The emergence of symbolic interaction is often cited together a an important step in the evolution of Homo sapiens, language, and also human-level cognition. It is a widely held assumption that humans are the only species that possess herbal symbolic communication schemes, back a range of other varieties can be teach to usage symbols. The origin of symbolic communication remains a controversial open up problem, obfuscated through the lack of a fossil record. Right here we show an unbroken evolutionary pathway indigenous a population of initially noncommunicating robots to the spontaneous appearance of symbolic communication. Robots evolve in a simulated world and are provided with only a single channel of communication. When their ability to give birth is urged by the need to uncover a mate, robots evolve indexical interaction schemes from initially noncommunicating populaces in 99% of every experiments. Furthermore, 9% the the populations evolve a symbolic interaction scheme permitting pairs of robots come exchange information about two live independence spatial dimensions over a one-dimensional channel, thereby boosting their possibility of reproduction. These results indicate that the capacity for symbolic interaction could have emerged spontaneously under natural selection, there is no requiring cognitive preadaptations or preexisting iconic communication schemes as formerly conjectured.

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Communication is commonly identified as an occasion mediated through the usage of indicators in i m sorry the action of an certified dealer or agents (the senders) causes a reaction in one or more agents (the receivers)1. Pets communicate making use of iconic or indexical signals to refer directly to objects or actions2, return some types can be taught to use symbols3. This type of interaction is identified by a one-to-one mapping in between the signal and the object or action. Iconic communication is mediated by signs (icons) which be affected by each other a similarity to the type of objects and also are instantly recognizable (e.g., as when a monkey opens up its mouth and also bears its this to threaten or as soon as two clues on a butterfly’s wings resemble the eyes of a predator) conversely, in indexical communication signs (indices) are just physically or temporally correlated with objects2,4. Because that example, to alert various other members in their troop of imminent danger, vervet monkeys have occurred alarm call directly linked with certain predators or, perhaps much more likely, to details fleeing responses5. The vervet monkey alarm calls qualify as indexical, as they execute not have any type of physical similarity with the predators to which they refer. If, however, the alarm for an eagle sounded choose (i.e., physically resembled) the speak to of an eagle, it would certainly qualify together iconic.

By contrast, humans appear to be the only types to have occurred a complex system of indications that interrelate v one another. This kind of communication—symbolic communication—is based upon sign-sign relationships fairly than the sign-object relationships of above or indexical communication. Symbolic interaction relies on one-to-many mappings in between a authorize or symbol and that to which it might refer. The meaning of symbols counts on a support agreed upon cultural context. Because that example, if one to write “bald eagle,” we know that we room talking about a varieties of bird of prey. If, however, one to write “eagle eyes,” we are instead talking about good vision. Thus, an interpretation arises indigenous the sign-sign relationships in between “eagle” and also the other indications (“bald,” “eyes”) and also not from any type of one sign in particular.

The transition from indexical to symbolic interaction is as such a an essential evolutionary change because it might signal the origin of language6,7,8 and also symbolic thought2,8,9. This change has no been observed in thedesigningfairy.com nor has actually it been reproduced in an synthetic evolutionary environment, hence the beginning of symbolic interaction remains an open problem10. Vault works11,12,13,14,15,16,17,18,19 have actually explored the evolution of communication in between robots making use of evolutionary algorithms. Such approaches employ discrete generations, whereby offspring change the entire parent populace thus removing the need for continuity of an evolving communication scheme in between generations. Furthermore, these viewpoints employ experimenter-defined objective features (used to evaluate the reproductive viability of people or teams of agents) which have the right to restrict the open-endedness that the evolution process20 and also can introduce far-ranging levels the experimenter bias21. These experiments have developed a selection of complex communication schemes; however, none has actually demonstrated the emergence of symbolic communication.

Digital simulation experiment have likewise been supplied to check out the development of communication. In a simulated world similar to the one gift here, agents developed indexical interaction using a 3-bit channel. Sighted but immobile females used these schemes to direct adjacent blind yet mobile males to their location on a two-dimensional grid22. Avida23, a software platform for research study on digital organisms, has likewise been supplied to study the introduction of experimenter-defined communication schemes among populations of self-replicating computer programs24.


