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    Synchrony and multimodality in the timing of Atlantic salmon smolt migration in two Norwegian fjords

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    Mutability of demographic noise in microbial range expansions

    Strains and growth conditionsSingle gene deletion strains were taken from the Keio collection [34] (Supplementary Table 1), which consists of all non-essential single gene deletions in E. coli K-12 strain BW25113. MreB and mrdA point mutant strains were from Ref. [35] (Supplementary Table 2). Plasmids pQY10 and pQY11 were created by Gibson assembly of Venus YFP A206K (for pQY10) or Venus CFP A206K (for pQY11) [31], and SpecR from pKDsgRNA-ack (gift from Kristala Prather, Addgene plasmid # 62654, http://n2t.net/addgene:62654; RRID:Addgene_62654) [36]. Plasmids pQY12 and pQY13 were created similarly but additionally with CmR from pACYC184.All E. coli experiments were performed in LB (Merck 110285, Kenilworth, New Jersey) with the appropriate antibiotics and experiments with S. cerevisae were performed in YPD [37]. All agar plates were prepared in OmniTrays (Nunc 242811, Roskilde, Denmark, 12.8 cm × 8.6 cm) or 12 cm × 12 cm square petri dishes (Greiner 688102, Kremsmuenster, Austria) filled with 70 mL media solidified with 2% Bacto Agar (BD 214010, Franklin Lakes, New Jersey). After solidifying, the plates were dried upside-down in the dark for 2 days and stored wrapped at 4 °C in the dark for 7–20 days before using.Tracking lineages with fluorescent tracer beadsIn order to track lineages, we spread fluorescent tracer beads with a similar size to the cells on the surface of an agar plate, allowed them to dry, then inoculated and grew a colony on top of the agar plate and imaged the tracer beads to track lineages. In this way, we are able to track lineages without genetic labels at low density (i.e. sparsely) in the colony so that we can distinguish individual lineages without needing high-resolution microscopy. We find that the bead trajectories track cell lineages over the course of one hour both at the colony front and behind the front (Figs. 1c, S1c, d, and S2). We chose to spread fluorescent tracer beads on the surface of the agar so that they could continue to be incorporated into the colony as it grew, which would allow us to track lineages even as existing beads and lineages get lost from the front. Even though behind the front many cells will be piled up on top of other cells rather than in contact with the agar, we don’t expect this to affect the ability of the beads to measure demographic noise, since lineages at the front (where cells are in a monolayer) are the most likely to contribute offspring to future generations [26].Fig. 1: Label-free method of measuring demographic noise in microbial colonies.a Schematic of bead-based sparse lineage tracing method for measuring demographic noise. b Schematic of existing method for measuring fraction of diversity preserved [26]. c (Top) The trajectory of a single bead (black) and the lineages of the cells neighboring it in the final-timepoint (colors) traced backwards in time in the Keio collection wild type strain. (Bottom) The deviation of the distance between the cell lineages and the bead from the final distance, backwards in time. Colors are the same as in the time series images. The gray shaded region shows a single cell width away or towards the bead. All cells that neighbor the bead in the final timepoint, except for one (orange), are neighbors of the bead in the first timepoint and stay within a single cell width of the final distance to the bead. d Example neutral mixtures of YFP and CFP tagged strains grown for 1 day and bead trajectories for strains highlighted in e. Black lines show the colony front at 12 and 23 hours. e Comparison of MSD at window size L = 50 µm to the fraction of diversity preserved for 3 E. coli strain backgrounds and 6 single gene deletions on the Keio collection wild type background (BW25113). Error bars in MSD represent the standard error of the weighted mean (N = 7–8, see Methods) and error bars in the fraction of diversity preserved represent the standard error of the weighted mean (N = 8) where weights come from uncertainties in counting the number of sectors.Full size imageFluorescent tracer beadsFor experiments with E. coli, 1 µm red fluorescent polystyrene beads from Magsphere (PSF-001UM, Pasadena, CA, USA) were diluted to 3 µg/mL in molecular grade water and 920 µL was spread on the surface of the prepared OmniTray agar plates with sterile glass beads. Excess bead solution was poured out, and the plates were dried under the flow of a class II biosafety cabinet (Nuaire, NU-425-300ES, Plymouth, MN, USA) for 45 min. The bead density was chosen to achieve ~250 beads in a 56x field of view. For experiments with S. cerervisiae, 2 µm dragon green fluorescent polystyrene beads from Bang’s labs (FSDG005, Fishers, IN, USA) were used at a similar surface density.Measurement of the distribution of demographic noiseWe randomly selected 352 single gene deletion strains from the Keio collection. For each experiment, cells were thawed from glycerol stock (see Supplementary Methods), mixed, and 5 µL was transferred into a 96-well flat bottom plate with 100 µL LB and the appropriate antibiotics. Plates were covered with Breathe-Easy sealing membrane (Diversified Biotech BEM-1, Doylestown, PA, USA) and grown for 12 h at 37 °C without shaking. A floating pin replicator (V&P Scientific, FP12, 2.36 mm pin diameter, San Diego, CA, USA) was used to inoculate a 2–3 mm droplet