PLoS Biol plos plosbiol PLOS Biology 1544-9173 1545-7885 Public Library of Science San Francisco, CA USA 10.1371/journal.pbio.3002644 PBIOLOGY-D-23-01915 Research Article Biology and life sciencesOrganismsEukaryotaAnimalsVertebratesAmniotesBirdsPigeons Biology and life sciencesZoologyAnimalsVertebratesAmniotesBirdsPigeons Biology and life sciencesPsychologyBehaviorAnimal behaviorAnimal migrationAnimal navigation Social sciencesPsychologyBehaviorAnimal behaviorAnimal migrationAnimal navigation Biology and life sciencesZoologyAnimal behaviorAnimal migrationAnimal navigation Biology and life sciencesPsychologyBehaviorAnimal behaviorAnimal sociality Social sciencesPsychologyBehaviorAnimal behaviorAnimal sociality Biology and life sciencesZoologyAnimal behaviorAnimal sociality Biology and life sciencesNeuroscienceCognitive scienceCognitionMemory Biology and life sciencesNeuroscienceLearning and memoryMemory Biology and life sciencesPhysiologyBiological locomotionAnimal flightBird flight Biology and life sciencesZoologyOrnithologyBird flight Biology and life sciencesPhysiologyBiological locomotionAnimal flight Biology and life sciencesNeuroscienceCognitive scienceCognitive psychologyLearning Biology and life sciencesPsychologyCognitive psychologyLearning Social sciencesPsychologyCognitive psychologyLearning Biology and life sciencesNeuroscienceLearning and memoryLearning Biology and life sciencesOrganismsEukaryotaAnimalsVertebratesAmniotesBirds Biology and life sciencesZoologyAnimalsVertebratesAmniotesBirds Cumulative route improvements spontaneously emerge in artificial navigators even in the absence of sophisticated communication or thought Cumulative route improvements as emergent property https://orcid.org/0000-0003-3241-0760 Dalmaijer Edwin S. Conceptualization Data curation Formal analysis Investigation Methodology Software Validation Visualization Writing – original draft Writing – review & editing * School of Psychological Science, University of Bristol, Bristol, United Kingdom Chittka Lars Academic Editor Queen Mary University of London, UNITED KINGDOM

The authors have declared that no competing interests exist.

 * E-mail: edwin.dalmaijer@bristol.ac.uk 6 6 2024 6 2024 22 6 e3002644 28 7 2023 26 4 2024 2024 Edwin S. Dalmaijer This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Homing pigeons (Columba livia) navigate by solar and magnetic compass, and fly home in idiosyncratic but stable routes when repeatedly released from the same location. However, when experienced pigeons fly alongside naive counterparts, their path is altered. Over several generations of turnover (pairs in which the most experienced individual is replaced with a naive one), pigeons show cumulative improvements in efficiency. Here, I show that such cumulative route improvements can occur in a much simpler system by using agent-based simulation. Artificial agents are in silico entities that navigate with a minimal cognitive architecture of goal-direction (they know roughly where the goal is), social proximity (they seek proximity to others and align headings), route memory (they recall landmarks with increasing precision), and continuity (they avoid erratic turns). Agents’ behaviour qualitatively matched that of pigeons, and quantitatively fitted to pigeon data. My results indicate that naive agents benefitted from being paired with experienced agents by following their previously established route. Importantly, experienced agents also benefitted from being paired with naive agents due to regression to the goal: naive agents were more likely to err towards the goal from the perspective of experienced agents’ memorised paths. This subtly biased pairs in the goal direction, resulting in intergenerational improvements of route efficiency. No cumulative improvements were evident in control studies in which agents’ goal-direction, social proximity, or memory were lesioned. These 3 factors are thus necessary and sufficient for cumulative route improvements to emerge, even in the absence of sophisticated communication or thought.

Homing pigeons improve their route efficiency in consecutive generations, potentially through social interaction. This study uses artificial agents with a highly limited cognitive architecture to show that although their only "social" capacity is to seek proximity, their behavior matches that of pigeons, and they show cumulative improvements in route efficiency.

 The author(s) received no specific funding for this work. Data Availability All code and data has been made publicly available through open repositories on GitHub (https://github.com/esdalmaijer/artificial_navigators) and Zenodo (data: https://doi.org/10.5281/zenodo.6944185; code: https://doi.org/10.5281/zenodo.10997495). Introduction

Cumulative cultural evolution occurs when individuals pass down adaptive innovations through social means (e.g., teaching or copying), leading to progressive increases in fitness over generations [1,2]. In humans, this “ratcheting” [3] of socially transmitted improvements is vital to human technological advancement [4] and has historically been attributed to uniquely human “high-fidelity” communication [5]. However, experimental work has shown simple emulative learning is sufficient for cumulative culture to occur [6,7]. Some argue that other species show cumulative culture, e.g., in transmission chains of songs in zebra finches [8] and humpback whales [9], tool use in crows [10] and chimpanzees [11–13], and pattern reproduction in great tits [14] and baboons [15]. One particularly striking example comes from pigeons, which seem to pass down route improvements [16].

Homing pigeons (Columba livia) are suboptimal navigators that develop and remember idiosyncratic routes when flying alone or in pairs [17]. While paired birds fly more efficient routes than individuals [18], pairs in which experienced pigeons are swapped for naive ones show “innovation”: beneficial modifications between generations [16] that meet criteria for cumulative culture [19]. Perhaps pigeons pool information between individuals, learn and decide through collective intelligence, and evaluate performance to prune worse innovations [16]; or develop intra-pair dynamics of communication and leadership [20].

An alternative explanation is that cumulative route improvements emerged as accidental by-product during navigation in groups. Here, I directly address this question using a minimal cognitive architecture in artificial agents that are bound by only 4 rules derived from avian navigation (Fig 1). The first is goal direction, akin to birds’ solar [21] and magnetic compasses [22] that allow them to orient towards their home even from unfamiliar release sites unless under total overcast with disorienting magnets glued to their head [23]. The second is social proximity, which birds seek when flying together [24]. The third is route memory, which in pigeons could depend on visual landmarks [25] and improves over consecutive flights [26]. The fourth is continuity, a tendency to continue along the current heading to avoid implausibly erratic patterns. Crucially, there is no communal decision-making, evaluation of outcomes, or deliberate social communication.

10.1371/journal.pbio.3002644.g001 The top panel shows paths from artificial agents (introduced here) and from pigeon data published by others [<xref ref-type="bibr" rid="pbio.3002644.ref020">20</xref>].

