and Zimmerman 1984) and abiotic conditions

(e.g. local weather conditions) (Cruden et al. 1983). Secretion depends on species- specific characteristics, flower age (Cruden et al. 1983, Torres and Galetto 1998), and sex(-phase) (Devlin and Stephenson 1985), whereas depletion results from pollinator visits, changes in ambient humidity and temperature, and resorption (Cruden et al. 1983).

Within a many-flowered plant (patch), variation in accumulated nectar (nectar standing crop, or NSC) depends largely on pollinator abundance and visitation (Pleasants and

Zimmerman 1979, 1983, Zimmerman 1988, Torres and Galetto 1998), but also on separation of sex roles within and among flowers (Devlin and Stephenson 1985, Torres and Galetto 1998). Among individuals, variation in mean NSC depends largely on local pollinator visitation (Zimmerman 1981a), but may also arise from genetic differences among plants (Leiss et al. 2004). Thus, bees visiting multi-flowered plants are highly suitable subjects for examining the consequences of structured variation on patch foraging.

In this chapter, I describe the results of a laboratory experiment using captive bumble bees to examine how the partitioning of resource variation among and within patches affects patch use by foraging animals. Responses of bees, in the form of floral visits and inspections, and the time spent probing and flying within and among artificial inflorescences (patches) were recorded in environments that differed in the proportions of the total nectar variance associated with within- or among-inflorescence components. In addition to characterizing these responses, I tested the prediction of the MVT that bees depart an inflorescence when their marginal intake falls to the average in the environment. As studies of bees support maximization of both RNEI (Hodges 1985,

Bautista et al. 1998, Charlton and Houston 2010) and FE (Schmid-Hempel et al. 1985,

Charlton and Houston 2010) and they have been shown to be equivalent theoretically and empirically (McNamara and Houston 1997, Charlton and Houston 2010), I considered both currencies.

Foraging bumble bees engage in a suite of observable behaviors while foraging.

The spatial distribution of plants obliges bees to fly among plants to encounter new aggregations of floral resources. Within plants, visits to flowers result in floral probes, the duration of which depends on floral depth and nectar volume (Harder 1983). As floral visits occur, bees deposit scent that they can detect subsequently to avoid revisiting flowers that they depleted recently (Schmitt and Bertsch 1990). After depleting a flower, if a bee remains on an inflorescence, it must fly to another flower. During flight, bees may inspect other flowers for the presence of scent, to assess the recent visitation history of those flowers (Schmitt and Bertsch 1990, Goulson and Stout 2000), which increases the duration of flight among flowers (Ishii et al. 2008, Robinson 2013, Amiot et al.

unpublished manuscript). Foraging benefits and costs depend on the incidence and duration of these behaviors, so understanding how these behaviors respond to partitioned variance enables prediction of how currencies vary in response to different environments, facilitating interpretation of observed patch exploitation behavior.

If bees employ a marginal-value inflorescence-departure rule, then as among- inflorescence variation increases, a bee’s ability to assess inflorescence quality should improve, enabling it to implement energetically appropriate foraging decisions.

Conversely increased within-inflorescence variation should hamper a bee’s ability to detect differences in patch quality. These contrasting effects may invoke a speed- accuracy trade-off (Gegear and Thomson 2004, Ohashi and Thomson 2012), which may cause deviations from the expectations of long-term currency maximization. Specifically, confronted with an apparently low-quality inflorescence, bees should forage quickly to assess inflorescence quality, whereas on an apparently high-quality inflorescence they should forage more slowly and visit more flowers to enhance nectar exploitation.

However, the uncertainty associated with within-inflorescence variation will constrain the applicability of this policy.

3.2 Materials and Methods

3.2.1 Experimental Design

To test the influence of structured variation on patch-exploitation, I observed the responses of worker bumble bees (Bombus impatiens [Cresson]) in environments with the same mean (µ = 1.5 µL) and total variance (1.0 µL2) in nectar volume, but which differed in the relative components of within- and among-“inflorescence” variance (Table 3.1).

The environment was a 100 cm x 120 cm x 90 cm (height) flight cage with Plexiglas 34

sides that contained a 2 x 3 array of six artificial inflorescences separated by 30 cm from their nearest neighbors. The inflorescences were vertical racemes with 12 flowers arranged in a dextral spiral, starting 16 cm from the base of the inflorescence and separated from the nearest orthogonal neighbors by 5 cm. Each flower consisted of 1 cm of the closed end of a 1-mL centrifuge tube, painted blue and glued to the head of a 3.5- cm insect pin.

A B

Figure 3.2 An artificial inflorescence (A) and a 2 x 3 array of artificial inflorescences arranged within the 100 cm x 120 cm x 90 cm (height) flight cage (B).

During an experimental trial, the inflorescences provided one of five treatments, with 0%, 25%, 50%, 75% or 100% of the total nectar variance associated with differences in mean nectar volume among inflorescences and the complementary component represented by among-flower variance within inflorescences. Except for the treatment with no among-inflorescence variation, the environment presented three high-

mean (high-quality) inflorescences and three low-mean (low-quality inflorescences) in randomized positions. Except for the treatment with no within-inflorescence variation, each inflorescence type comprised a randomized mixture of low-volume (low-quality) flowers and high-volume (high-quality) flowers. The number and nectar volume of each flower type differed among treatments and inflorescence types (details in Table 3.1: see the Appendix [§3.5] for a description of how the specific conditions were identified).

Table 3.1 Inflorescence and flower characteristic of the five treatments used to

2 2 assess the effects of within- and among- inflorescence variation (σ W and σ B , respectively) in nectar availability on foraging and energetics for Bombus impatiens workers.

Intended Treatment Inflorescence

2 Conditions States Flower states Actual σ W

2 2 σ W = 1.0 6 High-quality - 2.5 µL 1 µL 3 µ = 1.5 µL 2 σ B = 0.0 6 Low-quality - 0.5 µL 2 2 2 Variance (σ T = 1.00 µL 3 µ = 1.5 µL 2 High-quality - 3.7 µL 1.01 µL Mean (µ ) = 1.48 µL T 10 Low-quality - 1 µL

2 2 σ W = 0.75 3 High-quality 9 High-quality - 2.5 µL 0.75 µL

2 σ B = 0.25 µH = 2 µL 3 Low-quality - 0.5 µL

2 2 2 Variance (σ T ) =1.00 µL 3 Low-quality 3 High-quality - 2.5 µL 0.75 µL Mean (µ ) = 1.50 µL T µL = 1 µL 9 Low-quality - 0.5 µL

2 2 σ W = 0.50 3 High-quality 5 High-quality - 3.0 µL 0.48 µL

2 σ B = 0.50 µH = 2.18 µL 7 Low-quality - 1.6 µL

2 2 2 Variance (σ T ) =0.97 µL 3 Low-quality 5 High-quality - 1.6 µL 0.48 µL

Mean (µT) = 1.48 µL µL = 0.78 µL 7 Low-quality - 0.2 µL

2 2 σ W = 0.25 3 High-quality 7 High-quality - 2.8 µL 0.24 µL

2 σ B = 0.75 µH = 2.38 µL 5 Low-quality - 1.8 µL

2 2 2 Variance (σ T ) =1.02 µL 3 Low-quality 2 High-quality - 1.8 µL 0.27 µL Mean (µ ) = 1.51 µL T µL = 0.63 µL 10 Low-quality - 0.4 µL

2 2 σ W = 0 3 High-quality All 2.5 µL 0.00 µL

2 σ B = 1.00 µH = 2.5 µL

2 2 2 Variance (σ T ) =1.00 µL 3 Low-quality All 0.5 µL 0.00 µL

Mean (µT) = 1.50 µL µL = 0.5 µL 3.2.2 Forager Training

A total of fifteen bees from two colonies (4 bees from one colony and 11 from the second) served as subjects for the experiment. Each bee experienced all five treatments in randomized order, with three trials per treatment. A colony was connected to the flight cage with plastic and rubber tubing via a series of gates, allowing control of which bees entered the cage.

Bees were trained to forage on artificial inflorescences in three steps. To ensure that bees associated artificial flowers with food rewards, individuals were first trained to forage on a dense, horizontal array of artificial flowers with 2 µL of dilute (scented) honey solution. These conditions allowed bees to find rewards by olfaction without having to negotiate complicated inflorescence architecture during flight. Once a bee demonstrated an ability to associate the artificial flowers with food rewards, it was trained to visit six vertical racemes with 2 µL of 30% (unscented) sucrose solution. Bees that demonstrated an ability to navigate within and amongst vertical racemes were identified as experimental subjects, marked on the thorax with Testor enamel paint, and returned to the colony. During the third phase, test bees were subject to three training

runs during which data were not collected, under experimental conditions for a particular treatment, so that they were experienced with those conditions before observations began.

Training was repeated for every treatment for each individual. If an individual did not complete a particular treatment within a day, then the following day it was subject to the same training procedure before the remaining experimental trials were conducted.

3.2.3 Experimental Trials

Experimental trials were video-recorded using a Sony Handicam HDR-CX130 digital camcorder (1080p HD resolution; 60 frames s-1) and data were recorded during playback.

Immediately prior to a trial, 30% (unscented) sucrose solution was added to clean flowers according to the required volumes for the specified treatment (Table 3.1) with an

Eppendorf repeating pipettor. Once a test bee entered the flight cage, its behavior was video-recorded until either every inflorescence had been visited once, or the bee became satiated and ceased foraging.

I recorded the order and position of interactions with flowers, the type of interaction

(probe or inspection), the durations of flower visits and flights between inflorescences and flowers. Flower visits began when a bee landed on a flower, disengaged its wings and inserted its proboscis into the flower to drink the nectar contained within, and ended when the bee started vibrating its wings in preparation for departure from the flower.

Inspections occurred when a bee either hovered in front of a flower or briefly landed on a flower without disengaging its wings or inserting its proboscis to drink from the flower.

