Jean-Pierre Rospars
email: jean-pierre.rospars@inrae.fr

Nicole Meyer-Vernet
email: nicole.meyer@obspm.fr

How fast do mobile organisms respond to stimuli? Response times from bacteria to elephants and whales

Keywords: response time, startle response, locomotion, biophysical modelling, biological scaling

Quick responses to fast changes in the environment are crucial in animal behaviour and survival, 24 for example to seize prey, escape predators, or negotiate obstacles. Here, we study the 'simple 25 response time' that is the time elapsed between receptor stimulation and motor activation as 26 typically shown in escape responses, for mobile organisms of various taxa ranging from bacteria 27 to large vertebrates. We show that 95 % of these simple response times lie within one order of 28 magnitude of the overall geometric mean of about 25 ms, which is similar to that of a well-29 studied sensory time scale, the inverse of the critical flicker fusion frequency in vision, also lying 30 within close bounds for all the organisms studied. We find that this time scale is a few times 31 smaller than the minimum time to move by one body length, which is known to lie also within a 32 relatively narrow range for all moving organisms. The remarkably small 10 2 -fold range of the 33 simple response time among so disparate life forms varying over 10 20 -fold in body mass suggests 34 that it is determined by basic physicochemical constraints, independently on the structure and 35 scale of the organism. We thus propose first-principle estimates of the simple response and 36 sensory time scales in terms of physical constants and a few basic biological properties common 37 to mobile organisms and constraining their responses.

interpretation based on basic physicochemical and biological properties. Because the response 88 times of animals are expected to be hugely different from those of microorganisms, which are 89 subjected to very different constraints (e.g. [START_REF] Martens | Size structures sensory hierarchy in ocean life[END_REF], we also investigate the 90 timescales separately for single cells and for metazoans.

91

The empirical data are studied and discussed in sections 2 to 4. Section 5 proposes order-of-92 magnitude interpretations based on fundamental physicochemical constants and basic properties 93 of life, with conclusions given in Section 6. We define as "simple response time" (TS) the time to detect the occurrence of a simple and 100 sudden stimulus. These TS are delays from the time at which the stimulus reaches the organism to 101 either the onset of movement -measured by behavioural methods (for example with high-speed 102 cinematography), or to muscle activation -measured by electrophysiological methods with direct 103 recordings from muscles (electromyogram EMG). Since our study concerns minimum response 104 times, it does not include the "discrimination (or identification) and choice response times" (e.g. 105 [START_REF] Luce | Response Times[END_REF]. In these complex tasks, the subject, whether animal or human, is presented with one 106 of several stimuli and has to respond to only one of them (discrimination, e.g. [START_REF] Blough | Reaction times of pigeons on a wavelength discrimination task[END_REF] or to 107 perform different responses depending on the stimulus presented (choice between stimuli, e.g. 108 [START_REF] Abraham | 576 Maintaining accuracy at the expense of speed: stimulus similarity defines odor 577 discrimination time in mice[END_REF]). Likewise, for microorganisms, we only considered the response delay after 109 a stimulus (e.g. [START_REF] Block | Impulse responses in bacterial chemotaxis[END_REF] ambient conditions (e.g. [START_REF] Mitchell | The influence of cell size on marine bacterial motility and energetics[END_REF]). Thus, our definition of simple response times TS being 112 based on the simplicity of the task and the stimulus does not take into account the length, 113 variability or underlying sensorimotor mechanisms of the response delays (Roeder 1963, Koch 114 1999, [START_REF] Herberholz | Decision making and behavioral choice during predator 645 avoidance[END_REF][START_REF] Sillar | The Neuroethology of Predation and Escape[END_REF][START_REF] Roberts | 710 The decision to move: response times, neuronal circuits and sensory memory in a simple 711 vertebrate[END_REF]. It avoids the 115 operational difficulty to implement these multiple criteria and insures a better representativeness 116 of the sample.

117

We searched the Google Scholar database and extracted simple response times and other 118 relevant data (species names, stimuli, experimental conditions, etc.) published in refereed 119 journals. Our main objective being to investigate the interspecific variability, we kept all values 120 found for non-human species, but not for humans, for which we considered only a selection of 121 papers, either classical or illustrating the diversity of experimental paradigms. For a given species 122 and stimulus, we tabulated simple response times as the mean provided by the authors, or the 123 mean of the extremes when given as a range.

