Task allocation and site fidelity jointly influence foraging regulation in honey bee colonies

Abstract

Variation in behavior among group members often impacts collective outcomes. Individuals may vary both in the task that they perform and in the persistence with which they perform each task. Although both the distribution of individuals among tasks and differences among individuals in behavioral persistence can each impact collective behavior, we do not know if and how they jointly affect collective outcomes. Here we use a detailed computational model to examine the joint impact of colony-level distribution among tasks and behavioral persistence of individuals, specifically their fidelity to particular resource sites, on the collective tradeoff between exploring for new resources and exploiting familiar ones. We developed an agent-based model of foraging honey bees, parameterized by data from 5 colonies, in which we simulated scouts, who search the environment for new resources, and individuals who are recruited by the scouts to the newly found resources, i.e., recruits. We found that for each value of persistence there is a different optimal ratio of scouts to recruits that maximizes resource collection by the colony. Furthermore, changes to the persistence of scouts induced opposite effects from changes to the persistence of recruits on the collective foraging of the colony. The proportion of scouts that resulted in the most resources collected by the colony decreased as the persistence of recruits increased. However, this optimal proportion of scouts increased as the persistence of scouts increased. Thus, behavioral persistence and task participation can interact to impact a colony's collective behavior in orthogonal directions. Our work provides new insights and generates new hypotheses into how variation in behavior at both the individual and colony levels jointly impact the trade-off between exploring for new resources and exploiting familiar ones.

Full text

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Research
Cite this article: Mosqueiro T, Cook C, Huerta
R, Gadau J, Smith B, Pinter-Wollman N. 2017
Task allocation and site delity jointly
inuence foraging regulation in honeybee
colonies. R. Soc. open sci. 4: 170344.
http://dx.doi.org/10.1098/rsos.170344
Received: 12 April 2017
Accepted:25July2017
Subject Category:
Biology (whole organism)
Subject Areas:
behaviour/computational biology
Keywords:
Apis mellifera, collective behaviour,
exploitation, exploration, group composition,
persistence
Author for correspondence:
Thiago Mosqueiro
e-mail: thmosqueiro@ucla.edu
Electronic supplementary material is available
online at https://dx.doi.org/10.6084/m9.
gshare.c.3849760.
Task allocation and site
delity jointly inuence
foraging regulation in
honeybee colonies
Thiago Mosqueiro1,3, Chelsea Cook2, Ramon Huerta1,
Jürgen Gadau2,4,BrianSmith
2and
Noa Pinter-Wollman3
1BioCircuits Institute, University of California San Diego, La Jolla, CA, USA
2School of Life Sciences, Arizona State University,Tempe, AZ, USA
3Department of Ecology and Evolutionary Biology, University of California Los Angeles,
Los Angeles, CA, USA
4Institute for Evolution and Biodiversity,University of Münster, Münster, Germany
TM, 0000-0001-5808-8189
Variation in behaviour among group members often impacts
collective outcomes. Individuals may vary both in the task that
they perform and in the persistence with which they perform
each task. Although both the distribution of individuals
among tasks and differences among individuals in behavioural
persistence can each impact collective behaviour, we do not
know if and how they jointly affect collective outcomes.
Here, we use a detailed computational model to examine
the joint impact of colony-level distribution among tasks and
behavioural persistence of individuals, specifically their fidelity
to particular resource sites, on the collective trade-off between
exploring for new resources and exploiting familiar ones.
We developed an agent-based model of foraging honeybees,
parametrized by data from five colonies, in which we simulated
scouts, who search the environment for new resources, and
individuals who are recruited by the scouts to the newly
found resources, i.e. recruits. We varied the persistence of
returning to a particular food source of both scouts and
recruits and found that, for each value of persistence, there is
a different optimal ratio of scouts to recruits that maximizes
resource collection by the colony. Furthermore, changes to the
persistence of scouts induced opposite effects from changes
to the persistence of recruits on the collective foraging of the
colony. The proportion of scouts that resulted in the most
resources collected by the colony decreased as the persistence
of recruits increased. However, this optimal proportion of
scouts increased as the persistence of scouts increased. Thus,
behavioural persistence and task participation can interact to
2017 The Authors. Published by the Royal Society under the terms of the Creative Commons
Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted
use, provided the original author and source are credited.

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impact a colony’s collective behaviour in orthogonal directions. Our work provides new insights and
generates new hypotheses into how variations in behaviour at both the individual and colony levels
jointly impact the trade-off between exploring for new resources and exploiting familiar ones.
1. Introduction
Group composition impacts the emergence of collective behaviours. Individuals that comprise a group
vary both in which tasks they perform [1,2] and in how persistently they perform them, i.e. how many
times they repeatedly perform a task [3,4]. The effect of allocation of workers to different tasks on the
collective behaviour of colonies has been studied extensively [5] with the underlying assumption that
dividing the labour among group members will increase the overall efficiency of the group, as it does in
human industrial societies [6]. However, variation among individuals in how persistently they perform a
task is striking. This behavioural variation can undermine the efficiency that is often associated with task
specialization [7,8] because individuals that are not persistent either do not perform a large proportion of
the task or incur the costs of task switching [9,10]. Although recent work has begun to examine the impact
of variation in individual persistence in performing a particular task on collective behaviours [11,12], we
do not know how task allocation and variation in persistence interact to impact collective outcomes.