A bee’s response to the variation in conditions present on pristine inflorescences was of interest. Although bees commonly revisited inflorescences, revisits to flowers were rare

(1.31%); neither was of interest and both were ignored during playback. At the end of an 38

experimental trial, all flowers were removed from the inflorescences and thoroughly rinsed and dried overnight in a drying oven to remove residual nectar and scent. Once a bee had participated in all treatments, I weighed it to allow calculation of foraging energetics.

3.2.4 Statistical Analysis

3.2.4.1 Behavioral Responses

To provide context for assessing the relation of bee behavior to foraging currencies, I first analyzed the effects of treatment, inflorescence type and flower type on the components of foraging currencies, namely the numbers of floral visits and inspections per inflorescence visit, and the durations of flower visits and flights between inflorescences and flowers. All analyses used generalized linear mixed models (Stroup 2013) as implemented in SAS version 9.4 (2013) These analyses accounted for the repeated measurement of individual bees by adjusting the denominator degrees of freedom for F- tests for within-subject covariance, as represented by a model of compound symmetry, by the methods of Kenward and Roger (1997). For the analyses of flight durations, separate variance-covariance matrices were fit for the two bee colonies. The number of flower visits was analyzed as a Poisson response with a natural logarithm link function, the number of inspections per inflorescence was analyzed as a negative binomial response with a natural logarithm link function, and time components were analyzed as log-normal responses with an identity link function. I present least-squares means (Milliken and

Johnson 1984) and their standard errors or 95% confidence intervals of their back- transformed values. Inflation of type 1 error rates from post-hoc comparisons of least- squares means were corrected using the Dunn-Šidák procedure (Šidák 1967).

3.2.4.2 Foraging Currency Maximization

Analyses were conducted to determine whether bees departed from inflorescences when they had maximized either their rate of net energy intake (RNEI: net energetic benefits / time) or foraging efficiency (FE: net energetic benefits / energetic costs). According to the marginal value theorem (Charnov 1976), bees should depart a patch when their instantaneous (marginal) RNEI falls to the average expectation among patches. A similar relation seems appropriate for maximization of FE. To assess these predictions, I examined the differences between a bee’s “realized” RNEI (or FE) at departure from each inflorescence from the mean of all inflorescences that it had already visited

(including the current inflorescence) for the same treatment conditions. On average, this

“residual” RNEI (or FE) should equal 0 if bees foraged according to the marginal value theorem. I assessed this prediction by analyzing whether the residual RNEI and FE differed among treatments and inflorescence types with generalized linear mixed models that considered normal distributions and identity link functions (see §3.2.4.1 for additional details). To see these results in context, I applied similar analyses to realized

RNEI and FE at departure from individual inflorescences.

3.2.4.2.1 Rate of Net Energy Intake

RNEI is the ratio of net energetic gains (the difference of gross energetic gains, G, and energetic costs, C) to the time spent obtaining those gains (T),

! − ! !"#$ = !

For a given inflorescence type, the gross energetic gains (G) are

G e S n V = ρ ∑ i i i where ! is the energetic content in 1 mg of sucrose (16.48!!); ! is the density of nectar

(1.16!!"/!"); ! is the concentration of nectar (% mass of solute / mass of solution);!!!!is the volume of ingested nectar (!") per flower type i; and !! is the number of flowers of type i that were visited. The corresponding energetic costs (C) are

! = !!"#$!!!!"#$!! + !!"#$%&'!!"#$%&' = !(!!!!"#$!! + !!!!"#$%&')

!!"#$!! and !!"#$%&' are the cumulative times associated with flight on the current inflorescence and probing flowers after !! floral visits on the current inflorescence, respectively. The coefficient ! is the mass of the foraging bee (!); !! and !! are mass- specific rates of energy expenditure associated with flight and probing (!!!!!!!), respectively. I assumed that bees maintain a constant internal temperature throughout the

!! !! !! !! experiment (!! = 0.435!!! ! , !! = 0.034!!! ! ; Heinrich 1975). The state variables are more precisely defined:

!!"#$!! = ! !!!! + !!"# = ! !!!! + !!"#

!!"#$%&' = !!!! where !! is the average time spent flying between flowers of an inflorescence; !!"# is the average time spent flying among inflorescences; !! is the average time spent probing flowers. Combining the preceding equations provides a characterization of the rate of net energy intake,

! !"#! − !! ! ! + ! − !! ! ! !"#$ = ! !"#$%& ! ! ! !"# ! ! ! !!!!! + !!"# + !!!!

3.2.4.2.2 Foraging Efficiency

FE is calculated by taking the ratio of net energetic gains from visiting an inflorescence

(G - C) to the costs associated with acquiring that energy (C).

! − ! ! !"#! − !! ! ! + ! + !! ! ! !" = = ! !"#$%& ! ! ! !"# ! ! ! ! !!! !!!! + !!"# + !!!!!!!

The suitability of FE as the currency by which foraging decisions are made was assessed in a similar manner to assessing the suitability of RNEI.

3.3 Results

3.3.1 Behavioral Responses

Contrasting variation in nectar volume within and among inflorescence had pervasive effects on the behaviors of nectar collecting bumble bees. These responses largely represent reactions to variation in nectar volume that bees encountered in flowers, rather than their ability to detect inflorescence or flower quality remotely, as bees generally visited low- and high-quality flowers in the proportions in which they occurred inflorescences on in the foraging environment (Fig 3.3). Slight exceptions occurred when

25% of the total variance in the environment arose either within- or among- inflorescences, when Bees tended to visit a slightly higher proportion of low-quality flowers than expected (Fig 3.3).

The horizontal dotted lines denote the environmental frequency of low-quality flowers on the respective inflorescence types.

3.3.1.1 Probing Time

The duration of flower visits varied significantly among treatments, inflorescence types and flower types (Table 3.2). Much of this variation can be attributed to differences in nectar volume, as illustrated by largely corresponding patterns of the observed mean

durations and expectations based on a linear increase between the observed probe durations on flower types with the least and most nectar (Fig 3.4). However, the lack of complete correspondence between these expectations and the observed means indicates that differences in nectar volume were not the sole cause of variation in probe duration.

Indeed, if this was the only cause, probe duration would have been subject to a treatment x inflorescence type x flower type interaction, but this interaction did not have a statistically significant effect (Table 3.2). Instead, probe duration depended only on separate treatment x inflorescence type (Fig 3.4A) and treatment x flower type interactions (Fig. 3.4B). The most consistent deviation from expectations based on nectar volume involved longer than expected visits to low-quality flowers in the presence of within-inflorescence variation (Fig. 3.4B). In contrast, in the absence of such variation, bees spent longer than expected probing high-quality flowers.

Table 3.2 Results of generalized linear mixed models assessing the effects of variance conditions (Treat), inflorescence type

(Itype), flower type (Ftype) and covariates on temporal aspects of bee behavior on artificial inflorescences.

Inflorescence

Effect Probing time flight time Inter-flower flight time! Inter-flower flight time!

Treat F4,7615=9.38*** F4,859.2=0.79 F4,6390=3.40** F4,63222.39*

Itype F1,7593=326.4*** F1,861=2.65 F1,6379=3.56 F1,6297=11.40**

Treat x Itype F3,7587=89.88*** F4,858.6=1.04 F3,6372=3.09* F3,6290=8.96***

Ftype F1,7594=465.63*** F1,6376=22.15*** F1,6293=18.70***

Treat x Ftype F3,7588=18.63*** F3,6369=3.52* F3,6286=1.19

Type x Ftype F1,7598=0.13 F1,6378=1.36 F1,6296=0.0008

Treat x Itype x Ftype F3,7588=1.42 F3,6369=0.84 F3,6288=0.44

ln(Inspections+1) F1,6314=6612.11***

ln(visit number) F1,6390=30.50 F1,6320=75.77

* P < 0.05, ** P < 0.01, *** P < 0.001

3.3.1.2 Flight Time

On average, bees spent 2.57 s (mean; UCL: 2.64 s, LCL: 2.51) flying between inflorescences. Transit time did not vary with habitat-level variance treatment, inflorescence type or their interaction (Table 3.2), or the type of flower visited on the inflorescence immediately before the flight (P>0.15 for main effect and all interactions).

In contrast, the durations of flights between flowers varied significantly with two- factor interactions of variance treatment with both inflorescence type and the flower type that a bee had just visited (Table 3.2, Fig. 3.5). These interactions arose because inter- flower flight duration responded primarily to the dominant component of variance in nectar volume: flights lasted longer on high-quality inflorescences than on low-quality inflorescences when nectar varied primarily among inflorescences (Fig. 3.5A); whereas flights lasted longer after visits to high-quality flowers than to low-quality flowers when nectar varied primarily within inflorescences (Fig. 3.5B). This analysis also accounted for a general increase in inter-floral flight duration during inflorescence visits (partial regression coefficient ± SE for ln[visit number] = 0.048 ± 0.0086).

Floral inspection during a flight between visits greatly increased flight duration

(Fig. 3.6, Table 3.2; partial regression coefficient ± SE for ln[visit number] = 0.689 ±

0.0085). Inclusion of this effect in the analysis tended to weaken the pattern described above, except for the heightened difference between low- and high-quality inflorescences with equal within- and among-inflorescence variance (Fig 3.5A). In addition, the partial regression coefficient for ln(visit number) became negative (-0.054 ± 0.0062), indicating both: that the positive effect in the previous analysis arose primarily from the increasing

tendency of bees to inspect flowers with successive visits; and that after accounting for this effect bees flew faster between flowers with successive visits.

Figure 3.5 Relations of least-squares mean (± SE) duration of inter-floral flight by

15 B. impatiens workers to within- and among-inflorescence variation in nectar

volume per flower and inflorescence quality. Panels A and B depict relations among inflorescence and flower types, respectively.

Figure 3.6 Relation of the least-squares mean (± SE) duration of inter-floral flights by 15 B. impatiens workers to the number of flowers inspected during a flight.

Numbers indicate sample size. Results are illustrated for 99.5% of the flights: the remaining flights involved 4-6 inspections.