124

Our TS sample (Table S1) includes 175 measurements on 81 species. Behavioural (n = 134) 125 and electromyographic (EMG, n = 41) measurements (column M in Table S1) are not 126 significantly different (Fig. S2A and Table S10); thus, we pooled them together in subsequent 127 analyses. The data belong to two main classes: startle and non-startle. "A startle response is an 128 abrupt response, often of relatively short latency, to a sudden stimulus that we believe to be both 129 unexpected and alarming (i.e., of high valence)" [START_REF] Bullock | Comparative neuroethology of startle, rapid escape, and giant fiber-599 mediated responses[END_REF], so that threats that develop For TS and TL, we distinguished unicellular and multicellular organisms and spermatozoids (TL 151 only), as specified in column U of Tables S1 andS3. For the three timescales, column Cla of We characterized body size by the mass M for each species. Except for vertebrates with measured 162 CFFs from [START_REF] Healy | Metabolic rate and 643 body size are linked with perception of temporal information[END_REF] for which we used the mass provided by these authors, we 163 searched the original papers for mass, length or age. When given as a range, we took the mean.

164

We converted length in mass using either the length-mass relationship of the species when it is the scientific literature (for example, [START_REF] Bartholomew | A field study of flight temperatures in moths in 585 relation to body weight and wing loading[END_REF][START_REF] Byrne | Relationship between wing loading, 605 wingbeat frequency and body mass in homopterous insects[END_REF]Niven 169 and Scharlemann 2005, for insects; Falk-Petersen 1981, for shrimps) or in websites. We have not 170 considered in the analyses two TF data for which the mass could not be found (lines 24 and 87 in 171 Table S2). Otherwise, all body masses and their references are given in Tables S1-S3. Simple response times, TS, extend from 2.5 ms in the escape behaviour of the calanoid S7). 2).

266

Since the maximum metabolic rate of organisms affects their maximum speed (Meyer-Vernet

267

and Rospars 2016), we studied also the dependence of TL on maximum specific metabolic rates 268 (MSMR) in 14 species of mammals for which both values were determined (Table S5). The slope 269 of the regression lines of MSMR against body mass (Fig. S6A) and of TL against MSMR (Fig. Over the whole mass range, the variabilities of the timescales expressed by the ranges including 278 95 % of the data (δT95, Table 1), are so small compared to the mass ranges (δM, Response times (revised version) Phys. Biol.

Page 13 their ratios are always less than one in a million (10 δT95 /10 δM ). Indeed, 95 % of the simple 280 response times TS (Fig. 2), of the visual resolution times (TF = 1/CFF, Fig. 3) and of the minimum 281 locomotor times TL (Fig. 4) lie within less than a factor of ten, five and six respectively of their species (Fig. S3, S4, S5 and Table S6). For most groups, the mass scaling exponents are positive 306 with intercepts decreasing with mass, so that all the data still lie in a relatively narrow range, as 307 found previously for the mass specific metabolism [START_REF] Makarieva | Mean mass-specific metabolic rates are strikingly similar across life's major domains: 671 Evidence for life's metabolic optimum[END_REF][START_REF] Hatton | Linking scaling 641 laws across eukaryotes[END_REF]) and its 308 maximum value [START_REF] Makarieva | Energetics of the smallest: do bacteria 668 breathe at the same rate as whales?[END_REF]. For simple response times TS, the only exponent that 309 reaches statistical significance is that of mammals (Fig. S3) where the trend explains 42% of the 310 variance and agrees with previous studies (section 4.3). Although not significant, the trend in 335

Second, the evolution of different traits is correlated throughout a phylogenetic lineage so that 336 species values do not represent statistically independent data [START_REF] Felsenstein | Phylogenies and the comparative method[END_REF]. This leads to 337 overestimation of degrees of freedom, which artificially narrows confidence intervals. Our major 338 finding that timescales lie within close bounds and that for unicellular (for TS) and multicellular 339 organisms (for all timescales) they do not significantly depend on mass would not be adversely 340 affected by any widening of confidence intervals (on the contrary for TL in single cells) and is 341 therefore impervious to this criticism.

