Recursion in action: An fMRI study on the generation of new hierarchical levels in motor sequences

Abstract

Generation of hierarchical structures, such as the embedding of subordinate elements into larger structures, is a core feature of human cognition. Processing of hierarchies is thought to rely on lateral prefrontal cortex (PFC). However, the neural underpinnings supporting active generation of new hierarchical levels remain poorly understood. Here, we created a new motor paradigm to isolate this active generative process by means of fMRI. Participants planned and executed identical movement sequences by using different rules: a Recursive hierarchical embedding rule, generating new hierarchical levels; an Iterative rule linearly adding items to existing hierarchical levels, without generating new levels; and a Repetition condition tapping into short term memory, without a transformation rule. We found that planning involving generation of new hierarchical levels (Recursive condition vs. both Iterative and Repetition) activated a bilateral motor imagery network, including cortical and subcortical structures. No evidence was found for lateral PFC involvement in the generation of new hierarchical levels. Activity in basal ganglia persisted through execution of the motor sequences in the contrast Recursive versus Iteration, but also Repetition versus Iteration, suggesting a role of these structures in motor short term memory. These results showed that the motor network is involved in the generation of new hierarchical levels during motor sequence planning, while lateral PFC activity was neither robust nor specific. We hypothesize that lateral PFC might be important to parse hierarchical sequences in a multi‐domain fashion but not to generate new hierarchical levels.

Full text

RESEARCH ARTICLE
Recursion in action: An fMRI study on the generation
of new hierarchical levels in motor sequences
Mauricio J. D. Martins
1,2,3
| Roberta Bianco
2,4
| Daniela Sammler
2
| Arno Villringer
1,2,3
1
Berlin School of Mind and Brain, Humboldt-
Universität zu Berlin, Berlin, Germany
2
Department of Neurology, Max Planck
Institute for Human Cognitive and Brain
Sciences, Leipzig, Germany
3
Clinic for Cognitive Neurology, University
Hospital Leipzig, Germany
4
Ear Institute, University College London,
London, UK
Correspondence
Mauricio Dias Martins, Berlin School of Mind
and Brain, Humboldt Universität zu Berlin,
Luisenstrasse 56, Berlin 10117, Germany.
Email: diasmarm@hu-berlin.de
Abstract
Generation of hierarchical structures, such as the embedding of subordinate elements into
larger structures, is a core feature of human cognition. Processing of hierarchies is thought to
rely on lateral prefrontal cortex (PFC). However, the neural underpinnings supporting active
generation of new hierarchical levels remain poorly understood. Here, we created a new motor
paradigm to isolate this active generative process by means of fMRI. Participants planned and
executed identical movement sequences by using different rules: a Recursive hierarchical
embedding rule, generating new hierarchical levels; an Iterative rule linearly adding items to
existing hierarchical levels, without generating new levels; and a Repetition condition tapping
into short term memory, without a transformation rule. We found that planning involving gen-
eration of new hierarchical levels (Recursive condition vs. both Iterative and Repetition) acti-
vated a bilateral motor imagery network, including cortical and subcortical structures. No
evidence was found for lateral PFC involvement in the generation of new hierarchical levels.
Activity in basal ganglia persisted through execution of the motor sequences in the contrast
Recursive versus Iteration, but also Repetition versus Iteration, suggesting a role of these
structures in motor short term memory. These results showed that the motor network is
involved in the generation of new hierarchical levels during motor sequence planning, while
lateral PFC activity was neither robust nor specific. We hypothesize that lateral PFC might be
important to parse hierarchical sequences in a multi-domain fashion but not to generate new
hierarchical levels.
KEYWORDS
fMRI, hierarchy, motor, prefrontal cortex, recursion
1|INTRODUCTION
Much of what differentiates human behavior from that of other spe-
cies is related to an increased ability to represent and generate com-
plex hierarchies (Conway & Christiansen, 2001; Dehaene, Meyniel,
Wacongne, Wang, & Pallier, 2015; Everaert, Huybregts, Chomsky,
Berwick, & Bolhuis, 2015; Fitch, Friederici, & Hagoort, 2012). This is
evident across several domains, including language (Chomsky, 1957)
and music (Jackendoff & Lerdahl, 2006; Lerdahl & Jackendoff, 1977), but
also actions (Fitch & Martins, 2014; Lashley, 1951). While animal behav-
iorisforthemostpartseriallystructured,thatis,canbedescribedasa
Mauricio J. D. Martins and Roberta Bianco authors contributed equally to this work.
Significance Statement: Processing of hierarchical structures often activates lat-
eral PFC, across several domains. However, it remains unclear whether this
region supports the generation of new hierarchical levels, or other peripheral
mechanisms supporting structure encoding and externalization components,
such as motor execution. Using fMRI, here, we isolated (a) generative processes
by inspecting the planning of identical motor sequences based on different (hier-
archical and nonhierarchical) rules and (b) externalization processes by inspect-
ing their execution. The generation of motor hierarchies via application of
recursive hierarchical embedding rules was supported by a neural system used
for motor imagery and planning. No evidence was found for lateral PFC involve-
ment in the generation of new hierarchical levels. While lateral PFC might be
important to parse hierarchical sequences in a multi-domain fashion, it might not
be necessary to generate new hierarchical levels.
Received: 2 September 2018 Revised: 17 January 2019 Accepted: 30 January 2019
DOI: 10.1002/hbm.24549
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any
medium, provided the original work is properly cited and is not used for commercial purposes.
© 2019 The Authors. Human Brain Mapping published by Wiley Periodicals, Inc.
Hum Brain Mapp. 2019;40:2623–2638. wileyonlinelibrary.com/journal/hbm 2623