3.3.1.3 Floral Inspections

Bees typically inspected two or three flowers per inflorescence visit and generally inspected more flowers on high-quality inflorescences than on low-quality inflorescences

(Fig. 3.7A); however, this tendency differed among variance treatments (Table 3.3, treatment x inflorescence type interaction). Exceptions arose when nectar variation was distributed equally between within- and among-inflorescence components (F1,1020 = 0.46,

P>0.45), or when inflorescence types offered the same mean reward and nectar varied only within inflorescences (F1,861.1 = 0.23, P>0.6). Inspection frequency did not vary among variance treatments for visits to high-quality inflorescences (F4,831.3 = 0.79,

P>0.5), on which bees inspected an average of 3.16 (UCL: 3.40, LCL: 2.94) flowers.

During inflorescence visits, the occurrence of inspections varied with position in the visit sequence and interacting effects of variance treatment and flower type (Table

3.3). The incidence of inspections increased linearly with successive interactions with flowers (probes and inspections); however this effect was not significant (partial regression coefficients for ln[interactions] = 0.0909 ± 0.059; test of β = 1, t2831 = 1.55,

P>0.1). In addition, bees were more likely to inspect flowers after visiting a high-quality flower than a low-quality flower, but this effect was significant only when nectar varied primarily among flowers within inflorescences, rather than among inflorescences (Fig

3.7B).

Figure 3.7 Relations of least-squares mean (± SE) A) number of floral inspections at departure from inflorescences to within- and among-inflorescence variation in

nectar volume per flower and inflorescence quality, and B) incidence of inspection during inflorescence visits to nectar variance and flower quality.

3.3.1.4 Visits

The structure of variation in nectar volume per flower influenced the number of flowers that bees visited per inflorescence differently on high- and low-quality inflorescences

(Table 3.3, treatment x inflorescence type interaction; Fig. 3.8). This contrast resulted from effects of among-inflorescence variation in nectar volume, rather than of within- inflorescence variation. Specifically, bees visited equivalent numbers of flowers in the absence of such variation (F1,53 = 0.12, P>0.7), but with increasing among-inflorescence variation visit number diverged strongly and largely symmetrically. As a consequence, when nectar volume per flower varied only among inflorescences, bees visited 50% more flowers on high-quality inflorescences than on low-quality inflorescences. The number of flowers visited per inflorescence increased strongly with the number of floral inspections during an inflorescence visit (Table 3.3; Fig. 3.9); however, accounting for this effect did not alter the generally divergent influence of among-inflorescence nectar variation for low- and high-quality inflorescences (Fig. 3.8B).

panels A and B differ in that the latter account for the positive influence of the number of floral inspections during an inflorescence visit.

Figure 3.9 Influence of the number of floral inspections during an inflorescence visit on the least-squares mean (± SE) number of flower visits by 15 B. impatiens workers.

3.3.2 Foraging Currencies

3.3.2.1 Rate of Net Energy Intake

Overall, bees gained net energy at a rate of 1.73 ± 0.058 Js-1 during inflorescence visits, with relatively high (short-term) RNEI per inflorescence when 25% of the nectar variance occurred among inflorescences (Fig. 3.10A). Average RNEI at inflorescence departure

depended significantly on interacting effects of the partitioning of nectar variance and the type of inflorescence on which they were foraging (Fig. 3.10A), as well as on the type of flower that a bee visited immediately before departing (Table 3.4). When variation among inflorescences accounted for less than half of the total variation in the environment, realized RNEI did not differ among inflorescence types (P>0.3 in both cases). However, when resource variation among inflorescences dominated the partitioning of variation in the environment, bees realized almost 10% lower RNEI from low-quality inflorescences than from high-quality inflorescences (P<0.005 in all cases).

The RNEI that bees realized when they departed inflorescences after last visiting a high- quality flower (mean ± SE = 1.77 ± 0.060 Js-1) exceeded that when departing from a low- quality flower (1.71 ± 0.059 Js-1) by 3.5%.

In contrast to expectations of the marginal value theorem for long-term rate maximization, residual RNEI differed significantly among inflorescence types within a given variance treatment (P<0.01 in all cases), but the nature of this difference depended on the relative component of within-inflorescence nectar variation (Table 3.4, treatment x inflorescence type interaction; Fig. 3.10B). When nectar volume varied primarily among flowers within inflorescences, residual RNEI was highest on low-quality inflorescences, whereas the opposite was true with equal or greater among-inflorescence variation. As a result, residual RNEI equaled 0, as expected from long-term rate maximization, only when bees visited high-quality inflorescences and within-inflorescence variation accounted for >50% of total nectar variance (Fig. 3.10B). Not surprisingly, residual RNEI was lower when bees left inflorescences after visiting a low-quality flower, but this effect was stronger on low-quality inflorescences than on high-quality inflorescences (Table

3.4, inflorescence type x flower type interaction; Fig. 3.11).

line in B) indicates the expectation for long-term maximization based on the marginal value theorem.

Figure 3.11 Effects of inflorescence and the type of the last flower visited on an inflorescence on least-squares mean (± 95% CI) residual RNEI. The dashed line indicates the expectation for long-term maximization according to the marginal value theorem.

3.3.2.2 Foraging Efficiency

The (short-term) FE that bees realized per inflorescence depended on interacting effects of the partitioning of nectar variation and inflorescence type (Table 3.4) in a very similar pattern to that observed for realized RNEI (Fig 3.12). In general, bees foraged with equivalent efficiency when nectar varied mostly within inflorescences (P>0.5 in both cases), but when among-inflorescence variation accounted for at least half of the variation in the environment, bees realized higher FE on high- compared to low-quality inflorescences (P<0.001 in all cases). Unlike realized RNEI, realized FE was not significantly affected by the flower type from which a bee departed an inflorescence

(F1,1183 = 3.69, P>0.05), although this test was marginally non-significant.

Residual FE was subject to more complex influences than residual RNEI (Table

3.4), but again, the results are inconsistent with long-term maximization. In this case, the flower type from which a bee left an inflorescence affected interacting effects of variance treatment and inflorescence type (Table 3.4, treatment x inflorescence type x flower type interaction; Fig. 3.13). Residual FE generally increased from the expected value of 0 on high-quality inflorescences with an increasing component of among-inflorescence variation (Fig. 3.13A). In contrast, residual FE on low-quality inflorescences declined with increasing among-inflorescence nectar variation (Fig. 3.13B). In the absence of nectar variation among inflorescences, bees foraged in a manner that maximized long- term FE (i.e., residual = 0), except if they departed low-quality inflorescences from high- quality flowers. With increasing among-inflorescence variation, the difference between flower types generally increased on high-quality inflorescences, but decreased on low- quality inflorescences.

Figure 3.12 Relations of least-squares mean (± SE) foraging efficiency (FE) of 15 B. impatiens workers to within- and among-inflorescence variation in nectar volume and inflorescence quality.

3.4 Discussion

3.4.1 Behavioral Responses

The nature of nectar variation within the environment significantly influenced the behavioral responses of foraging bees. Inter-floral flight time, probing times and the number of flowers visited and inspected differed significantly between low- and high- quality inflorescences, indicating that bees both detected resource variation and modified their inflorescence exploitation in response.

Hierarchically-structured resource variation impacts the behavioral responses of foraging animals. Variation on multiple levels in a forager’s environment has been demonstrated (Real et al. 1982, Wilmshurst et al. 2000, Burns and Thomson 2005) to influence a forager’s estimation of patch quality, its patch-exploitation strategy, and how quickly it can process information that it has obtained from a patch. Many paradigms in foraging theory do not explicitly accommodate hierarchically structured resource variation, and empirical studies considering the influence of additional sources of resource variation are required to test patch departure rules rigorously in natural settings.

Moreover, observational studies need to account for all sources of resource variation at the patch and environment levels to prevent underestimation of resource variation, and thus an animal’s ability to understand and respond to the existing distribution of resources. Accounting for missing sources of variation may help explain deviations from existing models of animal behavior (Nonacs 2001) and foster the development of new models that place more reasonable expectations on foragers.

Visits to high-quality inflorescences generally resulted in longer inter-floral flights than visits to low-quality inflorescences, especially when quality differences were evident because of limited within-inflorescence nectar variation. This response arose largely because of an increased incidence of floral inspection on high-quality inflorescences. The energetic cost of this increased inspection was offset by a minimum

5-fold difference in nectar volume in flowers on high-quality inflorescences relative to the poorest quality flowers in the habitat. On low-quality inflorescences, flight duration was shorter, with fewer inspections, suggesting that encountering poor patches caused bees to make subsequent visits hastily within the patch to quickly assess patch-quality.

Correspondingly, bees visited fewer flowers on low-quality inflorescences and so generally experienced lower RNEI and FE at departure.

Bees also responded to variation in nectar volume among flowers within inflorescences by probing low-quality flowers longer than expected based on a linear relation between probe duration and nectar volume. This suggests that bees may have remained on poor-quality flowers either to ensure that a flower had been depleted; or while planning their next move, either within the present inflorescence or to another inflorescence. Additionally, bees made more floral inspections and longer flights after visiting high-quality flowers when there was extensive within-inflorescence variation.

This suggests that bees relinquished speed for accuracy in an attempt to locate remaining high-quality flowers. Realized RNEI and FE did not differ among inflorescence types when treatments comprised >75% of variation within-inflorescences; whereas with increasing among-inflorescence variation, realized RNEI and FE differed significantly among inflorescence types. When variation within-inflorescences was sufficiently high

relative to variation among inflorescences, differences in mean nectar available among inflorescence types were small, so failing to modify visit duration in response to inflorescence type had little effect on realized currency. In contrast, when among- inflorescence variation became more prevalent, so did differences in visit duration among inflorescence types, resulting in bees realizing higher currency on departure from high- rather than low-quality inflorescences.