342

A third possible objection is that several experimental factors affecting the measurements have 343 not been considered explicitly. The electrical or behavioural measurement methods play a minor 344 role and correcting them would have practically no effect (Fig. S2 and Table S10 show that their 345 difference is not significant). However, the effect of temperature, which is an important 346 determinant of metabolism and behaviour, should be checked. We thus studied how correcting worst-case scenario assuming that short time scales (T < µ*) were measured at 10 °C, and would 350 thus be still shorter if they had been measured at θ0, and that long time scales (T ≥ µ*) were 351 measured at 30 °C, these two temperatures being close to the extremes in our data (Fig. S7A). For 352 this preliminary test, we used the mean activation energy E = 0.66 eV observed in a wide range 353 of species and traits [START_REF] Dell | Systematic variation in the temperature 616 dependence of physiological and ecological traits[END_REF], and studied how the percentage of timescales lying outside 354 the range [µ*/10, µ*×10] would be affected by temperature in this worst-case scenario. For all 355 timescales, this percentage is less than 3 % without standardization (Table S11a) and less than 356 10 % with standardization (Table S11b), except for TS where it is 5 % and 22 % respectively.

357

Next, noting the greater sensitivity of TS, we applied a finer standardization procedure to this 358 timescale, for which the temperature is known in 72 % of our data for ectothermic species, based 359 on the different mean activation energies of movements away from and toward a stimulus (see

Methods). This procedure leads to no significant change neither in the distribution of TS values 361 (Fig. S7B) nor in the number of species beyond the limits (it remains the same, i. e. four, Fig.

S7

). This indicates that our results in mean, variability and overall trend are robust with respect to The variation of the simple response time, as well as the other time scales studied here, by less 398 than a factor of ten around their mean for organisms so diverse in structure and size suggests that 399 it may be determined by basic constraints set by the universal properties of living matter. We will 400 thus derive first-principle estimates, trying to capture the essential processes at play, whereas 401 neglecting specific details that should be considered in scaling studies over narrow ranges of 402 mass and taxa. Such simple analytic calculations are expected to yield only order-of-magnitude 403 results, that is to within a 10-fold or so accuracy, similar to the variability of the time scales in 404 our data, in the line of the so-called "Fermi problems" or of Weisskopf's physics courses 405 [START_REF] Weisskopf | Of atoms, mountains, and stars: a study in qualitative physics[END_REF][START_REF] Weisskopf | The Privilege of Being a Physicist[END_REF]. process. With L ∝ M 1/3 , this would yield a mass variation TS ∝M 2/3 , as observed for bacteria (see

424
the leftmost regression line in Figure S3 with slope α = 0.66, as given in Table S5). The median 425 mass of a bacterium of length L being M ≃ (3.3L) 3 (Meyer-Vernet and Rospars 2016), the length 426 of a bacterium of mass 10 -15 kg (µM*, Table S6) is L ≃ 3 µm. We deduce from Eq. ( 1) TS = 90 427 ms, which agrees to better than a factor of two with the empirical value for bacteria (µ* = 144 ms 428 in Table S5) and is close to the response time given by their regression line (TS = 100 ms for 429 M = 10 -15 kg, Table S6). Let us now estimate the timescale TF, assuming that it is limited by the membrane time constant 469 τm. For a surface S of membrane of width a and resistivity rm, the electrical resistance is 470 R = rm a/S and the capacitance is given by (2), so that the time constant τm = RC is given by 471 τm = rm ε0 εm.

(6)

472

To estimate a basic value for the resistivity rm, independent on the details of the system, we for M ≲ 50 kg, which agrees to better than a factor of two with the empirical value (59 ms, 497 geometric mean of TL for all organisms of mass M < 50 kg, Table 1). The increase in TL observed [START_REF] Garland | The relation between maximal running speed and body mass in terrestrial 638 mammals[END_REF][START_REF] Garland | The relation between maximal running speed and body mass in terrestrial 638 mammals[END_REF][START_REF] Iriarte-Diaz | Differential scaling of locomotor performance in small and large terrestrial 654 mammals[END_REF].

502

It is interesting to note that our estimates of the minimum times for response (4), for vision 503 (7), and for moving by one body length (8) all yield timescales proportional to the inverse of the 504 maximum mass-specific metabolic rate (per unit of active mass). This suggests that, since the 505 metabolic rate varies with mass within groups of related species, these time scales may depend 506 not only on body mass within groups of related species but also on metabolic rates. This is shown 507 for TL in mammals (Fig. S6B), which is inversely proportional to the maximum mass-specific

--------------------------------------------------------------------------- 735 Timescale n min max Q2.5 Q97.5 r95 δT95 med IQR µ* s* out95 out10 736 --------------------------------------------------------------------------- 737
T

741

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

742

T F all multic 106 2.5 250 4.2 100 24 1.37 24 27 25 2.14 5 1

743

--------------------------------------------------------------------------- Rows: same as in Table 1. Table S7): TF = TS ≠ TL.

