Cognitive simplicity drives collective route improvements in homing pigeons

For decades, humans have been intrigued by the remarkable ability of animals to navigate their environment (Krause and Ruxton, 2002; Wiltschko and Wiltschko, 2003; Åkesson et al., 2014; Wiltschko and Wiltschko, 2023). Fascinating examples include the annual pole-to-pole migration of Arctic terns (Egevang et al., 2010; Alerstam et al., 2019) and sooty shearwaters (Shaffer et al., 2006) that achieve flight distances spanning thousands of kilometers or the precise navigation of anadromous salmon, swimming from the open ocean to return to their natal spawning grounds (Thorpe, 1988; Quinn, 2018). To achieve these marvelous feats, animals utilize a variety of environmental information to guide their journey at different length scales–for example, polarized light (Muheim et al., 2006) or geomagnetic cues (Brothers and Lohmann, 2015; Karwinkel et al., 2024) can roughly guide animals across long length scales, while olfactory cues (Bett and Hinch, 2016) and visual landmarks (Dreyer et al., 2018) are more useful at shorter length scales.

Animals living in groups can further reduce directional uncertainty through social interactions. One way this can be achieved is by the direct social transfer of information. In such cases, the group leader (or a few members of the group, who are often older or more experienced) guide the rest of the group in their preferred direction via a leader-follower relationship (Couzin et al., 2005; Nagy et al., 2010; Nagy et al., 2013; Strandburg-Peshkin et al., 2015; Strandburg-Peshkin et al., 2018; Sampaio et al., 2024; Berdahl et al., 2018). For example, dominant female meerkats have higher influence in leading group movements, especially movement turn and speed, due to their experience and frontmost position in the group (Averly et al., 2022). Through these leadership dynamics, expertise can propagate through the group, allowing less knowledgeable individuals to exhibit improved navigational performance.

An alternative socially-mediated mechanism that can improve migration efficiency is the ‘wisdom of crowds’, where large groups improve their decision by averaging individual opinions (Berdahl et al., 2018). This mechanism benefits from the law of large numbers, whereby individual errors cancel each other out with increasing group size, resulting in greater collective accuracy (Galton, 1907; Simons, 2004) (assuming that the distribution of opinions is roughly centered around the optimal value; Kao et al., 2018). In contrast to the leadership mechanism described above, here the group outcome is emergent. In other words, the collective decision may be highly accurate even if there are no knowledgeable individuals in the group at all. Furthermore, this mechanism has low cognitive requirements, since it does not require group members to recognize differences in knowledge or experience. In both humans and non-human animals, across different behavioral contexts, the wisdom of crowds has been shown to improve outcomes as group sizes increase (Sumpter et al., 2008; Dell’Ariccia et al., 2008; Faria et al., 2009; Krause et al., 2011; Ward et al., 2011; Prelec et al., 2017).

However, the two mechanisms described above are not mutually exclusive. Weighted average strategies (Bahrami et al., 2010; Koriat, 2012), where more experienced, knowledgeable, or confident individuals hold greater influence in the collective decision, but other individuals still have some decision weight, may capture the benefits of both existing knowledge and emergent solutions. While sociality can theoretically support a multitude of distinct and non-mutually exclusive strategies for improving navigation efficiency, the extent to which animals use each strategy in practice remains unclear. In particular, how the optimal strategy depends on the type of decision that animals face, the cognitive ability of the animals, and other details of the species’ life history, remains poorly understood.

Learning through time

Many animals usually make repeated trips between two locations in a given period of time. At small spatial scales, these journeys may be between known locations within their home range (Strandburg-Peshkin et al., 2015), or at larger spatial scales, they may be seasonal migrations that occur annually (Flack et al., 2018). A solitary individual may improve its performance across bouts by sampling multiple routes and preferentially remembering better ones. However, the individual faces a classic exploration-exploitation trade-off (Mehlhorn et al., 2015) between spending time exploring new routes (which may be associated with unknown and possibly severe risks) or utilizing previously known routes that are less costly. Furthermore, an individual can attempt a trip only a finite number of times, ultimately limited by its lifespan, which sets an upper bound on the ability of a single individual to improve its learned route over time.

