Synergetic impacts of turbulence and fishing reduce ocean biomass

A universal scaling relationship exists between organism abundance and body size1,2. Within ocean habitats this relationship deviates from that generally observed in terrestrial systems2–4, where marine macro-fauna display steeper size-abundance scaling than expected. This is indicative of a fundamental shift in food-web organization, yet a conclusive mechanism for this pattern has remained elusive. We demonstrate that while fishing has partially contributed to the reduced abundance of larger organisms, a larger effect comes from ocean turbulence: the energetic cost of movement within a turbulent environment induces additional biomass losses among the nekton. These results identify turbulence as a novel mechanism governing the marine size-abundance distribution, highlighting the complex interplay of biophysical forces that must be considered alongside anthropogenic impacts in processes governing marine ecosystems.


Abstract: 55
A universal scaling relationship exists between organism abundance and body size 1,2 . Within 56 ocean habitats this relationship deviates from that generally observed in terrestrial systems 2-4 , 57 where marine macro-fauna display steeper size-abundance scaling than expected. This is 58 indicative of a fundamental shift in food-web organization, yet a conclusive mechanism for this 59 pattern has remained elusive. We demonstrate that while fishing has partially contributed to the 60 reduced abundance of larger organisms, a larger effect comes from ocean turbulence: the 61 energetic cost of movement within a turbulent environment induces additional biomass losses 62 among the nekton. These results identify turbulence as a novel mechanism governing the marine 63 size-abundance distribution, highlighting the complex interplay of biophysical forces that must 64 be considered alongside anthropogenic impacts in processes governing marine ecosystems. 65 66 marine ecosystems, the exponent for this relationship often differs from that in terrestrial 74 ecosystems 2 . Life-history, trophic strategies, altered productivity, and fisheries are all proposed 75 to alter the scaling slopes of both species size-abundance distributions and individual size 76 spectra 2-4,6 . Here, we quantify, empirically and with an independent model, how fishing and 77 ocean turbulence cause qualitatively distinct breaks in the global marine size-abundance 78 distribution. 79 80 For the scaling analysis we compiled size-abundance data for 2179 species, ranging from viruses 81 to blue whales. Analyses were undertaken on a database built from primary literature and online 82 databases ( = 15,146 datapoints), with secondary verification undertaken using the manually 83 curated literature data alone ( = 1719) to ensure there was not systematic bias in the online 84 sources (Methods); additionally, fits were undertaken through a balanced subsampling routine to 85 ensure a diverse spread of species and sizes (Methods). As previously observed within individual 86 size spectra 3 , nonlinearity was apparent in the log-transformed global size-abundance plot 87 ( Figure 1a). This coincided with a statistically verified break in the scaling value at the plankton-88 nekton transition of ≃ 0.1 m ( = 0.08 m, 95% CI (0.06, 0.1)) (Methods). The marine virus to 89 marine invertebrate slope at = −0.77 is comparable to terrestrial slopes 7 . However, for 90 organisms ≥ 0.1 m was −1.9 (Figure 1a, Table 1 scales rather than mass/density; it is to be noted that as the transformation of both axes is the 106 same, the relationship between size and abundance remains unchanged (Methods). (a) Size 107 versus abundance for viruses to blue whales. There is a break in the scaling relationship at 0.1m. 108 Blue triangles represent plankton ranging from viruses to zooplankton and invertebrates. Green 109 squares are fished nekton, ranging from small fish to whales. Line (i) is the best fit to the scaling 110 To find the cause of the break in the marine size-abundance relationship, we note that fishing has 116 reduced the abundance of fish, pinnipeds, sea turtles and marine mammals by up to 99% 8 . We 117 corrected for this by adjusting the abundances of impacted populations to pre-human impact 118 estimates 8 . This caused a significant ( < 0.01) upward translation of the scaling line, removing 119 the step break in the dataset and corroborating earlier findings 5 . However, whilst the translation 120 is indicative of a decreased abundance of animals larger than 0.1 m, correcting for fishing did not 121 result in a change in exponent, rather just a vertical shift in the data ( Figure 1b, Table 1). The 122 size-abundance distribution may be interpreted as an average or upper bound on local population 123 densities 2 . The slope change is thus indicative of a constraint limiting nekton abundances which 124 is not present in planktonic or terrestrial systems. To probe for a mechanistic explanation of the 125 exponent change, we note that many aquatic organism scaling laws break at ≃ 0.1 m 6,9,10 ; this 126 size corresponds to the laminar-turbulent transition, where the change in the physical fluid 127 environment causally affects the biology 6,10 . We subsequently tested the hypothesis that the 128 change in scaling value is due to implicit and explicit costs associated with turbulence: that is, 129 nekton must expend energy actively moving to match planktonic prey distributions, and that this 130 expenditure propagates through higher trophic levels. 131 132 Aquatic predators and grazers are challenged by the chaotic nature of turbulence. As absolute 133 abundances of resources scale similarly in three-dimensional aquatic and two-dimensional 134 terrestrial environments 11 , their statistical distribution is scarcer in the three-dimensional ocean. 135 Plankton live within patches created by an interplay of physical and biological processes 12 . 136 Within these resource hotspots, plankton foraging and movement is localised and constrained 137 within the patch, allowing them to use hunting strategies such as chemotaxis or rheotaxis to 138 maximise their food acquisition 13,14 ; that is, plankton move passively with the turbulence that 139 creates the aggregations. Beyond several millimetres and up to ten centimetres is a transition 140 zone where eddies play an increasingly important role. Whilst they are below the swimming 141 speeds of most fish, eddies on the scale of tens to hundreds of metres cause bulk transport and 142 dispersal. Mesoscale eddies reach hundreds of kilometres in diameter and can move organisms 143 hundreds or thousands of kilometres 15 . Food may not be transported, or it may be consumed and 144 not replaced due to low light, low temperature or other unfavourable conditions 16 . Thus, nekton 145 must migrate between patches to feed, which are continually and unpredictably dispersed, 146 meaning they have resource encounter rates that typically cannot be bettered using local 147 information 17 . Nekton live at a scale where the foraging landscape is highly fragmented and 148 disordered due to these physical processes, and operate on biological timescales which are 149 significantly longer than eddy lifespans 16,18 . As they are trophically linked to the plankton, they 150 must actively work to overcome the dispersal, ultimately increasing their locomotory costs, 151 which also grow with prey size 19 . Short distance dispersal within or just beyond local habitats is 152 difficult to quantify. However, at a global scale, physical dispersal -and consequently the spatial 153 distribution of plankton -follows the Kolmogorov power law for the turbulent energy cascade 12 . 154 The overall effect is that dispersal, encoded here as the separation distance, is a key factor in 155 nekton survival. We propose that resource acquisition forces nekton movement to follow the 156 turbulence-driven distribution of plankton, increasing energy expenditure 20 , and consequently 157 reducing available energy for growth and reproduction, which decreases abundances. The 158 positioning of the break in the scaling relationship at the laminar-turbulent transition is consistent 159 with this reasoning. Testing the hypothesis that turbulence increased the nekton slope by 160 adjusting for the Kolmogorov power law, which affected small fish the least and large pelagics 161 the most, removed the structural break in the distribution and resulted in a near-canonical 162 exponent of = −0.73 for the entire distribution ( Figure 1d, Table 1). 163