Each line represents the final flight in a generation. The first generation comprises a single individual; a naive individual was added in the second; and in all later generations the most experienced was replaced with a naive individual. Solid lines show lone or experienced individuals, dotted lines show naive ones. The bottom panel shows how agents navigated by sampling from a weighted mixture of Von Mises distributions. These were centred on bearings towards the goal (green), other agents (blue), landmarks along a memorised route (purple), and the previous heading (yellow). Bottom left shows these distributions in a radial plot, with arrows indicating component centres and weights. Bottom right shows the distributions and their weighted sum (black). Artwork used in this figure exists in the public domain or was released under a CC0 license and can be found on Wikimedia Commons (https://commons.wikimedia.org/) under file names F1_chequered_flag.svg, Google_Maps_pin.svg, RockDove.jpg, and Black_rock_pigeon.jpg.

The artificial navigator model is a weighted mixture of Von Mises distributions Φ, with weights w that add up to 1 (Eq 1). These are akin to normal distributions, but they are circular, so that the tails wrap around. To produce the next heading h in journey i at time t+1, an agent combines information from time t on bearings towards the goal bgoal, the next memorised landmark blandmark, and other agents’ estimated future position b^other. As in birds, not all bearings are equally precise, which is reflected in each component’s precision parameter κ. For example, there is uncertainty about where the (solar/magnetic compass) goal is [21,22], whereas pigeon visual acuity is good enough [27,28] to identify nearby visual landmarks along a well-memorised route (although they are not always used, [29]). To prevent unnaturally jerky movements, the final component ensures continuity by sampling from a narrow distribution that is centred on the current heading. For a full account of the algorithm, please refer to Materials and methods.

h(i,t+1)=wgoalΦ(bgoal,κgoal)+wsocialΦ(b^other,κsocial)+wmemoryΦ(blandmark,κmemory,i)+wcontinuityΦ(h(i,t),κcontinuity)

Agents travelled in 3 conditions that mapped onto work in pigeons [16]: solo, paired, and an experimental condition with generational turnover. In the solo and pair conditions, 1 or 2 agents made 60 consecutive journeys. The experimental condition also involved pairs, but a naive replaced an experienced agent every 12 journeys. A total of 50 repetitions were done for each condition and set of weight parameters. Precision parameters were fixed at κcontinuity = 8.69 (equivalent SD = 0.35), κgoal = 1.54 (1.0), κsocial = 2.18 (0.80), κmemory,1 = 0.85 (0.9) to κmemory,5 = 6.78 (0.40), based on model fits for pigeon data. Note that memory precision improves over journeys, as per evidence from pigeon flight [26].

What is (not) cumulative culture?

Human’s accumulated innovations are undeniably “superlative” [30] and many depend on combining physical phenomena (“Type II” cultural evolution), whereas nonhuman innovations typically optimise only within a phenomenon (“Type I”) [4]. An appealing framework describes 4 core criteria of cumulative cultural evolution: behaviour needs to (1) show variation introduced by interaction between individuals; (2) be passed on through social learning; (3) improve performance; and 4) repeat over generations [19]. Few examples of “cumulative culture” in animals meet all 4, and rarely are extended criteria (functional dependence, diversification into lineages, recombination across lineages, exaptation, or niche construction) met [19].

Route improvements in successive generations of pigeons were described as cumulative culture [16], and it was indeed listed as meeting all core criteria of the aforementioned framework [19]. However, whether animals genuinely show cumulative culture is controversial. An alternative explanation is that individuals attend to others’ actions, and then reinnovate a “latent solution” to produce similar outcomes [5]. Alternatively, apparent innovations could have previously been unobserved or learned not socially but in response to changing environments [31]. It is hotly debated whether these alternatives are valid and relevant; see [32] and the numerous responses for an overview of current opinions.

The agents employed in this study arguably do not meet the above standard. Their “innovation” is limited to an increase in efficiency, which is decidedly unlike the development of novel behaviour. While focussing on task efficiency offers insight into cumulative cultural evolution [33], a focus on task solutions can obscure that humans also actively discover new problems and generalise solutions between them, which nonhumans rarely do [34]. Agents also do not engage in “social learning” as it is traditionally defined: all they do is follow other individuals, without explicit demonstration or observation of a concrete task. Hence, I will refer to their outcome as “cumulative route improvements.”

 Results

Artificial navigators travelled in an “experimental” condition with generational turnover (pairs with replacement of an experienced for a naive individual each generation) or in control conditions without turnover (paired or solo). They showed various levels of route efficiency (Figs 2 and A in S1 File), which was computed as start-goal distance divided by travelled distance [16], and ranged between 0 (never reached the goal) to 1 (straight line from start to goal). Parameters could be optimised for final-route efficiency (Fig 2, top) or improvement between generations (Fig 2, centre), and compared well to empirical pigeon data (Fig 2, bottom).

10.1371/journal.pbio.3002644.g002 Progression of route efficiency as a function of flight number.

The top panel shows results for the optimum for final efficiency, the middle for the optimum for intergenerational improvement, and the bottom panel for pigeon data published by others [20]. Lines show mean values over independent runs, with 95% confidence intervals as shaded areas. In the experimental condition, a naive agent replaced an experienced one in each generation; in the solo condition, a single agent made all journeys with no generational turnover; and in the pair condition, 2 agents journeyed together without turnover. Parameters for the navigation model were the same between each of the 3 conditions, and weights are listed above each panel.

Cumulative route improvement was quantified as the increase in route efficiency between each generation. This occurred exclusively in the experimental condition (Figs A, B, and D in S1 File), replicating empirical data [16].

In the experimental condition, the average highest final-generation route efficiency was 0.884 (SD = 0.017, SEM = 2.47e-3) for parameters wgoal = 0.25, wsocial = 0.20, wmemory = 0.05, and wcontinuity = 0.50. Highest final efficiency (M = 0.875, SD = 0.021, SEM = 2.97e-3) was also achieved for these parameters in the pair condition, whereas final efficiency in the solo condition was highest at 0.863 (SD = 0.22, SEM = 3.10e-3) for parameters wgoal = 0.35, wsocial = 0.05, wmemory = 0.05, and wcontinuity = 0.55.

The highest average generational efficiency increase was 0.091 (SD = 0.014, SEM = 2.00e-3) and achieved at wgoal = 0.15, wsocial = 0.25, and wmemory = 0.40, wcontinuity = 0.20 in the experimental condition. For these parameters, intergenerational improvement was only 2.4e-5 (SD = 11.2e-3, SEM = 1.58e-4) in the pair condition, and 1.0e-4 (SD = 7.32e-4, SEM = 1.03e-4) in the solo condition. The highest generational turnover achieved in the pair condition was 0.013 (SD = 0.042, SEM = 5.90e-3 at wgoal = 0.15, wsocial = 0.15, and wmemory = 0.10, wcontinuity = 0.60) and 0.005 (SD = 0.019, SEM = 2.62e-3 at wgoal = 0.15, wsocial = 0.20, and wmemory = 0.10, wcontinuity = 0.55) in the solo condition. Out of 610 parameter combinations, 269 achieved a greater intergenerational improvement in the experimental condition than the highest pair control condition.

