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Acoustic measurementsA set of acoustic echo sounder data was used to analyze fish density. This was collected within the Mycto-3D-MAP program using split-beam echo sounders at 38 and 120 kHz. The Mycto-3D-MAP program included multiple large-scale oceanographic surveys during 2 years and a dedicated cruise in the Kerguelen area. The dataset was collected during 4 large-scale surveys in 2013 and 2014, both in summer (including both northward and southward transects) and in winter, corresponding to 6 acoustic transects of 2860 linear kilometers (see Table 1 for more details). Note that all legs except summer 2014 (MYCTO-3D-Map cruise) were logistic operations, during which environmental in situ data (such as temperature or salinity profiles) could not be collected. The data were then treated with a bi-frequency algorithm, applied to the 38 and 120 kHz frequencies (details of data collection and processing are provided in37). This provides a quantitative estimation of the concentration of gas-bearing organisms, mostly attributed to fish containing a gas-filled swimbladder in the water column38. Most mesopelagic fish present swimbladders and several works pointed out that myctophids are the dominant mesopelagic fish in the region39. Therefore, we considered the acoustic signal as mainly representative of myctophids concentration. Data were organized in acoustic units, averaging acoustic data over 1.1 km along the ship trajectory on average. Myctophid school length is in the order of tens of meters40. For this reason, acoustic units were considered as not autocorrelated. Every acoustic unit is composed of 30 layers, ranging from 10 to 300 meters (30 layers in total).The dataset was used to infer the Acoustic Fish Concentration (AFC) in the water column. We considered as AFC of the point ((x_i), (y_i)) of the ship trajectory the average of the bifrequency acoustic backscattering of 29 out of 30 layers (the first layer, 0-10 m, was excluded due to surface noise) AFC quantity is dimensionless.As the previous measurements were performed through acoustic measurements, a non-invasive technique, fishes were not handled for this study.Table 1 Details of the acoustic transects analyzed.Full size tableRegional data selectionThe geographic area of interest of the present study is the Southern Ocean. To select the ship transects belonging to this region, we used the ecopartition of41. Only points falling in the Antarctic Southern Ocean region were considered. We highlight that this choice is consistent with the ecopartition of42 (group 5), which is specifically designed for myctophids, the reference fish family (Myctophidae) of this study. Furthermore, this choice allowed us to exclude large scale fronts (i.e., fronts that are visible on monthly or yearly averaged maps) which have been the subject of past research works43,44. In this way our analysis is focused specifically on fine-scale fronts.Day-night data separationSeveral species of myctophids present a diel vertical migration. They live at great depths during the day (between 500 and 1000 m), ascending at dusk in the upper euphotic layer, where they spend the night. Since the maximal depth reached by the echo sounder we used is 300 m, in the analysis reported in Figs. 2 and 3 we excluded data collected during the day. However, their analysis is reported in SI.1. A restriction of our acoustic analyses to the ocean upper layer is also consistent with the fact that the fine-scale features we computed are derived in this work by satellite altimetry, thus representative of the upper part of the water column ((sim 50) m). Finally, we note that the choice of considering the echo sounder data in the first 300 m of the water columns is coherent with the fact that LCS may extend almost vertically in depth even at 600 m depth45,46 and with the fact that altimetry-derived velocity fields are consistent with subsurface currents in our region of interest down to 500 m20.Satellite dataVelocity current data and Finite-Size Lyapunov Exponent (FSLE) processing. Velocity currents are obtained from Sea Surface Height (SSH), which is measured by satellite altimetry, through geostrophic approximation. Data, which were downloaded from E.U. Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu/), were obtained from DUACS (Data Unification and Altimeter Combination System) delayed-time multi-mission altimeter, and displaced over a regular grid with spatial resolution of (frac{1}{4}times frac{1}{4}^circ) and a temporal resolution of 1 day.Trajectories were computed with a Runge-Kutta scheme of the 4th order with an integration time of 6 hours. Finite-size Lyapunov Exponents (FSLE) were computed following the methods in14, with initial and final separation of (0.04^circ) and (0.4^circ) respectively. This Lagrangian diagnostic is commonly used to identify Lagrangian Coherent Structures. This method determines the location of barriers to transport, and it is usually associated with oceanic fronts9. Details on the Lagrangian techniques applied to altimetry data, including a discussion of its limitation, can be found in10.Temperature field and gradient computation The Sea Surface Temperature (SST) field was produced from the OSTIA global foundation Sea Surface Temperature (product id: SST_GLO_ SST_L4_NRT_OBSERVATIONS_010_001) from both infrared and microwave radiometers, and downloaded from CMEMS website. The data are represented over a regular grid with spatial resolution of (0.05times 0.05^circ) and daily-mean maps. The SST gradient was obtained from:$$begin{aligned} Grad SST=sqrt{g_x^2+g_y^2} end{aligned}$$where (g_x) and (g_y) are the gradients along the west-east and the north-south direction, respectively. To compute (g_x), the