sequence of movements in which each element (e.g., gesture) is maxi-
mally connected to one preceding and one successive element, humans
can organize movements into superordinate clusters (Koechlin & Jubault,
2006), entailing several processing advantages. Humans, like other ani-
mals, use serial representations, for example, when we learn a motor
sequence (e.g., a dance) involving multiple steps: A àBàCàD. It fre-
quently occurs that, when one step is forgotten (say C), we need to
repeat the sequence from the beginning, because we are incapable of
transitioning from B to D. This is because each node in the sequence is
connected only to its adjacent successor but not beyond (Udden, Mar-
tins, Fitch, & Zuidema, in press). Hierarchy overcomes this limitation
because individual behavioral units can be connected to more than one
successor (or in hierarchical terminology, each parent node can be con-
nected to more than one child). This allows elements in a motor
sequence to be connected via a tree-like structure containing nonex-
pressed hidden nodes. For instance, take a procedure containing six steps
AàBàCàDàEàF where two steps always form a structural unit
[X[A,B], Y[C,D], Z[E,F]]. In a coffee-making procedure, X could be adding
water to the machine (A. taking the pot out and B. pour water in it), Y
adding coffee to the machine (C. get the coffee out and D. put coffee in
the filter), and Z operating the machine (E. turn it on and F. turn it off ).
When we already put coffee in the filter the day before, we can easily
transition from B to E because beyond the simple serial relations
between steps (from A to F) we also represent the higher-level structural
units containing these steps (X, Y, Z) and the connections between these
units. This capacity to represent hierarchies seems to be particularly well-
developed in humans, who can generate an unbounded number of hier-
archical levels (Hauser, Chomsky, & Fitch, 2002) in a number of different
domains.
Numerous studies in the domains of language, music, and vision
have investigated the discrimination of hierarchical structures by ask-
ing participants to evaluate whether sequences of items are well-
formed according to a previously learned system of rules (Bahlmann,
Schubotz, & Friederici, 2008; Bahlmann, Schubotz, Mueller, Koester, &
Friederici, 2009; Bianco et al., 2016; Friederici, Bahlmann, Friedrich, &
Makuuchi, 2011; Maess, Koelsch, Gunter, & Friederici, 2001; Sammler,
Koelsch, & Friederici, 2011). These studies suggest that lateral prefron-
tal cortex (PFC, particularly inferior frontal gyrus, IFG) might contribute
multi-domain resources to the processing of hierarchies (Fadiga, Craigh-
ero, & D'Ausilio, 2009; Friederici et al., 2011; Patel, 2003), in interaction
with areas along ventral visual/auditory streams that may store domain-
specific schematic information (Bianco et al., 2016; Martins et al., 2014;
Oechslin, Gschwind, & James, 2017; Pallier, Devauchelle, & Dehaene,
2011; Sammler et al., 2013). Recent anatomical research has shown that
IFG in humans is expanded (Schenker et al., 2010) and more strongly
connected with the posterior temporal regions in comparison to other
primates (Neubert, Mars, Thomas, Sallet, & Rushworth, 2014; Rilling
et al., 2008). If IFG supports the generation of hierarchies, these ana-
tomical differences could explain why this ability is enhanced in
humans. However, activity in this region across domains has also
been argued to reflect general processes such as cognitive control
and working memory, which might assist (but not be central to) hier-
archical generativity (Fedorenko, Duncan, & Kanwisher, 2012;
Matchin, Hammerly, & Lau, 2017; Novick, Trueswell, & Thompson-
Schill, 2005).
In the present study, we went beyond discrimination and investi-
gated the generation of hierarchically organized behaviors and their
neurocognitive bases in the motor domain, where the generation of
structures can be explicitly measured at the behavioral level. Previous
research mostly relied on comparing classes of stimuli (hierarchical
vs. nonhierarchical) that differ in their underlying generative rule sys-
tem but also in their surface serial structure. This hampers the ability
to separate processes involved in hierarchy generation from those
involved in stimulus peripheral encoding. To solve this issue, our novel
motor design experimentally separated generative act from execution:
We asked participants to execute identical motor sequences, hence
having identical surface structure, but to generate these sequences
using different rules.
Crucially, the identical surface structure of the motor sequences
could be represented as either being hierarchical or not. This enabled
us to focus on the generative process, that is, in how far participants
specifically represented a rule that generated new hierarchical levels
versus a flat rule that merely transformed preformed hierarchies with-
out generating new levels, and versus a mere repetition procedure
without a transformation rule. As first rule, we used a recursive hierar-
chical embedding rule in which participants were required to generate
connections between a parent node and a set of three children nodes
(such as X àX[A1, A2, A3]), thus generating a new hierarchical level.
In the second rule (Iteration), successor elements were added serially,
without generating new levels (A1 àA1–A2 àA1–A2–A3). Hence,
these trials could be solved without representing cross-level relations.
The third rule simply required to repeat the full sequence presented in
a previous step condition, hence tapping into short term memory. The
respective rule was revealed to the participants in a series of initial
generative steps that they had to generalize to complete the trial with
the correct motor sequence. We compared BOLD activity elicited by
the use of recursive hierarchical embedding versus nonhierarchical
iterative rules versus repetition separately during planning and execu-
tion of these motor sequences.
So far, behavioral and neural markers of action production have
been extensively studied in contexts of (a) fast production of simple
movement sequences without hierarchical relations (Elsinger, Harring-
ton, & Rao, 2006; Hardwick, Rottschy, Miall, & Eickhoff, 2013; Hétu
et al., 2013) and (b) representation of hierarchical relations within
action sequences but without active generation of new hierarchical
levels (Fazio et al., 2009; Koechlin & Jubault, 2006).
The first stream of research demonstrated that learning to exe-
cute simple motor sequences is supported by a network including
premotor and motor cortices (PMC and M1), superior parietal lobe
(SPL), supplementary motor area (SMA), pre-SMA, left thalamus and
right cerebellum (Hardwick et al., 2013). Furthermore, planning
(keeping a given motor sequence in short-term memory) recruited a
bilateral network comprising sensorimotor (M1S1) and premotor
cortices, cerebellum and basal ganglia (Boecker, Jankowski, Ditter, &
Scheef, 2008; Elsinger et al., 2006).
The second stream of research has focused on the neural bases
of hierarchical action processing (when acts are encoded as parts of
higher-order actions; Fazio et al., 2009; Koechlin & Jubault, 2006).
These studies typically compare higher versus lower levels of given
hierarchical action structures and have revealed posterior-to-anterior
2624 MARTINS ET AL.

