Ecological principles for the evolution of communication in collective systems
Abstract
Communication allows members of a collective to share information about their environment. Advanced collective systems, such as multicellular organisms and social insect colonies, vary in whether they use communication at all and, if they do, in what types of signals they use, but the origins of these differences are poorly understood. Here, we develop a theoretical framework to investigate the evolution and diversity of communication strategies under collective-level selection. We find that whether communication can evolve depends on a collective’s external environment: communication only evolves in sufficiently stable environments, where the costs of sensing are high enough to disfavour independent sensing but not so high that the optimal strategy is to ignore the environment altogether. Moreover, we find that the evolution of diverse signalling strategies—including those relying on prolonged signalling (e.g. honeybee waggle dance), persistence of signals in the environment (e.g. ant trail pheromones) and brief but frequent communicative interactions (e.g. ant antennal contacts)—can be explained theoretically in terms of the interplay between the demands of the environment and internal constraints on the signal. Altogether, we provide a general framework for comparing communication strategies found in nature and uncover simple ecological principles that may contribute to their diversity.
1. Introduction
Advanced collective systems, such as multicellular organisms and social insect colonies, have evolved myriad mechanisms by which individuals share information about their environment [1–10]. For example, honeybee scouts use the waggle dance to communicate the location of food sources to other workers [11–14]; immune cells use cytokines to relay information about attacking pathogens [15–17]; and plant cells use hormones to communicate about environmental stress, such as drought [18–21]. These communication mechanisms enable a collective to adjust appropriately to changing conditions without each member having to observe the environment independently [22–29].
Theoretical biologists have studied the evolution of communication extensively, but prior work has largely focused on scenarios where the evolutionary interests of senders and receivers may be in conflict (e.g. alarm calls, begging, warning colours, mating signals) [30–34]. In contrast, we know little about the factors that drive the evolution and diversity of communication strategies in collectives whose members’ evolutionary interests are largely or completely aligned, such as clonal multicellular organisms and eusocial insect colonies. While it is not necessarily surprising that communication would evolve in these advanced collectives, it is less clear why communication has evolved only in some contexts and why the evolved signals have diverse properties. For instance, some species of social bees, such as honeybees, share the location of food sources among colony members, while others, such as bumblebees, do not [35–38]. Moreover, some systems use indirect communication mediated by signals that persist in the environment, like ant trail pheromones, while others rely on direct communication mediated by individual-to-individual interactions, like antennal contacts in ants or the waggle dance in honeybees (Box 1).
Box 1. Communication in social insect foraging.
Honeybee dance language. The waggle dance in honeybees (Apis) is a pinnacle of animal communication. When returning to the nest, honeybee scouts perform a complex sequence of behaviours that inform foragers about the odour, quality and location of a profitable food source [11,13,14]. Empirical and theoretical work shows that in honeybees, the benefits of dancing strongly depend on the spatiotemporal distribution of resources, with dancing being particularly favoured when resources are clumped in space but difficult to find [39–41].
Ant pheromone trails. Various species of ants lay trail pheromones that allow the colony to visit food sources repeatedly [1,36]. Evidence suggests that variation in the persistence of trail pheromones across species reflects differences in the stability of their food sources [42,43]. For instance, the garden ant (Lasius niger), which feeds on honeydew from long-lasting aphid colonies, produces a highly persistent pheromone trail that can last for multiple days [43,44]. In contrast, the ant Pheidole oxyops, which specializes on ephemeral food sources (e.g. dead insects), employs a less-persistent trail pheromone that decays within 5−7 min [43,45]. Some species of ants use multiple pheromones with different degrees of persistence [3,36,42,43,46,47]. There is evidence that these pheromones may relay different types of information: for example a less-persistent recruitment pheromone may indicate the location of a currently available food source, while a more persistent exploration pheromone may serve as a form of external memory to indicate the location of a possibly depleted food source that has been visited previously [43,48,49].
Antennal contacts. Aside from indirect information transfer mediated by the environment (e.g. trail pheromones), some ants also use direct interactions to regulate foraging. For instance, in harvester ants (Pogonomyrmex barbatus), workers at the nest decide whether to go out and forage based on brief antennal contacts with foragers returning to the nest [50,51]. These antennal contacts allow individuals at the nest to obtain information about the current availability of food [52]. The resulting communication system allows harvester ant colonies to adjust their foraging activity rapidly, on a timescale of minutes to hours, to changes in food availability [51,53].