787 788

  , which only involves internal time scales of the organisms and 110 is shorter than the time based on the comparison of different measurements, which depends on 111 Response times (revised version) Phys. Biol. Page 6

218copepodFigure 1 Page

 1 Figure 1 compares as boxplots the (log-transformed) timescales TF, TS and TL. Their relative

  dependence of simple response times on body mass M for the whole data set 237 encompassing life's major domains, we plotted the pairs (M, TS) in log-log plots for 81 species 238 (Fig. 2), including microorganisms in the mass range 10 -16 (bacterium) to 5×10 -13 kg (green alga) 239 and multicellular organisms from 3×10 -9 (spider) to 3860 kg (elephant). Fig. 2A distinguishes the 240 taxonomic groups whereas Fig. 2B distinguishes the types of responses. Overall, the mass M 241 varies by a factor of about 10 20 whereas 95 % of the TS values lie between 4.7×10 -3 and 0.31 s 242 (

  270 S6B) are not significantly different from 0 and -1 respectively, suggesting independence of 271 MSMR on mass and inverse dependence of TL on MSMR. Variability and Mass Dependency of Timescales 276 277

  311bacteria stands out owing to the proportion of variance it explains (81 %) and its steep slope 312 (α = 0.66) which agrees with first-principle derivations (section 5). For the flicker fusion time, the 313 mass exponent of the small-scale regressions are not significantly different from zero. Finally, for 314 the minimum time to move by one body length, the positive mass scaling exponent of mammals 315 stems from large masses (the inflection point near 50 kg is apparent in Fig.4), as noted and 316 interpreted by Meyer-Vernet andRospars (2016); we shall return to this point in section 5. 317 318 4.2. Possible Errors Resulting from Biological, Methodological and Experimental Factors 319 320 Are our data and analyses adequate for supporting our conclusion that the simple response time 321 TS lies within less than a factor of ten from the mean for organisms varying by more than 20 322 orders of magnitude in mass, as previously shown for the minimum time to move by one body 323 length TL (Meyer-Vernet and Rospars 2016)? That a similar finding holds for TF over the smaller 324 10 8 -fold mass range for which this time could be measured? And that these time scales display systematic variation with body mass in uni-and in multicellular organisms? Several 326 criticisms could be raised. 327 First, one could object that the diversity of organisms, of sensory and motor mechanisms, and 328 of experimental procedures hides any trend in the data. However, it is unlikely that the restriction 329 to more homogeneous data would reveal trends presently hidden because the smaller size of 330 samples would decrease the statistical significance. On the contrary, the diversity of species, 331 measurements and systems is indispensable to estimate reliably the variability and mean of the 332 timescales, independently of the specializations and limitations of taxa and systems. Our aim is to 333 transcend mass scalings holding within groups by considering large ranges of mass and 334 taxonomic groups.

347Page

  the time scales of ectotherms to a standard temperature θ0 = 20 °C would change our results (see 348 Methods). First, the temperature being unknown in several measurements, we considered the 349

  a wide range of mass and life forms have found organisms' properties to 368 lie in a relatively narrow range, without mass scaling across groups, despite the size scaling 369 observed within groups. This is the case for the mass-specific metabolic rate(Makarieva et al. 370 2008[START_REF] Hatton | Linking scaling 641 laws across eukaryotes[END_REF], its maximum value per unit of active mass[START_REF] Makarieva | Energetics of the smallest: do bacteria 668 breathe at the same rate as whales?[END_REF], the 371 cross-section-specific forces exerted by muscles and molecular motors[START_REF] Marden | Review: Scaling of maximum net force output by motors used for 678 locomotion[END_REF][START_REF] Marden | Molecules, muscles, and machines: universal performance 676 characteristics of motors[END_REF] Meyer-Vernet 2016), and the minimum time to move by one body 373 length TL = L/Vmax[START_REF] Mcmahon | On Size and Life[END_REF][START_REF] Meyer-Vernet | How fast do living organisms move: Maximum 690 speeds from bacteria to elephants and whales[END_REF], 2016). 374 However, for the simple response time TS and the critical flicker fusion time TF, previous 375 studies concern only relatively small mass ranges and we have included these data. The mass 376 scaling of sensorimotor delays has been studied by More and Donelan (2018) in the particular 377 case of the stretch reflex -a monosynaptic reflex that governs the fastest neural response to 378 peripheral stimuli in terrestrial mammals, with a determination of the different components and a 379 comparison with stance and stride durations. In our TS sample, we have used the sum of these 380 components except the force generation delay (time between force onset and peak), in coherence 381 with the rest of our data, for which the response is measured by the onset of force production or 382 the onset of movement (which can begin before the production of peak force). These data points 383 lie within the range of our general data set TS for multicellular organisms, where the nerve 384 conduction delay is expected to be mainly responsible for the increase of TS shown in figure 2 at 385 large mass. Indeed, the increase in nerve conduction speed due to increase in fibre diameter and 386 to myelination is too moderate to compensate for the increase in distance of conduction, because 387 of the trade-off between responsiveness and compactness (Castelfranco and Hartline 2016), 388 resolution (More et al. 2013), and energy cost (Perge et al. 2012). Let us compare the nerve 389 conduction delay estimated by More and Donelan (2018) Tcond = 5.3 M 0.3 ms to the geometric 390 mean (TS = 22 ms) that we find for multicellular species (