activation gradients along lateral PFC with increasing hierarchy level.
For instance, sequences of simple movements (left and right button
presses) activate more anterior regions in lateral PFC when the move-
ments are organized in superordinate clusters compared to when they
are un-clustered (Koechlin & Jubault, 2006).
Overall, these studies provide neural evidence for (a) generative
capacity but restricted to linear motor sequences and (b) hierarchical
processing of actions, but without active generation of new hierarchi-
cal levels. Here, we combined these two approaches to go a step fur-
ther and probe the mechanisms underlying the internally driven
generation of hierarchically organized motor sequences.
Previous research on hierarchical representations in music,
language or goal-directed actions (Fadiga et al., 2009; Fitch & Martins,
2014) points to the lateral PFC and IFG as a candidate region that
may also be involved in the generation of new hierarchical levels in
motor sequences, even though these studies did not isolate the gener-
ative act from the processing of given hierarchies. On the other hand,
planning and imagery of complex motor sequences (independently of
execution) are known to be supported by a motor network comprising
M1S1, PMC, basal ganglia and cerebellum. In this study we will test
whether the latter areas also support the generation of motor hier-
archies, or whether this capacity requires dedicated systems in PFC
hypothesized to support generation of hierarchies across multiple
domains.
2|METHODS
2.1 |Participants
Twenty healthy participants (11 males and 9 females, age range
21–35 years, M= 26.5) took part in the study. All participants were
nonmusicians. None had more than 2 years of music training, and none
practiced regularly with a musical instrument. All had normal or
corrected-to-normal vision and audition, no history of neurological or
psychiatric disease. All participants were right-handed German native
speakers. Participants were recruited from a pool of subjects able to
perform all behavioral tasks successfully (see below). They gave written
informed consent before the experiment in accordance with the local
ethics committee that had approved this study (016-15-26012015) and
were paid 8 Euros/hour for their participation.
2.2 |Task and stimuli
Our approach involved the comparison of brain activity during active gen-
eration of motor sequences following two different rules –“Recursion”
and “Iteration”–which can be used to generate or transform hierar-
chies (Hulst, 2010; Martins, 2012; Martins, Martins, & Fitch, 2015).
Athirdrule–“Repetition”– controlled for simple action repetition and
working memory without any transformation rule. This framework
(discussed in detail in Fischmeister, Martins, Beisteiner, & Fitch,
2017; Martins, 2012; and Martins & Fitch, 2014) focuses on the con-
trast between “recursive hierarchical embedding”rules which can
generate new levels at different subsequent steps and “iterative”inser-
tions rules that do not. Importantly, our framework is orthogonal to
some previous formalizations (e.g., Formal Language Theory) which do
not specifically target the difference between hierarchical embedding
and linear operations (Martins, 2012, for a discussion).
Here, the “Iterative”rule adds items linearly within levels of a
given hierarchy without generating new levels. For example, with the
rule “add 1 B subordinate to A”, we can start from A[B] and, in the
subsequent steps, generate A[BB]], [A[BBB]], and so forth. Con-
versely, the “Recursive”rule allows the generation of new hierarchical
levels at each following step. For instance, with the rule “add 2 αsub-
ordinate to α”we start with “α”and generate the hierarchy “α[αα]”but
also “α[α[αα]α[αα]]”, and so forth. These recursive principles can be
described with a recursive notation αàα[αα], as in Lindenmayer
systems (Lindenmayer, 1968). This kind of rewrite rules have been
used to describe visual (Martins, Martins, & Fitch, 2016), melodic
(Martins, Gingras, Puig-Waldmueller, & Fitch, 2017), and rhythmic
fractals (Geambasu, Ravignani, & Levelt, 2016). To control for gen-
eral task-effects involving visual-motor planning, working memory
and movement sequence execution, our approach included a third
rule–Repetition–in which complete motor sequences had to be
repeated, without necessity to add any items or levels. This control
task taxed the processes involved in acquiring, buffering, and exe-
cuting a complete motor sequence.
In the motor task, participants were asked to produce sequences
of finger movements that followed these rules on a keyboard with
16 keys: they had to press a correct set of keys in the correct order,
and with the correct timing. The temporal structure (see Figure 1a)
was given by an auditory metronome sounding at 240 bpm (four
beats per second delivered through MR-compatible headphones). The
typical trial was composed of three steps (I, II, and III) that unfolded
according to one of the three rules: Recursion, Iteration, and Repeti-
tion (Figure 1b–d). In Steps I and II, participants executed the motor
sequences by following visual cues appearing on the keys of a virtual
keyboard displayed on the screen. The visual cues, used only in Steps
I and II, were colored circles with different colors denoting the
different fingers that participants had to use to press the keys (red:
thumb, green: index, and blue: middle finger). The relation between
Steps I and II revealed the underlying rule that participants had to
apply in order to actively generate a final motor sequence in Step
III without visual guidance and following the temporal structure
(Figure 1a). Crucially, in the recursive rule, only the first two hierar-
chical levels were present at Step II, and participants had to gener-
ate a third level consistent with the previous ones. This required
the simultaneous representations of the first two levels, and of the
relations between them. In particular, each set of three keypresses
[K −1, K, K + 1] at level n+ 1 derived from a particular key K
n
from which it was hierarchically dependent (see Figure 1d and cap-
tion for detailed illustration). The extraction of these cross-level
relations was essential to generate Step III using the proper set of
parameters.
The application of any of our three rules always generated a final
motor sequence of the kind [[K −2s,K−s, K], [K −s,K,K+s],
[K, K + s,K+2s]]. To increase stimulus variability, we introduced the
changeable parameters s(contour) and K (reference key, which in the
Recursive rule was also the initial key k
1
). The parameter scould be a
value within the set {−2, −1, 1, 2}. If swas positive (1 or 2), the
MARTINS ET AL.2625

sequences were ascending, meaning that they unfolded from left
to right on the keyboard (e.g., [K −1, K, K + 1]). If swas negative
(−1or−2), the sequences were descending, meaning that they
unfolded from right to left on the keyboard (e.g., [K + 1, K,
K−1]). When s=1or−1, the sequence (within each cluster) was
formed by adjacent keys (e.g., [K + 1, K, K −1]), and when s=2
and −2, the sequence was formed by nonadjacent keys, meaning
that there was a space of one key between a pair of elements
within the cluster (e.g., [K −2, K, K + 2]). The reference key K
(which is the spatial center to the pattern) could be one of the mid-
dle four keys of the keyboard {7, 8, 9, 10}. Overall, these variations
produced 16 different sequences, which were perfectly balanced
across conditions. Crucially, parameters sand K had to be recognized
during Steps I and II, in order to correctly generate the sequence in
Step III.
2.3 |Pretest
All participants took part in a behavioral session up to 1 week before
the fMRI experiment. The goal of this session was to instruct partici-
pants explicitly about the task rules, to assess their understanding of
those rules and to train them in the execution of the motor sequences.
FIGURE 1 Task principles. In this task, participants were asked to generate sequences of 9 finger movements (ordered from 1 to 9) by pressing
keys on the keyboard with the thumb, index, and middle finger (red, green, and blue). These sequences were formed in three Steps (I, II, and III)
which followed one of three rules: simple Repetition (B), Iteration (C), and Recursion (D). During Steps I and II, participants executed the motor
sequence guided by visual cues displayed on the screen. In Step III, they were asked to generate the final sequence of nine finger movements
without visual support. (a) Temporal structure: In Step III, all rules resulted in the same complete sequence of 9 movements, grouped in three
clusters, as here [[K −2, K −1, K], [K −1, K, K + 1], [K, K + 1, K + 2]], of 4 s duration each (total sequence duration = 12 s). K is the key in the
spatial center of the pattern. Hierarchical clustering within the sequence (three clusters of three key presses) was given by the fingering pattern
(red, green, and blue) and the temporal structure (1 s break after each cluster). To mark the temporal structure, the sequence was in fact aligned
with a metronome with four beats per second (1 strong and 3 weak) with key presses starting on the strong beat and being released at the onset
of the third weak beat (duration of each key press [d] of 0.75 s). (b) Repetition: consisted of the repetition of the complete sequence of nine
finger movements three times. (c) Iteration: Step I was composed of three key presses executed with the thumb, each with d= .75 s, on the first
(strong) beat of each cluster [[K −2, _, _], [K −1, _, _], [K, _, _]]. In Step II, a second key press with the index was added to each chunk: [[K −2,
K−1, _], [K −1, K, _], [K, K + 1, _]]. Thus, the iterative rule added elements to pre-existing hierarchical levels, without generating new levels.
Step III was simply the serial completion of the pattern with the middle finger [[K −2, K −1, K], [K −1, K, K + 1], [K, K + 1, K + 2]].
(d) Recursion: Step I was a single key press with the index finger (first finger, or 1) on key K with d = 12 s. Step II was a sequence of three key
presses [K −1, K, K + 1] executed with the thumb (1), index (2), and middle finger (3), respectively, each with d= 3 s and 1 s break after each key
press. The underlying Recursive rule was the substitution of each key press a(k,f)
n
(on key kand with finger f) in step n, with a sequence of three
key presses [a(k,1)
n+1
=a(k−1, f)
n
,a(k,2)
n+1
=a(k,f)
n
,a(k,3)
n+1
=a(k+1,f)
n
], in step n+ 1. In the time domain, each key press with
duration d
n
was substituted by three key-presses each with duration d
n
/4 and followed by a break d
n
/12. For simplification, we will refer to this
rule as k
n
![(k−1)
n+1
,(k)
n+1
,(k+1)
n+1
]. Step III was obtained by applying the same transformation rule to each key press in Step II thus
obtaining the complete sequence [[K −2, K −1, K], [K −1, K, K + 1], [K, K + 1, K + 2]]. Each set of key presses at level n+ 1 was clearly
subordinate to one key press at level n. Therefore, the representation of the underlying hierarchical structure was a necessary condition to solve
the task [Color figure can be viewed at wileyonlinelibrary.com]
2626 MARTINS ET AL.