Our evolution environment, called NoiseWorld, is shown in Fig. 1. The agents inhabiting this discrete-time world are stood for by evolvable mathematics models25 (EMMs) in the type of a mechanism of expandable distinction equations which explain the state the the agent, its motor duty and its communication output. The use of EMMs permits a direct analysis of a robot’s behaviour by investigate its administer equations.


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NoiseWorld.

Robots exist in a 2D world and can feeling their very own x and also y locations. They cannot sense any information about their neighbours. Robots can produce nondirectional sounds ωout and also can finding the sounds created by their nearest neighbour ωin. Robots live on among the archipelago in the world, and also when 2 robots meet, they immediately produce one offspring. A randomly selected robot dies whenever a brand-new offspring robot is born. Islands are arranged in a toroid. Offspring robots are periodically born on one of the 4 neighbouring islands.


The framework of EMMs is given by command tree graphs (see Supplementary Fig. S1), which offer as the agent’s genome, and evolve using the rule of genetic programming25,26,27. Certified dealer genomes space subject to inheritance and mutation. However, no objective fitness function is provided. Two agents sexually reproduce once they space in near proximity (see Methods and Supplementary Fig. S2). Hence NoiseWorld evolves asynchronously. Selection pressure arises from the reality that greater reproductive rates lead to lower median agent lifespans as each birth is attach by the random fatality of a robot. This to decrease in typical lifespan forces less reproductively viable genomes out of the population. There are no target functions, no discrete generations, and also no enforced group selection.

Each robot is offered with a one-dimensional communication channel over which the emits a signal omnidirectionally and receives a signal native its nearest neighbour. Relative robot positions are recalculated after ~ every timestep, ensuring that a obtained signal is constantly arriving from a robot’s present neighbour. Robots can not detect changes in the identification of your nearest neighbour. Additionally, a 3rd robot has the potential come overhear component of the communications in between two various other robots: In the case where two robots share a nearest neighbour, both robots will receive signals native their usual neighbour, but the usual neighbour will only receive the signal from the robot the is closest to it. Therefore, the closestly robot and the usual nearest neighbour can signal to one another, while the 3rd robot have the right to only “overhear” one half of the conversation between the other two robots.

Robots cannot identify the direction indigenous which a signal is received nor is there any variation in the intensity of a signal that could otherwise reveal the relative distance the the sender. Any kind of information extracted by the receiver need to reside in the contents of the signal and also not from information inherent in the medium. If the robots space equipped with number of mechanical preadaptations–in enhancement to the access of a interaction channel, the robots understand their location and have engine function–no cognitive preadaptation is provided a priori.

Since robots re-superstructure the common goal the reproducing, over there is no problem of interest present, and also thus no selection pressure because that deceptive communication. Communication schemes that have advanced without a pressure for deception have been observed in thedesigningfairy.com. For example, over there is no conflict of interest throughout the mating displays that blue-headed wrasses employ to name: coordinates the simultaneous release of gametes28.


Figure 2 shows a sample history of one simulation operation (see Supplementary Fig. S3 for others). Populace “snapshots” were taken as soon as per era (defined as 100,000 timesteps). Together the simulation begins, over there is no interaction on the island since an permitted communication channel go not provide any reproductive benefits (see Fig. 2c). Moreover, at era 48 because that example, ωin, the change containing a neighbour’s output signal, appears nowhere in an agent’s administer equations (see Supplementary Equations S1–S3). Robots cannot respond come incoming signals and thus reproduction occurs only by chance. Together time progresses, the population’s reproductive success enhances with the an initial stepwise increase occurring at about era 50. In ~ this point, initial communication emerges; statistically, as measured by the Pearson correlation coefficient, the robot communication output signals (ωout) are discovered to it is in highly correlated with your latitude (y) as displayed in Fig. 2d. Indeed, for an example agent at era 313 (see Fig. 2a), the calculation signal equation (see Supplementary Equations S4 and also S5) is


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A sample history of one island is examined and also top reproducing robots from two different eras are displayed interacting.