from each well of the liquid culture onto a prepared OmniTray covered with fluorescent tracer beads. Droplets were dried and the plates were incubated upside down at 37 °C for 12 h before timelapse imaging.To account for systematic differences between plates, we also put 8 wild type BW25113 wells in each 96-well plate in different positions on each plate. The mean squared displacement (MSD, see below) of each gene deletion colony was normalized to the weighted average MSD of the wild type BW25113 colonies on that plate, 〈MSD〉WT, and this “relative MSD” is reported. We performed three biological replicates for each strain (grown from the same glycerol stock, Fig. S3), and their measurements were averaged together weighted by the inverse of the square of their individual error in relative MSD. The reported error for the strain is the standard error of the mean. During the experiment, several experimental challenges impede our ability to measure demographic noise, including the appearance of beneficial sectors (identified as diverging bead trajectories that correspond to bulges at the colony front) either due to de novo beneficial mutations or standing variation from glycerol stock (see Supplementary Section 2.4, Figs. S4 and S5), slow growth rate leading to bead tracks that were too short for analysis, no cells transferred during inoculation with our pinning tool, inaccurate particle tracking due to beads being too close together, or out of focus images. In order to keep only the highest quality data points, we focused on the 191 strains that had at least 2 replicates free of such issues.Timelapse imaging of fluorescent beadsPlates were transferred to an ibidi stagetop incubator (Catalog number 10918, Gräfelfing, Germany) set to 37 °C for imaging. Evaporation was minimized by putting wet Kim wipes in the chamber and sealing the chamber with tape. The fluorescent tracer beads at the front of the colony were imaged with a Zeiss Axio Zoom.V16 (Oberkochen, Germany) at 56x magnification. A custom macro program written using the Open Application Development for Zen software was used to find the initial focal position for each colony and adjust for deterministic focus drift over time due to slight evaporation. Timelapse imaging was performed at an interval of 10 min for 12 h, during which time the colony grew about halfway across the field of view. Two z slices were taken for each colony and postprocessed to find the most in-focus image to adjust for additional focus drift. Subpixel-resolution particle tracking of the bead trajectory was achieved using a combination of particle image velocimetry and single particle tracking [38] and is described in detail in the Supplementary Methods.Measurement of bead trajectory mean squared displacementThe measurement of mean squared displacement (MSD) is adapted from [31] and is illustrated in Figs. 1a and S1a. Points in a trajectory that fall within a window of length L are fit to a line of best fit. The MSD is given by$$MSDleft( L right) = leftlangle {leftlangle {frac{1}{L}mathop {int}nolimits_l^{l + L} {left( {{Delta}wleft( {L^prime } right)} right)^2dL^prime } } rightrangle _{windows}} rightrangle _{trajectories}$$where Δw(L’) is the displacement of the bead trajectory from the line of best fit at each point, 〈〉windows is an average over all possible definitions of a window with length L along the trajectory (window definitions are overlapping), and 〈〉trajectories is a weighted average over all trajectories in a field of view, where the weight is the inverse squared standard error of the mean for each trajectory’s MSD(L) (Fig. S1a). We use 200 linearly spaced window sizes from L = 6 to 1152 μm. Window sizes that fit in fewer than 5 trajectories are dropped due to the noisiness in calculating the averaged MSD(L). The combined MSD(L) for all trajectories reflects that of bead trajectories at the colony front, which will have the largest contribution to the strength of demographic noise [26] (Fig. S6). Because we expect the trajectories to follow an anomalous random walk [31], the combined MSD(L) for all trajectories across the field of view is fit using weighted least squares to a power law, where the weight is the inverse square of the propagated standard error of the mean. Colonies with data in fewer than 5 window sizes are dropped due to the noisiness in fitting to a power law. The fit is extrapolated or interpolated to L = 50 µm to give a single summary statistic for each colony, and this quantity is reported as MSD(L = 50 µm) (see Supplementary Section 2.2, Figs. S7 and S8), and the error is calculated as half the difference in MSD (L = 50 µm) from using the upper and lower bounded coefficients to the fit. For calculating the distribution of demographic noise effects, only MSD values where the error is less than half of the value are kept.Measurement of phenotypic traitsFor the phenotypic trait measurements, in addition to the 191 single gene deletions, we also measured 41 additional strains of E. coli which included 4 strain backgrounds, 1 mreB knockout in the MC1000 background, 2 adhesin mutants, and 34 single gene knockouts from the Keio collection that we predicted may have large changes to demographic noise because of an altered biofilm forming ability in liquid culture [39] or altered cell shape from the wild type (using the classification on the Keio website, https://shigen.nig.ac.jp/ecoli/strain/resource/keioCollection/list). We normalized all phenotypic trait values to the average value measured from the wild type colonies on the same plate. The reported values for each strain are averages across 2–3 replicate colonies on different plates and the errors are the standard error of the mean. See the Supplementary Methods for more details of the specific phenotypic trait measurements.Measurement of neutral fraction of diversity preservedNeutral fluorescent pairs were created by transforming background strains with plasmids pQY10 (YFP, SpecR) or pQY11 (CFP, SpecR). Cells were streaked from glycerol stock and a single colony of each strain was inoculated into a 96 well plate with 600 µL LB and 120 µg/mL spectinomycin for plasmid retention. Plates were covered with Breathe-Easy sealing membrane and grown for 12 h at 37 °C without shaking. 