Naive individuals can benefit from the experienced

In the experimental condition, naive individuals could benefit from following an experienced agent with established route memory. Compared to the pair control condition, naive individuals showed more efficient paths (Fig 3) if their experienced counterpart relied more strongly on memory (wmemory). However, naive agents were worse off at low memory-reliance, particularly if the relative influence of goal-direction (wgoal) was low, and if they more strongly sought social proximity (wsocial).

10.1371/journal.pbio.3002644.g003 Each panel shows the difference in route efficiency between naive agents in the experimental condition (generational turnover) and the first 12 journeys from agents in the pair control condition (without generational turnover).

Positive differences indicate that naive agents had better route efficiency compared to control. Each panel represents a combination of wgoal and wsocial parameters, while darker lines indicate higher levels of wmemory. Lines represent averages across 50 independent runs and their shaded areas the 95% confidence interval.

 Experienced individuals benefit from the naive

While it is perhaps obvious that naive agents could benefit from following established paths, more surprising was that experienced individuals also benefitted from their naive counterparts. This occurred due to regression to the goal. Compared to extreme samples, random samples are more likely to be nearer a distribution’s centre; this is regression to the mean. Similarly, experienced agents draw from internal distributions, including for goal-direction and route memory. Naive agents sample from internal distributions too, but do not have route memory yet, and hence are more biased towards the goal than experienced individuals. Because agents aim for social proximity, naive navigators should thus subtly pull experienced agents towards the goal.

This was born out empirically, as relative bearings for experienced towards naive agents were more likely to also be in the direction of the goal (Fig 4). This was primarily true for lower values of wmemory and increased with wsocial. Regression to the goal thus allowed naive agents to memorise slightly more efficient routes than their paired experienced agent.

10.1371/journal.pbio.3002644.g004 Each panel shows the distribution of relative bearings towards the naive agent from the perspective of the experienced agent in generations 2–5 of the experimental condition.

Positive values on the x-axis indicate bearings towards the goal, and negative values bearings away from the goal. Distributions are generally right-heavy, indicating a bias of naive individuals to be positioned in the general direction of the goal. This tendency increases as a function of wsocial and to a lesser extent as a function of wgoal.

 Control experiments with lesioned agents

Agents were lesioned in control experiments to investigate which navigation components were necessary for cumulative route improvements to emerge (Table 1). Control experiments employed the same weights as those that achieved highest final efficiency or intergenerational efficiency increases in the experimental condition (described above). However, headings were sampled from uniform distributions (i.e., noise) instead of being influenced by goal-direction, social proximity, route memory, or continuity.

10.1371/journal.pbio.3002644.t001 Efficiency quantifies how close agents were to the direct path from start to goal.

Final efficiency is measured in the last generation and generational increase as the difference between generations. Cumulative route improvements are reflected by a positive intergenerational increase and occur in the “experimental” condition (“pair” and “solo” are control conditions). The “no lesion” column reflects optimal scores; the other columns reflect scores after replacing the goal, social, memory, or continuity component with a uniform distribution (noise).

No lesion Goal lesion(all) Goal lesion(gen>1) Social lesion Memory lesion Continuity lesion
Final efficiency
experimental 0.884 0 0 0.794 0.894 0.178
pair 0.875 0 0.143 0.782 0.897 0.170
solo 0.790 0 0.074 0.788 0.837 0.173
Generational increase
experimental 0.091 0 7.95e-3 5.23e-4 8.99e-4 0.068
pair 2.37e-5 0 −9.84e-4 1.96e-5 2.91e-3 2.96e-4
solo 1.05e-4 4.24e-6 −2.84e-5 −7.67e-5 −8.04e-4 7.82e-5

When goal-direction was lesioned for all generations, agents engaged in random walks that failed to reach the goal in time. When goal-direction was lesioned for all but the first generation, a path could be established within the first generation. This isolated goal-direction’s necessity for intergenerational improvement, which should not occur with lesioned goal-direction if it is dependent on regression to the goal.

When social proximity or route memory was lesioned, efficiency was barely reduced, but generational increase was nullified. When continuity was lesioned, efficiency was greatly reduced, but the pattern of generational increases remained intact: present in the experimental condition, but not in pair or solo controls.

In another set of control experiments (Table 2), the precision of each navigational component was varied from low (wide Von Mises distribution) to very high (narrow distribution). Wider distributions reduced intergenerational efficiency increases, and a wide goal component even prevented agents from completing their routes. Narrower distributions effected less change, although a more precise goal component did subtly reduce increases in intergenerational efficiency. The pattern of cumulative route improvements in the experimental but not in the pair and solo control conditions was apparent throughout.

10.1371/journal.pbio.3002644.t002 This table illustrates how the precision of each navigation component impacts cumulative route improvements, which are quantified by a positive intergenerational increase in path efficiency in the “experimental” condition (“pair” and “solo” are control conditions).

The “normal precision” column reflects scores from the current model parameters. The “high precision” and “low precision” reflect halving and doubling the standard deviation, which is then transformed back into precision parameter κ for a navigational component Von Mises distribution.

Generational increase Very high precision High precision Normal precision Low precision
Goal κgoal = 101 Κgoal = 4.55 Κgoal = 1.54 Κgoal = 0.27
experimental 0.073 0.085 0.091 0.058
pair 8.12e-4 1.05e-4 2.37e-5 −5.79e-4
solo 7.01e-5 8.19e-6 1.05e-4 −3.55e-5
Social κsocial = 101 Κsocial = 6.78 Κsocial = 2.18 Κsocial = 0.579
experimental 0.092 0.093 0.091 0.032
pair −1.76e-4 −3.05e-4 2.37e-5 3.02e-4
solo 1.69e-4 −9.04e-5 1.05e-4 5.22e-4
Memory κmemory = 1e12 Κmemory = 25.5 Κmemory = 6.78 Κmemory = 2.18
experimental 0.092 0.090 0.091 0.043
pair −2.63e-4 −2.53e-4 2.37e-5 1.28e-3
solo −2.90e-4 −5.69e-4 1.05e-4 2.56e-4
Continuity κcontinuity = 401 Κcontinuity = 33.2 Κcontinuity = 8.69 Κcontinuity = 2.67
experimental 0.080 0.095 0.091 0.084
pair −2.54e-4 −4.56e-4 2.37e-5 4.23e-4
solo 3.13e-4 −1.39e-4 1.05e-4 2.01e-4

The lesion experiments suggest goal direction, social proximity, and route memory were all crucial for cumulative route improvements to emerge in this model.

