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    Fluctuation relations and fitness landscapes of growing cell populations

    The backward and forward processes
    Let us consider a branched tree, starting with (N_0) cells at time (t=0) and ending with N(t) cells at time t as shown on Fig. 1. We assume that all lineages survive up to time t, and therefore the final number N(t) of cells corresponds to the number of lineages in the tree.
    The most natural way to sample the lineages is to put uniform weights on all of them. This sampling is called backward, (or retrospective) because at the end of the experiment one randomly chooses one lineage among the N(t) with a uniform probability and then one traces the history of the lineage backward in time from time t to 0, until reaching the ancestor population. The backward weight associated with a lineage l is defined as

    $$begin{aligned} omega _{text {back}}(l)=N(t)^{-1} ,. end{aligned}$$
    (1)

    In a tree, some lineages divide more often than others, which results in an over-representation of lineages that have divided more often than the average. Therefore by choosing a lineage with uniform distribution, we are more likely to choose a lineage with more divisions than the average number of divisions in the tree.
    The other way of sampling a tree is the forward (or chronological) one and consists in putting the weight

    $$begin{aligned} omega _text {for}(l)= N_0^{-1} m^{-K(l)} ,, end{aligned}$$
    (2)

    on a lineage l with K(l) divisions, where m is the number of offspring at division. This choice of weights is called forward because one starts at time 0 by uniformly choosing one cell among the (N_0) initial cells, and one goes forward in time up to time t, by choosing one of the m offspring with equal weight 1/m at each division. The backward and forward weights are properly normalized probabilities, defined on the N(t) lineages in the tree at time t: (sum _{i=1}^{N(t)} omega _{text {back}}(l_i) = sum _{i=1}^{N(t)} omega _{text {for}}(l_i) =1).
    Figure 1

    Example of a tree with (N_0=1) and (N(t)=10) lineages at time t. Two lineages are highlighted, the first in blue with 2 divisions and the second in orange with 5 divisions. The forward sampling is represented with the green right arrows: it starts at time (t=0) and goes forward in time by choosing one of the two daughters lineages at each division with probability 1/2. The backward sampling is pictured by the left purple arrows: starting from time t with uniform weight on the 10 lineages it goes backward in time down to time (t=0).

    Full size image

    Single lineage experiments are precisely described by a forward process since experimentally, at each division, only one of the two daughter cells is conserved while the other is eliminated (for instance flushed away in a microfluidic channel9, 10). In these experiments, a tree is generated but at each division only one of the two lineages is conserved, with probability 1/2, while the rest of the tree is eliminated. This means that single lineage observables can be measured without single lineage experiments, provided population experiments are analyzed with the correct weights on lineages.
    Link with the population growth rate
    Since the backward weight put on a lineage depends on the number of cells at time t, it takes into account the reproductive performance of the colony but it is unaffected by the reproductive performance of the lineage considered. On the contrary, the forward weight put on a specific lineage depends on the number of divisions of that lineage but is unaffected by the reproductive performance of other lineages in the tree. Therefore, the difference between the values of the two weights for a particular lineage informs on the difference between the reproductive performance of the lineage with respect to the colony.
    We now introduce the population growth rate:

    $$begin{aligned} Lambda _t=frac{1}{t} ln frac{N(t)}{N_0} ,, end{aligned}$$
    (3)

    which is linked to forward weights by the relation

    $$begin{aligned} frac{N(t)}{N_0}=sum _{i=1}^{N(t)} m^{K_i} omega _text {for}(l_i) = langle m^K rangle _text {for} ,, end{aligned}$$
    (4)

    where (langle cdot rangle _text {for}) is the average over the lineages weighted by (omega _text {for}), and (K_i=K(l_i)). Combining the two equations above, we obtain19:

    $$begin{aligned} Lambda _t=frac{1}{t} ln langle m^K rangle _text {for} ,, end{aligned}$$
    (5)

    which allows an experimental estimation of the population growth rate from the knowledge of the forward statistics only.
    Equation (4) can also be re-written to express the bias between the forward and backward weights of the same lineage

    $$begin{aligned} frac{omega _{text {back}}(l)}{omega _text {for}(l)}=frac{m^{K(l)}}{langle m^K rangle _text {for}} ,, end{aligned}$$
    (6)

    which is the reproductive performance of the lineage divided by its average in the colony with respect to (omega _text {for}).
    A similar relation is derived using the relation

    $$begin{aligned} frac{N_0}{N(t)}=sum _{i=1}^{N(t)} m^{-K_i} omega _text {back}(l_i) = langle m^{-K} rangle _text {back} ,. end{aligned}$$
    (7)