Behavioural persistence has now been documented extensively throughout the animal kingdom [3]
including in social insects [4]. Some ant workers are more persistent in performing a certain task
than others [13], and honeybee workers vary in how persistently active they are [14,15]. Behavioural
persistence can impact how individuals in a group interact with one another and therefore affect the
collective behaviours that emerge from these interactions [12,16]. A growing understanding of the
mechanisms that underlie behavioural persistence is paving a path for understanding how variation
in behavioural persistence affects collective outcomes. For example, the decision of a honeybee to leave
the hive and start foraging is influenced by the bee’s genome [17–22]. Furthermore, genetic variation
underlies individual differences in learning abilities, which might influence the likelihood of a bee to
make certain types of foraging decisions, such as staying at a resource patch [23–27].
Honeybees exhibit variation in foraging behaviours at both the worker and colony levels [28–30].
Understanding the mechanisms that underlie honeybee foraging decisions is especially important
because of their economic importance for honey production and crop pollination [31,32]. Consistent
behavioural variation across workers within honeybee colonies has potential fitness consequences [29].
Although the regulation of foraging behaviour in honeybees has been studied for a long time [33], and
much is known, for example, about how foragers respond to resource availability [21,34], we still do not
know what mechanisms may underlie variation among colonies in collective foraging.
Many tasks in honeybee colonies are related to foraging. For example, some foragers collect pollen,
while others specialize in collecting nectar [33,35], and an animal’s genotype influences a bias for one
or the other [36–38]. Nectar foragers further vary in their propensity to leave the nest to find new
food. Experienced foragers that spontaneously leave the hive to explore the environment are referred
to as ‘scouts’ or ‘primary searchers’ [39–42]. When these scouts return to the hive, they recruit other
foragers to the food patches they found, and these bees are referred to as ‘recruits’. Scouts communicate
to recruits the direction, distance and quality of newly found resources using the waggle dance [33,43],
thus reducing waste of energy spent when searching for food over both long and short timescales [44,45],
and dangers, such as predation [34,46,47]. Although exploration of the environment for new food
sources is a task exclusive to scouts, they can contribute to the exploitation of resources, alongside the
recruits, through repeated visits to the same source [21,48]. We define persistence of a forager as the
average number of repeated visits it performs to each particular resource, regardless of whether it is
a scout or a recruit. Thus, both scouts and recruits with lower persistence can contribute to a colony’s
exploration of the environment because low-persistence scouts will travel to different resources and low-
persistence recruits will stop foraging quickly and become available to be recruited to new locations.
High persistence of both scouts and recruits can contribute to the colony’s exploitation of resources
through repeated visits to a profitable source but can also hinder the efficiency of collective foraging
if other, more profitable resources are available. Honeybees choose between exploring for new resources
or exploiting familiar ones based on colony [41] and individual information [49,50]. Thus, the trade-off
between exploration and exploitation can be adjusted both at the colony level, through allocation of
foragers to either scouts or recruits, and at the individual level, through variation in the persistence of
visits to a known food source.

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Although the trade-off between exploration and exploitation has been previously examined in
honeybees by addressing the differences between scouts and recruits [21,51], the role of behavioural
persistence in visiting the same resource, i.e. site fidelity, has thus far been overlooked. Because foraging
is energetically costly [49,52], greater persistence does not always translate into greater efficiency. To
examine the joint role of task allocation and behavioural persistence in the regulation of foraging by
honeybees, we considered how the ratio between scouts and recruits and the persistence of returning to
a particular resource jointly affect the collective resource acquisition by a colony. Specifically, we examine
how behavioural persistence of (i) the entire colony, (ii) scouts or (iii) recruits affects collective foraging
when different proportions of foragers are allocated either to scouting or to being recruited. Our findings
provide new and realistic insights on how behavioural variation at more than one level of organization
impacts collective outcomes.
2. Material and methods
2.1. Agent-based model
To examine the joint impact of task allocation and behavioural persistence on collective behaviour, we
developed a spatially explicit agent-based model. Simulated honeybees foraged in an open, continuous,
two-dimensional space. The hive was set at the origin of the space and three unlimited resource patches
were uniformly distributed around it at a fixed distance of 15 m from the hive, with equal distances
between neighbouring sites. We simulated two types of foragers, scouts and recruits, which varied in
their flight patterns as detailed below. To determine the effects of behavioural persistence on colony
outcomes, we examined the proportion of scouts that leads to the maximum amount of resources
collected by the colony under different regimes of behavioural persistence. A description using the
Overview, Design concepts and Details (ODD) protocol [53] and the source code of our model can be
found on Github [54]. In the following sections, we define the flight dynamics of foragers (section ‘Flight
dynamics’) and describe the variables used to quantify colony success (section ‘Collective outcomes’)
within the agent-based model.