How can we explain this cross-system variation in whether and how members of a collective communicate environmental information? While this variation may in part reflect developmental or physiological constraints on the mechanisms for communication (e.g. signals may be restricted to a particular sensory modality), it has repeatedly been proposed that diverse communication strategies can be interpreted as adaptations to different ecological circumstances [13,14,38,48,54–57]. For example, differences in foraging environments may explain why honeybees, but not bumblebees, communicate about the location of food sources: honeybees forage on clustered, hard-to-find resources, such as fruiting trees, while bumblebees forage on scattered, easy-to-find resources, such as individual flowers [13,14,38,54]. Along similar lines, differences in environmental variability could explain why some systems have evolved to communicate information directly while others have evolved to communicate indirectly: individual-to-individual communication may be adaptive in environments that change quickly, whereas environment-mediated communication may be adaptive in stable environments [48,55]. However, the role of ecology in the evolution of communication has not been investigated systematically outside of system-specific contexts (e.g. honeybee dance [39–41], robot communication [58–60]). As a result, we lack a theoretical framework to explore whether and how ecology could explain the diversity of communication strategies across systems.
To address this gap, here we develop a mathematical model to investigate, from the collective’s perspective, the evolution of diverse strategies to communicate information about a changing environment. The model captures a range of possible signals as well as a range of possible ecological environments, characterized by how variable they are and how easily individuals can detect changes in environmental conditions. Using the model, we identify the ecological conditions that give rise to communication between individuals, and we study the types of signals that emerge when communication evolves. By design, our model applies primarily to advanced collectives that are predominantly under collective-level selection, such as clonal multicellular organisms and eusocial insect colonies. However, as we will discuss, it may also provide insights into more loosely integrated collectives where the evolution of communication also critically depends on selection at the individual level.
2. Model
We develop a mathematical model to study the evolution of collective strategies for obtaining and communicating information about a variable environment (figure 1; see table 1 for an overview of model parameters).

Figure 1. Model overview. (a) Summary of the main components of the model. (b) In a simplified model in which signalling is impossible, individuals become explorers at rate . Explorers observe the environment at rate . The environment changes at rate (dashed arrow). (c) In the full model, explorers become signallers with probability upon observing the environment. Signallers quit signalling at rate . Active individuals respond to signal at rate per unit of signal concentration, which may change whether they are informed. Signallers produce signal at rate ; signal decays at rate . In (b) and (c), the dashed arrows represent a change in the environmental state, which affects all individuals simultaneously. See electronic supplementary material, analysis 1 for a complete mathematical description of the model.
Parameters describing properties of the environment | |
---|---|
Rate of environmental change | |
Productivity benefit of having environmental information | |
Rate at which an explorer senses the environment (determines the cost of sensing ) | |
Parameters describing exploring and signalling decisions | |
Exploration rate | |
Probability that an explorer becomes a signaller upon sensing the environment | |
Parameters describing properties of the signal | |
Rate of signal production (in units of signal per unit time) | |
Rate of signal perception (per unit signal per unit time) | |
Rate of signal decay (determines the persistence of the signal) | |
Quitting rate of signallers (determines the duration of signalling) |
(a) Environmental variability
We consider a dynamic environment that can be in one of many discrete states at any time. These states could represent, for example, the availability and location of food near a social insect colony, or the presence and types of pathogens challenging an immune system. We assume that the environment randomly changes to a new state at a rate : the larger the value of , the more variable the environment. At any time, individuals within the collective can be either informed or uninformed about the state of the environment (figure 1a). For simplicity, we make the standard assumption that environmental states never repeat [61]. Under this assumption, the next environmental state cannot be predicted based on past environmental states, and all individuals instantaneously become uninformed when the environment changes (figure 1a).
(b) Sensing and signalling
Information about the environment can be obtained in two ways (figure 1a). Individuals can observe the environment directly, or they can receive signals from other individuals that have observed the environment.
(i) Sensing
Individuals can observe the environment directly by exploring it (figure 1b). At rate , individuals become explorers. Explorers successfully sense the environment at rate , upon which they become informed.