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To build a minimal model which captures this phenomenon, we note other scaling breaks for 165 aquatic organisms 6 also occur at 0.1 m due to movement changes at the laminar-turbulent 166 transition 10 . The classical assumption that swimming is more energetically efficient than 167 running 21 does not consider drag, which increases with the square of velocity and carries extreme 168 metabolic cost 22,23 . Research examining cost of swimming may also underestimate real-world 169 metabolic effort for nekton as it frequently uses theoretically 'optimal' size-speed scaling 9 rather 170 than utilising empirical values which are steeper 6 . Finally, relative consumption rates are higher 171 in oceanic than terrestrial environments, yet a steeper inverse scaling of nekton abundances in 172 marine systems exists even at high resource densities 11 . This discrepancy has not been resolved 173 but indicates there must be a significant energetic cost associated with living and feeding in 174 oceanic environments that has not been considered. We incorporated classical formulations of 175 swimming cost for organisms living in laminar and turbulent environments, together with 176 foraging effort, into a size-dependent predator-prey model to assess these effects ( Figure 2). In 177 short, we expand the trophic transfer efficiency parameter, , in the classical Rosenzweig-178 MacArthur predator-prey model to account for energy diversion toward locomotion (Equation 1). 179 As our model includes a parameter for resource density, direct impacts of overfishing may also 223 be incorporated. We find that whilst heavy fishing could theoretically perturb the size-abundance 224 scaling value by decreasing resource saturation , the search effort multiplier is 225 ~0.17 (relative to mass). This means it is a slow parameter, which also reaches an asymptotic 226 value as → 0. Hence, whilst fishing removes biomass, our integrated model indicates it could 227 only perturb the size-abundance scaling law by ≈ −0.2 before the asymptote is reached. This is 228 an order of magnitude less impact than turbulence effects, and entirely consistent with what we 229 observe with our data (Table 1). 230 231 a b A complicating factor with our analysis is that organisms and biomes are not fixed physical or 232 chemical variables. Their characteristics can change in response to environmental pressures. 233 Ecosystem-wide size shifts in size-abundance relationships may be exacerbated by compensatory 234 genetic changes, particularly when they have occurred under strong selection pressures such as 235 fishing. Such a fisheries-induced evolution (FIE) causes further size reduction and earlier 236 maturation age 26 , which could alter the scaling relationship. To assess the relative impact of FIE, 237 we extracted data from 113 time series for 10 commercially exploited species of fish, and 238 assessed global changes in size and age at maturation. There was a mean decline of 11% in size 239 or age at maturity, when accounting for gender, species, and length of study (Methods). The 240 results from 10 of the 14 studies led to the conclusion that these changes were attributable to 241 fishing pressure 26 . In considering FIE's contribution to universal size-abundance scaling, the 242 breadth and size of our dataset gives insight into the signal-to-noise ratio for this problem. It 243 would be extremely challenging to detect shifts in a global scaling law over the restricted size 244 range of 0.1 to 2 m used for FIE impacts. While prior research suggests that FIE can perturb 245 local scaling properties 27 , we argue an 11% impact (or even significantly greater) would not be 246 enough to shift the global size-abundance scaling value of nekton by −1 or more. We conclude 247 that scaling alterations occurring due to FIE would be small relative to the turbulence effect 248 explored in this paper. 249 250 Global size-abundance laws provide a different form of ecological insight to that given by local 251 scaling behaviour, as they capture macroscale, aggregate processes rather than examining small-252 scale drivers such as inter-and intra-specific trait variation 2 . In this context, we introduce 253 turbulence, and its impact on energy and movement cost for large organisms, as a novel but 254 important process to consider for ocean ecosystems. Climate change impacts have the potential 255 to exacerbate these costs, as current and predicted increases in ocean surface energy 28 will 256 increase nekton foraging and locomotion costs 29 , whilst warming temperatures increase 257 respiration rates, reduce global primary productivity 30 , and cause greater resource patchiness 31 , 258 forcing increased movement cost. Turbulence may thus reduce the capacity of nekton to 259 withstand fishing pressure as we begin to observe oceanic anthropogenic impacts classically 260 associated with terrestrial systems, including loss of large apex predators, shifts to smaller size, 261 and a faster onset of sexual maturity. We propose that a deeper understanding of the role 262 physical mechanistic processes play in structuring marine ecosystems will be necessary when 263 formulating strategies to preserve biodiversity and retain the productivity of ocean resources in

