1. Many bee species show flower constancy, i.e. a tendency to visit flowers of one type during a foraging trip. Flower constancy is important for plant reproduction, but the benefits of constancy to bees are unclear. Social bees, which often use communication about food sources, show particularly strong flower constancy.

2. We aimed to better understand the benefits of flower constancy in social bees and how these benefits depend on foraging conditions. We hypothesised that sharing social information increases the benefits of flower constancy because social foragers share information selectively about high-quality food sources, thereby reducing the need to sample alternatives.

3. We developed an agent-based model that allowed us to simulate bee colonies with and without communication and flower constancy in different foraging environments. By varying key environmental parameters, such as food source numbers and reward size, we explored how the costs and benefits of flower constancy depend on the foraging landscape.

4. Flower constancy alone performed poorly in all environments, while indiscriminate flower choice was often the most successful strategy. However, communication improved the performance of flower constant colonies considerably in most environments. This combination was particularly successful when high-quality food sources were abundant and competition was weak.

5. Our findings help explain why social bees tend to be more flower constant than solitary bees and suggest that flower constancy can be an adaptive strategy in social bees. Simulations suggest that anthropogenic changes of foraging landscapes will have different effects on the foraging performance of bees that vary in flower constancy.

We built an agent-based model (ABM) using the programming software NetLogo 6.1 (Wilensky, 1999). The model simulates an environment with a colony surrounded by food sources. The agents (“bees”) operate on a two-dimensional square grid with 400 x 400 patches. A single patch length corresponds to 5 meters and 1 tick corresponds to 1 second. Thus, the size of the virtual world corresponds to 2 x 2 km. The nest of the colony is positioned in the centre of the grid (x=0, y=0). In the default situation, environments contained two different flower types that differed in the rewards they offered. The model is an extension of a model built to study foraging distances in bees (Grüter and Hayes, 2022).

The model allows simulating a wide range of parameter values, but for the purpose of this study, we based our default parameters, such as the nest stay time (t_nest), flight speed (v_flight), metabolic costs of flying (M_cost), and crop capacity (Crop) on the Western honeybee Apis mellifera because we have accurate information about these relevant biological parameters in Apis mellifera. Other values were tested (see Table 1 and section Sensitivity analysis and model exploration).

Foragers in social bees use different behavioural mechanisms to transmit social information and, thereby, influence the food source preferences of their nestmates (see introduction). The model does not simulate a particular behaviour, but a generic process that biases the food preferences of nestmates, which could correspond to jostling runs, trophallaxis or the waggle dance.

Entities and state variables

Bees

The default colony size was 100 agents (forager bees), which corresponds to the size of the forager pool in many species of bumble bees (Westphal et al., 2006) and stingless bees (Grüter, 2020). Agents could assume any of the following states: (1) generalists, (2) feeding forager, (3) searching forager, (4) returning forager, (5) inside-nest-worker and (6) influencer (see Fig. 1).

Agents begin the simulation in the centre of the nest with energy = 0 as generalists. They then move at a flying speed of 1.4 patch/tick (v_flight), corresponding to a flight speed of Apis mellifera (7 m/sec, von Frisch 1967). Their random search behaviour follows a Lévy-flight pattern (with μ = 1.4 as default) (Reynolds, 2009; Reynolds et al., 2007). A Lévy-flight consists of a random sequence of flight segments whose lengths, l, come from a probability distribution function having a power-law tail, P(l)~l^-μ, with 1<μ<3 (Reynolds et al., 2007). The speed of agents moving inside the nest (v_nest) was arbitrarily chosen to be 0.1 (patch/tick). Flying has a metabolic cost (M_cost) of 0.032 Joule (J) per tick in the default condition (Heinrich, 1975; Willmer, 2011). Once an agent encounters a food source, they remain on the food source for 60 ticks (t_flower-stay) under default conditions (feeding foragers), irrespective of whether they were choosing indiscriminately or are flower constant. Thus, we assume that the time spent handling a flower or flowers in a patch and extracting the reward is the same for flower-constant and indiscriminate foragers. This was chosen as the default condition to explore whether flower constancy can be an adaptive strategy in the absence of cognitive constraints.