(ii) Signalling
When individuals observe the environment, they may share the newly acquired information by producing a signal indicating the state of the environment (figure 1c). Upon sensing the environment, explorers become signallers with probability . Signallers produce signal at rate , and they quit signalling at rate ; signal decays at rate (figure 1c). Active individuals (i.e. individuals not currently exploring or signalling) perceive the signal at a rate per unit of signal concentration. Uninformed individuals may become informed upon perceiving a signal. However, informed individuals may also become uninformed if the signal they respond to has become outdated owing to a change in the environmental state.
(c) Collective productivity
We assume that individuals are more productive when they are informed. For example, social insect foragers may bring in more food if they know the current location of food sources; similarly, immune cells may mount a more effective defence response if they have information about the pathogens attacking the host. The benefits of environmental information are captured by a parameter : each active individual has productivity when uninformed, and this productivity increases to when informed.
While being informed is beneficial, obtaining and sharing information about the environment may take time and energy. To incorporate such costs, we assume that individuals do not contribute to productivity (i.e. ) while they are exploring or signalling. As a result, the costs of sensing the environment are proportional to the average time that individuals spend exploring. Similarly, the costs of signalling are proportional to the average time that individuals spend signalling. In real systems, there may be additional costs of signalling, such as energetic costs associated with producing or responding to signals. In the electronic supplementary information (analysis 2), we analyse extended versions of the model that include such additional costs, and we show that their results are in qualitative agreement with the simpler model discussed here.
For advanced collectives such as social insect colonies and multicellular organisms, selection acts at the level of the collective rather than at the level of individual workers or cells. We therefore use the collective’s productivity, defined as the average productivity across all individuals, as a measure of fitness. Thus, our model assumes that the collective is always better off when more individuals are informed about the environment; we do not consider potential benefits of uninformed individuals, which may arise, for instance, in the context of collective decision-making [62]. Collectives can adopt different strategies, characterized by the frequency with which individuals explore their environment (determined by the exploration rate ), their likelihood of sharing newly obtained information with others (determined by the signalling probability ) and the properties of the signal they use to do so (determined by the signalling parameters , , and ). In our analyses below, we investigate what strategies maximize the collective productivity , depending on ecological conditions.
3. Results
(a) Sensing evolves when environmental variability is low and sensing costs are low
We begin by studying the evolution of sensing in the absence of signalling. To do so, we use a simplified version of the model with the signalling probability fixed at (figure 1b). In this sensing-only model, the productivity of the collective amounts to:
(see §5a). We use this expression to determine the optimal rate of exploration for given environmental parameters (i.e. environmental variability , sensing costs and benefits of being informed ).
We find that costly sensing evolves (i.e. ) only when the benefits of being informed outweigh the time costs of obtaining information from the environment, that is, when:
Thus, for sensing to evolve, the environment must change sufficiently slowly (low ) and environmental information must be sufficiently easy to obtain (low ) (figure 2a, green region). If these conditions are not met, the collective achieves maximum productivity by ignoring the environment altogether (; figure 2a, yellow region). The optimal exploration rate is maximized at an intermediate value of —that is when the environment changes sufficiently slowly for environmental information to be valuable but not so slowly that infrequent sensing suffices (figure 2b).

Figure 2. Evolution of sensing and signalling. (a) Optimal strategies when signalling is impossible ( fixed): ignoring the environment () or sensing the environment (). (b) Optimal exploration rate as a function of environmental variability when signalling is impossible. The rate of sensing the environment is fixed at (dashed line in (a)). (c) Optimal strategies when signalling is possible ( evolvable): ignoring the environment (), sensing only (, ), or signalling (). (d) Optimal exploration rate and signalling probability as a function of environmental variability when signalling is possible, with (dashed line in (c)). (e,f) Comparison of the optimal strategies when signalling is possible with the optimal strategies when signalling is impossible, for . (e) Fraction of time during which each individual is exploring. (f) Relative increase in productivity achieved with signalling. Parameter values: , , , , . See electronic supplementary material, figure S1 for the optimal values of and across the whole parameter space.
(b) Signalling evolves when environmental variability is low and sensing costs are intermediate
To investigate the evolution of signalling, we next turn to the full model, in which the signalling probability can be non-zero (figure 1c). The full model is still analytically tractable, and we derive a closed-form expression for collective productivity (see §5b). Using this expression, we determine what combination of exploration rate and signalling probability maximizes collective productivity. In other words, we allow the collective to simultaneously optimize how frequently individuals sense their environment and whether or not they share information with others upon doing so.