The top structure of these behaviour samples shows the trajectory that the 2 robots take, while the bottom structure shows their interaction outputs ωout over time. Auditory interpretations that ωout values are detailed in Supplementary Audio S1–S2. An era is 100,000 timesteps. (a) by era 313, indexical communication has emerged. One deserve to determine straight a robot’s absolute y place at a given timestep indigenous its ωout worth (y = ωout/4.36, check out text). (b) by era 937, symbolic interaction has emerged. Robot place information can no much longer be established from observing solitary ωout values. Instead, loved one robot positions are revealed through sign-sign relationships (i.e., by observing both agents’ ωout values, see text). (c) Reproduction rates are shown with (green) and also without (grey) interaction enabled. (d) also shown space the magnitudes the the Pearson product-moment correlation coefficients in between the place (y in red, x in blue) and also ωout of every era’s most reproductively successful agent.


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exhibiting a direct one-to-one relationship. This is indicative of an indexical interaction scheme. Simply as different vervet monkey alert calls show the existence of particular predators, robot ωout worths indicate certain robot y positions. Through era 600, reproduction rates have jumped to a brand-new plateau, whereas the correlation in between output signal and robot position has actually dropped precipitously. Certified dealer genomes expose that the output signals involve both latitude and also longitude yet there is no much longer a one-to-one relationship between signal and also robot location. Because that example, in ~ era 937 (see Fig. 2b) a typical output signal equation (see Supplementary Equations S6–S7) is


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A provided value that ωout corresponds to lot of (x, y) locations. That is a one-to-many relationship. Equally important, one input interaction signal ωin appears in the equation: the output is amendment by the input, describe a dialogue. This dialogue resolves the ambiguity in the signal’s meaning, implying a sign-sign partnership in comparison to the sign-object relationship obvious earlier in the evolution process. A qualitative shift in the communication scheme has clearly occurred. The indexical setting of interaction has advanced into a rudimentary kind of symbolic communication.

A common equation determining the orientation that the robots employing indexical symbols is


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The equations identify the orientation the the symbolically communicating robots space structurally similar:


This structural similarity in between these two species suggests that the complexification that the signal outputs in the direction of symbolic communication was may be to yield reproductive services by exploiting the minimal preexisting cognitive machinery crucial for indexical communication. The probability of these changes developing during a single reproductive event is little considering the simulation’s mutation rates (see Methods). That is far an ext likely that this transition occurred via a collection of mutations and/or sexual recombination occasions that were able to create reproductively viable transient interaction schemes the exploited preexisting hearne capabilities. Future step-by-step documentation the this change will call for snapshots taken in ~ a frequency several orders of magnitude higher than was supplied to capture the data gift here.

From a interactions perspective, the dialogue in between two robots indigenous era 937 reveals just how they space able come negotiate a meeting. They very first resolve their distinction in latitude (y). When a robot’s (the sender’s) calculation signal is bigger than that neighbour’s, ωout > ωin from the sender’s perspective, it is interacting that the sender is phibìc of the recipient (see Figs 2b and 3a). The resulting action is because that the sender to relocate south and the receiver to relocate north. As the 2 robots converge top top a common latitude, the size of your signals begins to increase. Smaller sized values that x interpret to much faster increases and larger communication output signals pressure the receiver earlier towards smaller outputs, hence “calculating” relative robot x positions (Fig. 3b). ~ this “discussion,” bigger output signals show that the sender is “west” that the receiver.


Various visualizations the the evolved communication output ωout.

(a) neighbouring robots recognize relative y location via their ωout/in (i.e., dialogue) values oscillating between the two different regions presented here. The ωout/in the the robot v the greater y value will clear up in the left an ar (resulting in a higher ωout), when the various other settles in the right region (resulting in a lower ωout), thus “deciding” relative north/south robot position. (b) as the two robots approach a typical y place (the nonlinear part of this plots), the robot through the smaller sized x position will see the magnitude of its ωout increase faster than the of that is neighbour, which in turn forces the neighbour’s ωout ago towards linear behaviour, hence “deciding” their relative east/west position.