One way in which animals can overcome the finite time horizon set by an individual lifespan is by genetically encoding migratory information—such as when and where to migrate—so that it can be inherited by future generations (Liedvogel et al., 2011; Väli et al., 2018). However, encoding information genetically can be slow and susceptible to environmental variations (Cavalli-Sforza and Feldman, 1973; Whiten et al., 2017; Whitehead et al., 2019). Alternatively, traveling in a group can allow less-informed individuals to incorporate information from others into their own learned route, thereby permitting information to pass across individuals (and time). When such social learning is coupled with the ability to recognize beneficial solutions and prune out costly mistakes, improved solutions can be preferentially spread horizontally and/or vertically. Such ‘ratchet’-like improvements are referred to as cumulative cultural evolution (CCE), in recognition of its functional similarity to genetic evolution (i.e., variation, heritability, and selection). CCE has been observed in humans and some non-human animals (Boyd and Richerson, 1996; Tomasello, 2009; Dean et al., 2014; Creanza et al., 2017; Miton and Charbonneau, 2018; Whitehead et al., 2019), including primates (Yamamoto et al., 2013; Whiten et al., 2022b; van Leeuwen et al., 2024), birds (Hunt and Gray, 2003; Sasaki and Biro, 2017; Aplin, 2019; Williams and Lachlan, 2022), and cetaceans (Krützen et al., 2005; Mann et al., 2012; Garland et al., 2022). CCE is usually inferred as the underlying process when improvements ‘accumulate’ over time, even though the social learning mechanism(s) that lead to these improvements have not been directly observed (see Mesoudi and Thornton, 2018 for core criteria required for CCE and Hunt and Gray, 2003; Claidière et al., 2014 for examples of such cases). Yet, as previously discussed, alternative mechanisms such as the wisdom of crowds could in principle also cause an increase in task performance, without the need for other components associated with CCE (Mesoudi and Thornton, 2018).

In this study, we build upon one such example, by Sasaki and Biro, 2017, in which homing pigeons (Columba livia) were shown to improve their navigational performance over time, but the mechanism by which they do so remains a mystery. Homing pigeons are a highly social species that have been extensively studied for their ability to develop idiosyncratic routes and recall them across repeated flights, making them an ideal model organism for studying navigational strategies (Matthews, 1951; Wallraff, 2001; Nagy et al., 2010; Flack and Biro, 2013; Nagy et al., 2013; Sasaki and Biro, 2017). In their experiment, Sasaki and Biro created ‘chains’ of birds, similar to a game of telephone, and allowed them to fly back home repeatedly from a release site 8.4 km away. In the experimental condition, each chain was composed of five ‘generations’, with each generation consisting of 12 flights home. In each generation, an experienced bird, having developed knowledge about the homing task from the previous generation, was paired with a naïve bird that lacked this information. At the end of the generation, the experienced bird was removed and a new naïve bird was paired with the remaining (now-experienced) bird (see ‘Methods’ for details). As control conditions, solo and fixed pairs of birds were flown for the same total amount of flights as in the experimental condition (60 flights) (Figure 1A). To quantify the performance of the birds, the route efficiency, calculated as the ratio of the beeline distance (straight line distance between the release and home sites) to the actual distance traveled by the pair, was measured (a value of 1 indicates a beeline flight, while a value of 0 indicates an infinitely long flight).