Data sourcing and aggregation 353
To assess the size-abundance scaling relationship, we examined data for over 2100 species, 354 encompassing over 800 genera (bacteria/viruses excluded from diversity counts) (Extended Data, 355 Table S1, S7). For quality purposes, we undertook analysis with two datasets. The first was 356 manually curated from over 200 articles to ensure there was not systematic bias within database 357 sources, and consists of 1719 size-abundance pairs across 700+ species (Extended Data, Table  358 S1). The second dataset expands on the first via the inclusion of a further 13,455 entries 359 predominantly sourced from online databases, for a total of 15,174 data points (Extended Data, 360 Table S7). Five databases were used: IMOS (flow cytometry and zooplankton) 32,33 , Tara Oceans 361 (flow cytometry) 34 , Phytobase 35 for phytoplankton, a global diatom database 36 , and a reef fish 362 dataset 37 . Size data was taken from the same source as the abundance data, or if it was not 363 included, we assigned the average adult size for that taxon referenced from WoRMS 38 , 364 fishbase 39 , or (36) for diatoms. All database entries which dated pre-2000 were removed to 365 reduce the chance of methodological/quality control problems being introduced from older data. 366 For Phytobase entries, any data with the flags 'unrealistic day or year' and 'presumably 367 sedimentary' were deleted; we note this particular database is otherwise well suited to this 368 application as capturing local diversity patterns is not critical for global size density analyses 2 . 369 For the flow cytometry data, any entries which had not undergone or passed quality control 370 checks were removed. 371 372 Next, we outline pooling information for taxonomic/sampling groups. For most nekton, 373 abundance estimates were given at the species level, with the exception of hard-to-differentiate 374 taxa, e.g. striped/common dolphins. Unless the data had been provided that way by the primary 375 source, no averaging or grouping was undertaken. For bacterial and viral abundances, we elected 376 to use flow cytometric data rather than DNA-based methods, as the high variance in copy 377 numbers of marker genes in prokaryotes precludes reliable estimates. (Note that size 378 measurements for bacteria and viruses were given by microscopy-based sources, not flow 379 cytometry.) In addition, defining 'species' grouping is inherently problematic for microbes. No 380 manually curated data was aggregated unless that was its original format. For the databases, we 381 pooled according to the following principles. Firstly, we took taxa abundance averages by year 382 and location. A single location was taken to be one station, or the same degree of 383 latitude/longitude. We averaged at the lowest available taxonomic level (usually genus for 384 organisms <5E-4m, and species for anything larger), and selected taxa which, together, provided 385 >90% of the total abundance of that sample to avoid skewing with singletons; this also aligns 386 with the principle of size-abundance distributions often being representative of abundance 387 average or upper bounds 2 . The exceptions to this pooling rule were for targeted flow cytometry 388 counts of abundant cyanobacteria (Prochlorococcus, Synechococcus), which we included as is. 389 390 Abundance data is localised, hence spatial and temporal variation across local snapshots captures 391 natural variability of populations across space and time. Therefore, the inclusion of data from 392 different environments, e.g. tropical/temperate, or low/high biomass regions, or across different 393 sampling efforts, is suitable -and even desirable -as the goal is to build the universal 394 distribution, which should ideally contain a broad spread of data 2 . Given the similarity between 395 the manually curated and complete database results, and the generally well-behaved nature of the 396 model statistics (Figures S1-S3), we elected not to transform or apply other corrections to the 397 data. We acknowledge there is certainly variance introduced from species trait differences, and 398 potentially from inconsistencies from underlying experimental methods. However, these impacts 399 would remain with noise factor of this dataset. Furthermore, whilst more targeted studies can be 400 sensitive to this variance due to scaling size range and data limitations (e.g. bony fish, at ~3 401 orders of mass magnitude) 2 , fitting the scaling exponent over 23 orders magnitude, with this 402 quantity of aggregated data, drastically mitigates the effect of any one source of error. Notably, 403 the noise was sufficiently low for a strong statistical signal without the need for any 404 manipulation, which could introduce other errors or biases, and reduce transparency of the result. 405