Even when signalling is possible, the two strategies identified previously—ignoring the environment () and sensing the environment without signalling (, )—remain optimal under some conditions (figure 2c,d). But we also find that signalling (, ) is evolutionarily optimal for a range of conditions (figure 2c, blue region). Similar to the evolution of sensing, signalling evolves only if the environment changes sufficiently slowly and the costs of sensing the environment are sufficiently low (figure 2c, blue region). However, for very low sensing costs, collective productivity is maximized when individuals sense the environment independently and avoid the costs associated with sharing information, which leads to the evolution of sensing only (without signalling; figure 2c, green region). Thus, for signalling to evolve, environmental information must be neither so costly to obtain that individuals evolve to ignore the environment entirely, nor so inexpensive that individuals can rely on independent observations.
The predictions in figure 2c are consistent with what is known empirically about the evolution of communication in bees. Some species of social bees, such as bumblebees, independently locate food sources (corresponding to the sensing-only strategy in our model), whereas others, such as honeybees, communicate about the location of food sources (corresponding to the signalling strategy in our model). The evolution of communication in honeybees is typically attributed to a foraging environment in which food patches are hard to find (i.e. sufficiently high sensing costs ) and they persist for long enough to allow repeated visits (i.e. sufficiently low environmental variability ) [14,38,54]. Indeed, higher sensing costs or lower environmental variability (or both) can move a collective from the sensing-only regime to the signalling regime in figure 2c.
The signalling regime in figure 2c largely falls within the sensing regime in figure 2a, but it also encroaches on the ignoring regime, such that signalling can be favoured even under conditions that do not favour sensing in the absence of signalling. When individuals cannot signal ( fixed, simplified model; figure 1b), sensing a fast-changing environment may not be favoured because the benefits of a single observation do not outweigh the costs of sensing. However, when individuals can signal ( evolvable, full model; figure 1c), the same environment may favour sensing because the benefits of sensing the environment are higher when individuals can share observations with others (figure 2e). This finding highlights a potential advantage of group living: collectives can extract information from their environment more efficiently than solitary individuals, which allows collectives to invest in learning about their environment even when solitary individuals cannot afford to do so [63,64].
Finally, our model predicts that the benefits of signalling are maximized in environments of intermediate variability (figure 2f). This finding sheds light on the relationship between the persistence of food patches and the benefits of dancing in honeybees. The nature of this relationship has remained controversial [14]: some studies have suggested that dancing is most beneficial when food sources are ephemeral and cannot be found independently [39,65], while others have suggested that dancing is most beneficial when food sources are long-lasting and provide sustained benefits [41]. Our model provides a way to reconcile these ideas: for the benefits of communication to be maximized, the environment should change neither so slowly that independent sensing is already effective, nor so quickly that communication provides only marginal benefits.
(c) Trade-offs between signal reach, signal quality and signalling costs shape the evolution of signalling
Our analysis has identified environmental conditions for the evolution of signalling, assuming that individuals communicate using a particular signal with exogenously fixed properties. However, the range of environments in which signalling can evolve may also depend on the properties of the signal, as determined by the signal production rate , signal perception rate , signal persistence and signalling duration . We will therefore next explore the impact of these parameters on the evolution of signalling.
The parameters , , and determine the values of two key signal properties that emerge naturally in the mathematical conditions for the evolution of signalling (electronic supplementary material, figure S2):
The reach of the signal is the average number of individuals that perceive the signal produced by a signaller. The quality of the signal is the probability that the signal carries up-to-date information about the state of the environment. The expression for signal quality reflects that information communicated in a signal can become outdated in two ways: the environment may change while the signaller is signalling, which occurs with probability , or it may change between the production and perception of the signal, which occurs with probability .
Signalling can only evolve when signal reach and signal quality are sufficiently high (electronic supplementary material, figure S2). This condition restricts the evolution of signalling to certain values of the signal parameters. First, because increasing the rate of signal production (or the rate of signal perception ) increases signal reach but does not impact other signal properties, (and ) must be sufficiently high for signalling to evolve (figure 3a, blue line). Second, increasing signal persistence also increases signal reach, but at the expense of signal quality: a signal that persists longer reaches more individuals, but it is also more likely to carry outdated information. Therefore, signalling can only evolve for intermediate levels of signal persistence (figure 3b, blue line). Third, the duration of signalling mediates a similar trade-off between signal reach and signal quality, and it also affects signalling costs. As a result, signalling can evolve if signalling duration is not too long (figure 3c, blue line), but the net benefits of signalling are maximized at intermediate levels of signalling duration (figure 3c, arrow). Thus, whether signalling can evolve depends on the properties of the signal.