Page

  simple response time TS of microorganisms. It includes the transmission delay 410 from the sensor(s) receiving external stimuli to the motor apparatus producing the response by 411 regulating the swimming behaviour. A basic process is the transport of a signalling molecule 412 through the cytoplasm (e.g. Bitbol and Wingreen 2015) via diffusion (e.g., Purcell 1977, 413 Dusenberry 2009). In water, of viscosity η ≃ 10 -3 kg m -1 s -1 , a sphere of diameter d at 414 temperature θ has a diffusion coefficient D = kB θ/(3π η d), where kB is Boltzmann constant. 415 Signalling molecules are small proteins of typical size d ≃ 3 nm, like the key signalling protein 416 CheY (Bren and Eisenbach 2000), yielding a diffusion coefficient in water D ≃ 150 µm 2 /s. 417 Assuming that the crowding of the cytoplasm decreases D by one order of magnitude (e.g. Dill et 418 and Poolman 2011) and that the sensor-to-motor distance equals the organism's 419 length L, we find the three-dimensional diffusion time L²/6D 420 τdif ≃ 10 L µm ² ms.(1)421This timescale is the minimum response time TS of a microorganism of size L if information is 422 transmitted through the cytoplasm by diffusion of signalling proteins, which is the most basic 423

430

  Consider now multicellular organisms. For most of them, the responses are mediated by 431 conduction of information via electric pulses propagating through neurons, whose membrane 432 regulates the permeation of ions via an insulating lipid bilayer and proteins. The proteins act as 433 active ion channels and pumps and the lipid bilayer acts as a capacitance that enables charges to 434 accumulate and produce a potential across it. Biological membranes are also involved in sense 435 organs, via the concentration gradients they enable which produce active transport, whereas ion 436 channels play an essential role in signal transduction[START_REF] Martinac | Mechanosensory transduction: Focus on ion channels[END_REF]. The role of ions 437 to alter charge and thus protein conformation is essential in signal transduction in both uni-and 438 multicellular organisms[START_REF] Clapham | Calcium signaling[END_REF]. For example, paramecia use Ca 2+ ions and show 439 dynamic changes in the electrical properties of their membrane in response to stimuli, as do the structures of their receptors are similar to those of vertebrates (e.g. Maegawa 441 2017). 442 A tentative first principle estimate of TS can be obtained from the inverse of the number of 443 action potentials sent along an axon per second, since this is the shortest possible time to send a 444 bit of information along an axon. Let us first evaluate the cost of generating an action potential U 445 per surface S of membrane, of width a and dielectric constant εm, so that the capacitance is 446 C ≃ ε0 εm S/a, (2) 447 where ε0 is vacuum permittivity. With the electric charge across the membrane CU, of energy 448 CU 2 , the cost of an action potential is obtained from (2) as ε0 εm S U 2 /a, which agrees with values 449 in the literature (Aiello 2000). Using two biological properties common to living matter: the mass 450 density ρ ≃ 10 3 kg/m 3 and the maximum metabolic rate per unit mass of active tissue 451 bM ≃ 2×10 3 W/kg (Makarieva et al. 2005), the maximum power available to this surface S of power by the cost of an action potential estimated above and using the 455 energy corresponding to one monovalent ion crossing the membrane eU ≃ W0, where 456 e = 1.6×10 -19 C is the electron charge and W0 is the energy released by one ATP molecule, we 457 deduce the maximum number of action potentials per unit time, whose inverse yields 458 TS ≃ ε0εmW0 2 /(ρbM e 2 a 2 ) (4) 459 Substituting the typical dielectric constant of lipids εm ≃ 2, a membrane width a ≃ 6 nm -similar 460 to the typical protein size (e.g. Erickson 2009), the above value of bM, and the first-principles 461 relation (Meyer-Vernet and Rospars 2016) 462 W0 ≃ e²/(4πε0a) obtain TS ≃ 14 ms, close to the empirical mean simple response time TS of metazoans (