3.4.2 Currency Maximization

Bees in this experiment did not forage in manners that maximized their long-term RNEI or FE, as indicated by the non-zero and divergent mean residuals with increasing among- inflorescence variation (Fig. 3.9B, 3.12). On high-quality inflorescences, bees realized higher RNEI or FE than expected, whereas the converse was true on low-quality inflorescences. This difference is more consistent with maximization of these currencies on a short-term, per inflorescence, basis (see Fig. 3.1). As was predicted by short-term currency maximization, bees consistently left high-quality inflorescences before resource depletion decreased their realized currencies to levels realized on average (long-term) in the environment. Conversely, on low-quality inflorescences, bees consistently stayed after resource depletion had depressed their realized currencies to the average for the environment. Similar responses have been observed in other tests of the MVT with other animals (Mellgren 1982, Ydenberg 1984, Lima 1985, Alonso et al. 1995), and so may occur commonly. Such responses may represent an inability of bees to formulate long- term expectations because of memory limitations (Real et al. 1990), or because overstaying is inevitable, as a foraging currency can be maximized only after it has fallen

below the level realized on average in the environment (Nonacs 2001). Alternatively, as I argue below, short-term maximization may be the best policy in variable environments when animals confront speed-accuracy trade-offs.

The MVT was derived explicitly for foragers in a heterogeneous environment composed of homogeneous patch types, each with characteristic gain functions (Charnov

1976). Although the MVT has been generalized to allow stochastic within-patch variation

(Charnov 1973), deterministic approximations of stochastic processes, such as patch exploitation, provide poor descriptors of optimal behavior (Oaten 1977, Green 1980). In this experiment, behavioral responses were consistent with long-term currency maximization when most of the variation in nectar volume occurred within inflorescences. However, in the absence of among-patch variation, short- and long-term maximization lead to identical optimal departure decisions, so this result is also consistent with short-term maximization. Incorporating within-patch variation may be a missing component of the MVT; diminishing returns may arise from variation within inflorescences due to the stochastic nature of the sequence of rewards incurred while foraging on an inflorescence. Specifically, encountering a poor-quality resource in a sequence of visits may signal depletion, motivating departure for currency maximizing bumble bees (Kadmon et al. 1991, Kadmon 1992, Kadmon and Shmida 1992). A field study of optimal foraging in bumble bees that qualitatively considered within- inflorescence variation found support for the MVT (Best and Bierzychudek 1982); however, nectar was measured concurrently with pollinator observations, potentially depleting the nectar available to foragers. Additionally, Best and Bierzychudek did not control for random variation among sampled plants, potentially biasing estimates of the

distribution of nectar rewards. Given the range of variance conditions in plant populations (Chapter 2), and the extent to which they vary during a season, the amount of total variation arising from variation within inflorescences in a plant population likely varies temporally. Foragers exhibit uncertainty while foraging in patches by adjusting visit duration, residing in a patch for a duration disproportionate with the quality of a given patch. When resource variance arises primarily within patches, foragers do not remain within a patch long enough to incur increased search costs or to experience resource depletion; thus these diminishing returns, required by currency maximizing foragers to motivate patch departures, provide less of an incentive to leave than a forager’s uncertainty of patch quality.

Among the foraging currencies that I investigated, the behavioral responses of bees were no more consistent with short-term maximization of RNEI than of FE. Many studies have found support for RNEI maximization in the behavioral responses of bees to their foraging environments (Pyke 1979, 1980, Hodges 1981, Best and Bierzychudek

1982). However, reanalysis of those studies found that FE maximization was consistent with both the observed responses of bees, and predicted departure based on RNEI maximization (Charlton and Houston 2010). Moreover, studies of honey bees (Schmid-

Hempel et al. 1985, Houston et al. 1988, Schmid-Hempel and Wolf 1988), squirrels

(Lima et al. 1985) and chickadees (Lima 1985) suggest behavioral responses consistent with FE maximization.

Previous studies of currency maximization in foragers (Pyke 1978a, Cibula and

Zimmerman 1984, Pleasants 1989, Kamil et al. 1993) have focused on the spatial separation of patches and its influence on patch residence time. However, if currency-

maximizing foragers make departures based on the depletion they impose on resource patches as they forage (Best and Bierzychudek 1982, Hodges 1985b, Ollason 1987,

Kadmon and Shmida 1992), emphasis should be placed on the distribution of the quality of resources within patches in the environment, rather than on distance travelled to the next patch, as the structure of resource variance will cause uncertainty in an animal’s estimation of diminishing returns. In this experiment, the behavioral responses of bumble bees did not consistently fall within expectations of the marginal value theorem. As treatments exhibited more variation among patches and less within patches, behavior responded by diverging increasingly from predictions made by long-term currency maximization. Instead, bees likely employ a heuristic departure rule combining their instantaneous response to resources with some aggregate measure of their foraging experiences in the recent past (Hodges 1985a, 1985b).

3.4.3 Speed-accuracy Tradeoffs

The suite of observed responses to among-inflorescence variation is consistent with a speed-accuracy trade-off (SAT) in the exploitation of many-flowered inflorescences (see

Chittka et al. 2009). The complexity of tasks in relation to an animal’s cognitive ability compels it to favor either accuracy or speed in task solution (Burns et al. 2011,

McNamara and Fawcett 2012, Cole et al. 2012). Simple tasks can be solved both quickly and accurately, whereas for difficult tasks, accuracy can be improved at a cost to speed, or vice-versa (Chittka et al. 2009, Latty and Beekman 2011). Given the three- dimensional structure of the inflorescences, variation in nectar content among flowers, and the high rate of energetic expenditure associated with flight in bumble bees, finding

and exploiting rewarding flowers in a hierarchically structured habitat is probably difficult enough to impose a SAT (Fauchald 1999).

In this experiment, SATs were manifest in the response of visit and inter-flower flight durations to environment-wide nectar variance. The observed resolution of the SAT bees experience is consistent with the expectation that bees forage to maximize net foraging gains on inflorescences. On high-quality inflorescences, bees apparently spent more time acquiring information regarding patch quality by making more floral inspections while searching for other high-quality flowers prior to departing from flowers and in transit to other flowers on the inflorescence. These responses suggest that encountering high-quality resources caused bees to favor accuracy over speed.

Conversely, encountering low-quality resources or patches caused bees to favor speed over accuracy, hastening the next encounter with a high-quality patch, where previous lost foraging opportunities could be rectified.

Experiments investigating SATs in realistic settings for foraging animals are rare.

Often these experiments provide either a binary food distribution, with food present or absent (Real et al. 1982, Dukas and Real 1993, Burns and Thomson 2005), or a penalty either in the presence or absence of a reward (Ings and Chittka 2008). In contrast, resource quality usually varies continuously on several scales (Wu and Loucks 1995,

Fauchald 1999), so experiments that ignore this pattern risk over-estimating the extent to which animals respond to neutral or negative signals by making poor choices under experimental conditions. Although my experiment did not reflect the continuous gradient of resource variation that bees generally experience, it did allow insight into context-

dependent decision making based on an option (nectar) varying in a single dimension

(volume; also see Morgan et al. 2012).

Short-term currency maximization probably accompanies profitable resolution of the SATs that have been observed in bees (Chittka et al. 2003, 2009), and are evident in the results of this experiment (§3.4.1). This association is especially relevant when within-patch variance generates uncertainty in patch quality, as there is little incentive to modify behavior as patches offer similar rewards on average (Real 1981, Harder and Real

1987, McLinn and Stephens 2006). However, as among-patch variance became dominant in the environment, short-term maximization resulted in higher realized foraging currencies on high-quality patches compared with low-quality patches. This is consistent with animals maximizing a foraging currency in the short-term. When food availability varies only among patches, long-term currency maximizers will be slow to adapt patch exploitation to variation at this scale, as their departure criterion is based on past foraging experience in the environment (Templeton and Lawlor 1981, however see: McNamara et al. 2013). In contrast, SATs allow foragers to respond to variation among patches by scaling time spent foraging in a patch with the relative magnitude of rewards offered by the patch, thereby maximizing foraging returns during individual patch visits (Harder and

Real 1987, Real et al. 1990, Stephens and Dunlap 2009, Saavedra et al. 2013). When habitats exhibit variation within and among patches, long-term maximizers struggle to identify relative patch quality. The speed-accuracy trade-off resulting from high within- patch variance resulted in bees not staying long enough to assess patch-quality accurately, ultimately exploiting patches quickly, regardless of their quality. When habitats possess structured variation, speed-accuracy shifts allow animals to maximize

short-term returns; however, the extent to which this is realized may depend on how well animals can discriminate the variation among resources.

In patchy environments with hierarchically structured variation, the accuracy with which high-quality resources are found and exploited is confounded by both the noise of less-rewarding resource patches in the environment and aggregations of poor-quality resources within rewarding patches (Real et al. 1982, Dukas and Real 1993). SATs arise in two ways in such environments. First, variation within resource patches means foragers need to use information about resources obtained from foraging in a patch to assess patch quality (Dreisig 2011). In this case, rapidly reaching a decision about patch quality can cause foragers to discount high-quality resource patches; the ability to quickly and accurately assess patch quality should vary negatively with variance within resource patches. Accurately determining patch quality requires a forager to overstay in a poor- quality patch and miss out on, or delay, better foraging opportunities elsewhere. Second, foragers must evaluate the distribution of resources remaining in the present patch relative to the distributions of resources in other patches (Charnov 1976, Cibula and

Zimmerman 1984, Kadmon and Shmida 1992). The trade-off in this case is likely less severe, as assessing the distribution of remaining rewards in a patch is a component of assessing patch quality; once patch quality is determined, a forager must determine how much longer to stay. In high-quality patches, foragers pay no penalty for slowly concluding that they are in a high-quality patch, as visit duration is proportional to patch quality. However, in low-quality patches, slow assessment of patch-quality is penalized by lost foraging opportunities elsewhere; animals that fastidiously assess patch quality overstay.