Figure 3. Trade-offs shaping the evolution of signalling. Benefits and costs of signalling as a function of the rate of signal production (a), signal persistence (b) and signalling duration (c). The benefits of signalling represent the increase in productivity due to active individuals being more informed (which can be negative for a low-reach or low-quality signal), while the costs of signalling represent the decrease in productivity due to individuals spending time signalling. Both the benefits and the costs of signalling are computed at ; their difference is equal to the (marginal) productivity gain (see electronic supplementary material, analysis 3 and figure S2a, condition I). Parameter values: , , , , , (b, c), (a, c), (a, b).
When we repeat the analysis in figure 2c for different signals, we indeed find that signals with different properties result in signalling regimes with different sizes and shapes. Consistent with figure 3a, signals with a higher signal production rate or signal perception rate have a larger signalling regime that is expanded in all directions (electronic supplementary material, figure S2a,b). On the other hand, signals that are more persistent (higher ), which have a higher reach but a lower quality (figure 3b), give rise to a signalling regime with a different shape (electronic supplementary material, figure S2c). We find similar results for signalling duration (electronic supplementary material, figure S2d). In other words, increasing signal persistence or signalling duration may, depending on the context, either facilitate the evolution of signalling where it was previously impossible or prevent the evolution of signalling where it was previously possible.
Altogether, we conclude that while our results on when signalling can evolve (figure 2) are qualitatively robust to changes in signal properties, the size and shape of the signalling regime depend quantitatively on the signal parameters. The effects of different signal parameters on the evolution of signalling can be understood through trade-offs between signal reach, signal quality and signalling costs (figure 3). Moreover, these trade-offs—and the resulting constraints on the signalling parameters—are qualitatively robust to extending the model to include additional costs to signal production or signal perception (electronic supplementary material, analysis 2, figure S4).
(d) Diverse signalling strategies emerge from the interplay between ecological conditions and internal constraints
We have found that the properties of the signal determine the range of environments that favour signalling. This suggests that, conversely, ecological conditions may select for particular types of signals. To explore this possibility, we allow the signal properties themselves to evolve and we ask what signals are optimal across different environments. Specifically, we vary the environmental parameters (environmental variability and cost of sensing ) and, for a given environment, compute the combination of signal probability , exploration rate , signalling duration and signal persistence that maximizes productivity (figure 4a and electronic supplementary material, figures S5, S6). In other words, we allow the collective to optimize how frequently individuals obtain and share environmental information, the duration of individuals' signalling and how long the signal persists. As before, we treat the rate of signal production and the rate of signal perception —the product of which determines the efficiency of signal transmission—as fixed constraints, because increasing these parameters always improves productivity. In addition, we assume an upper bound for signal persistence because it is unlikely that signals are able to persist indefinitely. The other parameters are left unconstrained.

Figure 4. Evolution of diverse signals. (a) Optimal signals across ecological conditions. The dashed lines delineate the boundaries of the signalling, sensing-only and ignoring regimes (see figure 2c). Each triangle represents the optimal signal for a combination of environmental parameters (environmental variability and sensing cost at the grey dot inside the triangle). Triangle width represents optimal signalling duration , and triangle height represents optimal signal persistence . Three strategies are highlighted that rely primarily on long signalling duration (strategy I), high signal persistence (strategy II) and high signalling frequency (strategy III). (b) Social insect communication systems illustrating strategies I–III. (c) Optimal signal persistence and signalling duration as a function of environmental variability , for a fixed sensing cost . (d) Optimal signal persistence and signalling duration as a function of sensing cost , for a fixed environmental variability . (e) Optimal signal persistence and signalling duration as a function of signal transmission efficiency , for a fixed sensing cost and environmental variability . In (c–e), bands indicate the range of values for which collective productivity is within of the optimal productivity. Parameter values: (all panels), , (all panels except (e)). See electronic supplementary material, figure S5 for the values of , , and . See electronic supplementary material, figure S6 for quantifications of emergent signalling properties (including reach, quality and frequency of signalling).