2.2. Flight dynamics
Flight dynamics of all foragers were modelled as a random walk with drift [55,56]. At the beginning of
each simulation (t=0), the position of each bee iwas xi(0) =(0,0), i.e. all bees were at the hive. Each bee
was assigned a different drifting vector vi, which determined its flight direction when leaving the hive,
and its flight pattern is described as
dxi(t)=vidt+σidWt, (2.1)
where σidWtis the random contribution to the distance and angle a bee moved. This term has a normal
distribution with a mean of zero and variance of σi, thus closely resembling a diffusion process [57].
Specifically, 1/σimeasures the precision of the flight. Because E[dWt]=0, the average velocity of the
ith bee was vi, and its magnitude vi=|vi|defined the average flight velocity. The stochastic dynamics in
equation (2.1) produce slight variation among bees in their flight patterns to avoid an unrealistic scenario
in which bees take a straight line between two points. Using the Euler–Maruyama method [58], equation
(2.1) can be solved numerically using
xi(t+t)=vit+√tσiWt+xi(t)=vit+˜σiWt+xi(t), (2.2)
with tbeing a fixed time step, and ˜σi=√tσi. At the beginning of each simulation (t=0), all scouts
left the hive, with drifting vectors viassigned from a uniform distribution, and continued flying until
they found a resource. Once a scout detected a resource, it returned to the hive to recruit other foragers,
referred to as ‘recruits’. Scouts and recruits differed in the precision of their flight: ˜σiof scouts was larger
(˜σi=5) than that of recruits, resulting in flight paths that covered a larger area than recruits (figure 1).
The dispersion of recruited bees (˜σi=2) was fitted using data from experiments with feeders positioned
at distances varying from metres to kilometres [33]. To differentiate between the flight patterns of bees
that are exploring the environment and those that are exploiting a resource patch, are familiar with their
location, and are therefore faster and more precise, we assigned vi=1toscoutsandvi=1.5 to recruits,
following [59]. Foragers that reached the limit of the simulated area were set back to the hive instantly to
start foraging again.

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resource
found
exploring
scouts Ewaiting
foragers W
food
collected F
recruited
foragers R
recruiting
scouts Srecruitment
exploring
scout hive
recruits and
persistent scouts
0.15
2.0
5.0
0.10
frequency
0.05
0
–0.2 0
angle
0.2
(a)(b)(c)
returns
straight to
the hive
gd (aN–S)
–gsS
g S((1 – a)N–R)
–grR
gfSgfR
Figure 1. Flightdynamics of scouts and recruits. (a) Scouts left the hive at the beginning of the simulation and once they found a resource,
they recruited other foragers, referredto as ‘recruits’. (b) Variance of the scouts’ deviations from a straight pathon outgoing trips ( ˜σ=5,
red) was larger than that of the recruits and persistent scouts ( ˜σ=2, blue), resulting in greater spatial dispersion. (c) System dynamics
approach based on a compartmental model, with square boxes representing the states of foragers and the green circle representing the
amount of food retrieved by all foragers. Black arrows are state-transition rates (see equations (2.6) and (2.7)); the blue dashed arrow
represents the recruitment of foragers by scouts; the green double arrows represent foragers delivering food to the hive.
During recruitment, scouts communicated the location and distance of the newly found resource. The
recruiting scout remained at the hive for 1min (approx. 50 time steps in the numeric simulations) to
simulate the time it would take to recruit foragers using the waggle dance [33]. During this period, an
average of five randomly selected recruits left the hive in the direction of the resource. Recruiting on
average 1, 5 or 10 foragers by each scout did not qualitatively change the results of our simulations.
For simplicity, only the recruitment by scouts is considered here, and we examine the effect of adding
recruitment by recruits in the electronic supplementary material, figure S1. Distance and quality of food
patches are also communicated in the waggle dance [33,60], and variation in distance and quality could
be easily incorporated in further investigations of our model by varying the number of recruits that
respond to each recruiting forager and the time that each scout spends recruiting.
Each of the newly recruited bees left the hive with their drifting vectors pointing exactly towards the
location reported by the recruiting scouts, analogous to previous experiments [61]. The direction of this
drifting vector is the deterministic portion of the flight dynamics (see vidtin equation (2.1)), which is
accompanied by a stochastic contribution from σidWt. Recruited bees exploited the first resource they
found during their trips. The dispersion of recruited bees (σ=2) was fitted using data from experiments
with feeders [32]. Because the stochastic element of the flight of a recruited bee is very small compared
with the size of the resource patches in our simulations, bees always exploited the same resource patch
that was reported to them. The effect of communicating the distance to the source was modelled by
slightly changing the dynamics in equation (2.1) to
dxi(t)=viα(|xr−xi(t)|)dt+σidWt, (2.3)
where α(x) is any function that goes to zero when x→0andxris the location of the resource reported.