3.5 Appendix – Determination of treatment conditions

To determine the number of high and low-quality flowers per inflorescence and the nectar volume for each flower type, I solved two systems of equations. First, the mean nectar volumes for the high and low-quality inflorescences, !! and !!, respectively were found as the solutions of:

!!"#!! + 1 − !!"# !! = !!"#$%&

! ! ! ! !!"#!! + 1 − !!"# !! − !!"#$%& = !!"# ,

! where pinf (=0.5) is the proportion of high-quality inflorescences, and !!"# is the among- inflorescence variance in nectar volume. An appropriate solution required that !! and

!! > 0. Second, the nectar volumes for the low- and high-quality flowers (!! and !!, respectively) on high-quality inflorescences with mean volume sH was given by the solution of the following system:

!!" !!! !! + 1 − !! = !! !!" !!"

!!" ! !!" ! ! ! ! !! + 1 − !! − !! = 1 − !!"# = !!" , !!" !!"

where: !!" is the number of high-quality flowers, and !!"!is the total number of flowers.

pfH and nfl were varied until non-negative values of !! and !! that could be used for the corresponding treatment were obtained. The same approach was used to determine the nectar volumes for high- and low-quality flowers of low-quality inflorescences by substituting !! for !!.

Chapter Four: Consequences and evolutionary significance of structured resource variation

4.1 Structured Variation and Foraging

This thesis considered how variation in floral nectar is structured in plant populations and its consequences for the behavioral responses of foraging pollinators. The survey of several many-flowered plants (Chapter 2) revealed considerable variation in the extent to which the total variation in nectar standing crop (NSC) is partitioned into within- and among-plant variation in a population. Moreover, bumble bee responses to this hierarchically structured variation in NSC suggest that speed-accuracy trade-offs help bees to maximize their short-term foraging returns (Chapter 3). It is unclear whether short-term currency maximization motivates patch departure in other animals, and subsequent tests of the Marginal Value Theorem should address this possibility as there is plenty of inconsistency in support of the model (Nonacs 2001).

Continuous-time Markov chain models may enable identification of heuristic departure rules appropriate to foraging in environments with structured resource variation. Continuous-time Markov chains are stochastic processes that alternate between various states (Ross 2010). Transitions among states are memory-less, meaning that the probability of moving from a current state to some other state is independent of any states that were inhabited in the past. Specifically, continuous-time Markov chains inhabit states for an exponential period, governed by a rate parameter specific to that state (Ross

2010). Transitions among states can thus be determined from the rates governing the time spent by a forager in each state. Although continuous-time Markov chains have not been

employed in the context of patch foraging, their discrete-time analogs have been successfully employed to explain social behaviors in primates (Janson 1990) and patch searching algorithms (Prasad and Borges 2006). Continuous-time Markov chains would allow accurate modeling of how behavioral responses change with time and a forager’s experience, without imposing the assumption that foragers track either of these quantities.

Finding and extracting food from rewarding flowers in a structured habitat confronts pollinators with speed-accuracy trade-offs (SAT; Biernaskie and Gegear 2007,

Muller and Chittka 2008, Biernaskie et al. 2009, Ohashi and Thomson 2012). SATs enable pollinators to increase information intake from the environment, while simultaneously allowing them to maximize their foraging returns. Behavioral responses of bees subject to SATs in the short-term may be consistent with following a heuristic patch-departure rule. Nevertheless, the range of accuracy to speed in the foraging responses of pollinators allows them to respond favorably to variation in NSC among- plants in a population. Pollinators likely exploit less-rewarding plants quicker than more- rewarding plants, transferring pollen between the two relative types; whereas precise exploitation of rewarding plants may increase geitonogamous pollen transfer as the visit persists (Harder and Wilson 1998a, Ohashi and Thomson 2009).

Speed-accuracy trade-offs commonly arise when animals lack the requisite perceptual cognitive and mechanical capacity to perform complex tasks. When the distribution of resources in a habitat exhibits structured variation within and among heterogeneous resource patches, foraging animals confronted by SATs may use their short-term foraging experiences as a heuristic patch-departure rule. Nectar resources in plant populations vary in the structure of variance within- and among-plants, sometimes

over flowering seasons. Bumble bees readily trade-off between speed and accuracy when this occurs. A plant’s reproductive success benefits when trade-offs arise in the speed and accuracy with which bees forage. SATs will result in increased geitonogamous pollen transfer when variation arises primarily among inflorescences (de Jong et al. 1993,

Biernaskie and Elle 2006); however, pollen export will be enhanced among inflorescences varying in mean NSC (Biernaskie and Elle 2006, Fisogni et al. 2011). For bees, SATs likely impose heuristic departure rules enabling them to maximize their own foraging gains in the short-term, and the fitness of the colony in the long-term.

4.2 Towards an Optimal Stalemate

Bees are somewhat atypical foragers, because their feeding typically benefits the plants from which they extract food, rather than being detrimental, as is the case with herbivory and predation. Therefore, the foraging characteristics of pollinators has likely influenced the reproductive characteristics of the plants they pollinate (Heinrich and Raven 1972,

Harder et al. 2004). Pollinators benefit from maximizing some measure of food consumption, primarily involving floral nectar and pollen, from their foraging among flowers (Pyke 1978b, Pyke and Waser 1981). In contrast, plants benefit from maximizing pollen export to and import from conspecifics, often while minimizing self-pollen transfer to their own flowers (de Jong et al. 1993, Harder and Barrett 1996). To the extent that these objectives are incompatible, plants and their pollinators are likely engaged in a coevolutionary arms race (de Jong and Klinkhamer 2005).

Optimal pollinator foraging may often not maximize the reproductive success of plants, promoting plant mechanisms that manipulate pollinator behavior. Longer visits to

individual flowers and entire plants by individual pollinators generally reduce total pollen transfer among plants if many pollinators are available, because of increased pollen loss and among-flower self-pollination (geitonogamy) (Harder and Barrett 1996, Harder and

Wilson 1998b). In addition, increased geitonogamy when individual pollinators visit multiple flowers can reduce seed production or performance in self-compatible plants owing to inbreeding depression (Harder and Wilson 1998b, Yang and Hodges 2010).

Given these effects, plants realize enhanced reproductive success only at some cost to the foraging returns of pollinators. For example, large floral displays increase visitation

(Ohashi and Yahara 2001, Makino and Sakai 2007), but inclusion of nectarless flowers can reduce the number of flowers visited per pollinator and their intake rate (Tindall

2006, Makino and Sakai 2007), leading to increased pollen export (Pyke 1978b, de Jong et al. 1993, Fisogni et al. 2011). Plants influence the duration of pollinator visits via the rate of nectar production (Best and Bierzychudek 1982, Kadmon et al. 1991, Boose

1997), including the production of empty flowers (Tindall 2006, Ishii et al. 2008).

However, the extent to which individual plants intrinsically determine the distribution of

NSC among their own flowers, or amongst other individuals in a population varies depending on pollinator abundance, as much of the variation in NSC arises from pollinator visitation history when flowers are visited frequently (Thomson 1982,

Castellanos et al. 2002), rather from gene by environment interactions of individuals

(Boose 1997, Leiss et al. 2004, Leiss and Klinkhamer 2005). Thus, plants and pollinators jointly contribute to the partitioning of total variation in NSC within- and among-plants in context-dependent manners.

The impact of NSC distributions on the evolution of pollinator characteristics, including their behavior, probably depends on the pollinator. For pollinators that are reproductively capable, such as solitary bees, flies, and birds, NSC and their related foraging decisions may significantly influence reproductive success and the evolution of their foraging. In contrast, for social bees, fitness resides in the queen and her mate(s), rather than in the non-reproductive workers. Therefore individual workers experiencing poor foraging returns on a particular plant species may have little impact on the reproductive success of the colony if other individuals forage productively on other species (Houston et al. 1988). The extent to which the fitness of plants or their pollinators is maximized in the long-term, will depend on how each creates and exploits the variation in NSC imposed by the other.

Plants likely have greater influence on the partitioning of variation in NSC than their pollinators for several reasons. First, pollinators tend to exhibit constancy to a particular plant species (Grant 1950, Goulson 1999, Gegear and Laverty 2005), because the behavioral requirements associated with different inflorescence architectures and floral morphologies increase energetic costs for pollinators that attempt to handle a variety of floral species (Gegear and Thomson 2004, Gegear and Laverty 2005).

Constancy arises as pollinators learn to associate the flowers of a particular plant species with nectar rewards (Grant 1950, Laverty 1994). As bees learn to exploit new flowers, they may reside too long on plants, which may lead to pollen discounting (Harder and

Wilson 1998b) or geitonogamous pollen transfer (Klinkhamer and de Jong 1993, de Jong et al. 1993), as they will not know when to anticipate diminishing returns in nectar from new species (Woodward and Laverty 1992, Laverty 1994). Over a plant’s flowering

period, variable nectar production may be adaptive; providing large nectar rewards, enabling plants to condition new pollinators to forage upon their flowers (Woodward and

Laverty 1992, Laverty 1994), while simultaneously imposing diminishing foraging returns, preventing extended visits (Tindall 2006, Dreisig 2011). Further, given that pollinator lifespans and plant flowering periods do not necessarily overlap (Thomson

1982, de Jong and Klinkhamer 1991), variable nectar production could ensure a stable population of experienced pollinators by providing ideal learning conditions for training new pollinators.

References

Alonso, J. C., J. A. Alonso, L. M. Bautista, and R. Muñoz-Pulido. 1995. Patch use in cranes: A field test of optimal foraging predictions. Animal Behaviour 49:1367– 1379.

Amiot, V., and L. D. Harder. 2009. Memory and energetics!: are bumble bees memory- limited foragers? University of Calgary.

Bateson, M., S. D. Healy, and T. A. Hurly. 2003. Context-dependent foraging decisions in rufous hummingbirds. Proceedings of the Royal Society of Biological Sciences 270:1271–1276.

Bateson, M., and A. Kacelnik. 1996. Rate currencies and the foraging starling: The fallacy of the averages revisited. Behavioral Ecology 7:341–352.

