Nonadjacent dependencies and sequential structure of chimpanzee action during a natural tool-use task

Introduction

Many behaviours of both humans and non-human animals (henceforth animals) can be considered sequences of discrete actions. Therefore, understanding how both humans and animals generate, store and retrieve such sequences is key to understanding the cognition supporting these serial behaviours. Humans in particular exhibit a number of sequential behaviours which are argued to be uniquely complex in comparison to the analogous behaviours of animals, including language (Hauser, Chomsky & Fitch, 2002; Bolhuis et al., 2014; Hauser et al., 2014; Berwick & Chomsky, 2015); the production and appreciation of music (Fitch, 2013; Fitch & Martins, 2014); and the manufacture and use of highly sophisticated tools (Greenfield, 1991; McGrew, 1993; Davidson & McGrew, 2005; Vaesen, 2012). Comparative research into the sequential behaviours of animals may offer key insights into the evolution of the elaborate structural features of human behaviours, particularly through the investigation of behaviours which are analogous to human communication, music and tool use (Matsuzawa, 1996; Hauser, Chomsky & Fitch, 2002; Fitch & Hauser, 2004; Berwick et al., 2012; Hayashi, 2015; Sainburg et al., 2019).

A key feature of human sequential behaviours is the emergence of nonadjacent dependencies. Nonadjacent dependencies emerge in sequences when elements co-occur with each other, despite being separated by intervening elements of a sequence (Lin & Tegmark, 2017; Sainburg et al., 2019; Watson et al., 2020). For example, in language, nonadjacent dependencies can emerge through subject-verb agreements, where the nature of the subject (gender, number, etc.) may influence the morphology of its corresponding verb, irrespective of how far separated they are in linear space and/or time (Mel’čuk, 1988; Rispens & Soto de Amesti, 2017). Of the various ways nonadjacent dependencies emerge in human behaviours, one commonly cited mechanism is through the hierarchical organization of sequences. During hierarchical organization, the atomic units of a behaviour (e.g., phonemes, musical notes, and manual actions) are organized into short subroutines (e.g., words, musical phrases, short goal-directed action sequences) which are themselves organized to produce wider strings of behaviour. Importantly, hierarchical organization can produce nonadjacent dependencies through embedding subroutines within each other. For example, in language, a clause can be embedded within another clause (Lashley, 1951; Chomsky, 1956, 2002; Jäger & Rogers, 2012; Fitch & Martins, 2014; Sainburg et al., 2019; Sainburg, Mai & Gentner, 2022); e.g., in the sentence “The weather is horrible!”, a prepositional phrase may be embedded to produce the sentence “The weather [outside the window] is horrible!”. In this example, the verb ‘is’ and adjective ‘horrible’ both relate to the noun at the head of the phrase (the weather), despite being closer to another noun (the window) in linear space and/or time. Likewise during sequential actions, nonadjacent dependencies occur when a series of actions addressing one subgoal are embedded within a sequence of actions addressing another goal. For example, when opening a door an actor may grasp, turn, and push the handle. However, if the door is locked, the actor may grasp the handle, then begin eliciting a number of actions to open the lock (thus completing the embedded subgoal: to undo the lock), before continuing to turn and push the handle to open the door. In such an example, grasping a handle always precedes turning a handle, and therefore these actions are linked within the sequence; however, they may be separated by an intervening embedded string of actions. Whilst debate continues surrounding the extent to which language and action share homologous systems of organization (see Coopmans, Kaushik & Martin, 2023 for a recent argument for the nuanced differences between these behaviours), the general ability to comprehend hierarchically organized information, and account for nonadjacent dependencies, are undoubtedly important for the performance of many complex human behaviours (Lashley, 1951; Chomsky, 1956, 2002; Rosenbaum et al., 2007; Jäger & Rogers, 2012; Fitch & Martins, 2014).

Whilst nonadjacent dependencies in human behaviours—including those produced by hierarchical organization—have been subject to many decades of study, comparatively less research has assessed whether animals exhibit similar structural properties in the sequential behaviours that they habitually perform in the wild. Until relatively recently, animal sequential behaviours were assumed to be produced through reflexive serial chains: when an action or call was externalised, it would trigger the externalization of the next action or call, and so on to produce an extended behavioural sequence (Hauser, Chomsky & Fitch, 2002; Terrace, 2005; Ten Cate & Okanoya, 2012). The rules which animals employed to create such behavioural sequences were therefore theorized to be extremely simple, requiring no knowledge of the calls or actions they produced other than the one produced most recently (thus, significantly reducing the burden on working memory due to the absence of long-range nonadjacent dependencies; Wilson et al., 2020). Such reflexive chains can be characterized using simple stochastic modelling approaches, such as Markov chains: network models where each node represents a different possible element in a sequence, and the edges between nodes are weighted based on the likelihood a sequence will contain an adjacent transition between element types (Gagniuc, 2017). Despite the historic pervasiveness of chaining models for explaining the sequential structure of animal behaviours, mounting evidence suggests that a number of different animal species produce behavioural sequences which, to varying degrees, contain hierarchical patterns. For example, hierarchical organization is found the songs of whales (Suzuki, Buck & Tyack, 2006; Miksis-Olds et al., 2008) and birds (Sainburg et al., 2019), as well as in the behaviours of several primate species, including perceptions of grouped, hierarchical social relationships in baboons (Bergman et al., 2003); the nested temporal organization of vocal elements during orangutan long calls (Lameira et al., 2024); and the mental organization of social games in chimpanzees (Mielke & Carvalho, 2022). For behaviours which are temporally organized, such as in the case of birdsong, these hierarchical patterns have been supported through the identification of nonadjacent dependencies, which span across sequential distances that match those predicted by hierarchical organization (Sainburg et al., 2019).