473

  consider again energy constraints. In an electrical circuit of resistance R, submitted to the 474 potential difference U, the power is U 2 /R. Using the maximum power available (3), we deduce 475 the resistance R ≃ U 2 /(bM ρ a S), whence the resistivity rm ≃ U 2 /(ρbM a 2 ). Using again the order 476 of magnitude U ≃ W0/e, we deduce τm, which yields the flicker fusion time TF ≃τm (reflecting the 477 ability of the membrane to resolve a time-varying signal) 478 TF ≃ ε0εmW0 2 /(ρbM e 2 a 2 ) ≃ TS ≃ 14 ms (7) 479 close to the empirical value of TF (25 ms), and in agreement with our empirical result TF ≃ TS. 480 The absence of significant increase of TF for the largest masses (Fig. 3), contrary to what is 481 observed for TS (Fig. 2) suggests that the signal conduction time and hence the organism length L 482 plays a minor role in TF, contrary to TS. magnitude estimate of the minimum time to move by one body length TL = L/Vmax 487 was derived by Meyer-Vernet and Rospars (2016) from the invariance over the whole domain of 488 life of the force per cross-sectional area exerted by molecular motors and muscles (f ≃ W0/a 3 ≃ 489 2×10 5 N/m², Rospars and Meyer-Vernet 2016), and the two basic quantities considered above, 490 mass density ρ and mass-specific (per unit mass of active tissue) metabolic rate at maximum 491 activity bM. The maximum speed was estimated as Vmax ≃ L ρ bM / f for swimming and running 492 organisms (including microorganisms) of length L satisfying L ≲ (f / ρ) 3/2 /bM ≃ 1.4 m -493 corresponding roughly to M ≃ 50 kg (Meyer-Vernet and Rospars 2016). This yields TL ≃ L/Vmax, 494 the minimum time to move by L 495 TL ≃ f / (ρ bM) ≃ W0 /(ρ bM a 3 ) ≃ 100 ms (8) 496

  Vernet and Rospars 2016), in agreement with the known maximum speed of about 15 501 m/s (e.g. McMahon and Bonner

543

  would be limited by sensory performance, so that in both cases, at least one component of the 544 nervous system would be out of tune and wasting energy or space[START_REF] Laughlin | Energy as a constraint on the coding and processing of sensory 661 information[END_REF]. Likewise, the 545 evolution is expected to favour organisms for which the sensory and response organs act fast 546 enough with respect to their moving performances. It is noteworthy that since the first-principle 547 estimate (8) of TL holds for both uni-and multi-cellular organisms (Meyer-Vernet and Rospars 548 2016), the estimate (1) of the minimal response time TS yields a maximal length L of a few 549 micrometres in order to ensure TS ≤ TL when the response is mediated by diffusion, as observed 550 for bacteria 551 These preliminary results encourage further research on the response times of mobile 552 organisms and their fundamental bases. They might also possibly be used to infer properties of 553 extinct species since the reconstructed speed (e.g. Hutchinson and Garcia 2002) and size (e.g. . 2011) of the giant dinosaur Tyrannosaurus rex yield a time to move by one 555 body length TL ≃ 1 s for a mass M ≃ 10 4 kg, which is close to the value expected from (9) and 556 would put Tyrannosaurus rex in the middle of the data of extent animals of this size in figure 4.

  ------------------------------------------------------------------------749 Rows: TS, simple response time; TF, flicker fusion time; TL, minimum time to move by one body 750 length. 751 Columns: n, number of species; minimum; maximum; Q2.5, percentile 2.5 %; Q97.5, percentile 752 97.5 %; r95, ratio Q97.5/Q2.5 including 95 % values; δT95 = log10(r25); med, median; IQR, 753 interquartile range; µ*, geometric mean (ms); s*, multiplicative standard deviation; out95, number 754 of values outside [Q2.5, Q97.5]; out10, number of values outside [µ*/10, µ*×10]. Dependence of timescales on body mass for unicellular, multicellular and all species 757 --------------------------------------------------------------------------------------------------------------------------------------------------765 T F all multic 106 -1.57 0.023 -0.01 0.06 -1.93 8.25 1.6 0.19 2 0.19 0 766 -----------------------------------------------------------------------------------------------------------------------------------------------------772