Bauer, P. J. 1983. Bumblebee pollination relationships on the Beartooth Plateau Tundra of Southern Montana. American Journal of Botany 70:134–144.

Bautista, L. M., J. Tinbergen, P. Wiersma, and A. Kacelnik. 1998. Optimal foraging and beyond: How starlings cope with changes in food availability. American Naturalist 152:543–61.

Best, L. S., and P. Bierzychudek. 1982. Pollinator foraging on foxglove (Digitalis purpurea): A test of a new model. Evolution 36:70–79.

Biernaskie, J. M., R. V. Cartar, and T. A. Hurly. 2002. Risk-averse inflorescence departure in hummingbirds and bumble bees: Could plants benefit from variable nectar volumes? Oikos 98:98–104.

Biernaskie, J. M., and R. V. Cartar. 2004. Variation in rate of nectar production depends on floral display size: A pollinator manipulation hypothesis. Functional Ecology 18:125 –129.

Biernaskie, J. M., and E. Elle. 2006. A theory for exaggerated secondary sexual traits in animal-pollinated plants. Evolutionary Ecology 21:459–472.

Biernaskie, J. M., and R. J. Gegear. 2007. Habitat assessment ability of bumble-bees implies frequency-dependent selection on floral rewards and display size. Proceedings of the Royal Society of Biological Sciences 274:2595–601.

Biernaskie, J. M., S. C. Walker, and R. J. Gegear. 2009. Bumblebees learn to forage like Bayesians. American Naturalist 174:413–23.

Boose, D. 1997. Sources of variation in floral nectar production rate in Epilobium canum (Onagraceae): implications for natural selection. Oecologia 110:493–500.

Bormann, F., and G. Likens. 1979. Catastrophic disturbance and the steady state in northern hardwood forests: A new look at the role of disturbance in the development of forest ecosystems suggests important implications for land-use policies. American Scientist 69:660–669.

Brown, M. F., J. a. Moore, C. H. Brown, and K. D. Langheld. 1997. The existence and extent of spatial working memory ability in honeybees. Animal Learning & Behavior 25:473–484.

Burns, J. G., J. Foucaud, and F. Mery. 2011. Costs of memory: lessons from “mini” brains. Proceedings of the Royal Society of Biological Sciences 278:923–929.

Burns, J. G., and J. Thomson. 2005. A test of spatial memory and movement patterns of bumblebees at multiple spatial and temporal scales. Behavioral Ecology 17:48–55.

Carlson, J., and K. Harms. 2006. The evolution of gender-biased nectar production in hermaphroditic plants. Botanical Review 72:179–205.

Carroll, A., S. Pallardy, and C. Galen. 2001. Drought stress, plant water status and floral trait expression in fireweed, Epilobium angustifolium (Onagraceae). American Journal of Botany 88:438–446.

Cartar, R. V. 1991. A test of risk-sensitive foraging in wild bumble bees. Ecology 72:888–895.

Cartar, R. V. 2004. Resource tracking by bumble bees: Responses to plant-level differences in quality. Ecology 85:2764–2771.

Cartar, R. V. 2009. Resource-tracking by bumble bees: What explains local responses to density of Bergamot (Monarda fistulosa) flowers? Ecoscience 16:470–475.

Castellanos, M. C., P. Wilson, and J. D. Thomson. 2002. Dynamic nectar replenishment in flowers of Penstemon (Scrophulariaceae). American Journal of Botany 89:111– 118.

Charlton, N. L., and A. I. Houston. 2010. What currency do bumble bees maximize? PloS one 5:e12186.

Charnov, E. L. 1973. Optimal foraging: Some theoretical explorations.

Charnov, E. L. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology 136:129–136.

Charnov, E. L., and J. R. Krebs. 1974. On clutch-size and fitness. Ibis 116:217–219.

Charnov, E. L., G. H. Orians, and K. Hyatt. 1976. Ecological implications of resource depression. American Naturalist 110:247–259.

Chittka, L., A. G. Dyer, F. Bock, and A. Dornhaus. 2003. Bees trade off foraging speed for accuracy. Nature 424:388.

Chittka, L., A. Gumbert, and J. Kunze. 1997. Foraging dynamics of bumble bees: Correlates of movements within and between plant species. Behavioral Ecology 8:239–249.

Chittka, L., P. Skorupski, and N. E. Raine. 2009. Speed-accuracy tradeoffs in animal decision making. Trends in Ecology & Evolution 24:400–407.

Cibula, D. A., and M. Zimmerman. 1984. The effect of plant density on departure decisions: Testing the marginal value theorem using bumblebees and Delphinium nelsonii. Oikos 43:154–158.

Cole, E. F., J. Morand-Ferron, A. E. Hinks, and J. L. Quinn. 2012. Cognitive ability influences reproductive life history variation in the wild. Current Biology 22:1808– 1812.

Corbet, S. A. 2003. Nectar sugar content: estimating standing crop and secretion rate in the field. Apidologie 34:1–10.

Corbet, S. A., I. Cuthill, M. Fallows, T. Harrison, and G. Hartley. 1981. Why do nectar- foraging bees and wasps tend to work upwards on inflorescences? Oecologia 51:79– 83.

Corbet, S., D. Unwin, and O. Prys-Jones. 1979. Humidity, nectar and insect visits to flowers, with special reference to Crataegus, Tilia and Echium. Ecological Entomology 4:9–22.

Cresswell, J. E. 1990. How and why do nectar-foraging bumblebees initiate movements between inflorescences of wild bergamot Monarda fistulosa (Lamiaceae)? Oecologia 82:450–460.

Cresswell, J. E., J. L. Osborne, and D. Goulson. 2000. An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees. Ecological Entomology 25:249–255.

Croy, M., and R. Hughes. 1991. Effects of food supply, hunger, danger and competition on choice of foraging location by the fifteen-spined stickleback, Spinachia spinachia L. Animal Behaviour 42:131–139.

Cruden, R. W., S. M. Hermann, and S. Peterson. 1983. Patterns of nectar production and plant-pollinator coevolution. Pages 81–125 in B. Bentley and T. S. Elias, editors. The Biology of Nectaries. Columbia University Press, New York.

Dall, S. R. X., L.-A. Giraldeau, O. Olsson, J. M. McNamara, and D. W. Stephens. 2005. Information and its use by animals in evolutionary ecology. Trends in Ecology & Evolution 20:187–193.

Denny, A. J., J. Wright, and B. Grief. 2001. Foraging efficiency in the wood ant, Formica rufa: Is time of the essence in trail following? Animal Behaviour 62:139–146.

Devlin, B., and A. Stephenson. 1985. Sex differential floral longevity, nectar secretion, and pollinator foraging in a protandrous species. American Journal of Botany 72:303–310.

Dreisig, H. 1995. Ideal free distributions of nectar foraging bumblebees. Oikos 72:161– 172.

Dreisig, H. 2011. How long to stay on a plant: the response of bumblebees to encountered nectar levels. Arthropod-Plant Interactions 6:315–325.

Dukas, R., and L. Real. 1993. Effects of recent experience on foraging decisions by bumble bees. Oecologia 94:244–246.

Emlen, J. 1966. The role of time and energy in food preference. American Naturalist 100:611–617.

Fauchald, P. 1999. Foraging in a hierarchical patch system. American Naturalist 153:603–613.

Fisogni, A., G. Cristofolini, M. Rossi, and M. Galloni. 2011. Pollinator directionality as a response to nectar gradient: promoting outcrossing while avoiding geitonogamy. Plant Biology 13:848–856.

Galen, C., and R. Plowright. 1985. The effects of nectar level and flower development on pollen carry-over in inflorescences of fireweed (Epilobium angustifolium)(Onagraceae). Canadian Journal of Botany 63:488–491.

Gegear, R. J., and J. D. Thomson. 2004. Does the flower constancy of bumble bees reflect foraging economics? Ethology 110:793–805.

Gegear, R., and T. Laverty. 2005. Flower constancy in bumblebees: A test of the trait variability hypothesis. Animal Behaviour 69:939–949.

Gibson, K., C. Hall, and D. Kramer. 2006. Time-concentrated sampling: A simple strategy for information gain at a novel, depleted patch. Canadian Journal of Zoology 84:1513–1521.

Gilliam, J. F., R. F. Green, and N. E. Pearson. 1982. The fallacy of the traffic policeman: A response to Templeton and Lawlor. American Naturalist 119:875–878.

Giraldeau, L.-A., and D. L. Kramer. 1982. The marginal value theorem: A quantitative test using load size variation in a central place forager, the Eastern chipmunk, Tamias striatus. Animal Behaviour 30:1036–1042.

Giurfa, M., and J. Núñez. 1992. Honeybees mark with scent and reject recently visited flowers. Oecologia 89:113–117.

Goulson, D. 1999. Foraging strategies of insects for gathering nectar and pollen, and implications for plant ecology and evolution. Perspectives in Plant Ecology, Evolution and Systematics 2:185–209.

Goulson, D., and J. Stout. 2000. Identity and function of scent marks deposited by foraging bumblebees. Journal of Chemical Ecology 26:2897–2911.

Grant, V. 1950. The flower constancy of bees. The Botanical Review 16:379–398.

Green, R. F. 1980. Bayesian birds: A simple example of Oaten’s stochastic model of optimal foraging. Theoretical Population Biology 18:244–256.

Harder, L. D. 1983. Flower handling efficiency of bumble bees: morphological aspects of probing time. Oecologia 57:274–280.

Harder, L. D., and S. C. H. Barrett. 1996. Pollen dispersal and mating patterns in animal- pollinated plants. Floral biology: studies on floral evolution in animal-pollinated plants 140:190.

Harder, L. D., C. Y. Jordan, W. E. Gross, and M. B. Routley. 2004. Beyond floricentrism: The pollination function of inflorescences. Plant Species Biology 19:137–148.

Harder, L. D., and L. A. Real. 1987. Why are bumble bees risk averse? Ecology 68:1104–1108.