Nevertheless, nonadjacent dependencies and hierarchical organization do not appear to be universal aspects of animal behaviours. For instance, the communication systems of many species can be readily approximated using Markovian, non-hierarchical dynamics (Hauser, Chomsky & Fitch, 2002; Fitch, Hauser & Chomsky, 2005; Ten Cate & Okanoya, 2012), and do not result in nonadjacent dependencies over long distances, suggesting that the use of supraregular grammars to construct communicative sequences may be limited to animal species that employ complex broadcast signals. Additionally, some behaviours can employ different systems of organization at differing temporal scales. This is even the case for humans. For example in language, whilst words are hierarchically organized based on the rules of a language’s syntax, the relationships between sound units within words (phonemes) can be characterized using their neighbouring associations (Kaplan & Kay, 1994; however see instances of nonadjacent dependencies through vowel harmony, such as Gonzalez-Gomez et al., 2019). Therefore, further research is required to understand whether animals are able to produce sequences which share similar structural features to those of humans, and if so, to identify the behavioural contexts in which these sequences are employed. This includes research into the behaviours of species which are phylogenetically proximate to humans—such as chimpanzees, bonobos, and other great apes—for whom these systems of sequential organization, if present, would have the highest likelihood of sharing homologous origins with similar behaviours of humans (Gruber & Clay, 2016).

Among the behaviours of wild chimpanzees—one of the most closely related great ape species to humans—tool use has been identified as a domain of behaviour which likely possesses high hierarchical complexity (Byrne & Russon, 1998; Byrne, Sanz & Morgan, 2013; Gontier, 2024), and consequentially, likely entails some form of nonadjacent-dependency generation. Previous descriptions of chimpanzee tool-use behaviours have included the possibility that some particularly complex forms of tool use require chimpanzees to understand hierarchical relationships between objects (Matsuzawa, 1991, 1996; Hayashi, 2007; Sanz & Morgan, 2010; Hayashi & Takeshita, 2022). Moreover, when considering how chimpanzees organize their behavioural sequences for tool use, previous models used qualitative descriptions of the stages of producing, using, and disposing of tools, over many hours of human observation (the chaîne opératoire; Byrne & Russon, 1998; Tonooka, 2001; Carvalho et al., 2008; Sanz & Morgan, 2010; Estienne, Stephens & Boesch, 2017; Boesch et al., 2020). These observations have been used to suggest that, when engaging in tool-use behaviours, chimpanzees (and other apes) generate behavioural sequences hierarchically, through the decomposition of tool-use behaviours into a series of nested subgoals, which are themselves addressed through the generation of short subroutines of manual actions (Byrne & Russon, 1998; Byrne, Sanz & Morgan, 2013). Hierarchical organization is theorized to offer an adaptive advantage for successful tool-use behaviours in comparison to associative chaining, as organizing sequences hierarchically would allow for apes to flexibly reorganize subgoals of behaviours based on the local context of their environments, rather than repeatedly following a ‘fixed action pattern’ (Byrne, Sanz & Morgan, 2013). For example when organizing actions hierarchically, an individual may omit optional steps (a chimpanzee may not need to puncture a hole in a termite mound if one already exists; Byrne, Sanz & Morgan, 2013), or through embedding extra steps within a behavioural sequence (e.g., an individual may interrupt a behavioural sequence to adjust or swap over tool items, which are not necessary for the behavioural sequence, but may help an individual manipulate objects more efficiently).

Despite chimpanzee tool use possessing many signs of hierarchical organization, the majority of evidence for hierarchical organization in chimpanzee tool use comes from qualitative descriptions of behaviours. Descriptive arguments for behavioural organization have been pointed out on numerous occasions to be at risk of subjective bias. Even though sequences can be described hierarchically, this does not stop them from being generated using computationally simpler mechanisms of sequence generation (Dawkins, 1976; Vereijken & Whiting, 1998; Girard-Buttoz et al., 2022). This argument is reinforced by the observation that humans are biased to perceive hierarchical relationships in sequences which lack any form of hierarchical organization (Fitch, 2014; Ferrigno et al., 2020), which in this instance could include the observation of animals’ behavioural sequences in the wild. There is consequently the need for new methodologies which are able to provide objective evidence that chimpanzee action sequences for tool use are organized hierarchically. Additionally, methodologies which also quantify the extent to which nonadjacent dependencies emerge between actions during such behavioural sequences would be particularly useful, as this is a property of chimpanzee tool use which has not yet been formally investigated.

To better characterise the sequential organization of actions during tool-use behaviours, and the extent to which such behaviours produce nonadjacent dependencies, we herein draw upon models of mutual information decay. Mutual information (MI) refers to the predictability of a given sequence element when the state of another element elsewhere in the sequence is known. MI often decreases between elements separated by greater distances; for example, looking out of a window at the weather one morning provides some information about the likely weather events that same afternoon. However, knowing the weather several days, or weeks prior would carry increasingly less information about the likely weather conditions in the upcoming afternoon. Whilst nonadjacent dependencies can be produced by a number of means during the generation of human sequential behaviours, several models have recently been developed that predict how MI decay with increasing sequential comparative distance, based on structural properties of sequences themselves (Lin & Tegmark, 2017; Sainburg et al., 2019; Sainburg, Mai & Gentner, 2020, 2022; Youngblood, 2024). As non-hierarchical, ‘regular’ grammar systems (such as reflexive chains, and Markov models) produce sequences based on neighbouring probabilistic dependencies, they exhibit exponential decreases in MI between elements separated by increasing sequential distances (Lin & Tegmark, 2017). Alternatively, sequences with hierarchical structures produce nonadjacent dependencies at greater distances. This is due to relationships between sequence elements imposed by higher-level aspects of a sequence’s organization, and consequentially, hierarchical organization results in a power-law decay of dependencies over greater sequential distances (Lin & Tegmark, 2017; Sainburg et al., 2019; Sainburg, Mai & Gentner, 2022; Youngblood, 2024). Hierarchical and non-hierarchical structuring mechanisms may also be combined to form a composite structure (Sainburg et al., 2019; Sainburg, Mai & Gentner, 2022; Youngblood, 2024), where shorter, non-hierarchical strings are hierarchically organized to produce longer sequences (see above example of phonemes being organized into words, and words into sentences; Sainburg et al., 2019). Sequences produced by composite structuring may then display MI decay dynamics that are best approximated by exponential decay for sequential elements at local scales, and power-law decays for elements separated further across sequences. MI decay dynamics have been used to evaluate corpora of human and non-human vocal behaviours (Sainburg et al., 2019; Sainburg, Mai & Gentner, 2022; Youngblood, 2024), as well as the sequential actions of humans, zebrafish and fruit flies (Sainburg, Mai & Gentner, 2020). However, they have not thus far been applied to the sequential tool-use behaviours of a nonhuman animal.