following expression was used:$$begin{aligned} g_x=frac{1}{2 dx}cdot (SST_{i+1}-SST_{i-1}) end{aligned}$$where the SST values of the adjacent grid cells (along the west-east direction: cells (i+1) and (i-1)) were employed. dx identifies the kilometric distance between two grid points along the longitude (which varies with latitude). The definition is analog for (g_y), considering this time the north-south direction and (dysimeq 5) km (0.05(^circ)).Chlorophyll field Chlorophyll estimations were obtained from the Global Ocean Color product (OCEANCOLOUR_ GLO_CHL_L4_REP_OBSERVATIONS_009_082-TDS) produced by ACRI-ST. This was downloaded from CMEMS website. Daily observations were used, in order to match the temporal resolution of the acoustic and satellite observations. The spatial resolution of the product is 1/24(^{circ }).Estimation of satellite data along ship trajectory For each point ((x_i), (y_i)) of the ship trajectory, we extracted a local value of FSLE, SST gradient, and chlorophyll concentration. These were obtained by considering the respective average value in a circular around of radius (sigma) of each point ((x_i), (y_i)) . Different (sigma) were tested (ranging from 0.1(^circ) to 0.6(^circ)), and the best results were obtained with (sigma =0.2^circ), reference value reported in the present work. This value is consistent with the resolution of the altimetry data.Statistical processingFront identification FSLE and SST gradient were used as diagnostics to detect frontal features, since they are typically associated with front intensity and Lagrangian Coherent Structures10. Note that the two diagnostics provide similar but not identical information. FSLEs are used to analyze the horizontal transport and to identify material lines along which a confluence of waters with different origins occur. These lines typically display an enhanced SST gradient because water masses of different origin have often contrasted SST signature. However, this is not a necessary condition. FSLE ridges may be invisible in SST maps if transport occurs in a region of homogeneous SST. Conversely, SST gradient unveils structures separating waters of different temperatures, whose contrast is often – but not always – associated with horizontal transport. Therefore, even if they usually detect the same structures, these two metrics are complementary. Frontal features were identified by considering a local FSLE (or SST gradient, respectively) value larger than a given threshold. The threshold values have been chosen heuristically but consistently with the ones found in previous works. For the FSLEs, we used 0.08 days(^{-1}), a threshold value in the range of the ones chosen in18 and47. For the SST gradient, we considered representative of thermal front values greater than 0.009({^circ })C/km, which is about half the value chosen in47. However, in that work, the SST gradient was obtained from the advection of the SST field with satellite-derived currents for the previous 3 days, a procedure which is known to enhance tracer gradients.Bootstrap method The threshold value splits the AFC into two groups: AFC co-located with FSLE or SST gradient values over the threshold are considered as measured in proximity of a front (i.e., statistically associated with a front), while AFC values below the threshold are considered as not associated with a frontal structure. The statistical independence of the two groups was tested using a Mann-Whitney or U test. Finally, bootstrap analysis is applied following the methodologies used in47. This allows estimating the probability that the difference in the mean AFC values, over and under the threshold, is significant, and not the result of statistical fluctuations. Other diagnostics tested are reported in SI.1.Linear quantile regression Linear quantile regression method48 was employed as no significant correlation was found between the explanatory and the response variables. This can be due to the fact that multiple factors (such as prey or predator distributions) influence the fish distribution other than the frontal activity considered. The presence of these other factors can shadow the relationship of the explanatory variables (in this case, the FSLE and the SST gradient) with the mean value of the response variable (the AFC). A common method to address this problem is the use of the quantile regression48,49, that explores the influence of the explanatory variables on other parts of the response variable distribution. Previous studies, adopting this methodology, revealed the limiting role played by the explanatory variables in the processes considered50. The percentiles values used are 75th, 90th, 95th, and 99th. The analysis is performed using the statistical package QUANTREG in R (https://CRAN.R-project.org/package=quantreg, v.5.3848,51), using the default settings.Chlorophyll-rich waters selection The AFC observations were considered in chlorophyll-rich waters if the corresponding chlorophyll concentration was higher than a given threshold. All the other AFC measurements were excluded, and a linear regression performed between the remaining AFC and FSLE (or SST gradient) values. The corresponding thresholds (one for FSLE and one for SST gradient case) were selected though a sensitivity test reported in SI.1. These resulted in 0.22 and 0.17 mg/m(^3) for FSLE and for SST gradient, respectively. These values are consistent among them and, in addition, they are in coherence with previous estimates of chlorophyll concentration used to characterise productive waters in the Southern Ocean (0.26mg/m(^3)52).Gradient climbing modelAn individual-based mechanistic model is built to describe how fish could move along frontal features. We assume that the direction of fish movement along a frontal