Harder, L. D., and W. G. Wilson. 1998a. Theoretical consequences of heterogeneous transport conditions for pollen dispersal by animals. Ecology 79:2789–2807.

Harder, L. D., and W. G. Wilson. 1998b. A clarification of pollen discounting and its joint effects with inbreeding depression on mating system evolution. The American Naturalist 152:684–695.

Heinrich, B. 1975. Thermoregulation in bumblebees II. Energetics of warm-up and free flight. Journal of Comparative Physiology 96:155–166.

Heinrich, B. 1979a. Bumblebee Economics. Page 245. Harvard University Press, Cambridge.

Heinrich, B. 1979b. Resource heterogeneity and patterns of movement in foraging bumblebees. Oecologia 245:235–245.

Heinrich, B., and P. H. Raven. 1972. Energetics and pollination ecology: The energetics of pollinators may have wide implications in floral biology and community ecology. Science 176:597–602.

Henry, M., and K. E. Stoner. 2011. Relationship between spatial working memory performance and diet specialization in two sympatric nectar bats. PloS one 6:e23773.

Hirao, A. S., and G. Kudo. 2004. Landscape genetics of alpine-snowbed plants: Comparisons along geographic and snowmelt gradients. Heredity 93:290–298.

Hodges, C. M. 1981. Optimal foraging in bumblebees: Hunting by expectation. Animal Behaviour 29:1166–1171.

Hodges, C. M. 1985a. Bumble bee foraging: The threshold departure rule. Ecology 66:179–187.

Hodges, C. M. 1985b. Bumble bee foraging: Energetic consequences of using a threshold departure rule. Ecology 66:188–197.

Hodges, C. M., and L. L. Wolf. 1981. Optimal foraging in bumblebees: Why is nectar left behind in flowers? Behavioral Ecology and Sociobiology 9:41–44.

Hodges, S. 1993. Consistent interplant variation in nectar characteristics of Mirabilis multiflora. Ecology 74:542–548.

Houston, A. I. 1995. Energetic constraints and foraging efficiency. Behavioral Ecology 6:393–396.

Houston, A. I. 1997. Natural selection and context-dependent values. Proceedings of the Royal Society of Biological Sciences 264:1539–1541.

Houston, A., P. Schmid-Hempel, and A. Kacelnik. 1988. Foraging strategy, worker mortality, and the growth of the colony in social insects. American Naturalist 131:107–114.

Ings, T. C., and L. Chittka. 2008. Speed-accuracy tradeoffs and false alarms in bee responses to cryptic predators. Current Biology 18:1520–4.

Ishii, H. S., and L. D. Harder. 2006. The size of individual Delphinium flowers and the opportunity for geitonogamous pollination. Functional Ecology 20:1115–1123.

Ishii, H. S., Y. Hirabayashi, and G. Kudo. 2008. Combined effects of inflorescence architecture, display size, plant density and empty flowers on bumble bee behaviour: Experimental study with artificial inflorescences. Oecologia 156:341–350.

Janson, C. 1990. Social correlates of individual spatial choice in foraging groups of brown capuchin monkeys, Cebus apella. Animal Behaviour 40:910–921.

De Jong, T. J., and P. G. L. Klinkhamer. 1991. Early flowering in Cynoglossum officinale L. constraint or adaptation? Functional Ecology 5:750–756.

De Jong, T. J., and P. G. L. Klinkhamer. 2005. Evolutionary Ecology of Plant Reproductive Strategies. Page 335. Harvard University Press, Cambridge.

De Jong, T. J., N. M. Waser, and P. G. L. Klinkhamer. 1993. Geitonogamy: The neglected side of selfing. Trends in Ecology & Evolution 8:321–325.

Kadmon, R. 1992. Dynamics of forager arrivals and nectar renewal in flowers of Anchusa strigosa. Oecologia 92:552–555.

Kadmon, R., and A. Shmida. 1992. Departure rules used by bees foraging for nectar: A field test. Evolutionary Ecology:142–151.

Kadmon, R., A. Shmida, and R. Selten. 1991. Within-Plant foraging behavior of bees and its relationship to nectar distribution in Anchusa strigosa. Israeli Journal of Botany 40:283–294.

Kamil, A. C., R. L. Misthal, and D. W. Stephens. 1993. Failure of simple optimal foraging models to predict residence time when patch quality is uncertain. Behavioral Ecology 4:350–363.

Kenward, M., and J. Riger. 1997. Small sample inference for fixed effects from restricted maxiumum likelihood. Biometrics 53:983–997.

Klinkhamer, P. G. L., and T. J. de Jong. 1993. Attractiveness to pollinators: A plant’s dilemma. Oikos 66:180–184.

Kotliar, N., and J. Wiens. 1990. Multiple scales of patchiness and patch structure: A hierarchical framework for the study of heterogeneity. Oikos 59:253–260.

Krebs, J. R., J. C. Ryan, and E. L. Charnov. 1974. Hunting by expectation or optimal foraging? A study of patch use by chickadees. Animal Behaviour 22:953–964.

Latty, T., and M. Beekman. 2011. Speed-accuracy trade-offs during foraging decisions in the acellular slime mould Physarum polycephalum. Proceedings of the Royal Society of Biological Sciences 278:539–545.

Laverty, T. 1994. Bumble bee learning and flower morphology. Animal Behaviour 47:531–545.

Leiss, K. A., and P. G. L. Klinkhamer. 2005. Genotype by environment interactions in the nectar production of Echium vulgare. Functional Ecology 19:454–459.

Leiss, K. A., K. Vrieling, and P. G. L. Klinkhamer. 2004. Heritability of nectar production in Echium vulgare. Heredity 92:446–451.

Lima, S. L. 1985. Maximizing feeding efficiency and minimizing time exposed to predators: A trade-off in the black-capped chickadee. Oecologia 66:60–67.

Lima, S. L., T. J. Valone, and T. Caraco. 1985. Foraging-efficiency-predation-risk trade- off in the grey squirrel. Animal Behaviour 33:155–165.

MacArthur, R. H. 1972. Geographical Ecology. Harper & Row, New York.

Makino, T. T., and S. Sakai. 2007. Experience changes pollinator responses to floral display size: from size-based to reward-based foraging. Functional Ecology 21:854– 863.

McLinn, C. M., and D. W. Stephens. 2006. What makes information valuable: signal reliability and environmental uncertainty. Animal Behaviour 71:1119–1129.

McNamara, J. 1982. Optimal patch use in a stochastic environment. Theoretical Population Biology 21:269–288.

McNamara, J., and A. Houston. 1997. Currencies for foraging based on energetic gain. The American Naturalist 150:603–617.

McNamara, J. M., and T. W. Fawcett. 2012. Optimal Strategies and Heuristics for Ecological Search Problems. Pages 301–315 in T. T. Hills and T. W. Robbins, editors. Cognitive Search: Evolution, Algorithms, and the Brain. MIT Press, Cambridge, Massachusetts.

McNamara, J. M., T. W. Fawcett, and A. I. Houston. 2013. An adaptive response to uncertainty generates positive and negative contrast effects. Science 340:1084–1086.

McNamara, J. M., R. F. Green, and O. Olsson. 2006. Bayes’ theorem and its applications in animal behaviour. Oikos 112:243–251.

McNamara, J. M., P. C. Trimmer, A. Eriksson, J. A. R. Marshall, and A. I. Houston. 2011. Environmental variability can select for optimism or pessimism. Ecology letters 14:58–62.

Mellgren, R. 1982. Foraging in a simulated naturla environment: There’s a rat loose in the lab. Journal of the Experimental Analysis of Behavior 38:93–100.

Michaud, J. 1990. Observations on nectar secretion in fireweed, Epilobium angustifolium L. (Onagraceae). Journal of Apicultrual Research 29:132–137.

Milliken, G., and D. Johnson. 1984. Analysis of messy data, vol. 1. Van Nostrand Reinhold, New York, NY.

Morgan, K. V, T. A. Hurly, M. Bateson, L. Asher, and S. D. Healy. 2012. Context- dependent decisions among options varying in a single dimension. Behavioural Processes 89:115–120.

Morse, D. 1980. The effect of nectar abundance on foraging patterns of bumble bees. Ecological entomology 5:53–59.

Muller, H., and L. Chittka. 2008. Animal personalities: the advantage of diversity. Current Biology 18:R961–3.

Murphy, E. J., D. J. Mossir, J. L. Watkins, and J. Priddle. 1988. Scales of interactions between Antarctic krill and the environment. Pages 120–130 in D. Sahrhage, editor. Antarctic Ocean and Resources Variability. Springer, Berlin.

Nonacs, P. 2001. State dependent behavior and the marginal value theorem. Behavioral Ecology 12:71–83.

Oaten, A. 1977. Optimal foraging in patches: A case for stochasticity. Theoretical Population Biology 12:263–285.

Ohashi, K., and J. D. Thomson. 2009. Trapline foraging by pollinators: Its ontogeny, economics and possible consequences for plants. Annals of Botany 103:1365–78.

Ohashi, K., and J. D. Thomson. 2012. Trapline foraging by bumble bees: VI. Behavioral alterations under speed-accuracy trade-offs. Behavioral Ecology 24:182–189.

Ohashi, K., and T. Yahara. 1999. How long to stay on, and how often to visit a flowering plant?: A model for foraging strategy when floral displays vary in size. Oikos 86:386–392.

Ohashi, K., and T. Yahara. 2001. Behavioral responses of pollinators to variation in floral display size and their influences on the evolution of floral traits. Pages 274–296 in L. Chittka and J. D. Thomson, editors. Cognitive Ecology of Pollination. Cambridge University Press.

Ohashi, K., and T. Yahara. 2002. Visit larger displays but probe proportionally fewer flowers: Counterintuitive behaviour of nectar-collecting bumble bees achieves an ideal free distribution. Functional Ecology 16:492–503.

Ollason, J. 1980. Learning to Forage-Optimally? Theoretical Population Biology 56:44– 56.