    Combining Eqs. (5) and (7) we obtain:

    $$begin{aligned} Lambda _t= – frac{1}{t} ln langle m^{-K} rangle _text {back} ,. end{aligned}$$
    (8)

    A similar equation as Eq. (6) can be obtained in terms of the backward sampling and reads: 

    $$begin{aligned} frac{omega _{text {back}}(l)}{omega _text {for}(l)}=frac{langle m^{-K} rangle _text {back}}{m^{-K(l)}} ,. end{aligned}$$
    (9)

    Combining Eqs. (1) to (3), we obtain the fluctuation relation13,17:

    $$begin{aligned} omega _{text {back}}(l)= omega _text {for}(l) e^{K(l) ln m – t Lambda _t} ,. end{aligned}$$
    (10)

    If we now introduce the probability distribution of the number of divisions for the forward sampling (p_text {for}(K)=sum _l delta (K-K(l)) omega _text {for}(l)) and similarly for the backward sampling, we can also recast the above relation as a fluctuation relation for the distribution of the number of divisions:

    $$begin{aligned} p_{text {back}} (K,t)=p_{text {for}} (K,t) e^{K ln m – t Lambda _t} ,. end{aligned}$$
    (11)

    Let us now introduce the Kullback–Leibler divergence between two probability distributions p and q, which is the non-negative number:

    $$begin{aligned} {{mathscr {D}}}_{text {KL}}(p||q)=int {mathrm {d}}x , p(x) ln frac{p(x)}{q(x)} ge 0 ,. end{aligned}$$
    (12)

    Using Eq. (10), we obtain

    $$begin{aligned} {{mathscr {D}}}_{text {KL}}(omega _{text {back}}|| omega _text {for}) = langle K rangle _{text {back}} ln m – t Lambda _t ge 0 ,. end{aligned}$$
    (13)

    A similar inequality follows by considering ({{mathscr {D}}}_{text {KL}}(omega _{text {for}}|| omega _text {back})). Finally we obtain

    $$begin{aligned} frac{t}{langle K rangle _{text {back}}} le frac{ln m}{Lambda _t} le frac{t}{langle K rangle _text {for}} ,. end{aligned}$$
    (14)

    In the long time limit, (lim nolimits _{t rightarrow + infty } t/langle K rangle _{text {back}} = langle tau rangle _{text {back}}), where (tau) is the inter-division time, or generation time, defined as the time between two consecutive divisions on a lineage. The same argument goes for the forward average. In the case of cell division where each cell only gives birth to two daughter cells ((m=2)), the center term in the inequality tends to the population doubling time (T_d). Therefore, this inequality reads in the long time limit:

    $$begin{aligned} langle tau rangle _{text {back}} le T_d le langle tau rangle _text {for} ,. end{aligned}$$
    (15)

    Let us now mention a minor but subtle point related to this long time limit. For a lineage with K divisions up to time t, we can write (t=a + sum _{i=1}^{K} tau _i), where a is the age of the cell at time t and where (tau _i) is the generation time associated with the ith division. Then (t/ K= tau _m + a/K), where (tau _m) is the mean generation time along the lineage. For finite times, all we can deduce is (t/ K ge tau _m). Therefore the left inequality of Eq. (15) always holds

    $$begin{aligned} langle tau rangle _{text {back}} le frac{t}{langle K rangle _{text {back}}} le frac{ln m}{Lambda _t} ,, end{aligned}$$
    (16)