When sensing is costly (high ), we find that evolution favours high-reach signals with high signal persistence and long signalling duration (tall and wide triangles in figure 4a). When sensing costs are sufficiently high, signals with the maximum possible persistence become optimal and signal reach can only be increased further by increasing signalling duration (figure 4a, strategy I). Collectives using the resulting strategy (I) thus deploy a high-reach signal that, owinghe constraints on signal persistence, relies primarily on prolonged signalling for efficient information transmission.
By contrast, when sensing is cheap (low ), selection on signal reach relaxes and collectives can reduce signalling duration to mitigate the costs of signalling. Slowly changing environments still favour highly persistent signals (narrow but tall triangles; figure 4a, strategy II), giving rise to a strategy that relies primarily on the signal’s persistence to transmit information. As environmental variability increases and information becomes outdated more quickly, optimal signal persistence decreases (shorter triangles), giving rise to low-reach signals with short signalling duration and low signal persistence (narrow and short triangles; figure 4a, strategy III). To compensate for the decrease in signal reach, collectives using strategy III signal more frequently (electronic supplementary material, figure S6c) and thus rely primarily on signalling frequently rather than high signal reach. Overall, strategies I–III highlight that optimal information transmission can be achieved in different ways: strategy I relies primarily on broadcasting the signal for an extended period, strategy II relies primarily on having the signal persist in the environment, and strategy III relies primarily on deploying the signal frequently.
Model strategies I–III resemble communication strategies found in social insects (figure 4b; see also Box 1). For example, similar to strategy I, honeybee scouts spend a considerable amount of time on the dance floor to share information about the location of resources. Similar to strategy II, garden ant workers guide others to food sources using persistent pheromone trails that can last up to days [43]. And similar to strategy III, in harvester ant colonies, returning foragers have brief interactions with workers at the nest to relay information about food availability [50]. Beyond social insects, we can also find parallels in the mammalian immune system: for example, dendritic cells exhibit signalling behaviour similar to strategy I by presenting antigens for an extended period—up to several days [66]—while neutrophils lay trails of chemokines to direct T cells to localized infections [67], similar to strategy II.
The parallels between theory and reality allow us to probe the ecological factors that may explain the properties of existing communication systems. For example, based on their relative positions in figure 4a, we predict that high sensing costs (e.g. hard-to-find resources) may have contributed to the evolution of prolonged dancing in honeybees; that low environmental variability (e.g. stable food sources) may have contributed to the evolution of persistent trail pheromones in garden ants; and that comparatively higher environmental variability (e.g. fluctuating food availability or weather conditions) may have contributed to the evolution of frequent but brief communicative interactions to regulate activity in harvester ants.
From the results in figure 4a, we can extract general predictions for how signal properties depend on environmental variability (figure 4c) and sensing costs (figure 4d). First, as environments change faster, optimal signalling duration and signal persistence generally decrease (figure 4c). In the environments that change most rapidly, this relationship reverses to compensate for the reduction in sensing rate (electronic supplementary material, figure S5a); however, this effect is weak and largely disappears when signalling is costlier (i.e. when additional, direct signalling costs are included in the model; electronic supplementary material, figure S7). The more robust prediction that signal persistence decreases with environmental variability is consistent with observed variation in the persistence of ant trail pheromones (box 1): stable environments tend to be associated with more persistent pheromones compared to more variable environments.
Second, we predict that signalling effort increases with sensing costs: as the costs of sensing increase, optimal signalling duration and signal persistence both increase (figure 4d). The dramatic increase in signalling duration, especially when maximal signal persistence is reached, results in extensive temporary specialization between signalling and non-signalling roles: individuals signal for a long time before they return to doing something else. We speculate that this temporary specialization may be a precursor to the evolution of dedicated signalling specialists, like sensory cells in multicellular organisms, especially when sensing or signalling costs differ between individuals.
Beyond ecological conditions, optimal signalling strategies are likely also shaped by physiological constraints, such as constraints on the efficiency of signal transmission (as determined by the fixed parameters and ) and constraints on the maximum persistence of the signal (as determined by the upper bound for ). As we have seen above, constraints on signal persistence may lead to the evolution of strategy I, which relies primarily on broadcasting a signal for a long time. The fact that dancing honeybees use such a strategy may therefore reflect not only an environment where observations are costly, but also the fact that visual signals, such as the waggle dance, are constrained in their persistence.