50 µL of culture from each strain in a neutral pair were mixed and a floating pin replicator was used to inoculate a 2–3 mm droplet from the liquid culture onto a prepared OmniTray covered with fluorescent tracer beads. Droplets were dried and the plates were incubated at 37 °C.Colonies were imaged after 24 h with fluorescence microscopy using a Zeiss Axio Zoom.V16 and the number of sectors of each color was manually counted. The fraction of diversity preserved was calculated as in Ref. [26] by dividing the number of neutral sectors by one-half times the estimated initial number of cells at the inoculum front (see Fig. 1b). The factor of one-half accounts for the probability that two neighboring cells at the inoculum front share the same color label. The initial number of cells is estimated by measuring the inoculum size of each colony (manually measured by fitting a circle to a brightfield backlight image at the time of inoculation) divided by the effective cell size for E. coli (sqrt(length*width) taken to be 1.7 µm, Ref. [26]).Colony fitnessThe colony fitness coefficient between two strains was measured using a colony collision assay as described in Refs. [26, 40] by growing colonies next to one another and measuring the curvature of the intersecting arc upon collision. Cells were streaked from glycerol stock and a single colony for each strain was inoculated into LB with 120 µg/mL spectinomycin for plasmid retention and incubated at 37 °C for 15 h. The culture was back diluted 1:500 in 1 mL fresh LB with 120 µg/mL spectinomycin and grown at 37 °C for 4 h. 1 µL of the culture was then inoculated onto the prepared 12cmx12cm square petri dishes containing LB with different concentrations of chloramphenicol (0 µg/mL, 1 µg/mL, 2 µg/mL, 3 µg/mL) in pairs that were 5 mm apart, with 32 pairs per plate, then the colonies were incubated at 37 °C. After half of a day, bright field backlight images are taken and were used to fit circles to each colony to determine the distance between the two colonies. After 6 days, the colonies were imaged with fluorescence microscopy using a Zeiss Axio Zoom.V16. The radius of curvature of the intersecting arc between the two colonies was determined with image segmentation and was used to calculate the fitness coefficient between the two strains (Fig. S9a).Measurement of non-neutral establishment probabilityWe transformed 9 gene deletion strains from the Keio collection (gpmI, recB, pgm, tolQ, ychJ, lpcA, dsbA, rfaF, tatB) and 3 strain backgrounds (BW25113, MG1655, DH5α) with pQY11 (CFP, SpecR) or pQY12 (YFP, SpecR, CmR). Cells were streaked from glycerol stock and a single colony of each strain was inoculated into media with 120 µg/mL spectinomycin for plasmid retention, then incubated at 37 °C for 16 h. The culture was back-diluted 1:1000 in 1 mL fresh media with 120 µg/mL spectinomycin and grown at 37 °C for 4 h. YFP chloramphenicol-resistant and CFP chloramphenicol-sensitive cells from the same strain background were mixed respectively at approximately 1:500, 1:200, and 1:50 and distributed in a 96-well plate. A floating pin replicator was used to inoculate a 2–3 mm droplet from the liquid culture onto prepared OmniTrays with varying concentrations of chloramphenicol (0 µg/mL, 1 µg/mL, 2 µg/mL, 3 µg/mL). Droplets were dried and the plates were incubated at 37 °C for 3 days, then imaged by fluorescence microscopy using a Zeiss Axio Zoom.V16.The establishment probability of the resistant strain can be measured by counting the number of established resistant sectors normalized by the initial number of resistant cells at the inoculum front [26], which gives the probability that any given resistant cell in the inoculum escaped genetic drift and grew to a large enough size to create a sector. Briefly,$$p_{est} = N_{sectors}/N_0$$
    (1)
    where Nsectors is the number of resistant sectors after 3 days (counted by eye) and N0 is the estimated initial number of cells of the resistant type at the inoculum front. Because the establishment probability can only be accurately measured when the initial number of resistant cells is low enough that the resistant sectors do not interact with one another, we only keep colonies where neighboring resistant sectors are distinguishable at the colony front. In cases where we could see that a sector had coalesced from multiple sectors, we counted the number of sectors pre-coalescence. We also did not find a clear downward bias in the establishment probability as a function of initial mutant fraction (Fig. S10), suggesting that the probability of sector coalescence is low in the regime of these experimental parameters. The initial number N0 of cells of the resistant type is estimated by multiplying the initial number of cells at the inoculum front (see measurement of neutral fraction of diversity preserved) by the fraction of resistant cells in the inoculum (measured by plating and counting CFUs). More