Figure 1

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The study found that the experimental chains of birds significantly outperformed both the solo and fixed pair controls by the end of the fifth generation (Figure 1B). The researchers proposed CCE as the mechanism driving this result, where chains of birds improve their routes by exploring different options and selectively choosing better ones. Valentini et al. examined the trade-offs between exploration and exploitation of new routes by the naïve and experienced birds (Valentini et al., 2021), showing that both birds had an equally likely chance of initiating collective explorations. Despite these insights, a detailed mechanistic understanding of how route improvements emerge in pigeon chains is still lacking. For instance, it remains unclear what (social and/or environmental) information birds are sensing and using, and what kinds of computations they are performing on that information to produce the observed increase in route efficiency across generations.

Here, we hypothesized several plausible learning mechanisms that bird pairs might employ during homing navigation. We simulated each of these mechanisms using artificial chains of birds composed of trajectories from the solo control dataset and applied a weighted averaging procedure (which depended on the mechanism under study) to mimic the outcome of paired flights in a generation, analogous to the actual experimental design. It is also important to clarify that we use the terms mechanism or strategy in a more abstract manner rather than in a purely mechanistic way. In other words, we model how two trajectories (representing the ‘preferred’ path of two birds) map to a new trajectory (representing the joint path of the two birds flying as a pair), rather than the moment-to-moment decisions of each bird. This is because neither the underlying biological basis of the birds’ decisions, nor different sources of noise (e.g., perceptual noise, decision noise, environmental noise) can be uniquely inferred using the available geospatial data. Moving forward, we will be using the terms mechanism(s) or strateg(ies) interchangeably to indicate these meta-mechanism(s), while the actual cognitive mechanisms that lead to these meta-mechanisms arising remain an open question. Our learning strategies can be organized into three classes based on the kind of information required to execute the strategy. We quantitatively compared the predictions generated by each strategy with the experimental data to infer which strateg(ies) real birds are most likely to be using. By doing so, we can assess what kind of information and cognition pigeons may be using during paired homing flights. In particular, we ask whether the cognitive requirements of CCE are necessary for the observed improvement in navigation ability.

The navigational model

To simulate the experimental condition, we created artificial chains of bird pairs—similar to the experimental design—using bird trajectories from the solo control condition. We used the 12th flight of each solo control bird, since birds typically established stable idiosyncratic routes by this point, with minimal improvements in subsequent releases. In our model, we assumed that when two birds are paired together, a shared route is formed from their individual routes, which is the outcome of the learning process that the two birds engage in over the course of 12 releases. We model this learning process using a weighted averaging procedure for each pair (see ‘Methods’ for details). The naïve bird in that pair replaces its idiosyncratic route with this new averaged trajectory and becomes the ‘experienced’ bird in the next generation, where it is paired with a new naïve bird drawn from the solo control condition to continue the sequence. This iterative process—sampling a bird, generating the averaged route, assigning it as the ‘experienced’ bird for the next generation, and pairing it with another bird—was repeated for five generations, matching the actual experimental chains. The weighting parameter $w_E$ used in our model quantifies the influence (i.e., leadership) of the ‘experienced’ bird. As a comparison, for the experimental birds, we measured leadership based on the relative front-back positions of the birds during flights (since leaders have been found to take frontal positions across many species; see ‘Methods’ for details). We compared the route efficiencies and social weights of the experienced bird resulting from each simulated strategy with the experimental data to identify which candidate strateg(ies) are compatible with the empirical data.

We simulated seven strategies, which can be categorized into three types based on the kind of information required to execute the strategy. The first type $(T_1)$ represents the simplest process, where birds have no knowledge of their partner’s level of experience or performance (Figure 2A). This includes only the averaging strategy, where both birds weigh their individual routes equally in each generation, regardless of their respective navigational abilities.

Figure 2

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The second type $(T_2)$ assumes that birds are capable of recognizing the more experienced individual within the pair and adjust their social weighting to maximize performance using this knowledge (Figure 2B). Indeed, empirical evidence suggests that individuals can rely less on social information as they gain more experience (Brønnvik et al., 2024). Within $T_2$, the experienced bird weighting strategy assumes that the experienced bird maintains a constant weight $w_E$ across all generations, where $w_E$ is chosen such that route efficiency, on average, is maximized for the fifth generation. Alternatively, the maximize generation strategy allows the experienced bird to adjust its weight $w_E$ based on the generation the bird is in, thereby maximizing the route efficiency for each generation.