    while the right inequality does not necessarily hold at finite time.
    Inspired by work by Powell6, the inequalities of Eq. (15) have been theoretically derived in12 for age models. In our previous work17, we have replotted the experimental data of12 which confirm theses inequalities and we have shown theoretically that the same inequalities should also hold for size models. In fact, as the present derivation shows, the relation equation (14) is very general and only depends on the branching structure of the tree, while the relation equation (15) requires in addition the existence of a steady state. These inequalities and Eq. (11) express fundamental constraints between division and growth, which should hold for any model.
    Stochastic thermodynamic interpretation
    The results derived above have a form similar to that found in Stochastic Thermodynamics18. According to this framework, Eq. (5) is an integral fluctuation relation (similar to Jarzynski relation) while Eq. (11) is a detailed fluctuation relation (similar to Crooks fluctuation relation). Furthermore, the inequalities equation  (14) represent a constraint equivalent to the second law of thermodynamics, which classically follows from the Jarzynski or Crooks fluctuation relations. It is known that these inequalities take a slightly different form when expressed at finite time or at steady state, which is indeed the case here when comparing Eq. (14) with Eq. (15). A difference between work fluctuation relations like Crooks or Jarzynski and equations (5) and (11), is that Crooks or Jarzynski describe non-autonomous systems which are driven out of equilibrium by the application of a time-dependent protocol, whereas the relations for cell growth derived here concern autonomous systems, in the absence of any external protocol.
    One of the main applications of Jarzynski or Crooks fluctuation relations concerns the thermodynamic inference of free energies from non-equilibrium fluctuations. Similarly, Eq. (5) or Eq. (11) can be used as estimators of the population growth rate. The specific advantage of Eq. (5) with respect to Eq. (11) is that it only requires single lineage statistics, which can be obtained from mother machine experiments. Let us now show how this can be done in practice. We use the data from20, where the growth of many independent lineages of E. coli have been recorded over 70 generations in a mother machine at three different temperatures (25 °C, 27 °C, and 37 °C), precisely 65 lineages for 25 °C, 54 for 27 °C, and 160 for 37 °C. For each temperature condition, we study the convergence of the estimator of the population growth rate based on Eq. (5), which we call (Lambda _{mathrm{lin}}) as a function of the length t of the lineages for a fixed number of independent lineages L, and as a function of the number of independent lineages for a fixed observation time.
    Figure 2

    Estimator of the population growth rate (Lambda _{mathrm{lin}}) based on Eq. (5), (a) as function of the the length t of the lineages and (b) as function of the number L of lineages used in the estimation. In (a), the curves for the three temperatures converge to a constant value. In (b), only the curve for 37 °C is shown and the horizontal dashed line represents the quantity (ln (2)/langle tau rangle _{text {for}}), which is smaller than the limit value of (Lambda _{mathrm{lin}}), as expected from the second law-like inequality, namely Eq. (15). In the inset, the purple histogram is the distribution of the number of divisions, while the green filled histogram is the histogram deduced from it by weighting it by a factor (2^K) and normalizing. All the 160 lineages were used to plot these histograms.