In the present study, we employ MI decay models to investigate two overlapping research questions, concentrating on the sequential organization of serial action in chimpanzee tool use:

(1) Do chimpanzees produce nonadjacent dependencies within their sequential actions during tool-use behaviours, and if so, how to they compare with sequences from comparable Markov models?

(2) What do the dynamics of MI decay in chimpanzee tool-action sequences suggest about their sequential organization (Markovian, hierarchical, or a composite system)?

To answer these questions, we focus on the sequential organization of actions used by wild West-African chimpanzees (Pan troglodytes verus) when engaging in one of their most complex natural tool-use behaviours: the cracking of hard-shelled nuts with hammer and anvil stones. Through MI estimations, we demonstrate that the sequences of actions performed during tool use by two thirds of all sampled adult chimpanzees possess dependencies at significantly greater distances than those predicted by simulated Markov models. For half of adults, this relationship remained once repeating actions were accounted for, suggesting that repeating actions alone could not account for dependencies at long distances for many adults. We also report that the sequences of actions used by the majority of chimpanzees during nut cracking yield MI decay profiles that are concurrent with previous qualitative descriptions of hierarchical structuring in the tool action of apes. Additionally, we note that there is detectable interindividual variability in the distances at which dependencies occur in action sequences, and the most likely mechanisms of sequence generation detected by MI decay. Whilst our results are observational—and therefore limit the extent to which we can make claims about the underlying cognition of wild chimpanzees in this study—we report that the MI dynamics found in action sequences for tool use support previous claims that chimpanzees organize these behaviours hierarchically; however, given interindividual differences, further research is required to understand if this is a universal system of behavioural organization possessed by chimpanzees. Thus, our findings provide additional evidence for the capacity of non-human apes to draw upon supraregular rules of sequence production, and produce nonadjacent dependencies during a natural behaviour: tool use. We discuss the need for further studies that will quantify the precise mental representations which permit chimpanzees to produce sequences that are organized across multiple temporal scales. In extension, our findings feed into the wider discussion surrounding the abilities of animals to produce complex sequential behaviours, including possibly homologous structural properties to those found in the behaviours of humans.

Methods

Portions of this manuscript were previously published as part of a preprint (https://doi.org/10.1101/2024.03.25.586385).

Results

Sampled sequence data

We analysed a total of 251.85 min of video data of chimpanzees engaging in nut cracking, yielding action sequences from nine individuals (see Table 1; see Table S1 for demographic data of sampled chimpanzees). Of these nine individuals, one (Velu) had fewer than 200 actions coded throughout the entire series of sampled videos. As entropy estimation from small sample sizes can be subject to high levels of error (Grassberger, 2003), this individual was omitted from our MI analyses. Subsequently, eight individuals were included in our MI analyses: two adult females (Fanle & Jire); four adult males (Foaf, Jeje, Peley & Tua); one juvenile female (Joya) and one infant male (Flanle).

Table 1:

Summary of sequence data collected from the 2011/2012 field season at Bossou (including all complete and incomplete sequences).

Individual	Sex	Age (years)	Sampled for MI analysis	Time coded (MM:SS)	Number of sequences	Sequence elements (Total)	Mean sequence length ± SE	Number of action types	Nuts cracked	Mean sequence length per nut ± SE
Fanle	F	14	✓	44:55	21	1,368	65.1 ± 1.8	34	85	13.9 ± 0.4
Flanle	M	4	✓	24:03	35	453	12.9 ± 0.6	59	1	48
Foaf	M	31	✓	07:22	8	299	37.4 ± 2.2	18	10	31.2 ± 1.8
Jeje	M	14	✓	40:33	18	1,373	76.3 ± 2.1	36	39	29.4 ± 0.9
Jire	F	53*	✓	19:27	12	482	40.2 ± 1.8	33	22	16.0 ± 0.9
Joya	F	7	✓	36:52	39	1,178	30.2 ± 0.9	55	22	36 ± 1.3
Peley	M	13	✓	34:05	15	1,168	77.9 ± 2.3	44	45	21.7 ± 0.7
Tua	M	54*	✓	55:33	15	1,940	129.3 ± 2.9	43	79	22.4 ± 0.5
Velu	F	52*	×	01:07	2	16	8 ± 2	12	0	0

DOI: 10.7717/peerj.18484/table-1

Note:

Eight individuals were included in MI decay modelling. ‘Time Coded’ relates to the total duration of time individuals were seen to be engaging with nuts, nut fragments and stone tools throughout all video footage. An ‘Element’ is defined as each action coded within a sequence, whereas ‘Action Types’ represent the different types of coded actions in a sequence (e.g., “Grasp Nut” “Place Nut” “Grasp Nut”—Number of elements: 3, Number of Action Types: 2). ‘Nuts Cracked’ marks the number of nuts observed to have been cracked by an individual across all available video footage. Mean Sequence Length Per Nut refers to the mean number of elements in a sequence that is directed at cracking open each individual nut. SE for all means were calculated via the normal approximation of the Poisson distribution. Ages marked with * are estimates, as these individuals were already present at Bossou when long-term monitoring began in 1976.

Across the eight individuals in our dataset, we recorded action sequences for the cracking of 303 individual nuts, using 8,261 individual actions, belonging to 82 unique classes of action (see Fig. 1 for a list of the most common classes of actions used by chimpanzees, and example sequences of actions performed during nut cracking). Flanle, the infant male, used the greatest variety of different actions during nut cracking (59 unique classes of action), followed by Joya, the juvenile female (55 unique classes of action). Both of these individuals interspersed short sequences of solo object play into their attempts at nut cracking, e.g., mouthing the hammer stone, coded as either ‘kiss HAMMER’ or ‘bite HAMMER’, depending on the force applied. For both of these individuals, we retained these actions as part of our coded action sequences, to avoid subjective bias of when individuals were or were not attempting to crack nuts.