 Artificial navigator model fits empirical data

When fitted on 10 repetitions of the experimental condition in pigeons (data published by [20]), average parameter estimates were wgoal = 0.12 (SEM = 0.03), wsocial = 0.16 (SEM = 0.03), wmemory = 0.09 (SEM = 0.01), and wcontinuity = 0.59 (SEM = 0.03). That these weights did not align with optima for intergenerational improvement or efficiency for agents suggests that the artificial navigator model is insufficient to capture the full complexity of pigeon behaviour, which agrees with interpretations put forward by others [16,20].

 Discussion

The minimal cognitive architecture of goal-direction, social proximity, and long-term memory was sufficient for the emergence of cumulative route improvements. It was driven by regression to the goal over generations: as agents in a new pair aligned and converged their headings, experienced agents travelled along a remembered route, while their naive counterparts introduced a subtle goal-directed bias.

These results suggest that stepwise improvement between generations can occur when individuals simply seek proximity to others. Agents had no capacity or intent to communicate, but information transferred between them as naive agents followed and memorised experienced agents’ routes, while their subtle goal-directed pull introduced stepwise improvement between generations. While previous work has demonstrated step-wise improvement between generations through emulative learning [6,7], tasks required strategic social learning and advanced cognitive skills. Another difference is that the current task presents a clear limit: when the direct path between start and goal is reached, no further efficiency improvements can be made. The current findings outline a minimal set of cognitive abilities that is necessary and sufficient for cumulative route improvements to emerge.

The identified minimal set of cognitive abilities predicts that species with similar architectures could also show cumulative improvements, with a potential example in social ants who navigate along idiosyncratic one-way routes using landmarks [35]. My results also demonstrate a role for naive individuals in cumulative improvements. This aligns with findings from bluehead wrasse, which use traditional mating sites (like paired agents stick to idiosyncratic routes), but adopt new sites upon complete population replacement [36,37]. It also aligns with empirical work in great tits, in which population turnover drove cumulative improvements in efficiency due to new naive individuals adopting efficient variants [38].

Do the current findings extend to cumulative cultural evolution?

Examples of behaviour described as “cumulative culture” in animals often do not meet core criteria of a particular framework [19], although cumulative route improvement in pigeons has often been interpreted as meeting all core criteria [16,19] at least for Type I cumulative culture [4]. While the current model reproduces cumulative route improvements in successive generations, it could be argued that its “innovation” is unlike human innovation, and that its “social learning” is without the traditional demonstrator or observer.

Not all human cumulative culture is Type II. For example, humans can increase a wheel’s speed over several generations without gaining understanding of the physics behind their solutions [39]. Another example is language, in which systematic structure can develop over generations that share the goal of communicating effectively for the benefit of naive individuals [40]. In these situations, there are clear goals (meaning efficiency can be optimised), memory in experienced agents, and transfer to naive agents through implicit means. While the current model does not readily extend to these situations as it is, there is opportunity to explore the overlap between following another individual along a route and following an individual’s actions or utterances.

The difference between cumulative culture in humans and other animals is typically described as a qualitative distinction [4,19]. Some simulations suggest that this distinction could arise from a quantitative difference in the fidelity of information communication [41]. Specifically, high fidelity reduced the loss rate of cultural traits, and if this breached a threshold it allowed traits to survive long enough to be recombined, which in turn led to cumulative culture. Through an optimistic lens, this could be taken to suggest that rudimentary aspects of cumulative culture found in animals are on the same continuum as cumulative culture found in humans. However, even if that holds for other nonhuman individuals, the artificial navigators introduced here fall well below the required fidelity threshold. Hence, if someone did consider the current model an example of rudimentary “cumulative culture,” it would never pass beyond simple optimisation of efficiency.

 Conclusions

In sum, artificial agents with minimal cognition reproduce cumulative route improvements previously shown in pigeons. This is qualitatively different from cumulative culture in humans, and it is unclear whether the current model extends to more complex situations. However, these findings do suggest that cumulative improvement across generations could be an emergent property in animals that work towards a goal alongside more experienced individuals.

 Materials and methods Artificial navigator model

Artificial navigators were agents that embarked on journeys from a set starting point to a set goal, although they did not always reach this goal. They were bound by 4 rules, each implemented as an iterative sampling process from a Von Mises distribution. The centre of each distribution was determined by a bearing, and the spread by certainty of information. At each time point, an agent’s heading was updated by sampling each distribution and computing a weighted circular mean (Eq 1). Weights were set at agent initialisation and added up to 1. Precision parameters were based on empirical data (see under “Experimental design”).

The first rule was goal direction. The centre of this distribution was the bearing towards the goal bgoal, its precision parameter was κgoal, and its weight wgoal. The bearing was computed from the coordinates of the goal (xgoal,ygoal) and agent at time t (xt,yt) (Eq 2). The purpose of this rule was to orient agents towards the goal, just like pigeons can orient homewards upon being released from unfamiliar sites. This ability likely depends on the sun, as starlings and pigeons can learn to use light and time-of-day to orient towards rewards [21], and pigeons orient homeward when the sun is visible [23]. They can even do so when it is overcast, but their initial orientation becomes more random when magnets are glued to the back of their heads [23], suggesting that pigeons also use an internal compass. For more comprehensive overviews, see [22] and [29].

bgoal=atan2(ygoal−yt,xgoal−xt)

The second rule was social proximity. This distribution is a weighted composite of a Von Mises distribution for social convergence that is centred on the bearing towards another agent’s estimated future position b^other and another Von Mises distribution for social alignment that is centred on another agent’s current relative heading. The alignment of headings between agents at close proximity is a crucial part of flocking behaviour [42], but at larger distances agents need to converge rather than align to achieve social proximity. Samples drawn from the convergence distribution were weighted with proportion p and those drawn from the alignment distribution with (1-p). Proportion p was drawn from a cumulative normal distribution with mean 0.5 and standard deviation 0.1, which is equivalent to a distance of 30 metres, at which pigeons are estimated to be able to recognise individuals [43]. Both composite distributions have precision parameter κsocial, and the combined distribution has weight wsocial.

Bearings towards other agents were computed from an agent’s position at time t, (xt,yt) and other agent j’s expected position at time t+1 (Eq 3). The expected position of agent j at time t+1 was estimated on the basis of their velocity v (which was kept constant) and their heading hj,t at time t (Eq 4).

b^other=atan2(y^j,t+1−yt,x^j,t+1−xt) (x^j,t+1,y^j,t+1)=(xj,t+vcos(hj,t),yj,t+vsin(hj,t))

The third rule was route memory. This was established during an agent’s first journey, in which passed landmarks were committed to memory. Across the map of 200 by 130 units, 6,500 landmarks were spread. This aligns with landmark detection using pigeon flight routes [26] and edge detection in aerial photography [25]. During consecutive journeys, an agent attempted to fly from one memorised landmark to the next by sampling from a Von Mises distribution centred on the bearing towards the next landmark blandmark, with spread κmemory,i for journey i, and weight wmemory (Eq 5; see Fig C in S1 File). There were no memorised landmarks in the first journey, so the spread for κmemory,1 was set to 0, resulting in a completely uniform distribution. For all following journeys, κmemory,i was set to 1.82, 2.29, 2.98, 4.19, and then plateaued at 6.78. This was analogous to a linear decrease in standard deviation from 0.9 to 0.4 and was based on model fits to pigeon homing data (see under “Data reduction and statistics: Pigeons”). Agents proceeded to navigate towards the next landmark l+1 if they came within a threshold distance of landmark l. This threshold was set as 10 times the distance agents could travel between time t and time t+1.