    Full size image

    Firstly, for each temperature, we take into account all the lineages available and truncate them at an arbitrary time t smaller than the length of the shortest lineage of the set. On these portions of lineages of length t, we compute (Lambda _{mathrm{lin}}) versus the time t as shown in Fig. 2a. We see that the estimator (Lambda _{mathrm{lin}}) starts from zero, increases and eventually converges rather quickly towards a limiting value. The limit we found agree with the independent analysis carried out in19, with only one caveat, these authors reported that their estimator started at high values and then decreased towards the limit, while in our case, the estimator starts at zero and later increases towards the limit. In our case, the estimator needs to be zero at short times, before the first divisions occur.
    Secondly, we truncate all the lineages at a fixed time equal to the length of the shortest lineage of the set, and compute (Lambda _{mathrm{lin}}) versus the number L of lineages considered for the estimation, which have been randomly selected from the ensemble of available lineages. As shown in Fig. 2b for the case at (37^{,circ } hbox {C}) (curves for the other temperatures look exactly the same), the convergence is also excellent in that case. Although the value of the population growth rate which is obtained in this way can not be measured independently from the evolution of the population in the mother machine setup, this convergence is indicative of the success of the method. The figure also confirms that the value of the population growth rate deduced from the estimator (Lambda _{mathrm{lin}}) is larger than (ln (2)/langle tau rangle _{text {for}}), as predicted by the right inequality of Eq. (15).
    Here, the estimator is found to provide an excellent estimation, but this is not always so. For instance, for the inference of free energies from non-equilibrium work measurements, the exponential average of the estimator is often dominated by rare values, which are not accessible or not well sampled21. To understand why this problem does not arise here, we show in inset of Fig. 2b, the distribution P(K) of the number of divisions together with the same distribution weighted by the factor (2^K) and normalized. The peak of that modified distribution informs on the dominant values in the estimator21. Here, we observe that both distributions have a narrow support and are close to each other. The weighted distribution is peaked at (K=67) while P(K) is peaked at (K=66), therefore typical and dominating values are very close, which explains why the estimator is good.
    Let us now further develop the Stochastic Thermodynamic interpretation of our results by analyzing the implications of the previous fluctuation relations when dynamical variables are introduced on the branched tree of the population. Let us introduce M variables labeled ((y_1,y_2, ldots ,y_M)) to describe a dynamical state of the system, then a path is fully determined by the values of these variables at division, and the times of each division. We call ({mathbf {y}}(t)=(y_1(t),y_2(t), ldots ,y_M(t))) a vector state at time t and ({{mathbf {y}}}={{mathbf {y}}(t_j)}_{j=1}^{K}) a path with K divisions. For cell growth models, the variables (y_i) can typically be the size and age of the cell, or the concentration of a key protein.
    The probability ({{mathscr {P}}}) of path ({{mathbf {y}}}) is defined as the sum over all lineages of the weights of the lineages that follow the path ({{mathbf {y}}}):

    $$begin{aligned} {{mathscr {P}}}({{mathbf {y}}},K,t)=sum _{i=1}^{N(t)} omega (l_i) , delta (K-K_i) delta ({{mathbf {y}}} – {{mathbf {y}}}_i) ,, end{aligned}$$
    (17)

    where ({{mathbf {y}}}_i) is the path followed by lineage (l_i). Using the normalization of the weights (omega) on the lineages, we show that ({{mathscr {P}}}) is properly normalized: (int mathrm {d}{{mathbf {y}}} sum _K {{mathscr {P}}}({{mathbf {y}}},K,t) = 1). We then define the number (n({{mathbf {y}}},K,t)) of lineages in the tree at time t that follow the path ({{mathbf {y}}}) with K divisions:

    $$begin{aligned} n({{mathbf {y}}},K,t)=sum _{i=1}^{N(t)} delta (K-K_i) delta ({{mathbf {y}}} – {{mathbf {y}}}_i) ,. end{aligned}$$
    (18)

    This number of lineages is normalized as (int mathrm {d}{{mathbf {y}}} sum _K n({{mathbf {y}}},K,t) = N(t)). Then, the path probability can be re-written as

    $$begin{aligned} {{mathscr {P}}}({{mathbf {y}}},K,t) = n({{mathbf {y}}},K,t) cdot omega (l) ,. end{aligned}$$
    (19)

    Since (n({{mathbf {y}}},K,t)) is independent of a particular choice of lineage weighting, we obtain

    $$begin{aligned} frac{{{mathscr {P}}}_{text {back}}({{mathbf {y}}},K,t)}{{{mathscr {P}}}_text {for} ({{mathbf {y}}},K,t)}=frac{omega _{text {back}}(l)}{omega _text {for}(l)}= e^{K ln m – t Lambda _t} , , end{aligned}$$
    (20)

    which generalizes Eq. (11). In our previous work17, we have derived this relation for size models with individual growth rate fluctuations (i.e. ({mathbf {y}}=(x,nu ))) but we were not aware of the weighting method introduced by13, and for this reason, we used the term ‘tree’ to denote the backward sampling, and the term ‘lineage’ to denote the forward sampling.
    This relation has a familiar form in Stochastic Thermodynamics. The central quantity called entropy production can indeed be expressed similarly as the relative entropy between probability distributions associated with a forward and a backward evolution. In this analogy, ({{mathbf {y}}}) is analog to the trajectory and (t Lambda _t – K ln m) is analog to the entropy production. Then, the equivalent of a reversible trajectory for which the entropy production is null is a lineage for which the number K of divisions is equal to (t Lambda _t / ln m), that is, a lineage having the same reproductive performance as that of the colony. When all the lineages in a tree have this property, there is no variability of the number of divisions among them. In that case, the forward and backward distributions are identical, and the cost function (t Lambda _t – K ln m) vanishes for all lineages. More