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    Light exposure mediates circadian rhythms of rhizosphere microbial communities

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    Anopheles ecology, genetics and malaria transmission in northern Cambodia

    Mosquito abundance, biting rate and morphological identificationsA total of 3920 Anopheles sp. females, 1167 and 2753 during the dry and rainy seasons respectively, were captured on a total of 60 collection days. Overall 81% (3187/3920) of the samples were collected in the cow odor-baited double net traps (CBNTs) and while this relative abundance was rather consistent between different collection sites for the CBNTs, 67% (490/733) of the Anopheles from the human odor-baited double net traps (HBNTs) were collected in the forest sites (Table S1).The biting rate (# of females/trap/day) for the HBNTs was consistently higher in the forest sites compared to all other locations during both the rainy and the dry seasons (Table 1). However, for the CBNTs, while the biting rate was the highest in the forest sites during the dry season, the tendency changed during the rainy season with a higher biting rate in the villages and the forests near the villages compared to the forest sites (Table 1).Table 1 Biting and infectious rates of Anopheles mosquitoes collected by HBNTs and CBNTs across sites and seasons.Full size tableA total of 3131 females were morphologically identified as 14 different Anopheles species or complexes of morphologically indistinguishable sibling species. Based on these morphological identifications, species thought to be primary vectors comprised only 10.2% of the collected mosquitoes: Anopheles dirus s.l. (8.1%, n = 319), A. minimus s.l. (0.4%, n = 15) and A. maculatus s.l. (1.7%, n = 67). The most abundant species (represented by more than a hundred individuals in our collection) constituted 75.8% of the collected Anopheles mosquitoes and were represented by 6 species complexes: A. barbirostris (21.2%, n = 831), A. philippinensis (14.6%, n = 571), A. hyrcanus (13.6%, n = 535), A. kochi (10.5%, n = 412), A. dirus (8.1%), A. aconitus (7.7%, n = 303).Molecular determination of mosquito speciesA total of 844 females were molecularly characterized for species in the random subset and represent 26 distinct Anopheles species as determined by ITS2 and CO1 (Table S2). The most abundant species (representing ≥ 5% of the samples; n ≥ 42) comprise 77.8% of the molecularly typed individuals and represent 8 species from 6 different species complexes. These most abundant species included A. dirus (13.2%, n = 112) from the Dirus complex. From the Barbirostris complex; A. dissidens (13.2%, n = 112), and A. campestris-wejchoochotei (8.1%, n = 69). From the Hyrcanus Group, A. peditaeniatus (12.8%, n = 108), and A. nitidus (5.7%, n = 48). The Annularis, Funestus, and Kochi Groups were each represented by a single species A. nivipes (9.2%, n = 78), A. aconitus (6.7%, n = 57), and A. kochi (8.7%, n = 74), respectively. The 18 less abundant species, represent by fewer than 42 samples and in many cases just a handful of samples included A. philippinensis (n = 17) and A. annularis (n = 1) from the Annularis Group, A. jamesii (n = 16), A. pseudojamesi (n = 1), and A. splendidus (n = 1) from the Jamesii Group and A. saeungae (n = 29) and A. barbirostris (n = 2) from the Barbirostris Group. From the Hyrcanus Group A. crawfordi (n = 40), A. argyropus (n = 1), An. nigerrimus (n = 28), and A. sinensis (n = 3) were sampled. Anopheles