The meanings inferred by one robot in the other’s signals arise from sign-sign relationships. Because that example, if we only observe little communication output signals indigenous a single robot, we would not have the ability to discern if this agent were indicating north, south or eastern (this is analogous come the “eagle” instance given above, where one word/sign is not sufficient to fix meaning). Since third parties may overhear one half of a dialogue between two robots, over there is a pressure to avoid eavesdroppers from extracting the ar of a potential mate indigenous one side of the conversation, as otherwise they could reach this mate first. This pressure might play a function in the development of these symbolic interaction schemes where definition cannot be extract from a solitary robot’s signals, return further experimentation is compelled to confirm this.

These sign-sign relationships are abstract; the is, what they define cannot it is in sensed straight by the robots (in this case, they cannot directly sense loved one position). Furthermore, this relationships room arbitrary; that is, different meanings can and also have emerged from other evolutionary runs. The example over produces a mainly “north/south” movement and is reflected in the interaction patterns which evolved; other populations, however, have developed to usage an inverted “south/north” communication scheme or even a generally “east/west” device (see Fig. 4, Supplementary Figs S4–S8 and Supplementary Equations S8–S54).


The genome of one agent with an advanced symbolic interaction scheme is embodied in 2 e-puck robots.

Agents are gave with your position info via one overhead webcam and also colour detection software. Advanced agents are run on a laptop (not shown) that handles communication in between agents and also sends instructions come the robots via Bluetooth. Two hardware experiments room shown, with photos taken in ~ 5 2nd intervals displayed in the very first row, and also the corresponding inter-robot communication data presented underneath. Listening interpretations of ωout values are noted in Supplementary Audio S3–S4.


These results carry out a new window ~ above a potential pathway because that the emergence and evolution the symbolic interaction (see Supplementary video clip S2), one the does not need preexisting brains through a high level of complexity as previously conjectured29. Lock moreover show an unbroken evolution pathway to straightforward symbolic interaction via indexical communication without the require for top communication, which has previously to be proposed as a possible evolutionary stepping stone to symbolic communication30. Basic indexical communication strategies comparable to the one described over emerged in 99 that 100 simulation runs wherein the communication channel was permitted (10 added runs to be performed v the communication channel disabled). Nine of this populations advanced further, emerging a rudimentary kind of symbolic communication, as suggested by the sign-sign relationships on which these interaction schemes rely2,4 (see Table 1 and also Supplementary Table S1). Fact is that course lot more complicated than these simulations, together organisms in thedesigningfairy.com do not typically know their pure coordinates and also natural communication systems contain inherent physical information. Moreover, human symbolic communication is mainly learned, whereas here behaviours, including communication schemes, space genetically encoded. Therefore, while this results demonstrate one feasible pathway come symbolic interaction via indexical communication and without an extensive preexisting cognitive complexity, this is no necessarily the evolutionary course that human communication took, no one does this prove the symbolic interaction cannot emerge from iconic communication or cognitive preadaptations. Nonetheless, this results show that an easy symbolic interaction can arise spontaneously from a populace of at first noncommunicating embodied agents in a reasonably short evolution timespan given a restricted capacity interaction channel, no dispute of interest, and a choice pressure for cooperation. The duty of overheard signal in shaping these symbolic communication schemes and the potential effects of deceptive signals on the evolutionary procedure are left to future work.


Given the cognitive simplicity of these symbolically communicating robots, one cannot help but wonder why humans are the only species to have evolved symbolic interaction in thedesigningfairy.com. One feasible explanation is that the an unified dimensionality the both verbal and nonverbal pet communication media, and also their inherent information (such together directionality), provide sufficient info transmission capacity for animal species’ communication needs. Us might likewise speculate that perhaps similar symbolic systems carry out exist in other species but that we have not yet found them. However, it may require the combination of various other specifically human skills that enable cultural evolution for such a straightforward system to be elevated into the sort of complicated communication mechanism we watch in person language.


Evolvable mathematical models

The evolvable mathematical models (EMMs) provided to represent the agents are identified by a mechanism of equations the the form


where vt is the state vector that the certified dealer at time t, vt + Δt = vt + Δvt+Δt at the following timestep, ϑt is the motor calculation governing the direction that the robot’s activity relative to a provided reference direction and also ωtin/out room the robot’s input (from the nearest neighbour) and also output interaction signals. Every state vector has the coordinates xt, yt the the robot. This equations space encoded in a collection of command tree graphs which serves together the agent’s genome (see Supplementary Fig. S1). Terminal nodes of the equation trees take on the values of one of the variables (variable leaves) or a numerical continuous (constant leaves) if nonterminal (branch) nodes perform one of the four simple arithmetic work (addition, subtraction, multiplication, division). We use the hatchet “evolvable mathematics model” to refer to the genomic representation of agents through equation tree as developed via hereditary programming.