This turned the flight dynamics into a purely random walk (i.e. without bias) near the location of
the reported resource. For simplicity, we used a Heaviside function that removed all bias in the flight
dynamics when the forager was less than 2 m from the resource:
α(xr−xi(t)) =1, if |xr−xi(t)|−2;
0, otherwise. (2.4)
During our simulations, scouts and recruits obtained resources for the colony. Upon obtaining a resource,
foragers (both scouts and recruits) returned to the hive in a straight line, with constant velocity vi,
carrying one resource unit, equivalent to 1.0 ±0.3 µl [33]. If a forager reached the boundaries of the area
considered in the simulation, it was reassigned to the hive, without bringing food, to begin foraging
again. For simplicity, this reassignment was instantaneous, but adding a return trip or changing the
distance explored by these foragers before they return to the hive did not change our findings (electronic
supplementary material, figure S2).
Each forager, scout or recruit, was assigned a persistence value πi, defined as the number of
consecutive trips it performed to each resource location. If the persistence of a scout was greater than 1,

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its viand σiafter the first trip were set to those of recruits and its flight dynamics was adjusted to follow
equation (2.2). Scouts that completed πitrips to the same location randomly changed their drifting vector
and began scouting again. Recruits that completed πitrips remained at the hive until they were recruited
again.
2.3. Collective outcomes
To examine the impact of colony composition on collective foraging success, we simulated colonies with
different ratios between scouts and recruits. For simplicity, we neglect the effect of inactive foragers [42]
and we fixed the number of scouts and recruits during each simulation. Simulated colonies consisted of
300 foragers that were allowed to forage for 7 h in an area equivalent to 36×36 m =1296 m2. These values
were selected based on empirical data on honeybee foraging [33]. Because each simulation reflected just
one day of foraging, we assumed that resources were never depleted during a simulation and that the
ratio between scouts and recruits was fixed.
The colony-level outcome was measured as the total amount of resources retrieved by all the bees in
the colony. For each simulation jthat we ran, we recorded the resources fj(t) collected over time. Because
of the stochastic nature of our simulations, the amount of resources collected at each time point over all
our nsimulations followed a bell-shaped distribution with a variance V. To ensure that all conditions
tested (i.e. proportion of scouts and various persistence values) produced the same 90% confidence
interval wfor the estimation of the average amount of resource collected (see shaded area in figure 3a,b),
we used the central limit theorem to set the number of simulation runs to n=4V2/w. Because the mean
of the total amount of resources collected was of the order of thousands of microlitres, we set w=50 µl,
resulting in nof approximately 120. We estimated the average amount of resources collected at every
time point in all nsimulation runs as f(t)=E[fj(t)] (see lines in figure 3a,b).
2.4. System dynamics model
To complement our understanding of how behavioural persistence and recruitment by scouts in the
agent-based model combine to result in complex outcomes, we used a coarse-grained formalism based
on ordinary differential equations that describe the system’s dynamics (figure 1c), similar to [62]. We
consider the following dynamical variables: E(t), the number of scouts exploring the environment; S(t),
the number of scouts that are bringing food back to the hive; R(t), activated recruits; and W(t), potential
recruits waiting inside the hive. Let Nbe the number of foragers in the colony; then αNis the total number
of scouts and (1 −α)Nis the total number of recruits. Thus, E(t)=αN−S(t)andW(t)=(1 −α)N−R(t).
Because S(t)andR(t) represent the total number of foragers collecting food at any given time, we refer to
them as active foragers.Ifwedefineγas the rate at which active scouts S(t) recruit inactive recruits W(t),
then the increase in the number of active recruits is described by γSW =γS((1 −α)N−R). A simple
model describing the rate of change in number of scouts and number of recruits can be defined by two
differential equations:
dS
dt=γd(αN−S)−γsS(2.5a)
and dR
dt=γS((1 −α)N−R)−γrR, (2.5b)
where γdis the rate at which scouts find a new resource and start exploiting it; γsis the rate at which
these scouts stop collecting food and resume exploring for new resources; and γris the rate at which the
recruited foragers stop collecting food and begin waiting to be recruited again. Finally, the cumulative
amount of food collected by active foragers F(t) can be formulated as
dF
dt=γf(S+R), (2.6)
with γfbeing the rate at which bees collect food while exploiting a particular resource.
In this compartmental model, behavioural persistence, in the form of repeated visits to a particular
resource site, is defined according to the rates at which foragers stop exploiting particular resources.
Both 1/γsand 1/γrrepresent the characteristic durations of exploiting a particular resource by scouts
or recruits. Dividing these characteristic durations by the average time interval between each visit
to the feeder (which was experimentally evaluated as described in section ‘Behavioural experiments and
parameter estimation’) gives the average number of visits to one resource. Thus, to link the rates at which

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05 10 15 20
persistence
3
6
9
12
15
counts
0 10 20 30 40 50
time (min)
3
6
9
12
15
cumulative number
of visits
0 2 4 6 8 10
inter-visit interval (min)
10
30
50
70
counts
(a)(b)(c)
Figure 2. Empirical results of 206 foraging trips per formedon one day by 33 dierent honeybee foragers from one representative colony
of the ve colonies we tested. The feeder was positioned 5 m from the hive. (a) Number of visits over time. Each line represents one
bee and t=0 reects the rst bee’s rst visit to the feeder. (b) Distribution of intervals between consecutive visits to a single feeder.