The gradual improvement in memory precision over several journeys and the anchoring to landmarks were based on Gaussian process models of pigeon navigation [26]. While the current implementation was less elegant than its inspiration, it was computationally inexpensive, and parsimonious with sampling from distributions of other bearings.

bmemory=atan2(ylandmark,l−yt,xlandmark,l−xt)

The fourth and final rule was continuity. This assured that during journey i, an agent’s next heading at time t+1 would be similar to their heading at time t. The continuity component was sampled from a Von Mises distribution centred on current heading h(t), with precision parameter κcontinuity, and weight wcontinuity.

Finally, agents set their next heading by drawing random samples a from each of the Von Mises distributions described above and computing their weighted circular mean (Eqs 6–8). h(t+1)=arctan2(y¯,x¯) Where: y¯=sin(agoal)wgoal+sin(aother)wsocial+sin(amemory)wmemory+sin(acontinuity)wcontinuity x¯=cos(agoal)wgoal+cos(aother)wsocial+cos(amemory)wmemory+cos(acontinuity)wcontinuity

Software was implemented in Python (version 3.10.12) [44] (for tutorials, see [45,46]), using external libraries Matplotlib (version 3.8.2) [47], NumPy (version 1.26.3) [48], SciPy (version 1.12.0) [49], and utm (version 0.7.0) [50].

 Experimental design

Agents travelled in 3 conditions that mapped onto work in pigeons [16]: solo, paired, and in an experimental condition with generational turnover. In the solo and pair conditions, 1 or 2 agents made 60 consecutive journeys. In the experimental condition, a naive replaced an experienced agent every 12 journeys.

Agents travelled 1 distance unit per 1 time unit, attempting to find a fixed goal from a fixed starting point that were 104 units apart. The maximum distance agents were allowed to travel was 2,506 units. Compared to the map used by pigeons in Sasaki and Biro’s study [16], this is equivalent to a flight of 200 km and approximately 5 h. This cut-off was chosen because pigeons would have suffered continuously increasing concentrations of uric acid and other metabolites [51], and a marked increase in reactive oxygen metabolites and decrease in serum antioxidant capacity [52].

Weight parameters wgoal and wsocial varied from 0.05 to 0.35 in steps of 0.05, and wmemory from 0.05 to 0.5 in steps of 0.05, resulting in 610 unique combinations. No combinations with weight sums over 1 were included, and wcontinuity made up the difference for all weight sums under 1. A total of 50 repetitions were done for each condition and each unique combination of parameters, resulting in a total of 30,500 simulations.

Precision parameters were fixed at κgoal = 1.54 (equivalent SD = 1.0), κsocial = 2.18 (0.80), κmemory,1 = 1.82 (0.9) to κmemory,5 = 6.78 (0.40), and κcontinuity = 8.69 (0.35); roughly based on model fits for stable pigeon pairs (see under “Data reduction and statistics: Pigeons”). This data [53] was published alongside an analysis on leadership in pairs of naive and experienced pigeons [20], and seems to have been the source data for an earlier publication on generational improvements in efficiency [16].

 Data reduction and statistics: Pigeons

Individual pigeon GPS data (defined by latitude and longitude) published by others [53] was converted to Universal Transverse Mercator (UTM) coordinates (grid zone 30U). Samples with velocities under 25 or over 150 km/h were excluded from flights, to filter breaks and apparent GPS glitches. Flights were completely excluded it they contained coordinates further than 17.03 km (twice the start-goal distance) away from the point midway between start and goal. Out of 2,176 files in the original dataset, 6 were excluded for straying too far off course, and 45 for not reaching the goal. Sasaki and Biro [16] also imputed several early incomplete flights with direct-to-home trajectories, which was not done here to avoid fitting models to imputed data, but the pattern of results matches nevertheless (Fig 2).

Best parameter fits for pigeon flight data were determined through maximum likelihood estimation. This is an established way of deriving parameter estimates for mixture models of Von Mises distributions, for example, in research on visual short-term memory [54]. To speed up the fitting process, GPS data was downsampled to 0.05 Hz (1 sample every 20 s).

Averages (standard errors and ranges) for weight parameter estimates in pigeons were wgoal = 0.12 (0.03, [0.04–0.34]), wsocial = 0.16 (0.03, [0.04–0.28]), wmemory = 0.09 (0.01, [0.01–0.17]), and wcontinuity = 0.59 (0.03, [0.49–0.74]) in the experimental condition (N = 10 repetitions of 5 generations each); wgoal = 0.04 (0.01, [0.00–0.09]), wsocial = 0.32 (0.10, [0.13–0.65]), wmemory = 0.16 (0.04, [0.04–0.33]), and wcontinuity = 0.47 (0.11, [0.13–0.75]) in the pair condition (N = 6 repetitions of 60 flights with 2 birds each); and wgoal = 0.31 (0.04, [0.15–0.58]), wmemory = 0.27 (0.06, [0.02–0.55], and wcontinuity = 0.43 (0.06, [0.25–0.83]) in the solo condition (N = 9 repetitions of 60 flights with 1 bird each).

Averages (standard errors and ranges) for spread parameter estimates in pigeons were SDgoal = 1.16 (0.08, [0.86–1.67]), SDsocial = 1.04 (0.21, [0.18–1.87]), Sdmemory,1 = 1.50 (0.21, [0.52–2.37]) to SDmemory,5 = 0.26 (0.08, [0.10–0.85]), and SDcontinuity = 0.33 (0.03, [0.21–0.54]) in the experimental condition; SDgoal = 0.85 (0.10, [0.56–1.20]), SDsocial = 1.03 (0.38, [0.21–2.61]), SDmemory,1 = 0.73 (0.26, [0.10–1.68]) to SDmemory,5 = 0.30 (0.11, [0.10–0.77]), and SDcontinuity = 0.44 (0.04, [0.32–0.64]) in the pair condition; and SDgoal = 0.69 (0.14, [0.10–1.37]), SDmemory,1 = 0.85 (0.15, [0.46–1.69] to SDmemory,5 = 0.75 (0.24, [0.16–2.02]), and SDcontinuity = 0.33 (0.08, [0.10–0.78]) in the solo condition. Note that these were fitted as precision (κ) parameters, but due to their nonlinear scale, I opted to report standard deviation equivalents for clarity.