The agent then continues to forage (searching foragers) until its crop is full, after which it returns to the nest (returning foragers) to unload its energy and stay in the nest for 300 ticks (t_nest-stay) (Farina, 2000; Seeley, 1986; von Frisch, 1967). In the default condition, only foragers visiting the high-quality food source could become influencers (i.e. bees that bias the food choice of other bees) upon return to the nest. Influencers target inside-nest-workers that are not yet flower-constant to the high-quality food type by changing the latter’s preference if they encountered each other on the same patch inside the nest. Following such an encounter, inside-nest-workers become flower-constant for the high-quality type.

Since recruitment behaviours often depend on the food source distance (with greater foraging distances lowering the probability of recruitment), we simulated recruitment curves where the probability of becoming an influencer decreased with increasing distance of the last visited food patch (Fig. S1).

Food sources

In the default condition, two different types of food sources offering nectar rewards can be found in the environment, mimicking the typical situation in experimental flower constancy studies (e.g. Chittka et al., 1997; Goulson & Wright, 1998; Grüter et al., 2011; Ishii & Masuda, 2014; Wells & Wells, 1983). The food source types differ in the rewards they offer per visit. Natural bee-visited flowers offer between 0.1 and 10 μL of nectar per flower (Willmer, 2011, p. 203). For the default condition, we chose 5μL (29.07 J) for the high-quality type and 2.5μL (14.535 J) for the low-quality type. This reward could represent an individual flower that offers a large reward or a small patch of several flowers, each offering smaller quantities, or it could represent a larger patch of flowers that is shared by several bees.

We tested different refill times (t_refill) for food sources: 0, 1200 and 3600 ticks (Stout & Goulson, 2002). When t_refill= 0, food sources became rewarding again immediately after the visit of a bee. This simulates conditions under which bees have a high probability of finding a reward after landing on a food source, which might occasionally occur at food patches. With t_refill= 3600, a food source (flower or patch) was empty for the equivalent of an hour after it had been visited by a bee, leading to intense exploitation competition among bees. The number of food sources per type in the simulated environment varied between 1500 (low abundance) and 4500 (high abundance). Default conditions simulated even numbers of food sources for both food source types, but we also explored uneven food source abundances (Table 1). We measured the average foraging distance of bees during a simulation run to confirm that the simulated conditions led to naturally realistic average foraging distances for many social bees (271 ± 130 m; range 63-581 m; N = 1800 simulations in default conditions) (Kohl et al., 2020; Van Nieuwstadt & Iraheta, 1996; Walther-Hellwig & Frankl, 2000).

The energy collected by agents with a full crop was estimated in the following way: Apis mellifera can carry up to ~70 μL of nectar in their crop, but they usually carry less (I’Anson Price et al., 2019; Núñez, 1966). The crop load has been shown to depend on the quality of the visited food source, with lower quality food sources leading to smaller crop loads (Núñez, 1966, 1970). Agents visiting the low-quality flower type foraged until their crop contained 25μL, whereas agents visiting the high-quality food type collected 50μL per foraging trip. Generalist bees that choose indiscriminately have an intermediate crop load, reflecting the relative number of high- and low-quality food sources in the environment. For example, in an environment with an even number of high- and low-quality food sources, they collect 37.5μL per foraging trip. Sugar concentration of collected nectar varies considerably from c. 10–70% (Seeley, 1986; Willmer, 2011). We chose an average sugar concentration of 35%, providing 5.814 J/μL.

Each simulation lasted 36,000 ticks (i.e. 10 hours), simulating a day with good foraging conditions. We measured the total energy collected by a colony during this period divided by the number of agents (Energy/bee). Our main questions were if the energy/bee depended on flower constancy (vs. indiscriminate choice), communication (vs. no communication), refill time, the number of food sources and reward size. We also tested situations when flower constancy was lower after visiting a low-quality food source (Constancy_LQ) (Grüter et al., 2011), when there were 4 food source types and when indiscriminate flower choice increased the time to extract a reward from a food source (i.e. to simulate cognitive constraints) (Chittka et al., 1999).

Sensitivity analysis and model exploration

We varied a range of other factors to explore how they affected our results. These included colony size, crop load size, flower stay time, metabolic costs, nest stay time, Lévy flight μ, selectivity of communication (i.e. bees foraging on low-quality food source become influencers with the same probability as those foraging on the high-quality type) and the shape of the recruitment curve (see Fig. S1).

We performed 30 runs per parameter combination. We do not provide p-values due to the arbitrariness of the simulation number but indicate 95%-confidence intervals to facilitate interpretation of effect sizes.