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    Anthropogenic stressors impact fish sensory development and survival via thyroid disruption

    Ethics statement
    This study did not involve endangered or protected species and was carried out in accordance with the guidelines of the French Polynesia code for animal ethics and scientific research (https://www.service-public.pf/diren/partager/code/). All protocols and experiments were approved by the CRIOBE-IRCP animal ethics committee (DL-20150214).
    Model species
    The convict surgeonfish Acanthurus triostegus (Linnaeus, 1758) is an abundant coral-reef-associated species found throughout the Indo-Pacific60, including around Moorea Island, French Polynesia11. It has a pelagic larval duration of ~53 days60 after which larvae move back to the reef61. A. triostegus is a well-studied species with regards to metamorphosis, with a well-defined developmental sequence11. The recruitment of A. triostegus larvae to reef habitats coincides with a true metamorphosis into juveniles, with this full process taking around 1 week11. Its metamorphosis is controlled by thyroid hormones (TH, the precursor thyroxine (T4), and the active hormone triiodothyronine (T3)), which is the same as other teleosts and other metamorphosing vertebrates such as amphibians11. TH signaling in larval A. triostegus is vulnerable to disruption by anthropogenic stressors, including the waterborne pesticide chlorpyrifos and artificial light at night11,17. Given the importance of TH during teleost metamorphosis10, and as metamorphosis coincides with recruitment in a taxonomically diverse range of coral-reef fishes (i.e., Acanthuridae, Apogonidae, Balistidae, Chaetodontidae, and Pomacentridae)11, we consider A. triostegus a representative teleost model for examining the effects of anthropogenic stressors on fish recruitment via their impacts on metamorphic processes.
    Study period and site
    This study was conducted from February 2015 to June 2018, at Moorea Island, French Polynesia (S17°32′16.4589″, W149°49′48.3018″). Sampling for the examination of sensory development under pharmacological treatments was conducted in 2015. Sampling for the investigation of behavioral preferences and survival to predation under pharmacological treatments, as well as sensory development under anthropogenic stressor exposure, were conducted in 2016. Sampling for the examination of survival to predation under anthropogenic stressors exposure, and TH levels under co-exposure to anthropogenic stressors were conducted in 2018. Sampling for the investigation of TH levels under single anthropogenic stressors was conducted in both 2016 and 2018.
    Fish sampling
    Settlement-stage A. triostegus (i.e., fully transparent individuals11, here define as day 0 (d0) individuals), were collected on the north–east coast of the island (S17°29′49.7362″, W149°45′13.899″) at night using a crest net11, as they transitioned from the ocean to the reef. Fish were then transferred to either in situ cages (for thyroid hormone signaling experiments) where they remained until d8, or to aquaria at the CRIOBE Marine Research Station (for increased temperature and chlorpyrifos exposure experiments) where they remained until d5.
    Thyroid hormone signaling experiment: control, T3- and N3 treatments
    To test the role of TH on sensory development, behavior (response to sensory cues), and survival (predation test) in metamorphosing A. triostegus, their TH pathway was pharmacologically manipulated. Fish were injected, at d0 immediately following capture, in their ventral cavity with 20 µl of a pharmacological treatment: (i) T3 + iopanoic acid (IOP) both at 10−6 M (T3 treatment), or (ii) NH3 at 10−6 M (N3 treatment). IOP was used as an inhibitor of deiodinase enzymes, following comparable work in mammals and amphibians62, and as routinely used in fish to prevent the immediate degradation of injected T348. The T3 treatment was therefore applied to promote TH signaling. NH3 is a known antagonist of TH receptors (TR) in vertebrates63 and in A. triostegus in particular11. NH3 prevents the binding of TH such as T3 to TR, therefore impairing the binding of transcriptional coactivators to TR, which therefore remain in an inactive and repressive conformation63,64. The N3 treatment was thus applied to repress TH signaling by disrupting the TH pathway. T3 and NH3 were initially suspended in dimethyl sulfoxide (DMSO), at 10−2 M, and then diluted in phosphate buffered saline (PBS) 1× to reach 10−6 M. Control fish were injected with 20 µL of DMSO diluted 10.000 times in PBS 1× to control for the effect of the solvent and injection. DMSO and NH3 non-toxicity has been previously determined11. Until subsequent sampling, all fish were re-treated each morning (i.e., at d2, d3, and d4 for fish sampled at d5) to maintain pharmacological activity11.