Ollason, J. 1987. Learning to forage in a regenerating patchy environment: Can it fail to be optimal? Theoretical Population Biology 32:13–32.

Oster, G. F., and E. O. Wilson. 1979. Caste and Ecology in the Social Insects. Page 372. Princeton University Press, Princeton.

Ott, J. R., L. a. Real, and E. M. Silverfine. 1985. The effect of nectar variance on bumblebee patterns of movement and potential gene dispersal. Oikos 45:333–340.

Pickett, S., S. Collins, and J. Armesto. 1987. A hierarchical consideration of causes and mechanisms of succession. Vegetatio 69:109–114.

Pleasants, J. 1981. Bumblebee response to variation in nectar availability. Ecology 62:1648–1661.

Pleasants, J. M. 1989. Optimal foraging by nectarivores: A test of the marginal-value theorem. American Naturalist 134:51–71.

Pleasants, J. M., and M. Zimmerman. 1979. Patchiness in the dispersion of nectar resources: Evidence for hot and cold spots. Oecologia 41:283–288.

Pleasants, J. M., and M. Zimmerman. 1983. The distribution of standing crop of nectar: What does it really tell us? Oecologia 57:412–414.

Plowright, R. C., J. D. Thomson, L. P. Lefkovitch, and C. M. S. Plowright. 1993. An experimental study of the effect of colony resource level manipulation on foraging for pollen by worker bumble bees (Hymenoptera: Apidae). Canadian Journal of Zoology 71:1393–1396.

Possingham, H., and A. Houston. 1990. Risk-Averse Foraging in Bees: A Comment on the Mode of Harder and Real. Ecology 71:1622–1624.

Prasad, B. R. G., and R. M. Borges. 2006. Searching on patch networks using correlated random walks: space usage and optimal foraging predictions using Markov chain models. Journal of Theoretical Biology 240:241–249.

Price, M., and N. Waser. 1979. Pollen dispersal and optimal outcrossing in Delphinium nelsonii. Nature 277:294–297.

Pyke, G. H. 1978a. Optimal foraging in hummingbirds: Testing the marginal value theorem. American Zoologist 18:739–752.

Pyke, G. H. 1978b. Optimal foraging in bumblebees and coevolution with their plants. Oecologia 36:281–293.

Pyke, G. H. 1978c. Optimal foraging: movement patterns of bumblebees between inflorescences. Theoretical Population Biology 13:72–98.

Pyke, G. H. 1979. Optimal foraging in bumblebees: Rule of Movement between flowers within an inforescence. Zoology 27:1167–1181.

Pyke, G. H. 1980. Optimal foraging in bumblebees: Calculation of net rate of energy intake and optimal patch choice. Theoretical Population Biology 17:232–246.

Pyke, G. H., H. R. Pulliam, and E. L. Charnov. 1977. Optimal foraging: A selecting review of theory and tests. The Quarterly Review of Biology 52:137–154.

Pyke, G., and N. Waser. 1981. The production of dilute nectars by hummingbird and honeyeater flowers. Biotropica 13:260–270.

Real, L. 1981. Uncertainty and pollinator-plant interactions: The foraging behavior of bees and wasps on artificial flowers. Ecology 62:20–26.

Real, L., S. Ellner, and L. D. Harder. 1990. Short-term energy maximization and risk- aversion in bumble bees: A reply to Possingham et al. Ecology 71:1625–1628.

Real, L., J. Ott, and E. M. Silverfine. 1982. On the tradeoff between the mean and the variance in foraging: Effect of spatial distribution and color preference. Ecology 63:1617–1623.

Redmond, D., and C. M. S. Plowright. 1996. Flower revisitation by foraging bumble bees: The effects of landmarks and floral arrangement. Journal of Apicultural Research 35:96–103.

Richards, S. A. 2008. Dealing with overdispersed count data in applied ecology. Journal of Applied Ecology 45:218–227.

Richards, S. a., and A. M. de Roos. 2001. When is habitat assessment an advantage when foraging? Animal Behaviour 61:1101–1112.

Ross, S. M. 2010a. Markov Chains. Pages 191–275 Introduction to Probability Models, 10th edition. Academic Press.

Ross, S. M. 2010b. Continuous-Time Markov Chains. Pages 371–411 Introduction to Probability Models, 10th edition. Academic Press.

Saavedra, S., R. D. Malmgren, N. Switanek, and B. Uzzi. 2013. Foraging under conditions of short-term exploitative competition: The case of stock traders. Proceedings of the Royal Society of Biological Sciences.

Saleh, N., K. Ohashi, J. D. Thomson, and L. Chittka. 2006. Facultative use of the repellent scent mark in foraging bumblebees: Complex versus simple flowers. Animal Behaviour 71:847–854.

Schmid-Hempel, P., A. Kacelnik, and A. I. Houston. 1985. Honeybees maximize efficiency by not filling their crop. Behavioral Ecology and Sociobiology 17:61–66.

Schmid-Hempel, P., and T. Wolf. 1988. Foraging effort and life span of workers in a social insect. The Journal of Animal Ecology 57:509–521.

Schmitt, U., and A. Bertsch. 1990. Do foraging bumblebees scent-mark food sources and does it matter? Oecologia 82:137–144.

Schoener, T. W. 1971. Theory of feeding strategies. Annual Review of Ecology and Systematics 2:369–404.

Šidák, Z. 1967. Rectangular confidence regions for the means of multivairate normal distributions. Journal of the American Statistical Association 62:626–633.

Stephens, D. W., and A. S. Dunlap. 2009. Why do animals make better choices in patch- leaving problems? Behavioural Processes 80:252–60.

Stephens, D. W., and J. R. Krebs. 1986. Foraging Theory. Page 248 (J. R. Krebs and T. Clutton-Brock, Eds.), 1st edition. Princeton University Press, Princeton, New Jersey.

Stroup, W. 2013. Generalized linear mixed models: Modern concepts, methods and applications. CRC Press, Boca Taton, USA.

Templeton, A., and L. Lawlor. 1981. The fallacy of the averages in ecological optimization theory. American Naturalist 117:390–393.

Templeton, J. J., and L.-A. Giraldeau. 1996. Vicarious sampling: the use of personal and public information by starlings foraging in a simple patchy environment. Behavioral Ecology and Sociobiology 38:105–114.

Thomson, J. 1982. Patterns of visitation by animal pollinators. Oikos 39:241–250.

Thomson, J. 1988. Effects of variation in inflorescence size and floral rewards on the visitation rates of traplining pollinators of Aralia hispida. Evolutionary Ecology:65– 76.

Thomson, J. D. 1996. Trapline foraging by bumblebees: I. Persistence of flight-path geometry. Behavioral Ecology 7:158–164.

Tindall, J. R. 2006, October. The Incidence and Functional Significane of Nectarless Flowers. University of Calgary.

Torres, C., and L. Galetto. 1998. Patterns and implications of floral nectar secretion, chemical composition, removal effects and standing crop in Mandevilla pentlandiana (Apocynaceae). Botanical Journal of the Linnean Society 127:207– 223.

Turelli, M., J. H. Gillespie, and T. W. Schoener. 1982. The fallacy of the fallacy of the averages in ecological optimization theory. American Naturalist 119:879–884.

Tversky, A., and I. Simonson. 1993. Context-dependent preferences. Management Science 39:1179–1189.

Valone, T., and J. S. Brown. 1989. Measuring patch assessment abilities of desert granivores. Ecology 70:1800–1810.

Valone, T. J. 1991. Bayesian and prescient assessment: Foraging with pre-harvest information. Animal Behaviour 41:569–577.

Waage, J. K. 1979. Foraging for patchily-distributed hosts by the parasitoid, Nemeritis canescens. The Journal of Animal Ecology 48:353–371.

Wajnberg, E., X. Fauvergue, and O. Pons. 2000. Patch leaving decision rules and the marginal value theorem: An experimental analysis and a simulation model. Behavioral Ecology 11:577–586.

Wilmshurst, J. F., J. M. Fryxell, and C. M. Bergman. 2000. The allometry of patch selection in ruminants. Proceedings. Biological sciences / The Royal Society 267:345–9.

Winter, Y., and K. P. Stich. 2005. Foraging in a complex naturalistic environment: Capacity of spatial working memory in flower bats. The Journal of Experimental Biology 208:539–548.

Wolf, L., and F. Hainsworth. 1990. Non-random foraging by hummingbirds: Patterns of movement between Ipomopsis aggregata (Pursch) V. Grant inflorescences. Functional Ecology 4:149–157.

Woodward, G., and T. Laverty. 1992. Recall of flower handling skills by bumble bees: A test of Darwin’s interference hypothesis. Animal Behaviour 44:1045–1051.

Wu, J., and O. Loucks. 1995. From balance of nature to hierarchical patch dynamics: A paradigm shift in ecology. Quarterly Review of Biology 70:439–466.

Yang, J. Y., and S. A. Hodges. 2010. Early inbreeding depression selects for high outcrossing rates in Aquilegia formosa and Aquilegia pubescens. International Journal of Plant Sciences 171:860–871.

Ydenberg, R. 1984. Great tits and giving-up times: Decision rules for leaving patches. Behaviour 90:1–24.

Ydenberg, R., C. Welham, R. Schmid-Hempel, P. Schmid-Hempel, and G. Beauchamp. 1994. Time and energy constraints and the relationships between currencies in foraging theory. Behavioral Ecology 5:28–34.

Zimmerman, M. 1981a. Nectar dispersion patterns in a population of Impatiens capensis. Virginia Journal of Science 32:150–152.

Zimmerman, M. 1981b. Patchiness in the dispersion of nectar resources: Probable causes. Oecologia 49:154–157.

Zimmerman, M. 1988. Pollination biology of montane plants: Relationship between rate of nectar production and standing crop. American Midland Naturalist 120:50–57.

Zimmerman, M., and G. Pyke. 1986. Reproduction in polemonium: Patterns and implications of floral nectar production and standing crops. American Journal of Botany 73:1405–1415.