Adults used a smaller repertoire of actions when engaging in nut cracking. This repertoire included a small subset of high-frequency actions to facilitate nut cracking, with the five most common actions including ‘Strikeonehand Hammer’ (24.6%), ‘Eat Kernel’ (11.8%), ‘Grasp Nut’ (10.5%), ‘Place Nut’ (8.6%), and ‘Grasp Kernel’ (8%;). In total, 63% of all actions within our dataset fell into one of these five action types. In addition to these frequently performed actions, an extended number of actions were performed less frequently, only where necessary, e.g., passing the hammer between the hands (pass HAMMER), or rotating the anvil stone to confer stability (reorient ANVIL; see Fig. 1C for more examples).

Maximum inter-element distance MI detected

To understand the most extreme extent to which chimpanzees produced nonadjacent dependencies in their sequential actions, we identified the maximum sequential distance at which dependencies occurred. For each individual, we compared this result to the maximum distances MI_Adj was positive in 100 sequences simulated from Markov models. This allowed us to determine whether dependencies in observed action sequences occurred at greater distances than those which can be produced through Markovian chaining of actions.

On average, the maximum sequential distances where MI_Adj remained above zero was 30.3 elements (N = 8, SD = 29.9; see Table 2). For Flanle, the infant male, MI_Adj did not fall to zero before the maximum distance of 100 sequence elements. When excluding Flanle from this average—for whom the maximum distance over which dependencies were detected was over two standard deviations higher than all other individuals—the mean maximum sequential distance at which MI_Adj was positive was 20.3 elements (N = 7, SD = 10.8).

Table 2:

Summary of maximum comparative distances, model preferences, and transition points for action sequences with repeating actions.

Individual	Sex	Age class	Maximum sequential distance MIAdj > 0	Preferred model	Transition point	Mean sequence length per nut ± SE (no. of nuts cracked)
Fanle	F	Adult	17	Power-Law	–	13.9 ± 0.4 (85)
Flanle	M	Infant	100	Composite	2	48 (1)
Foaf	M	Adult	9	Exponential	–	31.2 ± 1.8 (10)
Jeje	M	Adult	22	Composite	4	29.4 ± 0.9 (39)
Jire	F	Adult	11	Power-Law	–	16.0 ± 0.9 (22)
Joya	F	Juvenile	21	Composite	8	36 ± 1.3 (22)
Peley	M	Adult	42	Composite	2	21.7 ± 0.7 (45)
Tua	M	Adult	20	Composite	7	22.4 ± 0.5 (79)

DOI: 10.7717/peerj.18484/table-2

Note:

Transition point describes the element distance where the composite model switches from a primarily exponential decay dynamic to one which is better generalised by a power-law. For each individual, the transition point, and mean number of actions used to crack open individual nuts, is provided. Total sample size for nut sequence length (i.e., number of nuts cracked throughout the study period) is included in bracket.

For six individuals (Fanle, Flanle, Jeje, Joya, Peley and Tua), a positive MI_Adj was detected at sequential distances that were significantly greater than those found in counterpart Markovian sequences (identified by a higher maximum inter-element distance where MI_Adj was positive compared to the upper 95% CI of the corresponding Markov distribution; see Fig. 2 and Table S3). This result confirms that nonadjacent dependencies for these individuals occurred at distances greater than could be readily generated by comparative Markov models. Alternatively for two individuals, (Foaf & Jire), we found no difference between the maximum distance MI_Adj was detected in the observed action sequences compared to sequences simulated from Markov models.

To determine whether successive repeats of elements (e.g., repeatedly striking a hammer) influenced the maximum inter-element distance where MI_Adj was above zero, observed action sequences were passed through a condensing algorithm that removed repeated elements, and MI_Adj was estimated in the same way as before. Separate Markov models were also constructed from condensed data, and our analysis was repeated identically to before.

For the condensed action sequences, the mean maximum sequential distances where MI_Adj was detected was 13.3 elements (N = 8, SD = 5.9). Flanle, the infant male, showed the largest decrease in the maximum distance where MI_Adj was greater than zero, reducing from possibly over 100 elements down to nine sequence elements. This implies that dependencies were heavily influenced by repeating actions in Flanle’s action sequences, possibly through repeated play actions.

For three individuals (Fanle, Peley and Tua), the maximum distance at which MI_Adi was positive remained significantly greater than sequences produced by their corresponding Markov models (see Fig. 2; see Table S3). These three individuals represent half of all adults in our sample. Following sequence compression, three individuals no longer exhibited dependencies at sequential distances greater than simulated Markov sequences: Flanle (infant male), Joya (juvenile female) and Jeje (adult male).

MI decay analysis: observed action sequences

To understand how sequences of behaviours are generated, it can be informative to assess how mutual information decays between sequence elements which are progressively further apart (Lin & Tegmark, 2017; Sainburg et al., 2019; Sainburg, Mai & Gentner, 2020, 2022; Youngblood, 2024). For seven out of eight individuals, MI_Adj decay was best characterised by a model which included a power-law decay dynamic, which is a key indicator of hierarchical organization of elements across biological sequences (Sainburg et al., 2019; Sainburg, Mai & Gentner, 2020, 2022; Youngblood, 2024; see Fig. 3 and Table 2; see Table S4 for AICc values). The MI_Adj decay profiles of two individuals (Fanle and Jire) were best explained by a purely power-law model (predicted by solely hierarchical structuring); while for five individuals (Flanle, Jeje, Joya, Peley and Tua), the optimal decay model was identified as the composite model, which combines periods of exponential and power-law decay. These composite models follow decay profiles predicted by structuring mechanisms which involve concatenation of elements into short subroutines based on adjacent transition probabilities, which are themselves hierarchically organized into longer sequences. In the case of these five adult chimpanzees, this could be reflected by a two-stage process of generating short subroutines through chaining together a handful of actions, before hierarchically organizing these subroutines into longer sequences. For one individual (Foaf), the exponential model was identified as the optimal model, implying that Foaf organized his actions using non-hierarchical means.

