Convergent evolution in silico reveals shape and dynamic principles of directed locomotion
Curation statements for this article:-
Curated by eLife
eLife assessment
This study provides an important, original framework to study locomotion on the ground with physics-based simulations. Through numerical simulations, the authors propose that intermediate numbers of body modules and high body symmetry enhance speed. The current way discussions and conclusions are written is overly broad: evidence that evolution may favour bilateral symmetry and modularity for efficient directed locomotion is still incomplete as further performance metrics and a more accurate description of the dynamics in water are needed.
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Abstract
Active, directed locomotion on the ground is present in many phylogenetically distant species. Bilateral symmetry and modularity of the body are common traits often associated with improved directed locomotion. Nevertheless, both features result from natural selection, which is contingent (history-dependent) and multifactorial (several factors interact simultaneously). Based solely on the unique natural history on Earth, it is difficult to conclude that bilateral symmetry and modularity of the body are required traits for an improved locomotion ability as they can result from chance or be related to other body functions. As a way to avoid these caveats, we propose using physics-based simulations of 3D voxel-based soft robots evolved under different evolutionary scenarios to test the necessity of both traits for sustained and effective displacement on the ground. We found that an intermediate number of body modules (appendages) and high body symmetry are evolutionarily selected regardless of gravitational environments, robot sizes, and genotype encoding. Therefore, we conclude that both traits are strong candidates for universal principles related to improved directed locomotion.
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eLife assessment
This study provides an important, original framework to study locomotion on the ground with physics-based simulations. Through numerical simulations, the authors propose that intermediate numbers of body modules and high body symmetry enhance speed. The current way discussions and conclusions are written is overly broad: evidence that evolution may favour bilateral symmetry and modularity for efficient directed locomotion is still incomplete as further performance metrics and a more accurate description of the dynamics in water are needed.
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Reviewer #1 (Public Review):
The manuscript presents a framework for studying biomechanical principles and their links to morphology and provides interesting insights into a particular question regarding terrestrial locomotion and speed. The goal of the paper is to derive general principals of directed terrestrial locomotion, speed, and symmetry.
Major strengths:
The manuscript is a unique and creative work that explores performance spaces of a complicated question through computational modeling. Overall, the paper is well written and well crafted and was a pleasure to read.
The methods presented here (variable agents used to represent ultra-simplified body configurations that are not inherently constrained) are interesting and there's significant potential in them for a properly constrained question. For the data that is present here …
Reviewer #1 (Public Review):
The manuscript presents a framework for studying biomechanical principles and their links to morphology and provides interesting insights into a particular question regarding terrestrial locomotion and speed. The goal of the paper is to derive general principals of directed terrestrial locomotion, speed, and symmetry.
Major strengths:
The manuscript is a unique and creative work that explores performance spaces of a complicated question through computational modeling. Overall, the paper is well written and well crafted and was a pleasure to read.
The methods presented here (variable agents used to represent ultra-simplified body configurations that are not inherently constrained) are interesting and there's significant potential in them for a properly constrained question. For the data that is present here their hypotheses (while they can be anticipated from first principles) are very well validated and serve as a robust validation of these expectations and can help.
Of particular interest was the discussion of the transferability of morphologies designed under one system and moving to another. From a deep-time perspective, of particular interest is the transition from subaqueous to terrestrial locomotion which we know was a major earth life transition. The results of this study show that the best suited morphologies for subaqueous movement are ill-suited (from a locomotor speed standpoint at least) to fully terrestrial locomotion which begs the questions on if there are a suite of forms that have balanced performance in both and how that would differ from aquatic morphologies.
Major weaknesses:
(1) There is a major disagreement between target and parameters.
From a biomechanics perspective the target of this study, Directed Locomotion, is a fairly broad behavioral mode. However, what the authors are ultimately evaluating their model organisms on is a single performance parameter (speed, or distance traveled after 30s). Statements such as "bilateral symmetry showed to be a law-like pattern in animal evolution for efficient directed locomotion purposes" (p 12 line 365-366) are problematic for this reason.
Attaining the highest possible speed is a relevant but limited subset of ways one might interpret performance for directed locomotion. Efficiency, power generation, and limb loading/strain are equally relevant components.
The focus on speed coupled with selection for only the highest performing morphologies, rather than setting a minimum performance threshold fundamentally restricts the dynamics of the system in a way that is not representative of their specified target and pulls the simulations toward a specific, anticipatable, result.