773

  Columns: n, number of species; log10T0, intercept of least square regression line, log10 T = log10T0 774 + α log10 M; α, allometric coefficient; [IC1, IC2], 95% confidence intervals of slope α; µM*, mean 775 log10M; δM, mass range of the category, δM = log10(Mmax/Mmin), with Mmax and Mmin masses of 776 heaviest and lightest species in the category; rα, fitted ratio Tmax/Tmin with Tmax = T0(Mmax) α and 777 Tmin = T0(Mmin) α ; δTα = log10 rα; r 2 , coefficient of determination (percent); P, p-value of test of 778 slope α = 0; Sig, slope α of regression line significantly different from zero (1) or not (0).

Figure 1 .

 1 Figure 1. Boxplots of log-transformed flicker fusion times TF, simple response times TS, and

  786

  Lm 3.04 which applies to fusiform

165 known or a more generic relationship, for example Mkg = 11.2 166 fishes (Froese et al. 2014; see other relationships in Meyer-Vernet and Rospars 2016). When no 167 indication was provided in the papers, we searched the average mass (or length) of the species in 168

Table

  S8b, second line, p < 10 -8 ). In both groups TL increases slightly with mass, since the 95 %

Table

1

, first line). Although very small, the slope of the regression line is significantly different 243 from zero (95 % confidence intervals [-0.065, -0.010], Table

2

), but as shown in Table

1

, this 244 effect results from the larger simple response times in single cells (µ* = 129 ms) than in 245 multicellular organisms (µ* = 22 ms). Since this difference is significant (Table

S8c

, first line, 246 p < 10 -3 ), the two groups must be studied separately. The scaling exponents α of the power law 247 regressions in both groups are not significantly different from zero with 95 % confidence 248 intervals [-0.41, 0.49] for single cells and [-0.01, 0.08] for multicellular organisms, whereas the 249 intercepts differ by more than one order of magnitude (Table

2 and Fig

2A). 250 Flicker fusion times TF could only be measured in multicellular organisms. Therefore, the 251 body mass of the 106 species shown in Figure 3 only varies from 2×10 -6 kg (fruit fly) to 354 kg 252 (sea turtle), representing over eight orders of magnitude, whereas 95 % of the TF values lie 253 between 2.5×10 -3 s and 0.25 s (

Table 1). No effect of body mass on TF could be evidenced, since 254 the power law regression is TF = 0.026M α (Fig 3), with α in the 95 % CI [-0.01, 0.06] (Table 2). 255 Response times (revised version) Phys. Biol. Page 12 The times to move by one body length at maximum speed TL (Meyer-Vernet and Rospars 256 2016, Fig. 4) concern 426 species including microorganisms from 10 -16 kg (bacterium) to 257 1.3×10 -8 kg (ciliate eukaryotic cell) and multicellular organisms from 10 -9 (copepod) to 1.4×10 5 258 kg (blue whale). So, M varies by 21 orders of magnitude whereas 95 % of the TL values lie 259 between 21×10 -3 and 0.71 s. The times TL in single cells (µ* = 145 ms) are twice longer and 260 more variable than in multicellular organisms (µ* = 69 ms), this difference being significant 261 (262 CI of the slope of the regression line α is [0.020, 0.14] for single cells and [0.028, 0.060] for 263 multicellular organisms (Table 2). However, the trend of the multicellular group results from the 264 largest vertebrates since for species under 50 kg the slope of the regression law α is not 265 significantly different from zero (95 % CI is [-0.030, 0.11] (Table

Table 2

 2

	), that

  The small variation of the visual resolution times is remarkable, given the Although outside the scope of this paper, we examined narrower mass ranges, i.e. groups of 304 related species of the same class (or kingdom in microorganisms) including more than three

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	305
	282
	283	geometric mean, whereas the mass varies by 20, 8, and 21 orders of magnitude for TS, TF and TL
	284	respectively. This is noteworthy, given the diversity of sensorimotor systems and the huge mass
		range, and suggests that these times are strongly constrained by physics, as was previously
	303
		Response times (revised version)	Phys. Biol.	Page 14

285

proposed for TL. 286 variation in spatiotemporal optical quality with eye size, which is correlated to body size (e.g. 287 Currea et al. 2018), and the large diversity of visual systems (e.g. Fernald 2000) and of strategies 288 of spatiotemporal summations. Although CFF is unrivaled to quantify the ability of an organism 289 to track a moving object, whether it is representative of other sensory systems is an open question 290 for further investigation. However, as suggested by a few reports (for example in olfaction, 291 Rumbo and Kaissling 1989, Lemon and Getz 1997, Smear et al. 2011, Jacob et al. 2017), 292 temporal resolution might reflect properties common to diverse neural networks rather than 293 specificities of the receptors (Butts et al. 2007, Panzeri et al. 2010) and, hence, be similar in the 294 visual and other sensory systems.