maculatus (n = 22), A. sawadwongporni (n = 4), and A. rampae (n = 2) from the Maculatus Group. Anopheles tessellatus from the Tessellatus Group and A. interruptus from the Asiaticus Group were each sampled once. A. vagus (n = 12) and A. karwari (n = 3) were also present. There were 2 mosquitoes that had 99.9% identical ITS2 and 99.4% identical CO1 sequences but matched no species in the NCBI database. In addition to the random subset, 79 Plasmodium sp. infected samples were molecularly characterized for species which resulted in a total of 29 Anopheles species as determined by ITS2 and CO1.Day biting rateOverall 20.2 ± 1.2% of the Anopheles females were captured during the daytime (between 06:00 and 18:00). Indeed, while the majority of Anopheles mosquitoes bite at night, an important proportion was active during the day (Fig. 2). Excluding species with extremely low sample sizes and unidentified samples, day biting behaviour was observed for all the Anopheles species and varied from 13 to 68% (Table S3).Figure 2Average number of Anopheles females collected per trap per hour in the different collection sites in the HBNTs and the CBNTs.Full size imageThe day biting rate in the HBNTs was not different across collection sites (19.6 ± 2.9%; χ2 = 3.6, df = 3, p = 0.3; Fig. 3a) but was higher during the dry season (25.9 ± 4.6%) compared to the rainy season (13.8 ± 3.5%; χ2 = 19.08, df = 1, p  More

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    Diel niche variation in mammals associated with expanded trait space

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    Behavioural movement strategies in cyclic models

    In this work, we performed stochastic simulations of a cyclic nonhierarchical system composed of 5 species. To this purpose, we implemented a standard numerical algorithm largely used to study spatial biological systems11,13,41. We considered a generalisation of the rock-paper-scissors game for 5 species, whose rules are illustrated in Fig. 1a. The arrows indicate a cyclic dominance among the species. Accordingly, individuals of species i beat individuals of species (i+1), with (i=1,2,3,4,5).The dynamics of individuals’ spatial organisation occurs in a square lattice with periodic boundary conditions, following the rules: selection, reproduction, and mobility. We assumed the May-Leonard implementation so that the total number of individuals is not conserved43. Each grid point contains at most one individual, which means that the maximum number of individuals is ({mathcal {N}}), the total number of grid points.Initially, the number of individuals is the same for all species, i.e., (I_i,=,{mathcal {N}}/5), with (i=1,2,3,4,5) (there are no empty spaces in the initial state). We prepared the initial conditions by distributing each individual at a random grid point. At each timestep, one interaction occurs, changing the spatial configuration of individuals. The possible interactions are:

    Selection: (i j rightarrow i otimes ,), with (j = i+1), where (otimes) means an empty space; every time one selection interaction occurs, the grid point occupied by the individual of species (i+1) vanishes.

    Reproduction: (i otimes rightarrow i i,); when one reproduction is realised an individual of species i fills the empty space.

    Mobility: (i odot rightarrow odot i,), where (odot) means either an individual of any species or an empty site; an individual of species i switches positions with another individual of any species or with an empty space.