Locomotor efficiency is alluded to later in the manuscript as one of the observed outcomes, but speed is not equivalent to locomotor efficiency (in much the same way that it is not the sole metric for describing performance with respect to directed locomotion). Energy/work/power have not been accounted for in the manuscript so this is not a parameter this study weighs in on.
The data and analyses the others present do show an interesting validation of these methods in assessing first order questions relating the shape of a single performance surface to a theoretical morphology, which has significant potential value.
(2) There is significant population and/or sample size and biasing.
Thirty simulations of a population of 101 morphologies seems small for a study of this kind, particularly looking to investigate such a broad question at an abstract level. Particularly when the top 50% of morphologies are chosen to mutate. It would be very easy for artificial biases to rapidly propagate through this system depending on the parameters bounding the formation of the initial generation.
This strong selection choosing the best 50 morphologies and mutating them enforces an aggressive effect that simulates and even more potent phylogenetic inertia than one might anticipate for an actual evolutionary history (it's no surprise then that all of the simulations were able to successfully retrieve a suite of morphotypes that recovered the performance peak for this system within 1500 generations)
Similarly, why is it that a 4^3 voxel limit was chosen? One can imagine that an increase in this voxel limit would allow for the development of more extreme geometries, which might be successful. It is likely that there might be computational resource constraints involved in this, it would be useful for the authors to add additional context here.
Review of resubmission:
I appreciate the clarification of points dealing with the details of computational modeling and methods and clarifications throughout the text.
However, the authors have failed to address the major weaknesses that were previously identified, specifically regarding the broader conclusions of the work, that either 1) the authors need to use an additional metric besides average speed, or 2) the conclusions need to be significantly reigned in to reflect the very narrow nature of the work.
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Reviewer #2 (Public Review):
Summary:
I believe the authors have done a wonderful job at dissecting a very complex topic, starting with basic building blocks of locomotion and introducing a powerful simulation approach to the exploring the landscape of growth and form in intelligent behavior.Strengths:
This is a very original, timely, and robust piece of work that I believe can inspire further computational studies in evo-devo-etho.Weaknesses:
More detail on the simulations and also greater clarity regarding the generalizability of their claims would improve the message and further studies. -
Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Recommendations For The Authors):
We would like to see the major conclusions constrained to better fit the data presented in the manuscript. Speed is only a single performance metric of a very complicated, very diverse system of locomotion.
If the authors would like to maintain the broader conclusions, the study should be repeated with a number of different performance metrics to shore up the manuscript's results. Particularly with efficiency, speed is not a reliable measure of efficiency to begin with, so this needs to be explored in a more targeted and appropriate manner.
We agree with Reviewer 1 that we should be more precise about the fitness metrics used and more constrained about the conclusions. Considering the points raised in each …
Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Recommendations For The Authors):
We would like to see the major conclusions constrained to better fit the data presented in the manuscript. Speed is only a single performance metric of a very complicated, very diverse system of locomotion.
If the authors would like to maintain the broader conclusions, the study should be repeated with a number of different performance metrics to shore up the manuscript's results. Particularly with efficiency, speed is not a reliable measure of efficiency to begin with, so this needs to be explored in a more targeted and appropriate manner.
We agree with Reviewer 1 that we should be more precise about the fitness metrics used and more constrained about the conclusions. Considering the points raised in each paragraph, we’ve modified the text as follows:
- [line 17] “... to test the necessity of both traits for sustained and effective displacement on the ground.”
- [starting on line 105] “We generate the robot’s sample using an artificial evolutionary process that selects for better locomotion ability - defined as higher average speed as it is a proxy for organisms with sustained and effective displacement.”
- [starting on line 287] “We also found that different gravitational environments require different shape structures to optimize locomotion average speed.”
- [starting on line 311] “This consistency is evidence that a small number of sparsely connected modules is a morphological computation principle for an organism’s optimized average speed.”
- [starting on line 348] “Beyond that, extending the tests for other important aspects of locomotion behavior - as noise on the ground, energetic costs, and maneuverability - by using other locomotion metrics - as energy efficiency, stability margin, and dissipated power (Paez and Melo, 2014; Aoi et al., 2016 ) - would also be relevant to evaluate the principle’s robustness.”
- [starting on line 524] “As the robots with the highest average speed are the ones that succeed in maximizing displacement and having robust dynamics (they will not tumble with time), we defined $\bar s$ as the fitness value using it as a proxy of successful directed locomotion. Selecting for bodies that maximize speed is a common locomotion bias in natural selection, as both predators and prey and thus fecundity and mortality depend on it (Alexander, 2006). Other measures - such as energy efficiency - can capture distinct important aspects of the locomotion complexity (Paez and Melo, 2014) and would be worthy of investigating in future work.”