Similarly to our previous analysis of the maximum inter-element distances where we detected positive MI_Adj, we repeated the analysis above on condensed sequences to ensure power-law relationships were not simply a product of highly repetitive elements (see Table 3). When analysing condensed action sequences, we were able to identify an optimal decay model for the action sequences of six individuals. Of the eight individuals in our analysis, the action sequences of five individuals were best explained by a model which included a period of power-law decay (two by a purely power-law, and three by a composite model), predicted by composite or wholly hierarchical structuring. For two individuals (Jeje and Jire), multiple models offered competing explanations of decay dynamics: for action sequence data collected from Jeje, the composite and exponential models offered competing explanations of the data; whereas for Jire, the power-law and exponential models exhibited similar explanatory power. For these individuals, we therefore could not find conclusive support for any one structuring mechanism. For the MI_Adj decay profile for Foaf, the exponential model continued to offer the best explanation of the data following sequence compression, implying non-hierarchical means of action-sequence generation.

Table 3:

AICc scores for MI_Adj decay models, derived from condensed sequences.

Individual	Max element distance	Model	K	AICc	∆AICc	AICc.Wt	Cum.Wt	LL
Fanle	16	Composite	5	−70.5	0.0	0.93	0.93	43.6
		Power-Law	3	−65.2	5.3	0.07	1.00	36.7
		Exponential	3	−47.2	23.3	0.00	1.00	27.7
Flanle	9	Power-Law	3	−18.5	0.0	0.98	0.98	15.3
		Exponential	3	−10.3	8.2	0.02	1.00	11.2
		Composite	5	0.8	19.4	0.00	1.00	19.6
Foaf	10	Exponential	5	−36.7	0.0	1.00	1.00	23.8
		Power-Law	3	−22.7	14.0	0.00	1.00	16.8
		Composite	3	−14.1	22.6	0.00	1.00	22.1
Jeje	11	Composite	5	−43.0	0.0	0.72	0.72	34.0
		Exponential	3	−41.2	1.8	0.28	1.00	25.6
		Power-Law	3	−23.0	20.0	0.00	0.00	16.5
Jire	9	Power-Law	3	−22.7	0.0	0.54	0.54	17.4
		Exponential	3	−22.4	0.3	0.46	1.00	17.2
		Composite	5	10.7	12.0	0.00	1.00	25.4
Joya	9	Power-Law	3	−26.5	0.0	1.00	1.00	19.2
		Exponential	3	−15.0	11.5	0.00	1.00	13.5
		Composite	5	−2.3	24.2	0.00	1.00	21.2
Peley	26	Composite	5	−121.8	0.0	0.80	0.80	67.5
		Power-Law	3	−119.1	2.7	0.20	1.00	63.1
		Exponential	3	−80.0	41.8	0.00	1.00	43.6
Tua	16	Composite	5	−92.2	0.0	1.00	1.00	54.5
		Exponential	3	−70.7	21.5	0.00	1.00	39.4
		Power-Law	3	−49.0	43.2	0.00	1.00	28.6

DOI: 10.7717/peerj.18484/table-3

Note:

For each individual, Max Element Distance highlights the greatest element distance included in the MI_Adj datasets, and models are given in the order of preference (as determined by AICc—rows in bold indicate highest preferences; lower AICc values reflect better performing models). K represents the number of parameters estimated in each model. ∆AICc represents the difference between a given model’s AICc score and the optimal model’s AICc score for each individual. AICc.Wt describes the proportion of the total predictive power of all three models contained in each model, and Cum.Wt describes the accumulation of predictive power in order of model preference. LL represents the log-likelihood of each model given the data—AICc is estimated using both K and LL.

Transition points for composite models

For each individual for whom our analysis showed a preference for the composite decay model, we also identified the transition point between primarily exponential and primarily power-law decay dynamics using the second differential of the curve in log-space (see Fig. 4.; see Methods section Estimating Transition Points in Composite Model). The maximum comparative distance prior to the transition between exponential and power-law decay dynamics ranged from 2–8 elements (mean = 4.6 elements, N = 5; see Table 2; see Fig. S4 for transition point profiles for each individual whose MI_Adj is best explained by the composite model). This predicts that for individuals whose sequence structure is best approximated by composite models, non-hierarchical chaining of actions can be used to produce subroutines of 2–8 elements apart. In extension, the composite model predicts that these subroutines are combined hierarchically to produce extended behavioural sequences. Additionally, for all of these individuals, transition points were identified at distances which were significantly shorter than the sequences of actions used to crack open individual nuts (see Table 2). This result reaffirms that composite decay dynamics were not produced through concatenation of action sequences directed at individual nuts, but were likely produced through sequential structuring of actions by chimpanzees at much shorter timescales.

MI decay analysis: Markovian sequences

To understand the rate at which our analyses of MI decay would identify power-law decay dynamics in non-hierarchical sequences (akin to a false-positive rate for identifying signatures of hierarchies from non-hierarchical sequences), we simulated action sequences from community Markov models, and ran the same model selection process as conducted on chimpanzee action sequences. We estimated a false positive rate by identifying the proportion of Markovian sequences whose MI decay profiles were best described by models which contained power-law relationships.

For the Markov model trained on the entire corpus of action-sequence data, including repeating elements, all three decay models were successfully fitted for the MI_Adj decay profiles of 425 sequences. There was a significant, positive relationship between with the maximum sequential distance at which MI_Adj was detected, and the likelihood of successfully fitting all three models (Binomial GLM with Logit Link: Success ~ Maximum Sequence Length, N = 425; Intercept: −9.25; Maximum Length: 1.53; Z = 8.96; p < 0.001), and this relationship also held for the condensed data (see Table S5). Of the 425 model comparisons, AICc identified a single best model for characterising MI_Adj decay for 340 datasets (80% of all model comparisons). 52.6% of model comparisons identified the exponential model as highly competitive (see Fig. 5). In 37.6% of model comparisons the exponential model was identified as the sole best performing model, and in 15% of comparisons the exponential model was identified as one of multiple equally optimal models. 16.5% of comparisons showed a sole preference for the power-law model, and 25.9% of comparisons showed a sole preference for the composite model.