(c) Distribution of persistence, i.e. the number of return visits by each bee to one of two feeders. The average persistence was 6.1 ±0.3.
foragers stop exploiting a particular resource with the persistence parameter in the agent-based model,
we define
γs=¯γs
πs(2.7a)
and
γr=¯γr
πr. (2.7b)
Defining the relationship between γsand γrand persistence, as simulated in the agent-based model,
allows us to analyse the compartmental model without having to fit a different value of γs,r for each πs,r,
reducing the complexity of our compartmental model. The parameters ¯γs,¯γr,γfand γdwere fitted using
simulation data from the agent-based model.
2.5. Behavioural experiments and parameter estimation
To assess persistence empirically, we observed the visitation of 323 honeybee (Apis mellifera L.) foragers
from five different colonies during the winter (between 3 and 26 February 2016). Each colony was
tested on a different day and was presented with two feeders, each containing 1M sucrose solution
on which the foragers fed ad libitum. We trained bees to find feeders, positioned at 3, 5 or 10 m from the
hive, 1 day before the experiments began, following [18] and comparable to other studies that examine
20 m [63]. These resources were never depleted despite their proximity to the hive. During the time of our
experiments, there were few naturally blooming plants and our feeders were very attractive to the bees.
We marked workers for individual identification using water-based acrylic paint markers (Montana)
and recorded the time at which each bee visited a feeder using the software EventLog [64]. We recorded
1307 trips. Work with invertebrates does not require ethics committee approval and all fieldwork was
conducted on university property. All collected data are publicly available [65].
We estimated the values for the parameters in our model based on the empirical observations.
Interestingly, all bees exhibited the same rate of visits to the feeders (figure 2a), which was 0.4 ±0.2
visits per minute (figure 2b). This visitation rate allowed us to set the model parameter vifor flight
velocity to a constant value for all foragers after their first visit at a resource. The empirical distribution
of intervals between consecutive visits to the feeder (figure 2b) informed the visitation interval of our
model. The observed average visitation interval twas linearly related to the distance dbetween the hive
and the feeder (R=95%, electronic supplementary material, figure S3): =αd+β, with α=2.3 ±0.3
and β=0.28 ±0.05. Finally, the observed distribution of persistence was geometric or negative binomial
(figure 2c), with an average of ±90% CI =6.1 ±0.3. This means that making the decision to stop exploiting
a particular patch had a probability of 16%, based on the value of the lambda parameter of a geometric
distribution that was fitted to the data. Because the largest number of observed return visits by a single
bee was 22, we restricted our persistence parameter πito range between 1 and 30.
3. Results
The proportion of scouts that maximized the amount of resources a colony collected by the end of the
simulation, referred to as the ‘optimal proportion of scouts’, changed with the persistence of visiting a

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1.2
1.0
0.8
0.6
resource collected (ml)
0.4
0.2
0
(a)
% of scouts
90%
50%
10%
low persistence
01234
time (h)
567
4
3
2
1
0
resource collected (ml)
(c)
% of scouts
0 20406080100
persistence
1
3
5
10
15
20
high persistence
5.0
4.0
3.0
2.0
1.0
0
resource collected (ml)
(b)
01234
time (h)
567
80
optimal % of scouts
70
60
50
(d)
colony persistence (p)
010 20 30
colony persistence (p)
0 102030
5
4
3
2
1
maximum resource
collected (ml)
(e)
Figure 3. The relationship between colony persistence πand the proportion of scouts aects the amount of resources collected by a
colony. The amount of resources collected over time by a simulated colony in which all foragers have either (a) low persistence (π=1)
or (b) high persistence (π=20) for three dierent proportions of scouts. Shaded areas represent 1.5 s.d. (c) Total amount of resource
collected throughout the entire simulation as a function of the proportion of scouts in the colony for dierent values of persistence
of all foragers (π). Bars are the standard deviation across all simulation runs. (d) Optimal proportion of scouts plateaus near 50%
as πincreases. Points are the results from our agent-based model and the line is the result from the systems dynamics approach
(equation (3.4)). (e) Maximum amount of resources collected scales sublinearly with π. Points are the results from our agent-based
model, and the line is the result from the systems dynamics approach (equation (3.3)).
resource. The amount of resources collected in all simulations increased over time (figure 3a,b). The total
amount of resources collected at the end of the simulation was different among the various proportions
of scouts. When both scouts and recruits lacked persistence, i.e. each bee made only a single trip to the
feeder (π=1), more resources were collected as the proportion of scouts increased (figure 3a). However,
as the persistence of all foragers increased from π=1 to 20, a greater proportion of scouts in a colony
did not necessarily result in more resources collected. For example, when persistence was set at π=20,
colonies with 50% scouts outperformed colonies with 90% scouts (figure 3b,c). For each persistence value
π,we found the optimal proportion of scouts, i.e. the proportion of scouts that resulted in the most
resources collected by the end of the simulation (after 7h of foraging; figure 3c). This optimal proportion
of scouts decreased with persistence and saturated after π>20 (figure 3d). However, the absolute amount
of resources collected per colony continued to grow when persistence increased beyond 20 visits per
individual (π>20; figure 3e). Changing the number of resource patches impacted the total amount of
resources collected by the colony, but the optimal proportion of scouts still decreased with the persistence
of the colony (electronic supplementary material, figure S4). This result led us to further investigate the
relationship between the total amount of resources collected and the persistence of recruits and of scouts,
as detailed below.