Paper Premise/Mission Statement: As defined in the abstract and also called out in the text starting on line 59 is "investigate whether symmetry and modularity are features of an organism's shape need [authors italics] to have for better-directed locomotion..."
If we understood correctly the reviewer is asking for more precision in the statement. We modified the respective sentence in the following way:
- [line 62] “... need to have for optimizing average speed on the ground,”
Reviewer #2 (Recommendations For The Authors):
i) a lot of details that are in the captions should be moved in the main text;
Thank you for this comment. We reviewed all the captions and text making modifications to ensure that all the information in the captions is also present in the main text. Below, we highlighted some of the changes:
- [line 57] “Thus, locomotion on the ground is present in phylogenetically distant species (such as the maned wolf and frogfish in Figure 1A) and depends upon … “
- [starting on line 64] “Figure 1B shows a schematic representation of symmetry and modularity on the maned wolf and frogfish bodies.”
- [starting on line 277] “There is a negative correlation between the proportion of feet voxels and the robot’s locomotion transference capability when the robots go to an environment with higher gravity, i.e., water to mars (dark blue in Figure 5C), water to earth (light blue), and mars to earth (red) - with a Spearman correlation coefficients of r = -0.39, r = -0.43, and r = -0.32, respectively, all with p < 1e-08.”
ii) hypotheses should be spelled out more clearly;
We verified the experiments and certified that every experiment had a clear hypothesis statement in the original manuscript. Before each section defining the hypothesis and describing the experiment, we added the following statement:
- [starting on line 119] “ With this sample, we tested the hypotheses about the relationships between locomotion performance and body modularity and symmetry (Figure 1I).”
iii) performance metrics and other features should be better defined using mathematical terms if possible (for example, instability);
Thank you for the comment. We added a definition for instability in the text:
- [starting on line 218] “Nonetheless, locomotion requires a minimum instability - the dynamic possibility of translating the center of mass - in the direction axis to generate the necessary forward displacement (Bruijn et al., 2013; Nagarkar et al., 2021).”
Despite the different definitions of instability in literature (Bruijn et al., 2013, Paez and Melo, 2014; Aoi et al., 2016, Nagarkar et al., 2021), we didn’t find one mathematical definition that fits perfectly in our context.
Following the reviewer's comment, when necessary we expanded the definition for other features:
- [starting on line 199] “... the distribution of body weight. As the robots do not have sensory feedback abilities, the weight balance is defined as the body’s movement due to gravity forces (consequences of the weight distribution and surface contact points) (Benda et al., 1994). We hypothesized that the robots with the best directed locomotion ability would tend to have a symmetric body shape. A robot with a low XY shape symmetry (XY shape symmetry < 0.5) has a higher chance of having a poor weight balance, increasing the chance of the body tipping over, thus leading it to a lousy locomotion performance (blue dotted line in Figure 3C). “
iv) more details regarding the simulations should be included;
We thank the reviewer for this comment. If we understood correctly the Reviewer 2 is asking for more details regarding: “a) the adequacy of the spatial resolution, whereby I failed to see a compelling argument regarding the completeness of 64 voxels; b) the realism of the oscillatory patterns, whereby all the voxels are set to oscillate at the same, constant, frequency of 2Hz; and c) the accuracy of simulations in water where added mass effects seem to be neglected.”. We modified the text to better satisfy these concern:
a) [starting on line 96] “We choose to first explore exhaustively the $4^3$ space dimension, as it is the minimal possible space that allows meaningful body plans. We also did control experiments within 6^3 and 8^3 to check for dimension size effects.”
- [starting on line 432] “We did control experiments with robots within 6³ and 8³ dimensions to check for dimension size effects - and we found that the results found in 4³ remained valid. We choose to focus our analysis in the 4³ design space because we consider it the minimum coarse-grain to approach the biological question about the contingency of shape outcomes pressured for locomotion. Smaller spaces do not allow sufficient complexity in the body structures, and increasing spatial resolution reduces the extensiveness of the investigated search space.”
b) [starting on line 451] “… we used a fixed oscillation frequency of 𝑓 = 2 Hz (Kriegman et al.,2020). A fixed frequency value reduces the number of degrees of freedom in the search for solutions, but in return, it narrows the direct connection between the simulated organisms and animals. Exploring different frequency values in future work would be important to investigate the impact of varied oscillatory frequencies in the shape solutions for directed locomotion.”
c) The environment we call “water” is not an accurate modeling of aquatic habitats as we didn’t simulate essential forces such as draff effects. This choice is explained in text starting on line 110: “In the water-like environment the bodies have nullifying body weight but do not have drag effects. We did not add drag in our simulations because our aim is to study just the body weight influences in locomotion independently of other forces.”
v) a full paragraph about limitations should be included in the discussions, focusing on both simulation aspects (for example, the use of simple spring elements in the voxels) and theoretical assumptions (for example, addressing the potential role of non-locomotion-related aspects).