This rate suggests that, if chimpanzees were organizing sequences similar to non-hierarchical Markov models, we would expect composite and power-law models to be the sole best performing model in 42.4% of instances combined (approximately three of eight individuals in total). In the action sequence data, this value was over double (seven individuals; composite = five individuals; power-law = two individuals). Our simulation also predicts that, if generated through non-hierarchical means, the exponential model would be the best performing model for three individuals. However, our analysis of the action-sequence data revealed that the exponential model was preferred for a single individual, Foaf.

A similar result was found when using a Markov model trained on condensed action sequences (see Fig. 5). If action sequences were generated through non-hierarchical means, we would expect composite and power-law models to be the sole best performing model in 40.68% of instances (three of eight individuals). We identified five individuals for whom composite and power-law models were the sole preferred model (composite = three individuals; power-law = two individuals). Equally, we would expect the exponential model to be preferred in 53.4% of instances (four individuals); however, much like the analysis for action-sequence data containing repeating actions, the exponential model was preferred for a single individual, Foaf.

Discussion

Nonadjacent dependencies emerge during the performance of many elaborate sequential behaviours in humans, and can be the result of hierarchical organization (Lashley, 1951; Dawkins, 1976; Mel’čuk, 1988; Chomsky, 2002; Rosenbaum et al., 2007; Fitch & Martins, 2014; Rispens & Soto de Amesti, 2017; Wilson et al., 2020). However, these cognitively demanding aspects of sequential behavioural organization appear to be sporadically distributed across other animal taxa, and when present, may be restricted to specific behaviours. Given their close phylogenetic proximity to humans, characterizing how great-apes organize sequential behaviours is informative for understanding how human sequential behaviours evolved. The purpose of this study was to apply mutual information measures (estimates of dependency strength between sequence elements) to: (1) determine whether chimpanzees routinely produce nonadjacent dependencies between sequential actions during tool use, and if so (2) to determine whether the distance at which nonadjacent dependencies occurred in action sequences, and the dynamics of mutual information decay between increasingly separated elements, supports existing claims that chimpanzees hierarchically organize their action sequences during tool use. To answer both of these questions, we coded 8,261 actions of eight wild chimpanzees at Bossou, Guinea, as they spontaneously cracked 303 individual nuts using stone tools.

For six out of eight individuals, including two-thirds of adults (we take adulthood to be a proxy for experience and proficiency in tool use), nonadjacent dependencies were identifiable at sequential distances which significantly exceeded those produced in sequences simulated from Markov models. Thus, our data suggest that between the sequential actions produced by multiple chimpanzees during stone-tool use, nonadjacent dependencies occur at distances which exceed those found in comparable non-hierarchical sequences. For half of adults, the extended distances at which we detected dependencies could not be solely explained by repeating actions; however for the other half of adults, as well as for both the juvenile and infant individuals in our analysis, repeating actions contributed substantially to the emergence of nonadjacent dependencies. This finding does not preclude these individuals from generating some dependencies through supraregular means of action sequence generation, such as hierarchical structuring (see further discussion on MI decay below); however, it does suggest that repeated actions contributed to a greater proportion of nonadjacent dependencies which spanned larger sequential distances. These results therefore suggest that there is detectable interindividual variation in the means through which nonadjacent dependencies are generated within the action sequences of different chimpanzees, particularly between distantly separated actions.

Interindividual differences in the distances at which dependencies occurred in action sequences is consistent with previously described differences in nut cracking techniques between chimpanzees at Bossou (Berdugo et al., 2023). Additionally, our analysis reveals that younger individuals may be more likely to produce dependencies through repeating actions, such as in the case of Flanle who showed a drastic decrease in the maximum distance dependencies detected after sequence compression. As the youngest individual in our analysis, Flanle was highly inexperienced in nut cracking, and we only observed Flanle successfully cracking open a single nut during the entire period of observation (for contrast, the other seven individuals for our analysis cracked a total of 302 nuts; mean = 43 nuts each, SD = 26.9). Flanle demonstrated the highest number of action types (59), indicating a greater diversity of different action types compared to the action sequences of adult chimpanzees during nut cracking (for whom action sequences were highly stereotyped in their use of a small number of different actions). This diversity of actions, as well as their repetition and flexible assembly, may have contributed to the anomalous distance at which dependencies were identified in the action sequences for Flanle. Further research is required to understand how these factors influence the emergence of sequential dependencies in animal behaviours.

Once repeating actions were controlled for, half of adult individuals in our analysis produced dependencies at distances which exceeded comparable Markov models. This result suggests that nonadjacent dependencies are produced by a substantial proportion of chimpanzees who are proficient in tool use, at distances which exceed expectations if sequences were generated through non-hierarchical means. Among the sequential behaviours of wild chimpanzees, tool use is the first domain in which such nonadjacent dependencies have been detected. This data provides new context to results from experimental paradigms which have previously revealed that captive chimpanzees are able to identify nonadjacent dependencies in both visual and auditory sequences (Sonnweber, Ravignani & Fitch, 2015; Watson et al., 2020), by offering an ecologically-relevant domain of behaviour in which such cognition can be used. It is possible that, within the domain of manual actions, tool use is a unique behaviour of wild chimpanzees which leads to the production of nonadjacent sequential dependencies. In another study performed on the sequential play behaviours performed by chimpanzees at Bossou, the accuracy with which an action in a play sequence could be predicted was aided by considering the two most recent actions, but actions further back in the sequence offered no additional benefit (Mielke & Carvalho, 2022). This suggests that play behaviours do not produce long-range dependencies, such as those we have identified during tool use. However, to validate whether tool use is unique in its production of nonadjacent dependencies, it will be necessary to analyse a wider range of sequential manual behaviours of wild chimpanzees, and also to ensure that comparisons are made with data collected and analysed using directly comparable methodologies. These analyses should include sequential manual behaviours which vary in their technical complexity, and should include both complex, multi-stage manual behaviours (e.g., nest building and complex foraging tasks which do not require tools), as well as simpler feeding tasks which require fewer processing steps (Gontier, 2024).