The system dynamics model allows us to further evaluate the processes that determine the optimal
proportion of scouts using the stable solutions for scouts (S) and recruits (R),
S∗=S(∞)=αNγd
γd+γs(3.1a)
and
R∗=R(∞)=(1 −α)N1
1+γr(γd+γs)/γ γdαN. (3.1b)
The expressions inside the parenthesis in equations (3.1a) and (3.1b) represent, respectively, the
proportions of scouts and recruits that become active after a long time, i.e. asymptotically. These solutions

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reveal that the optimal proportion of active scouts is determined solely by the ratio between the rate
at which scouts discover new resource sites, γd, and the rate at which they abandon them, γs. For a
fixed rate of discovery, γd, the number of active scouts increases almost linearly with the persistence
of scouts, saturating for large values of persistence, i.e. when γs→0. However, the number of active
recruits does not depend directly on the persistence of scouts, but on the number of scouts, αN, and the
rate of recruitment, γ. From equation (2.7), the amount of food collected, F(t), grows asymptotically at a
fixed rate,
dF
dt=γf(S∗+R∗)=γfNχ2α1+χ1
1−α
1+αχ1χ2, (3.2)
where χ1=γN/γrmeasures the trade-off between recruitment and the persistence of recruits; and
χ2=γd/(γd+γs) is the ratio between the rate of discovering new resource sites γdand the rate of
abandoning a site γs(same expression as in (3.1a)). If there are no scouts, α=0, then no food is collected,
which agrees with the agent-based model (figure 3c). Because the rate γdat which new resources are
discovered is constant in our model, the amount of food collected, F(t), always grows and does not
present a stable solution. However, the asymptotic speed at which F(t) grows, shown in equation (3.2),
changes with the proportion of scouts in the colony, α. Thus, for long times, the amount of food collected,
F(t), grows linearly, and comparing the rate of increase among different persistence values is equivalent
to comparing the relative values of F(t) at a fixed time point t,asinfigure 3c,d. To simplify the dependence
of the rate of increase of F(t) on the proportion of scouts, α, in equation (3.2), we use the Taylor expansion
up to second order in α:
γf(S∗+R∗)=γfNχ2[α(1 +χ1)−α2χ1(χ1χ2+1)] +O(α3), (3.3)
with Obeing the ‘big O’ notation, i.e. it refers to the remaining terms that are polynomials in αof order
3 or higher, and have a small contribution to equation (3.3) because 0<α ≤1. Thus, the asymptotic rate
of resource collection is a concave function whose maximum depends on α, the proportion of scouts in
the colony, in accordance with the results from our spatially explicit agent-based model (figure 3c). The
optimal proportions of scouts predicted by the system dynamics agree perfectly with the results of the
agent-based model (lines in figure 3c,d). However, the curvature of the amount of resources collected in
relation to the proportion of scouts slightly differs between the system dynamics and the agent-based
models (electronic supplementary material, figure S5).
Changes in the persistence of scouts had the opposite effect from changes in the persistence of recruits
on the proportion of scouts that maximized collective resource collection. In the agent-based model,
while the optimal proportion of scouts decreased with the persistence of recruits πr(figure 4a), this
proportion increased with the persistence of scouts πs(figure 4b). This opposite dependence of the
optimal proportion of scouts on πsand πrwas observed for a wide range of both scout and recruit
persistence values (figure 4c,d). Our system dynamics model also reproduces this dependence (see lines
in figure 5). The combined scout–recruit persistence with the best collective outcome, i.e. greatest amount
of resources collected, resulted from the largest persistence values of both scouts and recruits (figure 4e)
when approximately 60% of the foragers were scouts (figure 4f). The opposing dependence of the optimal
proportion of scouts on scout and recruit persistence is captured by our system dynamics (figure 5),
through the relationship between γsand γrin equation (3.3). Interestingly, changes in the persistence of
recruits resulted in a 50% change in the optimal proportion of scouts, whereas changes in the persistence
of scouts resulted in only a 25% change in this proportion (figure 6).