 Data reduction and statistics: Agents

Simulation results were averaged between paired agents and over independent runs within the same condition and parameter settings. Efficiency for the final generation was computed as the highest out of 12 journeys in the fifth generation.

Generational efficiency improvement was computed as the average difference in route efficiency between consecutive generations. To reduce the impact of random fluctuations, the most efficient (typically the final) routes were taken as representative within each generation. The first generation in the experimental condition was omitted, to avoid comparisons between single and paired journeys.

To avoid trivial statistical significance that can be achieved through increasing the number of simulations, inferences on the basis of statistical tests were avoided and were instead made on the basis of holistic interpretation. Readers are invited to scrutinise figures, data, models, and software.

 Supporting information PDF document containing Figs A–D.

A single PDF file is provided with figures that offer additional information. Fig A shows measures of efficiency as a function of the wgoal, wsocial, and wmemory components. Fig B shows the relationships between component weights and efficiency outcomes. Fig C shows example journeys and the landmarks that individuals used across generations. Fig D shows histograms of final efficiency and the intergenerational changes in efficiency for each condition.

(PDF)

Thanks to Dr. Paul E. Smaldino, Dr. Takao Sasaki, and members of the Cultural Evolution Discord for feedback on an earlier version of this manuscript.

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J Vis. 2009 Sep 1;9(10):1–11. doi: 10.1167/9.10.7 19810788 10.1371/journal.pbio.3002644.r001 Decision Letter 0 Roberts Roland G Senior Editor 2024 Roland G Roberts This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 0

4 Aug 2023

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 10.1371/journal.pbio.3002644.r002 Decision Letter 1 Roberts Roland G Senior Editor 2024 Roland G Roberts This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 1

27 Sep 2023

Dear Dr Dalmaijer,

Thank you for your patience while your manuscript "Cumulative culture spontaneously emerges in social navigators with imprecise memory" was peer-reviewed at PLOS Biology. It has now been evaluated by the PLOS Biology editors, an Academic Editor with relevant expertise, and by four independent reviewers.

You’ll see that reviewer #1 is positive but wants more a substantial Intro and Discussion, some sensitivity analyses, and has some requests for clarification. Perhaps more seriously, s/he also thinks that your claim that goal direction is unnecessary cannot be true (and even did some modelling to explore this). Reviewer #2 is also positive, but like rev #1 wants significantly more meat in the Intro and Discussion; s/he also thinks that you are too uncritical about the claims of cumulative culture by Sasaki & Biro, and need to justify your choice of definition more rigorously. Reviewer #3 also wants broader context in the Intro, some exploration of parameter space where predictions fail to match empirical data, wonders what happens if only the first generation knows the goal location, and wants more clarity about how heading h is calculated. Like the other reviewers, reviewer #4 also has problems with how the literature is covered (especially human cumulative culture), makes a similar point to rev #2 about the lively debate in the field about definitions, and asks what the “continuity” parameter would correspond to in tasks other than navigation (and whether it’s essential for the findings to hold).

We now invite our reviewers to cross-comment on each other's reviews; during this process, at least one other agreed with the main concern raised by reviewer #1. Several re-emphasised the need for a more substantial Intro and Discussion, and the Academic Editor and I think that your article should be expanded to a full Research Article to give you the space to expand on the issues identified. Also, in case it's helpful, one reviewer said "I completely forgot to add this to the review, but there is a special issue in Phil Trans on CCE across species that would be a good starting place for the author to check https://royalsocietypublishing.org/toc/rstb/2022/377/1843"

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------------------------------------

REVIEWERS' COMMENTS:

Reviewer #1:

The author presents a mathematical simulation of the cumulative cultural improvement of route efficiency, as documented empirically in pigeons. They find that the sort of cumulative improvement observed empirically can be produced under specific parameter values. I very much enjoyed reading this paper, and I would like to see it published eventually. However I have a number of quite significant concerns that I will detail below, and so I will request that significant revisions are made.

Major points:

1. The introduction is far too short. I'm all for getting straight to the point, but the current manuscript does so in such a hurry that it skips over a lot of context that would help get across why the reader should be interested in this work. I'm not going to tell the author how to write an introduction (I assume they are well versed in this), but as one example, it seems pertinent to cover a few other theories about what cognition supports cumulative culture and why those might not be the whole picture. The introduction should be at least double its current length, and could comfortably be much longer still.

2. Introduction paragraph 6. The spread (i.e. precision) parameters are fixed according to an analysis, but there is no reporting of the uncertainty in these estimates. Measures of such uncertainty should be provided. Even better would be a sensitivity analysis - does cumulative culture depend on the specific values used?

3. Results regarding lesions of the goal directed component: "If they found the goal, this resulted in low-efficiency paths with ample room for inter-generational improvement. Indeed, inter-generational efficiency improvement still occurred in the experimental condition, but not in pair or solo controls. Hence, goal direction was not necessary for cumulative culture."

I found this result to be quite surprising, so surprising I think it must be incorrect. I've even built a few simple models to reproduce it while reviewing the manuscript and cannot do so. The issue is that that without the goal directed component I cannot see how there can be any means by which efficiency can ratchet upwards. For instance, suppose one pigeon completes a random walk, and they are then paired with another. The new pigeon will learn from the experienced pigeon, and will superimpose its own random walk on top, but this should be just as likely to worsen the route as to improve it. At first, I wondered if the information was coming from failed routes (those that never reach the goal) being discarded, but the manuscript makes clear this is not the case. Another option is pigeons are initialized facing in the right direction on their first run (making the random walks not truly random). Or perhaps, this is an artefact of the efficiency measure: the initial random walks are at such low efficiency that the only way is up. But maybe I am wrong - if so the author needs to really dig into what is going on here and where the information is coming from that enables the population of achieve progressively higher efficiency.

4. Discussion. Like the introduction the discussion is really short. There needs to be more of an effort to expand on how this work contributes to and interacts with other parts of the literature.

Minor points:

1. Introduction paragraph 3. There are semicolons between the first three rules, but a period (full stop) between the 3rd and 4th. Any reason for this inconsistency?

2. Introduction paragraph 3. Continuity is introduced but not defined, leaving the reader to ponder what it means.

3. Introduction paragraph 4. Von Mises distributions are introduced but not explained. I had to look them up on Wikipedia. It would be perfectly easy to explain they are basically circular normal distributions. It is important to explain this because these distributions are a core part of the model.

4. Introduction paragraph 4. The existence of b_goal needs more justification. As it is, it is magic knowledge of where the goal is. The author needs to justify why it is reasonable to simulate agents with this kind of knowledge. A more detailed discussion of solar/magnetic compasses would be a good step.

5. Introduction paragraph 4, and throughout. The k parameter is defined as a spread, but it's not, it's the reciprocal of a spread, more intuitively called concentration or precision.