The sequential manual actions of non-human apes—including those used in tool use—have previously been described using qualitative frameworks which either explicitly or implicitly encompass hierarchical organization (Byrne & Russon, 1998; Carvalho et al., 2008; Byrne, Sanz & Morgan, 2013; Estienne, Stephens & Boesch, 2017; Boesch et al., 2020; Gontier, 2024); however, it has thus far been empirically challenging to exclude the possibility that these action sequences are produced by simpler structuring mechanisms, such as serial chaining (Vereijken & Whiting, 1998), particularly as human observers carry cognitive biases for identifying hierarchical structures in non-hierarchical sequences (Fitch, 2014; Ferrigno et al., 2020). Through characterizing MI decay across observed action sequences, we identified a period of power-law decay for the majority of chimpanzees. Whilst our data is observational, we can confirm that this result matches the MI decay dynamics predicted by hierarchical organization of action sequences. Of the chimpanzees whose MI decay profiles included periods of power-law decay, the composite model was more frequently selected as the optimal model. We therefore found the greatest support for composite structuring systems, where actions are organized into short subroutines through association rules between neighbouring elements, which were then hierarchically organized to produce longer sequences of tool-action. Through analysing the curvature of composite models, we identified that these subroutines of actions were likely between 2–8 elements long. Our results are therefore consistent with previous descriptions of how great apes organize sequences of actions during food processing behaviours, including those which involve the use of tools (Byrne & Russon, 1998; Byrne, Sanz & Morgan, 2013; Gontier, 2024). Apes are theorized to decompose goals into subgoals which are addressed through short, stereotyped subroutines of actions (Byrne & Russon, 1998; Byrne, Sanz & Morgan, 2013), thus, these models of behavioural organization are identical to the composite structuring model for which our analysis provided the greatest support. Additionally, our analysis is able to objectively offer support to the hypothesis that apes organize sequences through the hierarchical organization of subroutines, without the presence of human bias for identification of hierarchical phenomena through subjective descriptions.

Despite the prevalence of the composite model in characterizing MI decay, our analyses did not provide conclusive results for all chimpanzees, as we could not resolve for a single best model for two individuals once we had accounted for repeating actions. For one individual, Foaf, the best model was identified to be the exponential model, which is associated with sequences which are produced using serial chaining. Such interindividual differences may be further evidence of differences in strategies for nut cracking behaviours between individuals, with a minority of individuals relying on alternative, finite-state mechanisms of sequence generation. However, it is also important to recognize that for Foaf—the only individual for whom the exponential model was solely preferred—a much smaller corpus of actions was collected compared to those of other individuals (see Table 1). We are not able to say for certain whether sample size would have influenced the model preference for Foaf. However, given that sample size can influence entropy estimations (Grassberger, 2003), we can only conclude that this is a possibility for our analysis. We recommend further research be conducted to investigate possible interindividual variability in the systems of sequential organization employed by chimpanzees.

Whilst our analysis provides the strongest evidence for composite mechanisms of action organization in chimpanzee tool use, it is important to emphasize that our study is observational. It is therefore outside of the scope of this study to determine what parsing rules chimpanzees may use to facilitate a structuring system which relies on regular and supraregular dynamics at different temporal scales (a limitation recognized in similar analyses on birdsong; Sainburg et al., 2019). For example, whilst we provide a prediction for the average length of subroutines (2–8 actions), we cannot identify the precise actions that subroutines contain, nor the amount of variation in subroutine length within sequences. Additionally, our study is unable to provide insight into the exact representational mechanisms and parsing procedures that chimpanzees use to produce successful sequences of tool action (Gruber et al., 2015). This includes the extent to which chimpanzees have conceptions of ‘parent-offspring’ relationships between higher-order goals and their constituent elements, or whether hierarchical patterns could emerge from comparatively simpler systems, such as those similar to stack-memory in automata that can generalize phrase-structure sequences (Ong, 2007). In the latter case, chimpanzees may construct hierarchical patterns by pausing the performance of action sequences directed at one goal, to embed in shorter subroutines of actions for corrective behaviours, before returning to the completion of the original sequence (for example, pausing the striking of a nut with a hammer to reposition a nut on the anvil, or to rotate stones into a more stable configuration). These limitations also extend to the degree to which working memory is employed to account for distant dependencies. For example, it is possible that during nut cracking, physical traces of previous actions are maintained in the environment, rather than in the mind, reducing demands on memory (e.g., a nut positioned on top of an anvil would suggest it has already been placed there in a previous action; Byrne & Russon, 1998). Furthermore, whilst the hierarchical organization of subroutines has long been theorized to be the most likely form of sequential action organization in chimpanzees, it is possible that a small number of alternative supraregular systems of sequence generation may generate nonadjacent dependencies (see Wilson et al., 2020). We did not include these models of sequence generation in our analysis for two reasons. Firstly, we do not currently have clear predictions of how these mechanisms of sequence generation would lead to mutual information decay over increasing sequence length. Secondly, these systems of sequence generation are not supported by theoretical literature to the same degree as hierarchical models of action organization for tool use. We therefore restricted our analysis to comparing models of sequence generation that are informed by substantial theoretical support, and conclude that the patterns of dependencies produced by chimpanzees generally follow those which are predicted by the hierarchical arrangement of subroutines. We strongly recommend alternative supraregular grammar systems are tested where and when suitable.

In contrast with other studies which employ analyses of MI decay (Sainburg et al., 2019; Sainburg, Mai & Gentner, 2020, 2022; Youngblood, 2024), we used sequence data from Markov models to identify the rate at which power-law relationships would be identified from linear sequences. This offered a false positive rate for misidentifying signatures of hierarchical organization. Power-law relationships were identified from linear sequences at a non-negligible rate, indicating that using MI decay analyses to identify signatures of hierarchy can produce false-positive results. However, this false positive rate was substantially lower than the rate at which power-law relationships were identified in observed action sequences. We therefore can conclude that the power-law dynamics identified in chimpanzee action sequences did not represent false positives. Instead, power-law dynamics in chimpanzee action sequences more likely reflect that actions are not combined by systems akin to Markovian sequence generation. Moreover, we strongly advise that future research employing MI decay analyses employ Markov models to estimate false positive rates of power-law detection. These false positive rates can then be compared with the rates of power-law detection from real-world sequential data to ensure that power-law model preferences are not statistical artefacts.