    Thyroid hormone signaling experiment: fish husbandry
    Following collection and subsequent treatment, larvae were transferred to a nursery area on the north coast of the island (S17°29′26.5378″, W149°53′29.2252″) where they were raised in in situ cages (cylindrical cages, diameter: 30 cm, height: 50 cm, 15 fish per cage). This allowed them to develop in in situ conditions11. As A. triostegus feeds on algal turf following settlement11,60, cages were stocked with a supply of turf-covered coral rubble that was replaced daily, ensuring both shelter and constant food availability. Fish were subsequently sampled on d2, d5, and d8, post collection to examine sensory development, behavior (response to sensory cues), and survival (predation test). Twelve in situ cages were used, and the use of any given cage was randomized prior each experiment.
    Increased temperature and chlorpyrifos (CPF) exposures: fish husbandry and treatments
    Following collection, d0 fish were maintained in groups of ten individuals at the CRIOBE Marine Research Station. Each group was held in a 30 L × 20 W × 20 H-cm aquaria containing 12 L of filtered (1-µm filter) seawater. All tanks were subject to a 12:12 h light–dark cycle (06:00–18:00 light period) and oxygenated with an air stone. Twelve aquaria were used (six for exposures to increased temperatures only, and six for exposures with CPF), and the use of any given aquarium was randomized prior each experiment.
    For increased temperature treatments, seawater was in an open system, and water temperature was maintained at either 28.5 °C, 30.0 °C or 31.5 °C. 28.5 °C was chosen as the basal temperature as this was the mean temperature in the Moorea lagoon at the time of the study, and corresponds to the mean annual lagoon temperature in this region (http://observatoire.criobe.pf). Subsequent increases of +1.5 °C and +3.0 °C were selected, as these are in line with end-of-century projections for tropical Pacific sea surface temperatures37. Fresh coral rubble was added to the tanks and replaced each day to provide both food and shelter. Heaters controlled by thermostats were used to maintain the temperature treatments. Before the experiment, each tank was in open circuit with temperature maintained at 28.5 °C. At the beginning of the experiment, fish were introduced in the aquarium, and the thermostat temperature was then set up to 28.5 °C, 30.0 °C or 31.5 °C according to the treatment. The temperature of interest was reached within 2 h. Temperature in each tank was then visually checked (on the thermostat controller) at least five times per day, and never differed from the target temperature by more than 0.2 °C.
    For CPF exposure, five different treatments were applied: unaltered seawater (control), seawater with acetone at a final concentration of 1:1.000.000 (CPF0, solvent control treatment, as CPF was made soluble using acetone), or seawater with CPF at a nominal concentration of either 1, 5, or 30 μg L−1 (CPF1, CPF5, and CPF30 treatments), based on the findings of recent studies of reef fishes exposed to CPF11,14,65. CPF was spiked in each tank from dilutions that were prepared in advance: 1 µg µL−1, 5 µg µL−1, and 30 µg µL−1. From these dilutions, 12 µL were pipetted and spiked in the 12-L exposure tanks, therefore reaching nominal concentrations of 1 µg L−1, 5 µg L−1, and 30 µg L−1. Similarly, 12 µL of acetone was spiked in the tank for the CPF0 condition. Spike was allowed to mix for 2 min (water mixing due to the air stone) before fish were introduced in the tank. At the end of the 32-h exposure, CPF concentrations in the water or in the fish tissues were not evaluated, as we were only interested in the effects of CPF spikes on fish metamorphic processes. Nevertheless, a previous study using similar methods and nominal concentrations of similar magnitude (i.e., ranging from 4 to 64 µg L−1) measured CPF levels corresponding to 80% of nominal concentrations after 24 h66, therefore suggesting a good stability of CPF levels in the condition of our study. Environmentally, these nominal concentrations represent high (CPF1) to extremely high (CPF30) exposures, as recorded contamination concentration in Australian and North American surface waters are generally below 1 µg L−1, with a few high outliers reaching up to 26 µg L−153. However, this shows that concentrations of up to 30 µg L−1 are possible on a short timescale (such as the 32-h exposure of this study), in particular in coastal and shallow areas such as fish nurseries. Aquaria used for CPF exposure treatments and associated controls were not equipped with coral rubble to prevent potential interaction with the pesticide11. This may explain the delay in trunk canal development observed in control fish from the CPF exposure treatments compared with control fish from the increased temperature treatments and control fish from the TH treatments (Figs. 1g and  3e). Water was replaced each day to ensure the maintenance of CPF concentrations11.