Note that none of the participants had experience in playing music, par-
ticularly not in playing on a piano. The session lasted approximately
2 hr. Participants started by performing a beat perception task (part of
the battery used in Müllensiefen, Gingras, Musil, & Stewart, 2014),
to evaluate whether they were able to understand the synchrony
between two temporal events (a metronome and a music piece).
Then, they were shown a slideshow explaining the task rules, and
video examples with the motor sequences they had to perform (see
Supporting Information).
After the instructions, participants performed a supervised ses-
sion comprising 10 trials following the Recursive rule. They executed
the sequences as depicted on the screen, that is, did not have to men-
tally generate the sequences by themselves, as Steps I, II, and III were
all presented visually on screen (unlike in the task used in the MR
scanner). A researcher was in the room supervising this session, incen-
tivizing the participants to follow the temporal structure and to use
the visual landmarks to find the correct keys. The goal of this phase
was to train the participants with correct exemplars. We repeated this
procedure for the Iterative rule.
If participants were able to execute the Recursive and Iterative
sequences adequately, they proceeded to a final session, similar to
the one used in the fMRI experiment. This session was composed of
20 trials including 8 trials following the Recursive rule, 8 trials follow-
ing the Iterative rule, and 4 trials following the simple Repetition. In
this last session, Step III was not cued visually, and participants had to
generate the sequence by themselves, without visual support, but fol-
lowing the metronome, as later in the MR scanner.
Participants with accuracy >80% in the last session, for all rules,
were invited to participate in the fMRI experiment. Accuracy was
measured as the number of correct keys pressed at the correct time–
within the interval [−0.25 s, 1 s] locked to the onset of the appropri-
ate beat. Each trial contained nine expected key presses in Step III.
Twenty-one out of thirty-nine participants performing the pretest ful-
filled this criterion. Note that, although only about 50% of our partici-
pants passed our selection threshold for the MRI experiment, those
50% were able to acquire a keypress accuracy above >80% after only
1 hr of training (roughly 64 trials). Despite the task being relatively dif-
ficult to learn in one training session, this is in line with previous
research showing that more extensive training is necessary to reach
adequate performance in simple, nonhierarchical motor tasks (Taubert
et al., 2010; Taubert, Lohmann, Margulies, Villringer, & Ragert, 2011),
and in artificial grammar learning in language (Opitz & Friederici,
2003). Recent behavioral data from our laboratory (unpublished) also
suggests that more training, in terms of number of training sessions,
increases keypress accuracy in our motor task.
In those participants who succeeded in the pretest, the “gener-
ation of new hierarchical levels”(i.e., in the Recursive rule condi-
tion) hence pertains to the application of well-learned hierarchical
rules, independently on how these were acquired (Lungu et al.,
2014). This may entail either the execution of combinatorial compu-
tations specifically involved in the generation of new hierarchical
levels, or the retrieval of previously formed hierarchical representa-
tions (Figure 2), which remain stored as “schemas”within the motor
network (Wiestler & Diedrichsen, 2013). Note that in case our task
FIGURE 2 With our design, we explicitly separated the processes underlying the generation of hierarchical levels (left) from those used to
externalize and execute motor programs (right). While the generation of new hierarchical levels in the Recursive rule involves hierarchical
branching (left) and then serialization (right), Iterative completion of motor sequences is strictly serial. It should be mentioned that activations
referring to the generation of new hierarchical levels can potentially involve either de novo combinatorial operations (upper cascade), or the
retrieval of previously formed hierarchical representations (lower transparent box). The products of hierarchy-generating rules (e.g., [[K −2s,
K−s,K][K−s,K,K +s] [K, K + s,K+ 2s]]) might become schematized and stored in domain-specific networks from which they are retrieved
during sequence generation. The schema would retain the clustered hierarchical structure and a set of free parameters binding different levels
(in this study the reference key K, and contour variable s). Importantly, even if the latter were the underlying mechanism, participants would have
to extract and apply the parameters from the second step of each trial, and obey the same hierarchically organized temporal cluster boundaries.
Thus, irrespective of whether processing is based on combinatorial operations or retrieval of schemas, only recursion would entail flexible
generation of hierarchical motor sequences [Color figure can be viewed at wileyonlinelibrary.com]
MARTINS ET AL.2627

hinges on schema retrieval rather than on-the-fly generativity,
these schemas are still not rigidly automatized: (a) they also entail a
generative act since their internal spatio-temporal hierarchical
organization needs to be constructed from the set of free parame-
ters (sand K), and (b) the transformations within the Recursive rule
are bounded by a hierarchical temporal clustering which is strictly
scale invariant–that is, the key press duration at a subordinate level
is exactly 1/4of that of a key press at the dominant level (Figure 1A).
2.4 |fMRI procedure
On the day of fMRI data acquisition, participants were again briefed
on the task rules, then positioned in the scanner and asked to perform
a short test session of six trials. If they were able to perform ade-
quately, we proceeded with the anatomical and functional data acqui-
sition. One participant was excluded due to inability to replicate the
experiment within the MR experimental apparatus. At the end of the
procedure, participants were given a questionnaire on their cognitive
strategies used to generate Step III across the different tasks. The
whole procedure (briefing, scanning, and questionnaire) had a duration
of approximately 2:30 hr.
The fMRI scan included four sessions, each with an approximate
duration of 15 min and composed of 20 trials–8 Recursion, 8 Iteration,
and 4 Repetition trials. For the sake of maximizing the number of trials
in the main tasks of interest, we kept the number of Repetition trials to
half. Trials following different rules were inter-mixed within each session
and pseudo-randomized. The trial sequence was determined using Opt-
seq2 (https://surfer.nmr.mgh.harvard.edu/optseq/) to maximize the effi-
ciency of fMRI signal acquisition.
Trial structure is depicted in Figure 3. We were interested in two
periods within each trial, namely the transition between Steps II and
III–the planning phase–and in Step III–the execution phase. The plan-
ning phase was important to capture the computations necessary to
transform Step II into Step III, and the neural systems instantiating
these transformations.
The experimental apparatus is depicted in Figure 4. Participants
performed the task while lying in the MR scanner, using a silent 16-key
MR-compatible piano (Figure 4a). The keyboard contained visual and
tactile markers on keys 3, 5, 7, 10, 12, and 14 (from left-to-right) for
spatial reference (see Figure 1). We used a dual mirror system, so that
participants were able to see both the virtual keyboard projected on
the screen, and the physical keyboard on which they executed the
motor sequences (Figure 4b). The position of the mirrors was adjusted
individually for each participant. Both keyboards had visual markers on
specific keys for visuo-spatial reference (Figure 4c). On the physical
keyboard, these references could also be detected by touch. All partici-
pants used their right hand to perform the motor sequences.
2.5 |Data acquisition
The experiment was carried out in a 3.0-Tesla Siemens SKYRA whole
body magnetic resonance scanner (Siemens AG, Erlangen, Germany)
using a 32-radiofrequency-channel head coil. During the four ses-
sions, functional magnetic resonance images were acquired using a
T2*-weighted 2D echo planar imaging (EPI) sequence with TE = 30 ms
and TR = 2000 ms. For each session, we acquired 450 volumes with a
square FOV of 192 mm, with 31 interleaved slices of 3 mm thick-
nessand30%gap(3×3×3mm
3
voxel size) aligned to the AC-PC
plane, and a flip angle of 90. T1-weighted images for anatomical
co-registration were either selected from the database of the insti-
tute or acquired using a 3D MP2RAGE sequence (TI
1
=700ms,
TI
2
=2,500ms,TE=2.03ms,TR=5,000ms)withamatrixsizeof
FIGURE 3 Trial structure (Recursion example). All trials had the same structure: First, a letter indicated the trial type. Then, Steps I and II of the
sequence were shown on screen, which participants had to execute simultaneously on a keyboard (colored circles indicated which finger to use).
This was followed by a 6 s planning phase composed of a 4 s blank screen and a 2 s crosshair during which participants planned execution of Step
III. Finally, in the execution phase, participants performed the correct continuation of the sequence without visual cues. Throughout all steps, a
metronome sound at 240 bpm guided participants' pace and the sequence's temporal structure [Color figure can be viewed at
wileyonlinelibrary.com]
2628 MARTINS ET AL.