To explore the effects of constraints on the efficiency of signal transmission, we determined optimal signal persistence and optimal signalling duration across a range of values of . We find that as the efficiency of signal transmission increases—for example because of increased receiver density (which is one way of increasing the rate of signal perception, )—optimal signal persistence and signalling duration both decrease, which in turn increases signal quality (figure 4e). We therefore predict that, all else being equal, low signalling duration and low signal persistence (i.e. signalling using brief communicative interactions, as in strategy III) are more likely to evolve when signal transmission is more efficient, for example in larger groups with a higher density of individuals.
Taken together, our analyses reveal that diverse signalling strategies—that differ in signalling duration, signal persistence and signalling frequency—can be evolutionarily optimal. The emergence of these different strategies is qualitatively robust to including additional costs to signal production or signal perception (electronic supplementary material, analysis 2, figure S7), although there are some quantitative differences. For example, when signal production is more costly, optimal signals rely less on increasing signalling duration and more on increasing signal persistence (electronic supplementary material, figure S7a,b).
4. Discussion
We have developed a mathematical model to explore the evolution of communication in advanced collective systems, such as multicellular organisms and social insect colonies. This model focuses on the role of ecology in shaping optimal communication strategies.
Our first set of results concerns when communication can evolve in the first place (figure 2). We find that even when members of a collective have aligned, rather than competing, evolutionary interests, communication does not necessarily evolve. Communication about some aspect of the environment—e.g. food availability—evolves only if two ecological conditions are met: that aspect of the environment must be sufficiently stable (low environmental variability), while the costs of observing it must be neither so high that it is better to ignore the environment altogether nor so low that individuals can afford to sense the environment independently (intermediate sensing costs).
The question of when social exchange of information can evolve has been addressed previously in theoretical models for the evolution of learning [61,68–72], in which individuals can adopt either individual learning (i.e. exploration) or social learning (i.e. imitation) to adapt to their environment. Our model differs from these models of learning in two ways. First, in learning models, evolution acts on individual receivers, whereas in our model evolution acts on the collective as a whole. Second, our model describes true communication that involves signals that are costly to produce, whereas learning models rely on cues rather than signals. Despite these differences, the two approaches agree that social exchange of independently obtained information can evolve when the environment is sufficiently stable and that independent exploration (or ignoring the environment altogether) becomes optimal when the environment is too variable [61,69].
Our second set of results develops expectations for how collectives evolve to communicate. We show that collectives face trade-offs between signal reach, signal quality and signalling costs (figure 3) and that diverse communication strategies can be evolutionarily optimal as a result (figure 4). Collectives may, for example, adopt communication strategies that rely primarily on a long duration of signalling (e.g. waggle dance in honeybees), persistence of the signal in the environment (e.g. trail pheromones in garden ants) or a high frequency of brief communicative interactions (e.g. antennal contacts in harvester ants; figure 4a,b). The conditions that favour each of these strategies can be understood in terms of the interplay between the demands of the collective’s external environment and internal constraints on the signal. For instance, an environment in which sensing costs are higher will generally favour more prolonged signalling to take maximal advantage of costly observations (figure 4d), while a collective constrained by a low density of potential receivers will generally evolve more persistent signals to allow for sufficient signal reach (figure 4e).
Testing the predictions of the model empirically is far from straightforward, as doing so requires deciphering what environmental information is contained in a signal and describing quantitatively the dynamics of both the environment and the signal. Nonetheless, when all this information can be obtained (as is currently the case for only a few systems, such as the most well-studied social insects), then model predictions can be evaluated by comparing communication strategies across different species, or by comparing a single collective’s communication strategies across time (e.g. [73]) or across contexts. Across species, for example, our model predicts that species tend to adopt signalling strategies in stable environments or when environmental information is costly, whereas they tend to adopt sensing-only strategies in variable environments or when information is inexpensive—a prediction that is consistent with evidence from social bees (§3b). Similarly, within species, our model predicts that collectives should use more persistent signals when communicating about environmental features that are more stable—a prediction that is consistent with evidence from ant species that have in their signalling repertoire multiple pheromones with different degrees of persistence (box 1; §3d).