We thank the reviewer for the comment. We edited some paragraphs of the discussion section to make more explicit some limitations of our work:
[starting on line 398] “We expect that including other important aspects of an animal's body as a developmental process and sensory functions could influence the shape's outcomes with other layers of principles. Although we based our simulations on an already successful transference of \textit{in silico} behavior to organisms made of biological tissue
\citep{kriegman_scalable_2020}, there is an intrinsic gap between spring-mass robots modeling and animal’s bodies that is worthy of exploring to ensure the generality of our results. Other methods, such as the inclusion of rigid body elements in the simulation (possible in Voxelyze), the use of finite element modeling (FEM) (Coevoet et al., 2019), and the construction of physical robots (Aguilar et al., 2016), are important complements to this work. Beyond that, principles on other scales as in the genotypes (Johnston et al., 2022) and in other behavioral phenotypes (Gomez-Marin et al., 2016) could also be investigated.”
To address the potential role of non-locomotion-related aspects, we revised the section
“Discussion - Contingency of evolutionary outcomes” where we discussed other functional and biological roles:
[starting on line 354 ] “Here we investigate how a specific functional cause - optimization of average speed during directed locomotion on the ground - externally defines the phenotypic space of shape possibilities.”
[starting on line 359] “For simplification purposes, we choose to not explicitly control other important factors of locomotion (i.e., energy consumption, maneuverability) that nonlinearly interact during locomotion. In future studies, it would be important to conduct similar studies on a wider range of factors to study the shape and dynamic principles in different conditions.“
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eLife assessment
This study provides an important, original framework to study locomotion on the ground with physics-based simulations. Through numerical simulations, the authors propose that intermediate numbers of body modules and high body symmetry enhance speed. The evidence that evolution may favour bilateral symmetry and modularity for efficient directed locomotion is still incomplete, however.
-
Reviewer #1 (Public Review):
The manuscript presents a framework for studying biomechanical principles and their links to morphology and provides interesting insights into a particular question regarding terrestrial locomotion and speed. The goal of the paper is to derive general principles of directed terrestrial locomotion, speed, and symmetry.
Major strengths:
The manuscript is a unique and creative work that explores performance spaces of a complicated question through computational modeling. Overall, the paper is well written and well crafted and was a pleasure to read.The methods presented here (variable agents used to represent ultra-simplified body configurations that are not inherently constrained) are interesting and there's significant potential in them for a properly constrained question. For the data that is present here …
Reviewer #1 (Public Review):
The manuscript presents a framework for studying biomechanical principles and their links to morphology and provides interesting insights into a particular question regarding terrestrial locomotion and speed. The goal of the paper is to derive general principles of directed terrestrial locomotion, speed, and symmetry.
Major strengths:
The manuscript is a unique and creative work that explores performance spaces of a complicated question through computational modeling. Overall, the paper is well written and well crafted and was a pleasure to read.The methods presented here (variable agents used to represent ultra-simplified body configurations that are not inherently constrained) are interesting and there's significant potential in them for a properly constrained question. For the data that is present here their hypotheses (while they can be anticipated from first principles) are very well validated and serve as a robust validation of these expectations and can help.
Of particular interest was the discussion of the transferability of morphologies designed under one system and moving to another. From a deep-time perspective, of particular interest is the transition from subaqueous to terrestrial locomotion which we know was a major earth life transition. The results of this study show that the best-suited morphologies for subaqueous movement are ill-suited (from a locomotor speed standpoint at least) to fully terrestrial locomotion which begs the question of if there are a suite of forms that have balanced performance in both and how that would differ from aquatic morphologies.
Major weaknesses:
1. There is a major disagreement between the target and parameters.From a biomechanics perspective the target of this study, Directed Locomotion, is a fairly broad behavioral mode. However, what the authors are ultimately evaluating their model organisms on is a single performance parameter (speed, or distance traveled after 30s). Statements such as "bilateral symmetry showed to be a law-like pattern in animal evolution for efficient directed locomotion purposes" (p 12 line 365-366) are problematic for this reason.