Standardisation and units 406
Due to the large mass range (> 23 orders of magnitude), measuring uncertainty in the body mass 407 of microorganisms 40 , and to ensure units were consistent in downstream analyses, we used body 408 length, (m), as the measure of organism size. To accurately compare data sets where abundance 409 measurements were presented either as species numbers per unit volume or per unit area, and to 410 account for organism behaviour, we calculated the separation distance, (m), between 411 organisms as a proxy measurement for abundance. To calculate separation distances, it was 412 assumed the spatial distribution of organisms followed a Poisson distribution. Thus, the 413 separation distance for organisms where abundance was measured per unit area was given by 414 = "* + ⁄ , and per unit volume, = "* -⁄ . Under the assumption that organism mass is 415 approximately proportional to organism volume, the transformation of both axes in the size-416 abundance plot is the same. Therefore, our standardisation to length does not change the 417 empirical scaling values, nor does it disproportionately impact one part of the distribution, but 418 instead ensures consistency with units in the physics-based processes and derivations used in the 419 analyses. We acknowledge that organism mass and length generally do not have a perfect cube 420 root relationship. However, this is a standard transformation utilised when investigating 421 bioenergetics of swimming organisms 9 ; we also note that any deviation from a cube root 422 relationship would be applicable across the full distribution and therefore not change the key 423 outcomes of our analysis relating to the structural break. 424

425
We now discuss the raw data and the potential errors that may have arisen due to this 426 standardisation. Plankton data was near universally presented by volume; we note that plankton 427 distributions are by definition patchy and this variance far exceeds that of methodological error. 428 Volume-based measurements in the reef fish dataset were based on study areas <30m deep and 429 already undergone significant quality controls for accuracy; we did not undertake any further 430 corrections. We assumed volume-based data for small nekton in the manually curated literature 431 data did not require further adjustments. We acknowledge some small amount of error may have 432 been introduced under this assumption in the event that depths were incorrectly measured, but 433 note that (a) in the context of incorrectly measured depths, the cube root transformation reduces 434 the impact of that error and (b) the data covers approximately 0.5 of an order of (length) 435 magnitude, meaning that impacts on the full distribution would be minimal, particularly after 436 log-transformation. For marine megafauna, only studies using standard methodologies according 437 to transect/aerial surveys were included. It is to be noted that most of the length-or area-based 438 abundance measurements in the dataset were aerial survey data of marine mammals, and not of 439 benthic organisms. 440