The third type $(T_3)$ introduces the highest level of cognitive complexity, requiring birds to actively evaluate their individual or paired performance (Figure 2C). The strategies in $T_3$ align with the mechanistic criteria required for CCE, where individuals can recognize and select for better-performing routes. Within $T_3$, the first strategy, better bird weighting, assigns the better bird (i.e., the bird in the pair that has a shorter individual route, regardless of its experience level) a weight $w_B$ that maximizes efficiency in the fifth generation. Here, information from the worse-performing bird is still incorporated in the weighting process (with a weight $1-w_B$) before passing to later generations. A more extreme version of this strategy is the all-or-nothing strategy, wherein the better bird takes full despotic control (i.e., $w_B=1$), propagating only the best-performing routes across generations, with no contribution from the worse bird. The remaining two strategies focus on adjusting ‘local’ aspects of a paired flight. In the maximize flight strategy, birds aim for finding the best achievable route as a pair. For a particular pair of birds, this is a unique pair of weights w and $1-w$ that maximizes the route efficiency of the resulting trajectory. Finally, the maximize time steps strategy assumes that birds can judge their joint performance moment-to-moment and make adjustments to their heading at each time step during a flight. In this strategy, the bird with a preferred route closer to the beeline at a given moment, on average, exerts greater influence over the paired flight, pulling the pair closer to the correct homing direction.

Collectively, these strategies range from the minimal cognitive requirement $(T_1)$ to recognizing one’s own experience level $(T_2)$ to evaluating the relative quality of the preferred routes of the two birds $(T_3)$. We systematically tested the seven strategies by generating all possible combinations of chains from the solo control trajectories and measured the resulting distribution of route efficiencies and social weights used by the experienced bird for each generation. Using a mixed modeling approach, we fitted two different models, one for the responses of route efficiency and one for the social influence of the experienced bird (see ‘Methods’ for details) and compared the results to the experimental data.

In this study, we investigated potential navigational strategies, which varied in the level of cognitive complexity required to execute them, to infer the mechanism of collective route improvements in homing pigeons. Our work builds upon a 2017 experiment which demonstrated that pairs of experienced and naïve pigeons could iteratively improve homing routes over generations. Specifically, our aims were threefold: (1) provide insights into the mechanism(s) pigeons use to improve route efficiency, (2) investigate how cognitive complexity, as well as experimental design (turnover of birds), relate to performance, and (3) investigate if the identified mechanism(s) fall under the criteria required for CCE. To achieve this, we developed seven plausible mechanisms, broadly categorized into three types ($T_1$, $T_2$, and $T_3$), with increasing cognitive complexity. We created a simple navigational model by artificially pairing solo bird trajectories, similar to the experimental design, and tested our strategies to identify candidate strateg(ies) that are quantitatively compatible with the empirical data. All of our strategies resulted in route improvements, regardless of their underlying complexity. However, when combined with the results from the social weight analysis, the experimental data overall aligned best with the simplest strategy: averaging individual routes.

The route efficiency achieved generally increased with the cognitive complexity of the strategy—strategies in $T_3$ tended to perform the best. However, this was not always the case. Specifically, the all-or-nothing strategy ($T_3$), where only the best route was passed to the next generation, performed no better than the simple averaging strategy ($T_1$). This can be explained by recalling that there are two sources of information: leadership from experts and emergent wisdom of crowds. The all-or-nothing and the averaging strategies, respectively, represent these two ‘pure’ strategies. By contrast, all of the other strategies represent mixed strategies, whereby individuals with better information have greater social weight, but individuals with worse information still contribute to the collective decision. The mixed strategies all outperformed the pure strategies, demonstrating the benefit of exploiting both sources of information.