MI estimation has previously been used to detect signatures of hierarchical organization in the intricate grooming behaviours of Drosophila flies (Drosophila melanogaster) over an hour, and the swimming behaviours of Zebrafish (Danio rerio) during phototaxis paradigms (Sainburg, Mai & Gentner, 2020), and for both species, the composite model was the best choice for explaining information decay over the action sequences of individuals. Given our analysis found the greatest support for the composite model, we believe that our results likely reflect a possible homologous structuring system between the tool use behaviours of chimpanzees during nut cracking, and in the organization of goal directed actions by other species, when performing sequential actions for behaviours which do not involve tools. Additionally, the hierarchical complexity of early hominin tool-related action is believed to have increased throughout the course of hominin evolution, with the production of more ancient Oldowan tools requiring less complex hierarchical organization than the production of more recent Acheulian stone tools (Stout et al., 2021). In light of our results, it is possible that the hierarchical organization of tool-use behaviours may have been an adaptation which was present in the evolutionary ancestor of humans and apes—stemming from more basal hierarchical systems of action—which was then elaborated across the course of human evolution into a state of higher complexity. Understanding the dynamics of this evolutionary transition would be greatly aided through further comparative research into the sequential organization of actions used by chimpanzees and humans during a greater variety of tool-use tasks, as well as everyday behaviours which require careful sequencing of manual actions (Gontier, 2024). This includes establishing whether nonadjacent dependencies emerge in other manual behaviours of great apes, and if so, whether these nonadjacent dependencies are the product of hierarchical organization.

As previously mentioned, outside of tool use, the presence of hierarchical thinking in primates may also manifest within alternative behavioural contexts and social cognition, including in species other than chimpanzees (Bergman et al., 2003; Mielke & Carvalho, 2022; Lameira et al., 2024). In all of these instances, comparative research across domains of behaviour would be of interest, both within and between species. This research will be useful for determining whether hierarchical behaviours share common cognitive resources, or if these behaviours involve fundamentally different conceptions of hierarchies (see similar arguments made in human behaviours; Coopmans, Kaushik & Martin, 2023). For example in apes, comparisons of chimpanzee play sequences and tool use may be informative for understanding when nonadjacent decencies can be expected in sequential manual actions, and how this expectation can be linked to fast-changing goals (such as in play behaviours) or goals which are sustained over extended periods of time (such as in tool use). Additionally orangutans offer an excellent opportunity to investigate whether the hierarchical complexity of vocal sequences, and the sequences of manual actions performed during tool use, covary between individuals. Orangutans would be particularly suitable for such an analysis, given their habitual use of hierarchically organized long calls (Lameira et al., 2024), and that they spontaneously manufacture and use tools in the wild (Van Schaik, Fox & Sitompul, 1996).

Further research comparing the structure of sequential behaviours within ape species will clarify the extent to which these putatively hierarchical phenomena are supported by domain general cognition. This question is currently central to a number of hypotheses surrounding the evolution of cognition for hierarchical syntax and nonadjacent dependencies in human behaviours, such as language and tool use. For example, the statistical scaffolding hypothesis (Sainburg, Mai & Gentner, 2020) posits that long-range statistical dependencies in non-linguistic behaviours—and a generalised sensitivity to such behaviours—has led to a scaffold onto which language could evolve, where complex syntax and semantics can be understood as later additions that exploit such structures and sensitivities. Similarly, the Cognitive Coupling hypothesis suggests that the pre-existing cognitive architecture responsible for hierarchical tool behaviours was coupled with cognitive machinery responsible for communication, where such coupling occurred in multiple steps across hominin evolutionary history, driven by the need to socially learn and transmit increasingly more complex tool behaviours (Kolodny & Edelman, 2018).

We believe that the findings of our study are consistent with, but not confirmatory of, both the statistical scaffolding hypothesis, and the cognitive coupling hypothesis. We have presented data herein that supports the presence of nonadjacent dependencies in the sequential action of chimpanzee tool use, as well as decay dynamics of MI that are readily generalised by models associated with the hierarchical organization of action. Evidence for these structural features of sequential organization in chimpanzee tool use imply homologous origins with the sequential organization of actions in humans, suggesting that these structural features may also have been present in their last common ancestor. The emergence of highly hierarchical organization within communicative behaviours, and the resultant production of frequent nonadjacent dependencies in communication, may then have evolved as human-specific traits, following the evolutionary divergence of the human and Pan lineages. Further empirical investigation into the sequential organization of calls and gestures in chimpanzees and bonobos would offer further clarity on this matter.

Conclusion

In sum, we have identified that chimpanzees produce nonadjacent dependencies within their sequential tool-use behaviours, and exhibit interesting interindividual variability in the distances at which dependencies occur and in the means through which they are generated. These dependencies include those which extend past the maximum distance dependencies that were detected in sequences generated by Markov models, which for half of adult chimpanzees, cannot be explained by repeated actions. Our results of MI decay also support previous descriptions that chimpanzees organize their actions during tool-use through the hierarchical arrangement of subroutines of actions, and through analysing the curvature of composite decay models, we estimate that these subroutines are between 2–8 actions in length. However, we also note that this result was not universal to all individuals, with MI decay following alternative patterns for several individuals. We discuss this result in light of possible interindividual differences in systems of sequence organization by chimpanzees during tool use. Further research will determine whether primates’ other sequential behaviours exhibit nonadjacent dependencies similar to those we have found in tool use, and will clarify that these dependencies are generated through hierarchical means. This research will reveal the true extent to which nonadjacent dependencies, and the hierarchical systems of sequence organization that we provide evidence for, are the product of domain general cognition in nonhuman primates. In extension, this research will be informative for understanding whether the cognition supporting the generation of processing of nonadjacent dependencies in human behaviour, including through hierarchical structuring, were exapted across behavioural domains during hominin evolution.

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