6. Introduction paragraph 4. The author states that uncertainty in the location of the goal is greater than uncertainty in the location of the next landmark. Is this an assumption of the model or an empirically documented fact? It needs greater explication and justification.

7. Introduction paragraph 5, and throughout. It is never really stated that the experimental condition also involves pairs. Rather, turnover is mentioned, but not the group size.

8. Introduction paragraph 6. The term "runs" needs to be more clearly defined.

9. Methods. Is it plausible that b_other pulls you towards the other pigeons projected location? At high enough weights this will cause pigeon collisions. My recollection of the flocking literature is that individuals align their headings with those of nearby individuals, and not that they explicitly fly at them.

10. Methods. Route memory. It is important to make clear here that the landmarks are therefore unique to each agent. This is not intuitive, as in the real-world landmarks are typically conspicuous features (a lake, or tower etc) and so agents cannot freely choose their locations. But here, part of the reason that efficiency can improve is that each agent generates its own landmarks from a continuous landscape allowing for gradual improvements. This sort of thing would be suitable for an expanded discussion.

11. Methods. Experimental design. It is not clear how the choice of speed (70 units per 1 time unit) affects the results. This needs an expanded justification (or clarification of why it doesn't matter). If it does matter, a sensitivity check would be helpful.

12. Methods. Experimental design, Weight parameters. How are all these weight parameters possible? Many combinations would exceed a sum of 1? In the supplementary figures it looks like only valid combinations are considered, but this needs to be stated.

13. Methods, Data reduction. How many samples (and what %) were discarded for either GPS glitches or excessive distance from the route?

14. Methods, Data reduction. There is a reference to "the original paper", but which paper is this? What exactly is the subtle deviation? How can we be sure it doesn't matter?

15. Methods, Data reduction. Why is efficiency computed from the best of 12 journeys? Why not the average across all 12? Does this matter?

16. Figures S1 and S2. These figures are pretty, but the nested circles render them almost incomprehensible. I'm not sure what the best solution is, but perhaps separating the plots by w_memory is the only option.

Reviewer #2:

This article, "Cumulative culture spontaneously emerges in social navigators with imprecise memory", describes an avian navigation model where agents follow just four rules. Navigators that were paired outperformed solo navigators, and when the composition of the pairs was varied rather than fixed, efficiency improved even further. Interestingly, both the experienced and naive individuals benefitted from each other, which was somewhat unexpected: one would not think (at least initially) that the naive individual would be of much benefit to the experienced one.

This model and the findings of this paper pose a provocative question to the field of non-human culture, where there is a lot of debate currently about this topic (see Whiten 2023 Physics of Life Reviews, and the slew of responses). I think there is a lot of value in papers like this, which challenge the prevailing lines of thought in the field, which has at times become stagnated, and has always been too anthropocentric for its own good. It's an interesting time for the field, with a lot of new findings emerging (or on the brink of doing so). So, I would be happy to see this article published, and I do think that PLOS Biology would be a good fit. However, I do have some comments for the authors to consider first.

I am admittedly not an expert in modelling, so cannot really comment on the exact ins and outs of the model itself - although I can't see any glaring issues with it, the parameters are quite thorough and the controls seem reasonable. Hopefully, the other reviewers will be able to comment more thoroughly on this. My comments will therefore focus mainly on the introduction and discussion, which are at present, very brief, and could use expansion (or, at least reference to certain points - I am aware this is a short report, so won't necessarily be able to include much depth, but at least referencing would be helpful).

The original paper by Sasaki and Biro, which involved releasing pigeons (as singles or pairs, of either fixed or variable composition) is one of my favourites. While I am personally inclined to agree that Sasaki and Biro demonstrat

 10.1371/journal.pbio.3002644.r003 Author response to Decision Letter 1 Submission Version 2

27 Feb 2024

Submitted filename: Dalmaijer_response_letter_cumulative_culture.pdf

 10.1371/journal.pbio.3002644.r004 Decision Letter 2 Roberts Roland G Senior Editor 2024 Roland G Roberts This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 2

10 Apr 2024

Dear Dr Dalmaijer,

Thank you for your patience while we considered your revised manuscript "Cumulative culture spontaneously emerges in artificial navigators that have goal-direction and route memory, and seek social proximity" for publication as a Research Article at PLOS Biology. This revised version of your manuscript has been evaluated by the PLOS Biology editors, the Academic Editor and the original reviewers.

Based on the reviews, we are likely to accept this manuscript for publication, provided you satisfactorily address the remaining points raised by the reviewers and the Academic Editor. Please also make sure to address the following data and other policy-related requests.

IMPORTANT - Please attend to the following:

a) Please address all of the remaining requests from the reviewers.

b) The Academic Editor has also provided some comments, in which s/he firmly requests that you avoid the term "cumulative culture" for most of the paper, including the Title.

c) After some discussion with my team-members, who found the current Title rather obscure, and with the Academic Editor, we suggest that you change it to something like "Cumulative route improvements spontaneously emerge in artificial navigators even in the absence of sophisticated communication or thought" (perhaps "in silico navigators" would be clearer?)

d) My team-mates also found the Abstract rather difficult to comprehend, and this will need to be improved, especially for our broader readership. Specifically, two things were very unclear. Firstly, what are the "artificial agents" that you use - my understanding is that these are in silico or simulated entities, and this should be made clear in language that will be clear not only to those in your own field but also to general biologists (the majority of our readership). The second thing, which does not seem to appear in your abstract, is that you compare your model to real-life data from pigeons, finding a good fit - this should be mentioned in the Abstract, and overall the Abstract should be re-worked with the broader reader in mind.

e) you say in the financial declaration that you received no specific funding for this work. Can I just confirm that this is the case?

f) Many thanks for supplying the data and code. My understanding (correct me if I'm wrong) is that the data are in Zenodo, and that the code is in Github. Because Github depositions can be readily changed or deleted, please make a permanent DOI’d copy of the code (e.g. in Zenodo) and provide this URL (see below).

g) Please cite the location of the data clearly in all relevant main and supplementary Figure legends, e.g. “The data underlying this Figure can be found in https://zenodo.org/records/XXXXXXXX" or "The data and code required to generate this Figure can be found in https://zenodo.org/records/XXXXXXXX"

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------------------------------------------------------------------------

REVIEWERS' COMMENTS:

Reviewer #1:

The author has revised and resubmitted their model of the cumulative cultural evolution of efficient flight paths in pigeons. I previously enjoyed reading this paper and continued to do so following its revisions. The author should be commended for their thorough improvements to the manuscript. I was particularly appreciative of their deep dive into the role of goal-direction and the results of the model now make sense (to me at least). Below I have a few minor concerns, however, overall I have no reservations in recommending this manuscript for publication.

L.54. Through the symbol for b^_other does not render correctly, appearing as an empty cube.