Furthermore, the strategies in $T_3$ are compatible with the definition of CCE (Tomasello, 2009; Mesoudi and Thornton, 2018) but showed a quantitative mismatch with the experimental data. Therefore, an improvement in route efficiency alone is not sufficient evidence for cultural transmission, as the experimental birds did not exhibit evidence of some of the criteria of CCE (evaluation of performance, for instance). This is because of the possibility of the wisdom of crowds improving routes ‘for free’ without the need for individuals to specifically recognize and maintain improvements. In other words, the wisdom of crowds functions like a statistical ratchet, rather than a deterministic one. Moreover, as evidenced from our social weighting analysis, we did not find direct evidence of social learning in terms of imitative copying of prior routes (see Pettit et al., 2013 for similar results). Birds in this experiment, on average, equally influenced each other’s routes disregarding any differences in experience. This observation raises broader questions about which social learning mechanisms truly align with the requirements for CCE (Whiten et al., 2022a; Dalmaijer, 2024).

We note that the wisdom of crowds is beneficial in some but not all task types (Anderson et al., 2001; Sasaki et al., 2022; Langridge et al., 2008). In the context of the homing task, the pigeons apparently have a general (noisy) tendency to find their way home. Because of this, averaging the flights of multiple pigeons is an effective way of canceling out noise, resulting in an increasingly efficient route (on average). Hence, averaging routes can lead birds to stumble upon the best routes by chance. By contrast, in human cultural evolution, complex innovations are unlikely to arise de novo by averaging existing behaviors (Creanza et al., 2017; Migliano and Vinicius, 2022). In these types of tasks, selection on novel behaviors at the tails of the distribution—not the average—is probably necessary to ‘evolve’ towards improved solutions. Future work should investigate the range of tasks that group-living animals typically face, and categorize them into ones that can benefit from the wisdom of crowds and ones that require CCE (Gruber et al., 2022).

This study also reveals that collective strategies must be understood within the context in which they are implemented. Specifically, here the experimental design caused birds to fly in pairs in a particular chain structure. Combined with the averaging strategy, this resulted in a geometric dilution of influence over generations. This progressive loss of information due to repeated turnover of birds reflects an inefficient version of the ‘wisdom of crowds’, where instead of equally incorporating the knowledge of all past individuals, information from early generations is disproportionately lost. This is further supported by our effective group size analysis, which we developed as a reference metric to quantify the effective number of individuals contributing towards route improvements in each generation. We find this to be a potentially valuable metric to quantify such chained experimental design, which are usually proposed for studying CCE (Caldwell and Millen, 2008). Using this method, we showed that despite consisting of five birds, experimental chains of birds exhibited an effective group size only slightly better than two individuals. We expect the behavior of animals to be adaptive in the conditions in which they evolved. The chain structure of this experiment may approximate the dynamics of fission-fusion groups, and additionally forced group sizes to be just two birds. While urban pigeon flocks are highly fluid, they are typically of sizes much larger than two (Lefebvre, 1985). The averaging strategy that the experimental birds exhibited may have performed relatively poorly within this chain structure, but it should exhibit higher performance in larger groups, where there is more scope for the wisdom of crowds. A simple strategy such as the averaging strategy may also be beneficial in large temporary groups, where recognizing experienced or more knowledgeable individuals may be difficult.

It is also important to consider what the pigeons themselves are trying to optimize (Gruber et al., 2022). While our analysis focused on route efficiency, pigeons may not necessarily prioritize minimizing travel distance. Indeed, the average difference in travel distance between the best-performing and worst-performing strategies is only a few hundred meters. Previous studies have shown that pigeons rely on specific landmarks for navigation, suggesting that familiar, slightly longer routes may be preferable to unfamiliar, shorter ones (Meade et al., 2005; Guilford and Biro, 2014; Biro et al., 2004). In this context, birds may be prioritizing maximizing their probability of successfully returning home rather than minimizing flight distance per se (which would require exploring alternative routes, with an associated risk of getting lost). The averaging strategy may be best for birds to maximize the probability of returning home.