240 ×256 ×176, with 1 mm isotropic voxel size, flip angle
1
of 4,
flip angle
2
of 8, and GRAPPA acceleration factor of 3.
2.6 |Data analysis
fMRI data were analyzed with statistical parametric mapping (SPM8;
Welcome Trust Centre for Neuroimaging; http://www.fil.ion.ucl.ac.
uk/spm/software/spm8/). Anatomical data from high-resolution
T1-weighted images were obtained by masking the uniform tissue-
contrast image with the second inversion image from the MP2RAGE
sequence. Functional data were preprocessed by following standard
spatial preprocessing procedures. They consisted of: slice time correc-
tion (by means of cubic spline interpolation method), spatial realign-
ment, co-registration of functional, and anatomical data. Then, we
performed spatial normalization into the MNI (Montreal Neurological
Institute) stereotactic space that included resampling to 2 ×2×2mm
voxel size. Finally, data were spatially low-pass filtered using a 3D
Gaussian kernel with full-width at half-maximum (FWHM) of 8 mm
and temporally high-pass filtered with a cut-off of 1/128 Hz to elimi-
nate low-frequency drifts.
Statistical parametric maps were generated for the whole brain
data in the context of the general linear model (GLM). For each rule,
we modeled three “trial phase”regressors at first level: (a) Steps I and
II together, (b) planning, and (c) execution phase of Step III. This way
we could control for potential activity spill-over between phases. The
evoked hemodynamic response to the onset of each phase was mod-
eled for the Recursive rule, Iteration rule and simple Repetition condi-
tions as boxcars convolved with a hemodynamic response function
(HRF). We added estimated motion realignment parameters as cov-
ariates of no interest to this design to regress out residual motion
artifacts and increase statistical sensitivity. Furthermore, we added
two regressors to account for potential differences in difficulty
between Recursion, Iteration, and Repetition: As a measure of plan-
ning difficulty, we modeled the average asynchrony between the first
metronome beat (when participants should press the key) and the
actual first key presses of Step III. As a measure of execution
difficulty, we modeled the average asynchronies between the metro-
nome beats and the actual key presses across all 9 key presses of
Step III (mean response times for each key press are depicted in Sup-
porting Information Figure S1). If participants pressed an incorrect or
no key, we assigned the value 1 s, which is the highest possible
value, that is, reflects maximal difficulty.
For random effects group analyses, two within-subject flexible
factorial ANOVAs (with the factor RULE) were performed (for Step III
planning and execution, separately) on whole brain data with binary
gray matter masks thresholded at intensity value of 0.25. A main
effect of RULE (Recursion, Iteration, Repetition) was detected in both
FIGURE 4 fMRI apparatus. (a) The keyboard was placed on a custom-made wood stand. This stand provided a degree of inclination that
increased the visibility of the keyboard. The metronome sound was delivered through MR compatible headphones. (b) We used a double mirror
system mounted on the head coil, which allowed participants to see both the virtual keyboard on screen (top mirror, left arrow), and the physical
keyboard under their right hand (bottom mirror, right arrow). We adjusted the position of the mirrors for each participant to maximize visibility
and comfort. (c) The keyboard was an adapted MR compatible piano in which the black keys were covered. We added visual and tactile cues on
specific keys that the participants could use for reference. Importantly, pressing the keys on the keyboard did not generate any sound, and
therefore key-tone associations could not be used in our task, which was purely visuo-motor [Color figure can be viewed at
wileyonlinelibrary.com]
MARTINS ET AL.2629

planning and execution phases of Step III. To resolve these effects, sta-
tistical parametric maps with t-contrasts between each RULE were cal-
culated. We controlled family-wise error rate (FWER) of clusters below
0.05 with a cluster-forming height-threshold of 0.001.
To test for the involvement of lateral PFC, particularly IFG, we
performed small volume corrected (SVC) analyses within regions of
interest (ROIs) comprising the left and right Brodmann areas (BAs)
44 and 45 based on the Harvard-Oxford probability maps (thresholded
at 50%). Anatomical labels are based on Harvard-Oxford cortical and
sub-cortical structural atlas implemented in FSL (http://neuro.debian.
net/pkgs/fsl-harvard-oxford-atlases.html). In addition, we used REX
toolbox (http://web.mit.edu/swg/software.htm) to extract the mean of
the single-subject beta values across each ROI mask and calculated the
t-contrasts between each RULE (Recursion, Iteration, Repetition), sepa-
rately in the planning phase and the execution phase.
3|RESULTS
In the present fMRI study, participants generated sequences of finger
movements in three Steps (I, II, III) following one of three rules
(Figure 1): (a) a linear Iterative rule, (b) a Recursive hierarchical embed-
ding rule, or (c) simple Repetition. In the first two Steps (I, II) participants
executed sequences guided by visual cues on the screen. Then, they
were asked to generate Step III according to the respective rule without
visual support (Figure 3). The fMRI analysis focused on the transi-
tion between Steps II and III, the planning phase reflecting the gen-
erative act, and on Step III, the execution phase reflecting the
externalization. Importantly, motor sequences were identical in
their surface structure across tasks. Hence, any difference in brain
activation during execution is likely to derive from the different
outcomes of the generative phase.
Overall, we found that during action planning, the generation
of new hierarchical levels in Recursion, compared to both Iteration
and simple Repetition, yielded significantly stronger activity in a
bilateral network of brain areas involved in motor planning and
imagery (Hardwick et al., 2013; Hétu et al., 2013), including M1S1
and PMC, cerebellum, lateral occipital cortex (LOC), and left puta-
men (Figure 5). Crucially, regions of interest (ROI) analyses within
left and right IFG lent no evidence for involvement of lateral PFC
in the generation of new hierarchical levels (Figure 6). In the execu-
tion phase, no activation was specific for Recursion (i.e., stronger
than in Iteration and Repetition). Instead, execution of sequences
formed by both Recursion and simple Repetition rules showed sim-
ilarities when compared with Iteration in form of bilateral basal
ganglia and thalamus activity (Figure 7). This suggests that other
than planning, which required specific additional resources for
Recursion, sequence representation during execution was not
Recursion specific.
3.1 |Generation of new hierarchical levels is
supported by general networks of motor planning
By measuring brain activity in the planning phase,wesoughtto
identify neural networks underlying the cognitive processes that
are relevant for the transition between Steps II and III, that is, the
generative act as such. In simple Repetition, this process consisted
in holding the full sequence of Step II in memory until its repeated
execution in Step III (Figure 1B). In the Iterative rule, this process
FIGURE 5 Brain activations during the planning phase (between Steps II and III). Application of the Recursive rule yielded stronger activations
compared to both simple Repetition and Iteration in a bilateral network known to be involved in motor learning, planning, and imagery, including
sensorimotor and premotor cortices, cerebellum, and lateral occipital cortex. The reverse contrasts (Iteration > Recursion and
Repetition > Recursion) did not yield significant activations [Color figure can be viewed at wileyonlinelibrary.com]
2630 MARTINS ET AL.