Our framework applies primarily to advanced collectives that are predominantly under collective-level selection, such as clonal multicellular organisms and eusocial insect colonies. Nevertheless, our findings may also have implications for more loosely integrated collectives that are largely shaped by individual-level selection, such as groups of cooperatively breeding vertebrates [74,75]. While our model cannot explain why communication evolved in these collectives, it can be used to ask how information is communicated. Indeed, when a communicative interaction is mutually beneficial, senders and receivers share an interest in optimizing that interaction, and our model predicts how they would do so depending on ecological circumstances. At the same time, however, individual incentives present various challenges to the robustness of the predicted communication strategies. Individuals may avoid paying the costs of collecting and sharing information while reaping its benefits (cheating) [76]; signallers may mislead receivers by sharing inaccurate information (deception) [77,78]; and third-party receivers may intercept signals (eavesdropping) [79–83]. These behaviours are likely to impact some signals more than others: for example, signals that are costly to produce may be particularly susceptible to cheating, while indirect signals that persist in the environment may be particularly susceptible to eavesdropping. Deciphering the resulting consequences for the evolution of communication will require an integrated approach that combines the classical, individual-level perspective on the evolution of communication [30–34] with the complementary, collective-level approach developed here.
5. Methods
(a) The evolution of sensing
When signalling is impossible (), individuals independently obtain information about their environment. In this simplified version of the model (figure 1b), collective productivity (i.e. the average productivity of individuals) is equal to:
The first factor represents the proportion of time that individuals are active, which depends on the rate at which individuals become inactive to explore the environment and the rate at which individuals sense the environment and return to being active. The second factor represents the average productivity of active individuals, which depends on the benefits of being informed, the exploration rate and environmental variability .
Using expression (5.1), we find that sensing the environment is favoured when
which is equivalent to . For , the optimal rate of sensing is . For , the optimal rate of sensing is given by
which is maximized at intermediate environmental variability .
(b) The evolution of signalling
In the electronic supplementary information (analysis 1), we show how to derive the following expression for collective productivity in the full model:
The expression has a similar structure to the corresponding expression (5.1) for the simplified model (and reduces to it for ). The first factor, , represents the proportion of time individuals are active, which depends on how much time individuals spend sensing and signalling. The second factor represents the average productivity of active individuals, which depends on their access to environmental information.
(c) Numerical optimization
We used quasi-Newton optimization (implemented in the function nlminb in R v. 4.1.2 [84]), a standard numerical technique, to maximize expression (equation 5.4) under different constraints. In each analysis, we fixed most of the parameters and then numerically determined what values of the remaining ‘evolvable’ parameters maximize .
For the evolution of sensing and signalling (figure 2c,d), the evolvable parameters were and . For each parameter combination, we ran the optimization algorithm from 15 initial points, corresponding to all possible combinations of and .
We ran the optimization on rather than itself because we found that the optimal varied over multiple orders of magnitude across simulations. When the optimal was found to be equal to the minimum allowed value, we treated it as if it was .
For the evolution of signal properties (figure 4), the evolvable parameters were , , and . For each parameter combination, we ran the optimization from 825 initial points, corresponding to all possible combinations of: , , , .
Formally, we cannot exclude the possibility that there are global optima that our optimization procedure is unable to find. We consider this possibility unlikely, however, given the large grid of initial points and the fact that the objective function has a simple mathematical form. Therefore, we treat the optimum found across all runs of the optimization procedure as the evolutionary outcome.
Ethics
This work did not require ethical approval from a human subject or animal welfare committee.
Data accessibility
Code to run the simulations and generate the figures is provided in [85]. Supplementary material is available online [86].
Declaration of AI use
We have not used AI-assisted technologies in creating this article.
Authors’ contributions
M.S.: conceptualization, formal analysis, investigation, methodology, visualization, writing—original draft, writing—review and editing; C.E.T.: supervision, writing—review and editing; M.K.: conceptualization, methodology, writing—review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration
We declare we have no competing interests.
Funding
M.K. gratefully acknowledges support from James S. McDonnell Foundation (Postdoctoral Fellowship Award in Understanding Dynamic and Multi-scale Systems, doi:10.37717/2021-3209).
Acknowledgements
We thank Andrea Graham and members of the Tarnita lab for helpful discussions and suggestions.