Another assumption of our model is that the birds execute the strategies perfectly. In other words, the birds are able to accurately identify who is the more experienced bird or the bird with the shorter route, and can apply the optimal social weight for that strategy. Real animals, if they did implement these strategies, would have some error rate (either in differentiating the birds or applying the optimal social weight), resulting in a lower measured performance. If the error rate is high enough, the performance could even be worse than that exhibited by the averaging strategy. Therefore, the averaging strategy could be a less risky one, guaranteeing (statistically) some measure of improvement.

Our results highlight the need for a more general framework for understanding CCE, calling for a critical re-evaluation of its definition and evaluative criteria, especially in the context of non-human animals. Innovations can be the emergent outcome of collective behavior, rather than necessarily originating from a single individual (Berdahl et al., 2013). In that case, these collectively generated innovations can transmit within the group, without necessarily relying on social learning or leadership. When individuals lack the ability to recognize beneficial innovations, there is no ratchet in a strict sense, but a ratchet may nonetheless exist statistically, due to the wisdom of crowds. Moreover, CCE and the wisdom of crowds are not necessarily mutually exclusive, and social animals could, in principle, simultaneously exploit both sources of innovation, as illustrated in the mixed strategies we explored. We therefore recommend that future empirical studies of CCE in non-human animals clearly distinguish between these mechanisms and incorporate additional criteria for evaluation. Marrying the fields of collective intelligence and CCE could provide a powerful framework for understanding how social animals can improve their fitness across a range of task types and cognitive abilities.

In conclusion, our study opens avenues for future research into collective decision making across time (Biro et al., 2016). Collective performance is the emergent outcome of the social structure, task type, and social strategy. Understanding how these interact with each other could improve our predictions about what collective strategies we should expect to observe in nature given uncertain shifts in timings of events in the future (Kao et al., 2024). For this navigation task, simple averaging is sufficient to quantitatively explain the experimental results, but other tasks may be less amenable to the wisdom of crowds. It is crucial to understand collective strategies within the context in which they evolved, including typical group sizes, turnover rate, error rate, and how many times a task is repeated. While more cognitively complex strategies can result in greater performance, they may not be necessary, and, indeed, mixed strategies that draw on both individual and collective sources of intelligence may result in the highest levels of performance.

The dataset and code used for this study have been deposited in figshare with identifier "10.6084/m9.figshare.28950032" and can be accessed through this link: https://doi.org/10.6084/m9.figshare.28950032.v1.

1. 1. Banerjee S
   2. Kao AB
   3. Francisco F

   (2025) figshare

   Dataset and supporting code for manuscript: "A tale of two birds: cognitive simplicity drives collective route improvements in homing pigeons.

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   Data and code from: Naïve individuals promote collective exploration in homing pigeons.

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Author details

1. Shoubhik Chandan Banerjee

   Department of Biology, University of Massachusetts Boston, Boston, United States

   Contribution

   Conceptualization, Formal analysis, Visualization, Writing – original draft, Writing – review and editing, Investigation, Methodology, Software, Validation

   For correspondence

   shoubhik.banerjee001@umb.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4533-2140

2. Fritz A Francisco

   Department of Biology, University of Massachusetts Boston, Boston, United States

   Contribution

   Formal analysis, Writing – review and editing, Methodology

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8258-2221

3. Albert B Kao

   Department of Biology, University of Massachusetts Boston, Boston, United States

   Contribution

   Conceptualization, Writing – original draft, Writing – review and editing, Investigation, Methodology, Supervision

   For correspondence

   albert.kao@umb.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8232-8365

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