Attaining the highest possible speed is a relevant but limited subset of ways one might interpret performance for directed locomotion. Efficiency, power generation, and limb loading/strain are equally relevant components.
The focus on speed coupled with selection for only the highest performing morphologies, rather than setting a minimum performance threshold, fundamentally restricts the dynamics of the system in a way that is not representative of their specified target and pulls the simulations toward a specific, anticipatable, result.
Locomotor efficiency is alluded to later in the manuscript as one of the observed outcomes, but speed is not equivalent to locomotor efficiency (in much the same way that it is not the sole metric for describing performance with respect to directed locomotion). Energy/work/power have not been accounted for in the manuscript so this is not a parameter this study weighs in on.
The data and analyses the others present do show an interesting validation of these methods in assessing first-order questions relating the shape of a single performance surface to a theoretical morphology, which has significant potential value.
2. There is a significant population and/or sample size and biasing.
Thirty simulations of a population of 101 morphologies seems small for a study of this kind, particularly looking to investigate such a broad question at an abstract level. Particularly when the top 50% of morphologies are chosen to mutate. It would be very easy for artificial biases to rapidly propagate through this system depending on the parameters bounding the formation of the initial generation.
This strong selection choosing the best 50 morphologies and mutating them enforces an aggressive effect that simulates an even more potent phylogenetic inertia than one might anticipate for an actual evolutionary history (it's no surprise then that all of the simulations were able to successfully retrieve a suite of morphotypes that recovered the performance peak for this system within 1500 generations).
Similarly, why is it that a 4^3 voxel limit was chosen? One can imagine that an increase in this voxel limit would allow for the development of more extreme geometries, which might be successful. It is likely that there might be computational resource constraints involved in this, it would be useful for the authors to add additional context here.
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Reviewer #2 (Public Review):
Acknowledging practical difficulties in teasing out the principles behind animal locomotion from the body's functions and survival needs, the authors embark on a computational experiment to replay the "tape of life." Specifically, the chief objective of the study was to explore the necessity of symmetry and modularity for better-directed locomotion on the ground.
Towards this important goal, the authors put forward a comprehensive computational study using physics-based simulations of 3D voxel-based robots. Such a simulation environment allows one to capture salient dynamics behind locomotion, including interactions with the environment. The authors undertake simulations for three different gravitational environments, water, Earth, and Mars. The work has several methodological strengths, with respect to the …
Reviewer #2 (Public Review):
Acknowledging practical difficulties in teasing out the principles behind animal locomotion from the body's functions and survival needs, the authors embark on a computational experiment to replay the "tape of life." Specifically, the chief objective of the study was to explore the necessity of symmetry and modularity for better-directed locomotion on the ground.
Towards this important goal, the authors put forward a comprehensive computational study using physics-based simulations of 3D voxel-based robots. Such a simulation environment allows one to capture salient dynamics behind locomotion, including interactions with the environment. The authors undertake simulations for three different gravitational environments, water, Earth, and Mars. The work has several methodological strengths, with respect to the ingenuity of the approach and the elegance of the analysis; I was particularly intrigued by the use of graph theory in the context of modularity. Results point to a complex, rich role of modularity and symmetry in locomotion, modulated by the gravitational environment.
The association between "locomotion ability" and average speed is, in my view, tenuous, whereby locomotion is a complex phenomenon that should be assessed across a range of intertwined dynamic metrics that include, for example, stability with respect to external perturbations and energy efficiency. I also am not fully convinced of i) the adequacy of the spatial resolution, whereby I failed to see a compelling argument regarding the completeness of 64 voxels; ii) the realism of the oscillatory patterns, whereby all the voxels are set to oscillate at the same, constant, frequency of 2Hz; and iii) the accuracy of simulations in water where added mass effects seem to be neglected. Overall, dynamics and control aspects could be improved in both the methods and the interpretation of the results. Finally, I believe that a stronger connection between the hypotheses of the study and the literature (in animal or robot locomotion) would help frame the narrative better. I would be particularly curious to see some tie with human bipedal locomotion.
The work bears important implications in the study of locomotion, shedding light on the role of modularity and symmetry, beyond what one could gather from mere observations. Not only do I expect these new insights to stimulate further research in the area of locomotion, but also I envision other communities embracing a similar computational approach to address related questions in life sciences and robotics.
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