    For combined increased temperature and CPF exposure treatments, fish were also maintained without coral rubble with water replaced daily.
    For treatments where fish were exposed to an anthropogenic stressor and provided with supplemental T3, fish were maintained in either the elevated temperature or CPF exposure treatments as described above, but were also injected with either T3 (T3 treatment) or with DMSO (control, to control for solvent and injection). These injections were done as described above (thyroid hormone signaling experiment: control, T3- and N3-treatments).
    Sample preparation and fish measurements
    For thyroid hormone quantifications and histological analyses, fish were first euthanized in freshly prepared MS222 at 0.4 mg ml−1 in filtered seawater at 4 °C, and instantly placed on ice. Following euthanasia, all fish except those for histological analyses were weighed (W) then placed on a scale bar and photographed for standardized measurements (e.g., height (H) and standard length (SL)). These measurements were used to calculate Fulton’s condition factor K = 100*(W/SL3) (with SL, in cm, and W, in g) for each individual67. Weight measurements were performed using a precision balance (Ohaus Adventurer Precision), and length measurements were taken using the imageJ software.
    Retinas
    The retina is the light-sensitive tissue within the eye, and is composed of different cell layers organized ventrally and dorsally around the optic nerve (Fig. 1c). To analyze the retina’s cell layers, we removed the head region of euthanized fish in a way that allowed us to distinguish the right retina from the left retina, and the dorsal and ventral sides of the retina. This region was then fixed in Bouin solution before being embedded in paraffin for microtome sectioning (5 µm). Sections were then stained using hematoxylin and eosin. We chose cross-sections of the retina that were done at similar depth by selecting sections at the level of the optical nerve (Supplementary Fig. 5a). These sections enabled us to identify different cell segments, types, and layers, among which (i) photoreceptor external segments (perceiving light signals), (ii) photoreceptor nuclei, (iii) bipolar cells (which integrate the synaptic signals originating from the photoreceptors), and (iv) ganglion cells (which integrate signals from bipolar cells and create action potential toward the optic nerve) were easily distinguishable (Supplementary Fig. 5b). We only investigated the right eye of A. triostegus fish, as evidence suggests this species is visually lateralized at recruitment, and predominantly uses its right eye to examine visual predator stimuli14. Also, we only examined the dorsal side of the retina, as the ventral side (vs) was shown to not undergo change at metamorphosis in another coral-reef fish species, the goatfish Upeneus tragula13 (Supplementary Fig. 5a). To compare the developmental state of the retina between treatments, we looked at the peripheral area of the dorsal side (see the dotted square in Supplementary Fig. 5a, magnified in Supplementary Fig. 5b) as settlement-stage individuals in another acanthurid species (Naso brevirostris) showed weak if any spatial specialization of the retina, in particular on this axis68. We prioritized the examination of bipolar cell densities as important changes in bipolar cell density was observed during U. tragula metamorphosis13. However, we also examined the densities of photoreceptor external segments, photoreceptor nuclei, and ganglion cells along metamorphosis and across TH treatments, revealing for photoreceptor external segments (Supplementary Fig. 6) and nuclei (Supplementary Fig. 7) a TH-dependent density increase at metamorphosis, while ganglion cells showed no density variation during metamorphosis (Supplementary Fig. 8). Cell counting was performed in a 50-µm wide area perpendicular to the retina cell layers (Supplementary Fig. 5b). The measure of bipolar cell density corresponds to the number of bipolar cells per 0.001 mm² in the inner-nuclear cell layer (INL), after measuring the mean thickness of this INL (average of three measurements at random non-overlapping locations within the 50-µm wide area) (Supplementary Fig. 5b). The prn and ggc densities were obtained in a similar manner after measuring the mean width of their respective cell layer. Pes density corresponds to the exact number of pes in the 50-µm wide area as the pes cell layer is monocellular (Supplementary Fig. 5b). Cells that were located on the edges of the 50-µm wide area were included in the counts.