required the serial addition of one key press to each cluster within
a fixed hierarchical level (Figure 1C), without generation of new
levels. The Recursive embedding rule entailed the generation of
new hierarchical levels (Figure 1D) by recursively substituting
each key press k
n
instepnwithanewsequenceofthreekey
presses [(k-1)
n+1
,(k)
n+1
,(k+1)
n+1
]instepn+1(seeFigure1
for a detailed explanation). The parameters of the transformation
rule to be applied in each trial's planning phase,sand initial key k
1
,
could be inferred from the transition between Steps I and II (see
Section 2 for details).
3.1.1 |Behavioral data
According to the postexperiment questionnaires (see Supporting Infor-
mation Table S1), participants considered it equally difficult to extract
the rule parameters in Recursion (mean ± SD: 6.15 ± 0.88) and Iteration
(6.40 ± 0.75; Wilcoxon signed-ranks:z=−1.30, p= 0.19), while it was
easier to do so in Repetition (6.80 ± 0.41), than in the other two condi-
tions (Wilcoxon signed-ranks:z=−2.51, p=0.01, and z=−2.13,
p= 0.03, respectively).
In addition, in Recursion trials, participants relied more on Step II
for the generation of Step III (6.00 ± 1.52) than in both Iteration
(5.20 ± 1.74) and Repetition (4.90 ± 1.75; Wilcoxon signed-ranks:
z=−2.35, p= 0.02, and z=−2.32, p= 0.02, respectively). Finally, in
comparison with Repetition, during Recursion participants (a) imagined
more where the hand should go in key space, (b) prepared the
sequence more consciously, and (c) thought more explicitly about
the rule (Wilcoxon signed-ranks:allps < 0.05). For detailed means and
pairwise comparisons see Supporting Information Table S1.
To account for potential differences in task difficulty, we included
the asynchrony between first metronome beat and first key press of
Step III as a planning difficulty measure in our first level model (see
Section 2). Averages of these asynchronies did not differ between
tasks (Iteration: 0.30 ± 0.10s; Recursion: 0.31 ± 0.09 s; Repetition:
0.30 ± 0.09 s; F(2,38) = 0.14, p= 0.868, ηp2= 0.01).
3.1.2 |fMRI
Whole-brain results of the planning phase are depicted in Figure 5
and Table 1. We found increased activity in Recursion in comparison
with both Repetition and Iteration. The generation of new hierarchi-
cal levels in motor sequences using the Recursive rule was supported
by a bilateral network known to be involved in motor learning
(Hardwick et al., 2013), motor planning (Elsinger et al., 2006) and
imagery of motor sequences (Hétu et al., 2013). More precisely, this
network included a large bilateral cluster with peaks in the cerebel-
lum and extending through LOC, superior parietal lobe, M1S1 and
left PMC (see Supporting Information Table S2 for more extensive
enumeration and labeling of the peaks within this cluster). Further
clusters included left putamen and pallidum, and right PMC (all clus-
ters p< 0.05, FWE corrected). These activations were present in
both contrasts Recursion > Iteration and Recursion > Repetition,
and despite correcting for planning difficulty. Additionally, the contrast
Recursion > Iteration but not Recursion > Repetition yielded stronger
activation in right Pallidum and Putamen.
FIGURE 6 Global activity within the 4 IFG ROIs. Percent signal change (globally scaled) was higher in right BA 44 during planning in both
Recursion and Repetition versus Iteration. However, this activity did not survive FDR threshold at p< 0.05. No significant differences were found
during execution [Color figure can be viewed at wileyonlinelibrary.com]
MARTINS ET AL.2631

Conversely, no activations were found for the Iterative rule or
Repetition, that is, the contrasts Iteration > Repetition, Iteration >
Recursion, and Repetition > Recursion did not yield significantly
active clusters. Only Repetition > Iteration revealed activity in
bilateral inferior lateral temporo-occipital cortex and frontal pole
(Table 1), which may support mental practice and working mem-
ory for motor sequence (Jackson, Lafleur, Malouin, Richards, &
Doyon, 2003).
3.1.3 |ROI analyses
To test whether there were specific activations for the Recursive rule
within lateral PFC, particularly IFG, we performed four Small Volume
Corrected (SVC) analyses within left BA 44, left BA 45, right BA 44, and
right BA 45. Planned contrasts between rules yielded no significant
differences (with uncorrected p< 0.01). The comparison of global activ-
ity within each ROI (see Figure 6) revealed stronger right BA 44 activity
in both “Recursion > Iteration”(T=2.15, p-uncorrected =0.04) and
“Repetition > Iteration”(T=2.41, p-uncorrected = 0.02). However,
these effects did not survive FDR threshold at p<0.05.
We assumed participants engaged in specific computations to
transform Step II into the final Step III in the Recursive condition,
using an explicit motor-spatial rule. We found these specific com-
putations were supported by general networks associated with
motor planning and imagery but did not recruit IFG. The trend of
greater activity in right IFG in both Recursion and Repetition ver-
sus Iteration suggests that these conditions may pose greater strain
on working memory and motor control system (Aron, Robbins, &
Poldrack, 2014).
3.2 |Execution of recursion- and repetition-based
sequences (vs. iteration-based) recruits thalamus and
basal ganglia
3.2.1 |Behavioral data
In the execution phase, sequences were motorically identical
across all conditions. Importantly, key press accuracy did not differ
between conditions (Recursion: mean ± SD = 87% ± 20%; Itera-
tion: 89% ± 18%; Repetition: 87% ± 23%; generalized χ2score =
1.8, p= 0.400), suggesting that the execution was equally difficult.
In addition, participants reported similar confidence in the correct-
ness of their performance (regarding rhythm, keys pressed, and
fingers used) in Recursion and Iteration (Wilcoxon signed ranks:ps >
0.400; see Supporting Information Table S1 for full details on
means and pairwise comparisons).
Finally, we measured the asynchrony between metronome beats
and key presses in Step III. Average asynchronies across the 9 key
presses (Iteration: 0.21 ± 0.13 s; Recursion: 0.24 ± 0.14 s; Repetition:
0.30 ± 0.12 s) did not differ between the three tasks (F(2,38) = 1.27,
p= 0.291, ηp2= 0.06). To account for residual difficulty differences
between tasks, we included the mean asynchronies for each trial as
parameter into our fMRI statistical model.
3.2.2 |fMRI
In the execution phase, we found clear similarities between Recur-
sion and Repetition that both dissociated from Iteration (Figure 7
and Table 2). We found significant activations in subcortical clusters
including pallidum, putamen, and thalamus in both Recursion > Iter-
ation and Repetition > Iteration contrasts. These clusters extended
FIGURE 7 Brain activations during the execution phase (Step III). Participants executed sequences of nine key presses that were identical at the
motor output but were generated according to different rules (Recursion, Iteration, and Repetition). Compared to Iteration, both Recursion and
Repetition (C and D) activated the pallidum, putamen, and thalamus bilaterally. These clusters extended posteriorly into hippocampus and
parahippocampus (left panel), and anteriorly into right orbitofrontal cortex (right panel; BA10 and BA47). In the contrast Recursion > Iteration we
found an additional cluster in left LOC [Color figure can be viewed at wileyonlinelibrary.com]
2632 MARTINS ET AL.