NoiseWorld

When 2 robots come into close proximity come each various other (within a prespecified “reproduction distance” ρ, here ρ = 0.139), one offspring is born by sexual reproduction using hereditary programming. Throughout reproduction, offspring genomes are subject come a variety of genetic operators. For each equation the the 2 parents have actually in common (the equations have distinct identification tags based upon when they an initial appeared via mutation in the simulation), one of two people the equation from parental 1 or parent 2 will go to the offspring. Which equation is inherited is determined randomly for each equation in common. An offspring should receive at the very least one equation from each parent, for this reason sexual reproduction is enforced at the equation level. If an offspring receive an equation that consists of a variable modified by another equation the is not typical to both parents, the offspring will certainly inherit that equation also (see Supplementary Fig. S2 for several examples).

A mutation will happen in one equation tree through a probability of pm; here pm = 0.025β/n, whereby n is the number of trees in the genome and also β is separately calculated on each island every 10,000 timesteps as 500/b through b being the number of births on the island in the previous 10,000 timesteps. The parameter β saturates at 100 but has no minimum; it is provided in an initiative to save the variety of mutations per unit time constant.

A tree mutation is a point or subtree mutation with equal probability. A allude mutation take away the kind of a perturbation that a consistent leaf (if any kind of exist in the tree) or the mutation of one more node with equal probability. A perturbation of a consistent is drawn from the Guassian circulation N(μ, σ); here, μ = 0 and also σ = 0.5. A mutation to a branch-node reassigns the to an additional arithmetic operation and a mutation come a variable leaf transforms it to another variable or a brand-new constant, k; here, k ∈<−5, 5>. A subtree mutation replace instead instead a randomly selected node with a randomly produced subtree (generated via the ramped half-and-half method, see below). There is a 5% possibility that the randomly generated subtree will change the entire original tree, through the original tree climate being spliced onto a randomly selected node on this brand-new subtree. A hereditary splice procedure occurs through a probability pm through which a randomly selected node is changed with a randomly selected subtree indigenous a parental genome.

Initial problems of the state, v0, are also subject to mutation v probability pm; in this mutations, the initial state values room either augmented by a perturbation taken indigenous N(0, 0.25) or totally replaced through a random value drawn from the interval <−1, 1> with equal probability.

Finally, for each tree in one offspring genome, over there is a probability 0.5pm the a brand-new state equation will be added to the offspring’s genome, v a reference to the corresponding brand-new state variable placed into a randomly selected place on the tree. The equation tree for the new variable is initialized in the very same manner together for the primordial population (see below).

There is a full of 100 archipelago in NoiseWorld, each v a huge two-dimensional expanse (−20 x y NoiseWorld is toroidal whereby every island is surrounded by eight adjoining islands, 4 sharing a “border” and four sharing a “corner” ~ above a two-dimensional manifold. Each island is seeded with 50 agents and also each agent is initialized v a arbitrarily genome utilizing the “ramped half-and-half” method27 to create trees with a preferably depth of 1 or 2. Ramped half-and-half is a combination of 2 methods, the “full” method and the “grow” method. In the “full” method, nonterminal nodes are randomly produced until the maximum depth is reached. At the maximum depth, just terminal nodes room created. In the “grow” method, as in the “full” method, just terminal nodes are created at the best depth. The difference is that prior to the maximum depth is reached, randomly created nodes deserve to be one of two people terminal or nonterminal nodes, allowing for a broader range that potential tree shapes. The ramped half-and-half method chooses to create a random subtree using either the “full” or “grow” an approach with equal probability.

Each agent is offered with two immutable equations, Δxt+Δt = aΔt cosϑt and Δyt+Δt = aΔt sinϑt in Δvt+Δt, i beg your pardon govern its movement; a is attracted from N(1, 0.025) and Δt = 0.0005 in dimensionless time units. Each robot to know its latitude and also longitude, x and also y, but has no straight information around any of its fellow robots. The angle ϑt is measured loved one to either “east” (+x direction) or “north” (+y direction).