Power law model fitting methods 441
To determine the scaling relationship across the dataset, organism length was plotted against the 442 inverse of the separation distance 1⁄ (m -1 ) on a logarithmic scale, so that ∝ ". , where is a 443 scaling exponent. Note that we consider a global, bivariate, size-abundance distribution more 444 commonly applied in terrestrial settings, and not the univariate size distribution often studied in 445 aquatic environments 2 . As the data is bivariate, the methods developed for univariate distribution 446 fits are not directly applicable 41 . Regression methods are standard for the bivariate case, and may 447 be used provided the dependent variable contains higher measurement error than the independent 448 variable 42 . Therefore, following a residuals analysis, the models for plankton and nekton were 449 fitted using ordinary least squares on the log-transformed data (residuals plots provided in 450 Figures S1-S2). For the fits, a balanced subsampling routine was used to ensure an even spread 451 of data across the distribution and improve fit quality 43 . We did not use a naive with-replacement 452 bootstrapping routine as this would simply bias the sampling towards whichever data (taxa 453 and/or sizes) were most frequent in our database. Furthermore, as large databases typically had 454 large groups of data clustered together (e.g. Figure 1a, where various clumps of data may be 455 observed), subsampling mitigated against one database, taxon, or size class dominating the fit. 456 The data was stratified by organism sizes, and by taxa. We then randomly sampled data points 457 (without replacement) such that the quantity of data per (log)bin was uniform across the full size 458 range and balanced the probabilities of sampling from different taxonomic groups. The optimal 459 subsampling size is denoted by = / , where is the size of the dataset being drawn from, 460 = 3, and = 0.5 (43, 44). We then generated 10,000 parameter estimates for each model, 461 where each estimate was created from subsampled data, for the laminar regime < 0.1, turbulent 462 regime ≥ 0.1, or complete size range. Percentile confidence intervals (95%) were created from 463 the bootstrapped statistics. Representative linear model statistics are available in Tables S5-S6,  464 and bootstrap histograms in Figure S3. For the -estimates from the Rosenzweig-Macarthur 465 simulated data, we randomly generated datapoints (matching the empirical subsample sizes) 466 for the laminar, turbulent, and full size ranges. Confidence intervals were generated from fitted 467 linear models on 10,000 model runs for each -estimate. 468

469
Structural break 470 We used MATLAB's fminbnd function to find the segmented regression breakpoint which 471 minimised MSE. This was bootstrapped for a percentile-based confidence interval on log-472 transformed, subsampled data (sampling method as for regressions). 473

474
Correction for Fishing 475 To investigate the impact of fishing on the observed scaling relationships, organisms were 476 assigned to groups of impacted large marine animals according to standard conventions 8 . These 477 included organisms such as fish, sharks, pinnipeds, whales, sea turtles and sea birds. Separation 478 distances were corrected for each group to reflect theoretical historical abundance values, 479 assuming losses ranging between 50 and 99.7% 8,45 . Where no specific loss estimate was 480 available, the mean decline for all large marine species (89%) was allocated 8 . 481 482 483 484 size was given by (standardised) length in m and abundance was defined as organisms per meter 508 ( . m "* ), i.e. the inverse of separation distance, rather than mass (kg) and biomass (density, 509 kg. m "-). The base ordinary differential equation contains strictly positive parameters and is 510 where and are resource and consumer (predator) abundances, respectively. The parameter ℎ 514 denotes the half saturation, whereas is the carrying capacity, and are birth and death rates, 515 the conversion efficiency, and the maximal consumption rate. 516 517 Each of the parameters follows scaling models according to the size ( , m) of the resource ( 2 ) or 518 consumer ( 3 ), such that = 4 5 ! , for some parameter , coefficient 4 and exponent 6 . Scaling 519 properties can change according to factors such as primary production rates, temperature, habitat 520 complexity, among many others 3 . A constant temperature was assumed, and resource-consumer 521 size ratios between 0.01 and 0.5 (corresponding to prey-predator mass ratios of 1E-6 and 0.1 522 respectively), as scaling laws can change when the predator is smaller than the prey. Exponents 523 were given by representative values from previous research, which was typically specialised on 524 deriving empirical scaling for that specific parameter (Extended Data, Table S2). As our dataset 525 ranges over more than 23 orders of mass magnitude, where there was some variability across 526 literature scaling models, our study used the exponent values which were most consistent across 527 the size range. Values chosen were (i) frequently reported with consensus ( , , 7 , ), (ii) mid-528 range (ℎ) or (iii) specifically calculated for aquatic vertebrates ( 8 ). Noting that rate-related 529 parameters ( , , 7,8 ) will scale faster with length than mass, the scaling values are given as 530 follows: = 4 2 "4.;1 ; = 4 2 "4.;1 ; ℎ = ℎ 4 3 "4.;1 ; 7 =  Table S2 for more information. 544