posteriorly into hippocampus and parahippocampus, and anteriorly
into right orbitofrontal cortex (including BA10 and BA47). In
Recursion > Iteration an additional cluster was found in left LOC.
Finally, Iteration > Recursion did not yield significant activations
that survived cluster level correction. However, one cluster in left
primary somatosensory cortex (BA1) was significant with FWE-
correction at voxel level (Z=4.53, voxel p-FWE =0.04, x=−50,
y=−16, z=48).
3.2.3 |ROI analysis
Similar to the planning phase, we performed small volume corrected
(SVC) analyses within IFG ROIs comprising left BA 44, left BA 45, right
TABLE 1 Effects of rule in the planning phase
Region Hem. BA kxyzZ-value
Recursion > Iteration
Cerebellum VI R - 23,865 26 −50 −30 5.97
-32−42 −30 5.60
-8−70 −34 5.44
Putamen L - 1,199 −26 −6 8 4.95
-−12 −18 2 4.79
-−24 −14 4 4.56
Pallidum R - 879 18 −2 0 4.71
-26−8 10 4.67
- 24 0 10 4.59
Precentral gyrus R 6 1,108 42 −6 60 4.63
624−2 54 4.63
632−4 66 4.13
Brain stem - 461 −6−28 −22 4.01
-−4−30 −30 3.69
-10−26 −24 3.65
Recursion > Repetition
Cerebellum VI R - 1,764 26 −52 −30 5.27
L- −24 −50 −26 4.32
R32−42 −30 4.10
Precentral gyrus R 6 6,173 44 −6 56 5.00
L6 −24 −4 54 4.94
L3 −40 −20 54 4.85
Putamen L - 471 −20 12 −2 4.16
-−24 −4 6 3.93
Postcentral gyrus R 3 1,057 32 −32 48 4.15
254−18 42 3.88
240−30 48 3.79
Lateral occipital cortex R V5 819 44 −62 8 4.13
V5 52 −64 6 4.02
-34−68 22 3.83
Repetition > Iteration
Cerebellum I R 2,466 48 −66 −22 5.31
48 −56 −14 5.27
26 −42 −42 4.75
Frontal pole R 10 1,291 18 38 −16 5.22
10 26 42 −8 4.63
10 34 48 −4 4.36
Lateral occipital L V5 4,760 −42 −66 −10 4.81
R- 8−70 −36 4.53
V3 −28 −90 2 4.52
Occipital pole R V4 704 30 −90 2 4.42
17 14 −94 12 3.87
V4 38 −80 0 3.78
Whole-brain activation cluster sizes (k), MNI coordinates (x,y,z), and Z-scores for the rule contrast in the planning phase (p
voxel
< 0.001; p
cluster
< 0.05,
FWE corrected). BA: Brodmann area; Hem.: hemisphere.
MARTINS ET AL.2633

BA 44, and right BA 45. We found no significant differences between
rules (with uncorrected p< 0.01). Global activity within each area was
also not significantly different across rules (all uncorrected p> 0.10;
Figure 6).
4|DISCUSSION
To our knowledge, the present study is the first to investigate the
neural systems involved in the generation and overt production of
motor hierarchies, which clearly separates these two phases (genera-
tive act and externalization components). To do so, we developed a
novel paradigm that contrasted (a) sequences of finger movements
formed according to a hierarchy-generating Recursive rule with
(b) identical sequences formed according to rules that did not require
generation of new hierarchical levels (Iteration and Repetition). Each
trial was composed of two initial Steps (I and II) that established
the rules and a set of parameters which participants had to apply to
correctly generate Step III. Thus, during planning, Repetition implied
buffering of the given motor sequence [[K −2s,K−s,K][K−s,K,
K+s] [K, K + s,K+2s]] and Iteration required the completion of a
pattern [[K −2s,K −s, __] [K −s,K,__][K,K+s, __]] using within-
level transformations. Only the Recursive rule entailed the genera-
tion of new hierarchical levels through the recursive substitution of
each finger movement k
n
with a sequence of three finger move-
ments [(k−s)
n+1
,(k)
n+1
,(k+s)
n+1
]. Accordingly, participants
reported mostly for the Recursive condition that they relied on
Step II to consciously prepare the final sequence and imagined the
sequence prior to execution. This entails that in the Iteration condition
participants may have engaged less in active planning of Step III.
Nevertheless, Recursive and Iterative conditions did not differ in cor-
rectness of their execution or in subjective reports of general
difficulty.
Our first important finding was that the generation (i.e., planning)
of new hierarchical levels using the Recursive (compared to Iterative)
rule was supported by a network of areas involved in motor learning,
planning and imagery (Elsinger et al., 2006; Hardwick et al., 2013;
Hétu et al., 2013). This bilateral network included M1S1 and PMC,
cerebellum, LOC, pallidum, putamen, and thalamus. Interestingly, in
this study, which focused on the motor domain, we did not find
evidence that these generative processes recruited IFG, an area
thought to play an important role in the processing of hierarchies
across domains (Fadiga et al., 2009; Fitch & Martins, 2014; Jeon,
2014). Although there was higher global activity within right BA
44 in Recursion compared with Iteration, this activity neither
survived multi-comparison p-value correction, nor was it specific
for Recursion, being present also in the Repetition > Iteration con-
trast. Therefore, right BA44 activity, if any, is not likely caused by
computations specific to the generation of hierarchical levels using
recursive rules.
Our second relevant finding was that execution of identical motor
sequences generated by the Recursive rule or by simple Repetition of
a given sequence, both involved bilateral subcortical areas including
putamen, pallidum, and thalamus, extending posteriorly to hippocam-
pus and parahippocampus, and in the right hemisphere anteriorly to
orbitofrontal cortex, including BA47 and BA10. This suggests that
identical sequences might be represented differently depending on
their generative process. Notably, the similarity between Recursion
and Repetition (vs. Iteration) suggests that these representations are
TABLE 2 Effects of rule in the execution phase
Region Hem. BA kxyzZ-value
Recursion > Iteration
Pallidum R - 2008 16 −6−6 5.53
- 26 6 14 5.02
- 22 14 10 4.69
Putamen L - 432 −22 4 14 4.95
-−22 12 12 4.73
-−22 −10 −4 3.86
Lateral occipital cortex L 19 1,438 −30 −90 6 4.92
19 −18 −94 −12 4.58
18 −20 −94 8 4.29
Thalamus L - 1,117 −12 −6 2 4.17
-−26 −32 −32 4.03
-−4−30 −28 4.02
Repetition > Iteration -
Pallidum R - 2,229 16 −6−6 5.01
- 26 0 14 4.69
-28−28 −4 4.68
Putamen L - 1848 −24 4 12 4.61
-−10 −22 −18 4.48
-−22 −10 −4 4.26
Whole-brain activation cluster sizes (k), MNI coordinates (x,y,z), and Z-scores for the Rule contrast in the execution phase (p
voxel
< 0.001; p
cluster
< 0.05,
FWE corrected). BA: Brodmann area; Hem.: hemisphere.
2634 MARTINS ET AL.