    In our stochastic simulations, selection, reproduction, and mobilities interactions occur with the following probabilities: s, r and m, respectively. We assumed that individuals of all species have the same probabilities of selecting, reproducing and moving. The interactions were implemented by assuming the von Neumann neighbourhood, i.e., individuals may interact with one of their four nearest neighbours. The simulation algorithm follows three steps: i) sorting an active individual; ii) raffling one interaction to be executed; iii) drawing one of the four nearest neighbours to suffer the sorted interaction (the only exception is the directional mobility, where the neighbour is chosen according to the movement tactic). If the interaction is executed, one timestep is counted. Otherwise, the three steps are redone. Our time unit is called generation, defined as the necessary time to ({mathcal {N}}) timesteps to occur.In our model, individuals of one out of the species can move into the direction with more individuals of a target species. The choice is based on the strategy assumed by species. We assumed three sorts of directional movement tactics:

    Attack tactic: an individual of species i moves into the direction with more individuals of species (i+1);

    Anticipation tactic: an individual of species i goes towards the direction with a larger number of individuals of species (i+2);

    Safeguard tactic: an individual of species i walk into the direction with a larger concentration of individuals of species (i-2).

    In the standard model, individuals of all species move randomly.We considered that only individuals of species 1 perform the directional movement tactics, as illustrated in Fig. 1b. The solid, dashed, and dashed-dotted lines represent the Attack, Anticipation, and Safeguard tactics, respectively. The concentric circumference arcs show that individuals of species 2, 3, 4, and 5 always move randomly. For implementing a directional movement, the algorithm follows the steps: i) it is assumed a disc of radius R (the perception radius), in the active individual’s neighbourhood; ii) it is defined four circular sectors in the directions of the four nearest neighbours; iii) according to the movement tactic, the target species is defined: species 2, 3, and 4, for Attack, Anticipation, and Safeguard tactics, respectively; iv) it is counted the number of individuals of the target species within each circular sector. Individuals on the borders are assumed to be part of both circular sectors; v) the circular sector that contains more individuals of the target species is chosen. In the event of a tie, a draw between the tied directions is made; vi) the active individual switches positions with the immediate neighbour in the chosen direction. The swap is also executed in case of the neighbour grid point is empty.To observe the spatial patterns, we first performed a single simulation for the standard model, Attack, Anticipation, and Safeguard tactics. The realisations run in square lattices with (500^2) grid points, for a timespan of 5000 generations. We captured 500 snapshots of the lattice (in intervals of 10 generations), that were used to make the videos of the dynamics of the spatial patterns showed in https://youtu.be/Ndvk6Rg57m4 (standard), https://youtu.be/JGhkDAHSo74 (Attack), https://youtu.be/ZZp9QlOfv2Q (Anticipation), and https://youtu.be/eFxWdLhIOuQ (Safeguard). The final snapshots were depicted in Fig. 2a–d. Individuals of species 1, 2, 3, 4, and 5 are identified with the colours ruby, blue, pink, green, and yellow, respectively; while white dots represent empty spaces. The simulations were performed assuming selection, reproduction, and mobility probabilities: (s = r = m = 1/3). The perception radius was assumed to be (R=3).The population dynamics were studied by means of the spatial density (rho _i), defined as the fraction of the grid occupied by individuals of species i at time t, i.e., (rho _i = I_i/{mathcal {N}}), where (i=0) stands for empty spaces and (i=1,…,5) represent the species 1, 2, 3, 4, and 5. The temporal changes in spatial densities of the simulations showed in Fig. 2 were depicted in Fig. 3, where the grey, ruby, blue, pink, green, and yellow lines represent the densities of empty spaces and species 1, 2, 3, 4, and 5, respectively. We also computed how the selection risk of individuals of species i changes in time. To this purpose, the algorithm counts the total number of individuals of species i at the beginning of each generation. It is then counted the number of times that individuals of species i are killed during the generation. The ratio between the number of selected individuals and the initial amount is defined as the selection risk of species i, (zeta _i). The results were averaged for every 50 generations. Figure 4 shows (zeta _i,(%)) as a function of the time for the simulations presented in Fig. 2. The ruby, blue, pink, green, and yellow lines show the selection risks of individuals of species 1, 2, 3, 4, and 