Offspring begin life in a randomly selected ar on that parents’ island (within a circle, below of radius 1.13, centred ~ above the origin) although there is a little probability (pb = 0.001) the it will show up on a bordering island (diagonal movements are not permitted). A minimum distance (here the reproduction street ρ) to the offspring’s nearest neighbour is enforced. Parents are additionally moved to brand-new random places on their island (in the exact same manner as described above for your offspring) and also reinitialized. Migration permits the spread out of genes among islands. Otherwise, robots are limited to remain on their native islands. To keep a constant population, as soon as a bear occurs, another robot randomly dies.

A newly developed offspring genome has a 10% opportunity of gift selected to undergo equation reduction. In together an event, the adhering to operations are used recursively across all of the agent’s equation trees:

The subtraction, addition, multiplication or department of 2 constants is diminished to a single constant by performing the encoded operation.

The amount of two identical subtrees is diminished to 2× a solitary version the the subtree.

The subtraction of two similar subtrees is diminished to 0.

The multiplication of a subtree through 0 is reduced to 0.

The department of 0 by a nonzero subtree is decreased to 0.

An agent’s genome is minimal to a maximum of 200 nodes throughout all the its equation trees. An offspring born with an ext than 200 nodes die immediately.

If one or much more of an agent’s output variables exceed the minimum or preferably representable floating-point number, the agent will have actually that output collection to a arbitrarily floating-point number and also will be selected to die as soon as the next birth occurs.

It is worthwhile note that additional investigation and also observation that the robots’ behaviour show the evolutionary procedure to be developing a straightforward control mechanism. Taking again the developed agent of era 937 as our example (see Supplementary Equations S6–S7), we view that the common dynamics that two similar agents (1 and also 2) own the fixed suggest x1 = x2, y1 = y2. Moreover, this allude behaves in a steady fashion. Native a control-theoretic viewpoint, then, the advancement produces a steady controller in i m sorry the objective is bring two agents to consensus in position and where ϑt is the regulate variable and ωout/in serves together the measure up variable.

Computational experiments

All simulation experiments were run for 48 wall surface clock hours on a specialized Linux server v an Intel Xeon E5540 at 2.53 GHz. Every island is implemented as a separate process so that the algorithm have the right to take full benefit of the parallel style of the Intel Xeon CPU (8 cores/16 threads). A master/slave parallel implementation is used, wherein a “master” procedure handles the synchronization that “slave” processes (i.e., the islands). Islands space synchronized and also migrants exchanged every 10,000 timesteps. Islands introduce incoming migrants into their subpopulations in ~ a price of η =10,000 migrants every timestep (in a randomized order). Migration occasions are cure as brand-new births on the receiving island, thus engendering a random death on the island in ~ the complying with timestep. When migration isn’t essential for symbolic interaction to emerge, it has the impact of boosting the probability of a operation achieving symbolic communication, and reducing the buildup of neutral mutations in agent genomes, thus significantly increasing the variety of eras that have the right to be simulated in 48 wall clock hrs (Supplementary Table S2).

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To test how an island snapshot performs with and also without communication enabled (i.e., ωin = 0), as well as to collection data because that the correlation calculations (Fig. 2d and Supplementary Fig. S3), a regulate test simulation to be performed. The expression of a manage test run is one era (100,000 timesteps) and the genomes supplied are taken indigenous a photo of an island population. The robots are initially placed randomly in the check world and also initialized. If during the manage test run two robots accomplish one another (within the street ρ, watch above), the occasion is counted as a reproduction event however no offspring genome is created. Instead, the two parent robots are relocated to new random locations and reinitialized. This prevents any kind of evolution during the control runs. The results of births and deaths were simulated by moving a robot to new random position and also reinitializing it v a probability the 0.001 every robot every timestep.

For correlation calculations, the communication outputs and position info of the optimal reproducing certified dealer in the photo are taped throughout the test simulation, yielding 100,000 set of input/output worths per test. The Pearson product-moment correlation coefficient r (“correlation” in Fig. 2d and Supplementary Fig. S3) to be calculated as