4. Discussion
Social groups constantly adjust their collective behaviour to changes in their surroundings. However,
an understanding of how these adjustments emerge is still scant. Our models show that both colony-
level composition, i.e. the ratio between scouts and recruits, and individual-level traits, such as the
persistence of foragers, interact to impact collective foraging. We found that the balance between the
proportion of bees scouting and behavioural persistence allows a colony to acquire more resources and
allocate fewer individuals to the potentially costly activity of scouting. Scouts may expend considerable
energy flying around in search for new resources, and they can be preyed upon or potentially lose
their way home [34]. In our simulations, colonies with high persistence, π=20, collected almost five
times more resources than those with low persistence, π=1(figure 3c). The trade-off between exploring
for new resources and exploiting known ones resulted in a different optimal proportion of scouts for
each value of persistence (figure 3). As persistence increased, the proportion of scouts required for

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4
3
2
1
0
0 20406080
% of scouts
100 0 20406080
% of scouts
100
resource collected (ml)
(a)4
3
2
1
0
resource collected (ml)
(b)
recruit persistence
20
15
10
5
1
(e)
1 5 10 15 20
scout persistence
6
5
4
3
2
max. resource collected (ml)
100
80
60
40
20
optimal % of scouts
100
80
60
40
20
optimal % of scouts
(c)
0 10 20 30 0 10 20 30
recruit persistence scout persistence
recruit persistence
20
15
10
5
1
(f)
1 5 10 15 20
scout persistence
optimal % of scouts
90
80
70
60
50
40
30
(d)
recruit
persistence
1
5
10
15
20
scout persistence
1
5
10
15
20
scout
persistence
1
5
10
15
20
recruit persistence
15 15
31020
Figure 4. Dierences in collective foraging due to the persistence of either scouts (πs)orrecruits(πrin the agent-based model). Total
amount of resources collected by a colony as a function of the proportion of scouts when (a) the persistence of scouts is set to πs=5
for the following values of persistence of recruits: πr=1,5,10,15,20 and (b) the persistence of recruits is set to πr=5forthefollowing
values of persistence of scouts: πs=1,5,10,15,20. Bars are the standard deviation across all simulation runs. Proportion of scouts that
resulted in maximal amount of resource collected as a function of (c) recruit persistencefor dierent values of xed scout persistence πs
and (d) scout persistence for dierent values of xedrecruit persistence πr.(e) Heat map of the maximum amount of resources collected
for dierent values of scout πsand recruit πrpersistence jointly. (f) Heat map of the proportion of scouts that led to the maximum
amount of resources collected for dierent values of scout πsand recruit πrpersistence jointly.
100
80
optimal % of scouts
60
40
100
80
60
40
0 5 10 15 20
recruit persistence
0 5 10 15 20
scout persistence
optimal % of scouts
scout
persistence
recruit
persistence
(a)(b)
1
5
10
15
20
1
5
3
10
15
20
Figure 5. The systems dynamics approach captures the opposing eects of scout and recruit persistence on the optimal proportion of
scouts. (a) Change in optimal per cent of scouts due to change in the persistence of scouts. (b) Change in optimal per cent of scouts due
to change in the persistence of recruits.
collecting the maximal amount of resources decreased to a minimum near 50% (figure 3b,c), because
exploiting known resources required fewer scouts to find new resources. Previous studies estimated that
the percentage of scouts in honeybee colonies is between 5 and 35% [39]. These numbers are slightly
lower than the optimal proportions we found in our simulations. This difference between empirical
and simulated results can be eliminated by increasing the number of bees that respond to a waggle
dance in our simulations (electronic supplementary material, figure S6) and without changing any other
parameter in the model, or affecting any of our conclusions regarding persistence and task allocation
(compare figure 3 with electronic supplementary material, figure S6). Changing the number of foragers
(from 100 to 1500) did not qualitatively change how persistence and colony composition interacted to
achieve optimal resource collection (electronic supplementary material, figures S7 and S8), although, in
agreement with previous modelling efforts [59], larger colonies did induce faster collection of resources.
Lastly, the effect of including recruitment by recruits on the optimal proportion of scouts was the same as

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60
50
40
30
difference in optimal % of scouts
20
10
0
recruit
persistence
scout
persistence
Figure 6. The eect of increase in recruit persistence on the proportion of scouts that resulted in an optimal amount of resource collected
was double that of the eect of increase in scout persistence. Bars are the standard deviation across all persistence values.
that of increasing the number of recruited foragers by scouts per waggle dance (electronic supplementary
material, figure S1).