5, respectively.To quantify the spatial organisation of the species, we studied the spatial autocorrelation function. This quantity measures how individuals of a same species are spatially correlated, indicating spatial domain sizes. Following the procedure carried out in literature41,42,44,45,46, we first calculated the Fourier transform of the spectral density as (C({{vec{r^{prime}}}}) = {mathcal{F}}^{{ – 1}} { S({{vec{k}}})} /C(0)), where the spectral density (S({{vec{k}}})) is given by (S({{vec{k}}}) = sumlimits_{{k_{x} ,k_{y} }} {mkern 1mu} varphi ({{vec{kappa }}})), with (varphi ({{vec{kappa }}}) = {mathcal{F}}{mkern 1mu} { phi ({{vec{r}}}) – langle phi rangle }). The function (phi ({{vec{r}}})) represents the species in the position ({{vec{r}}}) in the lattice (we assumed 0, 1, 2, 3, 4, and 5, for empty sites, and individuals of species 1, 2, 3, 4, and 5, respectively). We then computed the spatial autocorrelation function as$$C(vec{r^{prime}}) = sumlimits_{{|{{vec{r^{prime}}}}| = x + y}} {frac{{C({{vec{r^{prime}}}})}}{{min (2N – (x + y + 1),(x + y + 1))}}}.$$Subsequently, we found the scale of the spatial domains of species i, defined for (C(l_i)=0.15), where (l_i) is the characteristic length for species i.We calculated the autocorrelation function by running 100 simulations using lattices with (500^2) grid points, assuming (s = r = m = 1/3) and (R=3). Each simulation started from different random initial conditions. We then captured each species spatial configuration after 5000 generations to calculate the autocorrelation functions. Finally, we averaged the autocorrelation function in terms of the radial coordinate r and calculated the characteristic length for each species. We also calculated the standard deviation for the autocorrelation functions and the characteristic lengths. Figure 4 shows the comparison of the results for Attack, Anticipation, and Safeguard strategies with the standard model. The ruby, blue, pink, green, and yellow circles indicate the mean values for species 1, 2, 3, 4, and 5, respectively. In the case of standard model, the mean values are represented by grey circles, which are the same for all species. The error bars show that standard deviation. The horizontal black line represents (C(l_i), =, 0.15).To further explore the numerical results, we studied how the perception radius R influences species spatial densities and selection risks. We calculated the mean value of the spatial species densities, (langle , rho _i,rangle) and the mean value of selection risks, (langle , zeta _i,rangle) from a set of 100 simulations in lattices with (500^2) grid points, starting from different initial conditions for (R=1,2,3,4,5). We used (s,=r,=,m,=1/3) and a timespan of (t=5000) generations. The mean values and standard deviation were calculated using the second half of the simulations, thus eliminating the density fluctuations inherent in the pattern formation process. The results were shown in Fig. 6, where the circles represent the mean values and error bars indicate the standard deviation. The colours are the same as in Figs. 3 and 4. Furthermore, to verify the precision of the statistical results, we calculated the variation coefficient – the ratio between the standard deviation and the mean value. Supplementary Tables S1 and S2 show statistical outcomes for species densities and selections risks, respectively.We studied a more realistic scenario where not all individuals of species 1 can perform the directional movement tactics. For this reason, we defined the conditioning factor (alpha), with (0,le ,alpha ,le ,1), representing the proportion of individuals of species 1 that moves directionally. For (alpha =0) all individuals move randomly while for (alpha =1) all individuals move directionally. This means that every time an individual of species 1 is sorted to move, there is a probability (alpha) of the algorithm implementing the directional movement tactic, instead of randomly choosing one of its four immediate neighbours to switch positions. To understand the effects of the conditioning factor, we observed how the density of species 1 changes for the entire range of (alpha), with intervals of (Delta alpha = 0.1). The simulations were implemented for (R=3) and (s,=r,=,m,=1/3). It was computed the mean value of the spatial density of species 1, (langle , rho _1,rangle), and its standard deviation from a set of 100 different random initial conditions. The results were depicted in Fig. 7, where the green, red, and blue dashed lines show (langle , rho _1,rangle) as a function of (alpha). The error bars indicate the standard deviation.Finally, we aimed to investigate how the directional movement tactics jeopardise species coexistence for a wide mobility probability range. Because of this, we run 2000 simulations in lattices with (100^2) grid points for (0.05, More

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    High turbidity levels alter coral reef fish movement in a foraging task

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