L55. Typo. "in components' precision" should be "in each component's precision" (note shift of apostrophe).

E1. It is not clear why k_memory is indexed by i. This is explained in the methods, but I would mention here it is because the precision of memory increases across flights.

L90-98. Typos. W_goal and w_social are presented as integers (e.g. 15) instead of decimals (e.g. 0.15).

L129-150. This section is hard to follow and could be improved. Specifically:

L130-132. What is meant by "identical" is it that the same weights are used?

L135. Typo. ", .".

L136-137. Note that this necessity can be seen in that efficiency did not improve when the goal-direction system was lesioned.

L157. In what way do these results not align with agents?

L201. "demonstrates" should be "demonstrate".

Reviewer #2:

I would like to thank the author for their clear and detailed responses, particularly to the more technical modelling queries. For my part, the rewritten article has addressed my concerns regarding the lack of background information and need for wider context, and I am happy to recommend it be published in its current form. Although, as I mentioned previously, I'm no expert in modelling, so please do defer to the more knowledgeable reviewers' opinions regarding the responses to these queries. However, I did find the author's responses to these questions (and changes made as a result) to be clear and plausible to me, and I at least was satisfied that they were addressed sufficiently.

Reviewer #3:

Many thanks to the authors for their clear responses to my comments--the manuscript is greatly improved in clarity and contribution, and I can recommend this for publication. I especially liked that the ms now highlights the mechanism as regression to the goal, and is a nice formalization of this mechanism that can lead to CCE.

I only have some lingering minor comments below, which I do not need responses to:

L133: "instead of goal-direction, social proximity, route memory, or continuity Von Mises distributions, headings were sampled from uniform distributions"

"continuity Von Mises distributions" sounds wrong here and might confuse readers. Suggest instead to avoid it: However, headings were sampled from uniform distributions (i.e. noise) instead of being influenced by goal-direction, social proximity, route memory, or continuity.

L179: "While focussing on task efficiency offers insight into cumulative cultural evolution (Gruber et al., 2021), solutions are only one side"

I think authors meant "one-sided", although I still don't quite get what that means. Maybe meant to say something like "evolutionary paths are limited?"

L203: "but adopt new sites upon population refresh"

I like the turn of phrase, but maybe something like "upon complete population replacement" would be clearer.

L205: "naive individuals conforming to efficient variants"

Would recommend "adopting efficient variants", since as I remember there was no evidence of conformity in this experiment

L330-345: all of these reported metrics might be better off in a table, and in the supplementary. Will save you some space.

Reviewer #4:

The paper has shown clear improvements, and I believe the author has appropriately addressed most of the raised comments. However, there are still some areas that need attention:

Major comments:

While the revised introduction does a better job of citing existing work, the structure remains poor, making it difficult to follow. For example, the first sentence defines cumulative culture, followed by a sentence about underlying mechanisms (line 6), then a discussion on cumulative culture in animals (lines 8-12), followed by paragraphs on alternative mechanisms/explanations (lines 13-17), and more definitions of cumulative culture later on. I recommend the author streamline the material from line 1 to 36 for greater clarity.

The author cites the Mesoudi & Thornton definition of cumulative culture to argue that the documented phenomenon constitutes an instance of cumulative culture. However, the second criterion of this definition specifies that the behavioral variant must be passed to others via social learning. Typically, this involves a cultural demonstrator (an individual with experience) and a cultural learner (an individual naive to the task). Here, the only social mechanism is social proximity. I am not convinced this qualifies as social learning, which should be discussed further. As I mentioned in my previous review, it is crucial to articulate these results within the existing literature.

Minor comment:

Line 135: Part of the sentence/paragraph is missing.

COMMENTS FROM THE ACADEMIC EDITOR:

I do find, however, that the author has not sufficiently addressed reviewer 2's comment - that the paper is not in fact about cumulative culture by most people's reading of the term. Readers might be misguided by the title to think that a human-like phenomenon is under examination: the building of new technological or cultural innovations on previously existing ones. Instead it refers to a single study on gradual flight route improvements in pigeons that come about by social learning. The authors of that study have indeed argued that this qualifies as cumulative culture, but this is not widely accepted: indeed it does not contain the innovation of any novel behavioural routines (e.g. the use of a tool that spreads via social learning) - much less the building of a further unique innovation on top of another. There are more impressive examples about the gradual improvement of spatial information in animal groups - e.g. the consensus decision making in honeybee swarms (cf work by Martin Lindauer in Tom Seeley), and no one has seen the need to label these as cumulative culture. I don't think that the modelling in the present study would generalise to other cases than the particular phenomenon in pigeon navigation. So I think the author would do himself a favour if he removed "cumulative culture" from the title and instead indicated a clear focus on the specific phenomenon under investigation: route improvements in navigation via social learning. The same applies to elsewhere in the study. It's fine to discuss the study in its relation to cumulative culture, but readers will be disappointed if it's pitched as it currently is.

[...and in response to Roli Roberts' suggestion that the Title should be changed to something like "Cumulative route improvements spontaneously emerge in artificial navigators even in the absence of sophisticated communication or thought" and the whether it would be fair/appropriate to ask the author to substitute "cumulative route improvements" for "cumulative culture" throughout...:]

....yes, you have my full support for this change of the title, and the terminology throughout. I think an interesting finding has to stand on its own no matter whether one sticks a fancy label on it or not. I think it's fine if he wants to have a brief discussion of cumulative culture somewhere, e.g. "such cumulative route improvements have even been discussed as bearing some of the elements of cumulative culture as occurs in species X, Y and Z; I suggest that my modelling might also apply to phenomenon x if the following conditions are met" or something like this.

 10.1371/journal.pbio.3002644.r005 Author response to Decision Letter 2 Submission Version 3

22 Apr 2024

Submitted filename: point-by-point_response.pdf

 10.1371/journal.pbio.3002644.r006 Decision Letter 3 Roberts Roland G Senior Editor 2024 Roland G Roberts This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 3

26 Apr 2024

Dear Dr Dalmaijer,

Thank you for the submission of your revised Research Article "Cumulative route improvements spontaneously emerge in artificial navigators even in the absence of sophisticated communication or thought" for publication in PLOS Biology. On behalf of my colleagues and the Academic Editor, Lars Chittka, I'm pleased to say that we can in principle accept your manuscript for publication, provided you address any remaining formatting and reporting issues. These will be detailed in an email you should receive within 2-3 business days from our colleagues in the journal operations team; no action is required from you until then. Please note that we will not be able to formally accept your manuscript and schedule it for publication until you have completed any requested changes.

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Thank you again for choosing PLOS Biology for publication and supporting Open Access publishing. We look forward to publishing your study. 

Sincerely, 

Roli Roberts

Roland G Roberts, PhD, PhD

Senior Editor

PLOS Biology

rroberts@plos.org