545
The parameter scaling coefficients were standardised against phytoplankton/zooplankton models 546 to ensure the boundary value for primary producers was feasible. The smallest primary producer 547 (i.e. 0.7 − 1 m in length) was assumed to be the cyanobacterium Prochlorococcus 51 . For 548 coefficients, biomass was divided by species mass to obtain the number of organisms. Model 549 equilibria were calculated using analytical formulae solutions. 550

Locomotion cost: biophysics derivations for the model 552
To derive the biophysics portion of the model we integrate models across several disciplines. We 553 use scaling of mass throughout this section to remain consistent with the literature, unless 554 otherwise specified. To account for movement cost in the Rosenzweig-MacArthur system, we 555 consider locomotion energy budgets across the whole size range (bacteria to whales). If 556 movement energy usage scales equivalently to basal metabolic processes, its impacts would not 557 be noticeable. However, if it scales differently, some of the energy previously used to create new 558 biomass would instead be diverted to locomotion. Alternately, if locomotion were to become 559 more efficient, additional energy could be provided for biomass. This can be seen by examining 560 the gross metabolic power of an organism: 561 Normalising by CDBDE results in: 563 If there is a discrepancy between the power exponents, the (relative) locomotory power 565 consumption will change across the size distribution. 566 567 This deviation can be captured within the parameter for biomass transfer efficiency . To achieve 568 this, we use a classical ecological relation, which links basal and locomotory metabolic cost to 569 abundance 24,52 : 570 In this master equation, is the population abundance, and is the relative transport cost 572 scaling. We have ∶= − , where is basal metabolic scaling, and is the scaling of transport 573 cost ( ) ) defined below. The term ( − ) describes search effort, including , swim speed 574 scaling, and the parameters and , which describe density/fragmentation and dimensionality of 575 the resource space. Note that if the term -+ ( − ) equates to zero, classical population 576 dynamics apply. That is, the standard Rosenzweig-MacArthur system, with a typical value of 577 e.g. the prey-predator size ratio. However, when it is non-zero, it captures the shift in locomotion 578 energy allocation across the size distribution. This provides the following relationship for : 579 In the subsequent derivations for the exponents of , we use empirical swim speed scaling results 581 from Andersen et al.'s (2016) review of marine scaling laws: 1/4 and 1/6 for viscous and inertial 582 swimmers respectively. This is important because it suggests the scaling of real-world nekton 583 swimming speed is steeper than what would be theoretically derived for maximum efficiency. 584 'Optimal' speed scaling would be given as 5/24 and 1/12 for viscous and inertial regimes 585 The parameter is the scaling of swimming speed. The dimensionality of the space, , is taken 591 as 3 for the turbulent regime. In the laminar/viscous regime, we consider = I = 2.4, to 592 account for the patch constraint and the fact that organisms can use local information to optimise 593 their hunting strategies 24 . We set the fractal dimension of the space, , to a mid-range value of 594 1.9 24 . 595 596 Transport cost scaling ( , ) 597 In this section, and denote the viscosity and density of the liquid respectively. Fishing-induced evolution 630 Fishing-induced evolution (FIE), specifically, quantifying phenotypic change, was assessed by 631 extracting size/age at maturity data from 113 time series taken from 15 studies (Extended Data, 632 Table S3). In some cases, this was provided as probability norms of weight or length at 50% 633 maturity (Wp50 or Lp50). Time-series with large gaps or fewer than 20 measured time points 634 were excluded. Data was manually extracted using WebPlotDigitizer (v 3.12) and visually 635