not specific to the processing of hierarchical relations, but to some
other processes, which we discuss below.
According to the discrete sequence production framework
(Verwey, 2001; Verwey, Shea, & Wright, 2014), performance
involves (a) sequence generation and motor loading during plan-
ning, followed by (b) fast execution of the motor buffer content by
effector-specific motor processors. The generation of new hierar-
chical levels in the Recursive rule puts particular strain on stage (a),
the planning of the final sequence, by strongly relying on cortical
resources. Unlike in Repetition and Iteration where the motor pro-
gram is (partly) available already in Step II, performers have to use
their rule knowledge in the Recursive condition to construct or
retrieve motor schemas (see legend of Figure 2 about these alterna-
tives) for appropriate sequence continuation. Interestingly, they
seem to do so by means of general mechanisms of visuo-motor
imagery and planning, as shown by stronger activity in bilateral
visuo-motor networks (Hardwick et al., 2013).
Once formed, these motor programs are buffered in striatal areas
and sent to the motor effectors for execution (Doyon et al., 2009;
Miyachi, Hikosaka, Miyashita, Kárádi, & Rand, 1997). Our activity pat-
terns in the execution phase speak for a similar buffering during
Recursion and simple Repetition, but not during Iteration. Both
Recursion and Repetition activated a fronto-striatal-thalamic circuit
with the additional contribution of hippocampus/parahippocampus,
and right orbitofrontal cortex (BA47 and BA10). The fronto-striatal-
thalamic circuit supports motor control and working memory during
sequence production (Humphries & Gurney, 2002; Schroll, Vitay, &
Hamker, 2012; Vitay, 2010), and fronto-hippocampal areas have
been associated with a global versus incremental representation of
motor sequences (Lungu et al., 2014). According to these previous
findings, we surmise that during production in both Recursion and
Repetition conditions, a global representation of the full sequence is
retained in working memory and used to optimize motor control,
hence a correct motor sequence. It is very likely indeed that the
sequence of nine finger movements was fully present during execu-
tion, being generated during planning in the Recursive condition (see
paragraphabove)andcarriedoverfromStepIIinRepetition(see
activity in right orbitofrontal cortex during planning). Conversely,
during planning, we did not observe increased activity in Iteration in
comparison with Recursion or Repetition. This may indicate less
strain on the motor buffer, either because a sequence of only six
finger movements had to be carried over from Step II to be linearly
completedinStepIII,orbecauseparticipantsusedagenerallydif-
ferent execution strategy that was less hinging on the motor buffer
(although it fell short off significance at the cluster level, there was
higher activity in left somatosensory cortex in Iteration during Step
III than in Recursion). Overall, the results suggest that execution of
a sequence formed by an incremental Iterative rule poses less
demands on the motor control system compared to buffering and
releasing the complete motor sequence in the Recursion and Repe-
tition conditions.
In sum, we found that while generating new hierarchical levels
in the Recursive rule demands more planning resources, serial com-
pletion of motor sequences in the Iterative rule might be achieved
using sensorimotor areas during execution. Interestingly, these
additional planning resources in Recursion were instantiated by the
motor imagery network, and they did not require IFG.
4.1 |Prior hypotheses: The role of lateral PFC/IFG
Based on current views that IFG is involved in the processing of hier-
archies across many domains (e.g., language, music and action, as
reviewed by Fadiga et al., 2009; Fitch & Martins, 2014; Jeon, 2014)
and in line with models of a posterior-to-anterior gradient of lateral
PFC for hierarchical organization of actions (Badre, 2008; Koechlin &
Summerfield, 2007), we hypothesized lateral PFC, and particularly
IFG, to support motor generation of new hierarchical levels in our
Recursive rule condition. However, we did not find evidence for
involvement of this area in the generation of new hierarchical levels.
How can our results be reconciled with the previous literature?
On the one hand, the absence of evidence for lateral PFC activa-
tion in our task might indicate that this region is sensitive to hierar-
chies of action goals (or other nonmotor contextual dependencies;
Badre, 2008), rather than to transparent rules describing cross-level
relations in motor hierarchies (i.e., inducible without prior instruc-
tion) as tested in our task. Alternatively, the resources necessary to
discriminate hierarchical sequences may not completely overlap with
those used for the generation of new hierarchical levels, in that dis-
crimination recruits numerous additional cognitive mechanisms
that are not relevant during generation but may well account for
IFG effects. For example, representing hierarchies from sequential
input during discrimination also poses demands on resources required
more generally for sequence encoding, buffering and template match-
ing (Bornkessel-Schlesewsky, Schlesewsky, Small, & Rauschecker,
2015; Fitch & Martins, 2014), that may not be taxed to the same
degree during the generation of hierarchical structures in the motor
domain. Importantly, most discrimination studies found greater IFG
involvement in material that drew strongly on these general resources,
for example, by using sequences that were violations (Bianco et al.,
2016; Molnar-Szakacs, Iacoboni, & Koski, 2005; Novick et al., 2005),
had greater ambiguity (Rodd, Vitello, Woollams, & Adank, 2015;
Vitello & Rodd, 2015), longer dependencies or posed higher demands
on working memory than respective control sequences (Baddeley,
2003; Braver et al., 1997). This makes it difficult to dissociate the con-
tribution of specific hierarchical generativity and general cognitive
control/sequence encoding processes to the observed IFG activations
(see also Fedorenko et al., 2012). Our design not only balanced the
amount of required cognitive control across conditions (recall that
final sequences were always correct, unambiguous and identical
across conditions, although based on different rules); it also allowed
us to study hierarchy processing stripped off general processes
required for parsing temporally evolving sequences by specifically tar-
geting hierarchy generation (in the planning phase). Consequently, the
fact that we did not find evidence for lateral PFC involvement does
not support the notion of multi-domain hierarchical generativity in
IFG (Fadiga et al., 2009; Fitch & Martins, 2014) and rather argues for
its more general function during encoding of structured sequences.
It is important to note that while we did not find evidence for the role
of IFG in the generation of hierarchies in the motor domain, this
region could play a pivotal role in other domains such as language.
MARTINS ET AL.2635

Since we focus on both generation of motor hierarchies (in contrast
with, for instance, processing of linguistic syntax), we cannot draw
strong conclusions about other domains. Although recent experiments
in the music domain seem to suggest a similar absence of specialized
IFG activity in the generation of new hierarchical levels versus serial
iteration (Martins, 2017) further work is needed.
5|CONCLUSION
In this study, we isolated the processes involved in generating
motor hierarchies while separating them from other motor externali-
zation components. Our results suggest that the generation of
motor hierarchical structures via the application of recursive rules
was supported by a neural system used for motor imagery and
motor planning. Conversely, we did not find evidence that a puta-
tive multi-domain hierarchical processor in the lateral PFC is neces-
sary for the generation of hierarchical levels in motor sequence
production. While lateral PFC might be important to parse hierarchi-
cal sequences in a multi-domain fashion, due to encoding and exter-
nalization processes, it might not be necessary for the generation of
new hierarchical levels.
ACKNOWLEDGMENTS
The authors are grateful to Sven Gutekunst and Jöran Lepsien for
technical support.
AUTHOR CONTRIBUTIONS
Mauricio J.D. Martins and Roberta Bianco contributed project concep-
tion, experimental design and setup, data acquisition and analysis, data
interpretation, writing the manuscript; Daniela Sammler and Arno
Villringer contributed supervision of the project, project conception,
data interpretation, writing the manuscript.
DATA AVAILABILITY
The data that support the findings of this study are available from the
corresponding author upon request. Authors can confirm that all rele-
vant data are included in the article.
ORCID
Mauricio J. D. Martins https://orcid.org/0000-0003-0247-8473
Roberta Bianco https://orcid.org/0000-0001-9613-8933
Daniela Sammler https://orcid.org/0000-0001-7458-0229
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How to cite this article: Martins MJD, Bianco R, Sammler D,
VillringerA. Recursion in action: An fMRI study on the generation
of new hierarchical levels in motor sequences. Hum Brain Mapp.
2019;40:2623–2638. https://doi.org/10.1002/hbm.24549
2638 MARTINS ET AL.