295

Most of the overall variability results from variations at smaller mass ranges. Within uni-and 296 multi-cellular organisms considered separately, the mass-scaling exponents are not significantly 297 different from zero or result from a small-scale trend (TL in large metazoans), so that the TL 298 (small) mass dependency in single cells appears as an exception that will need further data to be 299 interpreted. For TS and TL, differences between single cells and metazoans contribute to the 300 overall variability. The twice longer geometric mean of TL in single cells (Table

1

) is well 301 documented (n = 70 species) but the six times longer one of TS (n = 7) should be confirmed on a 302 larger sample.

Table 1

 1

	). This yields

  We have shown that across the whole of mobile life, from bacteria to large vertebrates, the simple 517 response time TS lies in a relatively narrow range, with 95 % of species reacting in a time that 518 differs by less than one order of magnitude from the mean, in striking contrast to the 20 orders of 519 magnitude difference in body mass. The simple response time does not display significant scaling It is fair to note that the agreement between these simple estimates of minimum time scales For example, one tenth of second is in the middle of the range of protein 537 folding time scales, which however spans six orders of magnitude (e.g.[START_REF] Lane | Inferring the rate-length law of protein folding[END_REF]

	Page 23 of 39	AUTHOR SUBMITTED MANUSCRIPT -PB-101280.R1 AUTHOR SUBMITTED MANUSCRIPT -PB-101280.R1	Page 22 of 39
	509 532	metabolic rate, as expected from (8) if the proportion of active tissue in the body mass does not tentative simple estimates of TS and TF based on fundamental physicochemical constants and
	510	vary in the range considered in the regression. basic properties common to motile organisms.
	511 534	Finally, it is noteworthy that Eqs. (4), (5) and (8) yield TL/TS ≃ 4π/εm ≃ 6 in order of
	512 535	magnitude, to be compared to the empirical ratio TL/TS = 78/26 = 3, suggesting that fast reacting (for sensing, for reacting and for moving) and the measurements is only indicative of the
	513 536	species are also fast moving. dominant constraints in play (e.g. Phillips and Milo 2009), since several mechanisms may be
	514	operating in parallel.
	515	6. CONCLUSIONS
	516
	520
	521	with body mass across groups in unicellular organisms nor in multicellular ones, although it is
	522	almost six times larger in the former life form. The absence of large-scale trend does not preclude
	523	-and is indeed compatible with various scalings valid in narrower ranges of size and taxa, as is
	524	known for the specific metabolic rate. However, within narrow ranges, the detailed characteristics
	525	of the organisms must be considered and it is only on larger scales that these variations can be
		transcended.
	527
	528	critical flicker fusion frequency for vision) TF, and is a few times smaller than the minimum time
	529	to move by one body length TL, with all time scales lying in a relatively narrow range. Since this
	508	narrow range suggests that these time scales may be strongly constrained by physics and basic
	531
		Response times (revised version) Response times (revised version)	Phys. Biol. Phys. Biol.	Page 23 Page 24

526

This simple response time TS is close to a well-studied sensory timescale (the inverse of the 530 properties of life, independently of the structure or mass of the organism, we have performed 533 538

and close to the maximal turn-over rate of the most abundant enzyme in the biosphere (e.g. 539

[START_REF] Flamholz | Revisiting trade-offs between Rubisco kinetic parameters 634[END_REF]

. The relation TS ≃ TF < TL found from the data (Fig.

1

) and tentatively 540 interpreted from first-principles, is reminiscent of symmorphosis

[START_REF] Weibel | The concept of symmorphosis: A testable 726 hypothesis of structure-function relationship[END_REF]

and 541 expected to be favoured by evolution since it is indicative of an optimum state. Indeed, if TS < TF 542 the sensory resolution would be in excess over motor control whereas if TS > TF the response

TABLE 1 .

 1 Summary statistics of timescales (in ms) for unicellular, multicellular and all species

	734