gradient is influenced by the noise of the prey field (SI. 2). Specifically, we consider a Markovian process along the (one dimensional) cross-front direction. Time is discretized in timesteps of length (varDelta tau). We presuppose that, at each timestep, the fish chooses between swimming in one of the two opposite cross-front directions (“left” and “right”). This decision depends on the comparison between the quantity of a tracer (a cue) present at its actual position and the one perceived at a distance (p_R) from it, where (p_R) is the perceptual range of the fish. We consider the fish immersed in a tracer whose concentration is described by the function T(x).An expression for the average velocity of the fish, (U_F(x)), can now be derived. We assume that the fish is able to observe simultaneously the tracer to its right and its left. Fish sensorial capacities are discussed in SI.2. The tracer observed is affected by noise. Noise distribution is considered uniform, with (-xi _{MAX}{tilde{T}}(x_0-varDelta x)), the fish will move to the right, and, vice versa, to the left. We hypothesize that the observational range is small enough to consider the tracer variation as linear, as illustrated in Fig. S7 (SI. 3). In this way:$$begin{aligned}&{tilde{T}}(x_0+varDelta x)=T(x_0)+ p_R,frac{partial T}{partial x}+xi _1 \&{tilde{T}}(x_0-varDelta x)=T(x_0)- p_R,frac{partial T}{partial x}+xi _2 ;. end{aligned}$$In case of absence of noise, or with (xi _{MAX}p_R,frac{partial T}{partial x}). If (T(x_0+varDelta x) >T(x_0-varDelta x)) (as in Fig. S7), and the fish will swim leftward if$$begin{aligned} xi _1-xi _2 >2p_R,frac{partial T}{partial x}; . end{aligned}$$Since (xi _1) and (xi _2) range both between (-xi _{MAX}) and (xi _{MAX}), we can obtain the probability of leftward moving P(L). This will be the probability that the difference between (xi _1) and (xi _2) is greater than (2p_R,frac{partial T}{partial x})$$begin{aligned} P(L)&=frac{1}{8xi _{MAX}^2} bigg (2 xi _{MAX} – 2 p_R,frac{partial T}{partial x}bigg )^2\&=frac{1}{2} bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2 end{aligned}$$.The probability of moving right will be$$begin{aligned} P(R)&=1-P(L) end{aligned}$$and their difference gives the frequency of rightward moving$$begin{aligned} P(R)-P(L)&=1-2P(L)=1-bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2\&=frac{p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg ); , end{aligned}$$where the absolute value of (frac{partial T}{partial x}) has been added to preserve the correct climbing direction in case of negative gradient. The above expression leads to:$$begin{aligned} U_F(x)=frac{V p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg );. end{aligned}$$
(1)
We then assume that, over a certain value of tracer gradient (frac{partial T}{partial x}_{MAX}), the fish are able to climb the gradient without being affected by the noise. This assumption, from a biological perspective, means that the fish does not live in a completely noisy environment, but that under favorable circumstances it is able to correctly identify the swimming direction that leads to higher prey availability. This means that$$begin{aligned} p_R*frac{partial T}{partial x}_{MAX}=xi _{MAX},. end{aligned}$$
(2)
Substituting then (2) into (1) gives:$$begin{aligned} U_F(x)=V frac{frac{partial T}{partial x}}{frac{partial T}{partial x}_{MAX}}bigg (2-frac{big |frac{partial T}{partial x}big |}{frac{partial T}{partial x}_{MAX}}bigg );. end{aligned}$$
(3)
Finally, we can include an eventual effect of transport by the ocean currents, considering that the tracer is advected passively by them, simply adding the current speed (U_C) to Expr. (3).The representations provided are individual based, with each individual representing a single fish. However, we note that all the considerations done are also valid if we consider an individual representing a fish school. (U_F) will then simply represent the average velocity of the fish schools. This aspect should be stressed since many fish species live and feed in groups, especially myctophids (see SI.2 for further details).Continuity equation in one dimension The solution of this model will now be discussed. The continuity equation is first considered in one dimension. The starting scenario is simply an initially homogeneous distribution of fish, that are moving in a one dimensional space with a velocity given by (U_{F}(x)).We assume that in the time scales considered (few days to some weeks), the fish biomass is conserved, so for instance fishing mortality or growing rates are neglected. In that case, we can express the evolution of the concentration of the fish (rho) by the continuity equation$$begin{aligned} frac{partial rho }{partial t}+nabla cdot mathbf{j },=,0 end{aligned}$$
(4)
in which (mathbf{j }=rho ;U_{F}(x)), so that Eq. (4) becomes$$begin{aligned} frac{partial rho }{partial t}+nabla cdot big (rho ;U_{F}(x)big ),=,0;. end{aligned}$$
(5)
In one dimension, the divergence is simply the partial derivate along the x-axis. Eq. (5) becomes$$begin{aligned} frac{partial rho }{partial t}=-frac{partial }{partial x} bigg (rho ;U_{F}bigg ) end{aligned}$$
(6)
Now, we decompose the fish concentration (rho) in two parts, a constant one and a variable one (rho ,=,rho _0+{tilde{rho }}). Eq. (6) will then become$$begin{aligned} frac{partial rho }{partial t}=-U_Ffrac{partial {tilde{rho }}}{partial x}-rho frac{partial U_F}{partial x};. end{aligned}$$
(7)
Using Expr. (3), Eq. (7) is numerically simulated with the Lax method. In Expr. (3) we impose that (U_F(x)=V) when (U_F(x) >V). This biological assumption means that fish maximal velocity is limited by a physiological constraint rather than by gradient steepness. Details of the physical and biological parameters are provided in SI.6. More