Changing the persistence of scouts had a different impact on collective foraging from changing the
persistence of recruits. We found that an increase in the persistence of recruits resulted in a decrease
in the proportion of scouts required for collecting the maximal amount of resources. By contrast, an
increase in the persistence of scouts resulted in an increase in the proportion of scouts required for
collecting the maximal amount of resources (figure 4a–d). This result suggests that the persistence of
recruits was the predominant factor impacting the optimal proportion of scouts when varying the
persistence of all foragers (figure 3). Indeed, the effect of the persistence of recruits on the proportion
of scouts that resulted in an optimal collective outcome had double the impact of persistence of scouts
(figure 6). Because recruits spend much time inside the hive, their persistence may change in response to
information about the amount of resource stocks in the hive [42,66]. Furthermore, recruits may acquire
information from several scouts that are returning from different locations and decide which one to
follow and how many trips to make to each location, depending on their relative quality [33,67,68]. If the
persistence of recruits is flexible and is determined by integrating information about resources inside and
outside the hive, the substantial impact of their persistence on collective foraging that we found suggests
that recruits may be the ones driving the adjustment of the colony’s exploration–exploitation strategy in
response to both external and internal conditions. However, if behavioural persistence is not a flexible
trait, perhaps because it is regulated by genetic or epigenetic/developmental factors [17–20,69], our
simulations show that a colony can compensate for having highly persistent scouts by allocating more
foragers to the scouting task. Interestingly, colonies with comparable persistence for scouts or recruits
collected almost the same amount of resources (compare curves with the same colour in figure 4a,b),
but the optimal proportion of scouts required to achieve the maximal amount of resource collection
differed between the two cases. Recent work suggests that persistence can be genetically determined [23],
thus one could create colonies with high persistence and examine the proportion of scouting bees
emerging in these manipulated colonies. Our model predicts that with high enough persistence, the
proportion of scouts should drop by about 40%. Alternatively, because evidence shows that scouting
is genetically determined [18], one could also manipulate the proportion of scouts in a colony, and
examine if colonies with a greater ratio between the proportion of scouts and persistence gather
fewer resources.
Learning the location of a resource did not affect the relationship between persistence and the
proportion of scouts. In our simulations, bees communicated the location of newly discovered resources,
which is known to increase resource collection in patchy environments [59,60]. Our incorporation of
behavioural persistence further enhanced this positive effect of communication by effectively simulating
‘learning’ of the target location. Return flights of scouts to a particular resource became more precise than
their initial flight during which they located the resource (figure 1a,b). Interestingly, when this learning
was removed, i.e. flights did not become more precise, the relationship between the optimal number
of scouts and persistence was unchanged but the rate of resource collection substantially decreased
(electronic supplementary material, figure S9). Thus, when repeatedly returning to the same location

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does not increase collection efficiency, the total benefits are reduced, but the collective dynamics which
dictate the relationship between persistence and optimal proportion of scouts are unchanged. It would
be interesting to further investigate the effect of increase in collection efficiency on collective dynamics
in primitively social bees that exhibit division of labour but do not share spatial information during
recruitment, e.g. bumble bees [44], or halictine bees in which there are no known mechanisms of
recruitment [68]. The effects of communication on these dynamics can also be studied in honeybees,
for example, by hindering communication through tilting their hive [69], which substantially impairs
foraging. Our model predicts that the proportion of scouts that optimizes collection of resources drops
by half if recruitment is reduced by a factor of 10 (electronic supplementary material, figure S6). This
prediction can be tested by reducing communication in the hive, for example, by turning the hive on its
side or capturing recruited bees.
The spatial and temporal abundance of resources can substantially impact foraging behaviour
[26,59,60,70]. Indeed, during the development of our model we found that an increase in the number
of resource patches caused the total amount of resources collected by the colony to increase for all
proportions of scouts, and the optimal proportion of scouts to decrease with the number of patches
(electronic supplementary material, figure S4). This finding is consistent with a model of collective
foraging in ants [71] which also found that the optimal proportion of scouts is inversely related to
the amount of resources in the environment. To examine the relationship between the proportion of
scouts in a colony and behavioural persistence, without the confounding effects of resource distribution,
we focused only on one spatial setting in our final model. The simulations we present have biological
significance for foraging in patchy resources that cannot be depleted in a single day.
In conclusion, we showed that both colony-level composition and individual-level traits interact to
impact collective outcomes. The way these levels of organization interact are not affected by the number
of resources or colony size (electronic supplementary material). Other complexities, such as the depletion
of resources, can be further added to adapt our model to more specific scenarios. Further investigation
of the mechanisms that underlie behavioural persistence and task allocation, and examination of the
timescales on which these processes act in different species and in different environments will advance
our understanding of the collective trade-off between exploration and exploitation. Our model serves as
a springboard for such investigations and can be used to generate hypotheses for further empirical work
on the regulation of collective behaviour and its response to various environmental conditions.
Data accessibility. All data collected on behavioural persistence are publicly available on FigShare [65]: https://figshare.
com/articles/Task_allocation_and_site_fidelity_jointly_influence_foraging_regulation_in_honey_bee_colonies/361
9779. Details and source code of our simulations are publicly available on Github [54]: https://github.com/
thmosqueiro/ABBAS.
Authors’ contributions. T.M. and N.P.W. designed the simulations. T.M. and R.H. designed the ODEs; and T.M. performed
all the computations. C.K. collected the data. T.M., C.K., N.P.W. and R.H. analysed the data. All authors participated
in writing the paper and gave their final approval for publication.
Competing interests. The authors declare no competing interests.
Funding. Funding for this work was generously provided by NIH grant R01GM113967 to B.H.S., N.P.W., J.G. and R.H.
T.M. acknowledges support from CNPq grant 234817/2014-3.
Acknowledgements. We thank the social insect research group at ASU for helpful comments and Dr Byron Van Nest for
comments on a previous version of the manuscript.
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