    Olfactory organ lamellae
    In fish, the olfactory organ is a fluid-filled blind sac that contains the ciliated sensory epithelium, which forms a rosette comprise of a number of folds, i.e., lamellae44. In A. triostegus, the left and right olfactory organs can be found in two cavities on the dorsal surface, between the eye and the snout edge, with water moving through each cavity from the anterior nostril to the posterior nostril (Supplementary Fig. 3). Pictures (e.g., Supplementary Fig. 3) were obtained using SEM microscopy following specialized tissue preparation involving the dissection of the olfactory organ (removal of the thin skin layer between the two nostrils) and fixation in a sodium cacodylate + glutaraldehyde solution (2.5% glutaraldehyde in 1 M sucrose and 0.1 M sodium cacodylate, pH 7.4) for a week at 4 °C. Samples were then washed (10% sucrose in 0.1 M sodium cacodylate solution, pH 7.4) 15 × 15 min at room temperature (RT). Samples were then dehydrated using successive ethanol (EtOH) baths (30%, 50%, 70%, 85%, 95%, 100%, 100%, 100%, each time during 15 min at RT). Samples were then placed in EtOH:HMDS (1:1) 15 min at RT, in 100% HMDS for 15 min at RT, and lastly in 100% HMDS for 30 min at RT. HMDS was used to replace critical point drying. Samples were not metalized. SEM pictures were obtained using a MiniMEB Hitachi TM3030 (University of French Polynesia). Given that lamellae are well formed and have a macroscopic size in A. triostegus at recruitment, lamellae counting was performed on tissues samples identically prepared, but observed under a simple binocular stereomicroscope. Lamellae counting was performed on both left and right olfactory organs to then have a measure of the average number of lamellae per olfactory organ. In the case where one of the left or right olfactory organ was damaged and thus accurate lamellae counts were not possible, we used the count from the other olfactory organ as the average number, as no significant difference was observed between the number of lamellae in the left and right olfactory organs in our preliminary observations.
    Lateral line trunk canal pores
    The lateral line system enables fish to detect water motions and pressure gradients, such as those caused by other fish (e.g., movement from other fish in the shoal or predator strikes). It is composed of superficial and canal neuromast receptor organs, which are the functional units of the lateral line system and are ciliary sensory organs, composed of hair cells, like those in the inner ear, located either on the skin or embedded in lateral line canals43. Canal neuromasts are found in the epithelium lining the bottom of the lateral line canals, and one canal neuromast is usually found within the short canal segments between two adjacent canal pores43. The development of neuromasts and the morphogenesis of lateral line canals and their pores initiate in late-stage larvae and continue through metamorphosis43. Counting the number of pores on the trunk canal is thus an appropriate way to rapidly characterize the development of the lateral line system when one cannot perform more advanced histological analyzes of the neuromasts. In d0 to d8 A. triostegus at recruitment, a fully formed trunk canal corresponding to a complete arched canal can be observed on each of the fish body flanks (Supplementary Fig. 4a). At this stage, A. triostegus does not exhibit scales69, and the trunk canal is therefore only composed of soft tissue (Supplementary Fig. 4a). Following the same preparation protocol as used for olfactory organs, we investigated the development of the lateral line system of A. triostegus by counting the number of pores on the trunk canal (Supplementary Fig. 4a-b). Counting was performed either on the left or the right side of the body, depending on tissue preservation. Indeed, as fish body frequently curved when dried to a critical point in HMDS, only one side of the body was generally accessible for counting trunk canal pores. We did not consider this an issue, as preliminary observations revealed no significant difference between the numbers of trunk canal pores present on the left or right flanks of the body. Variation in the number of pores cannot be attributed to variation in the length of the fully formed trunk canal (measured from the vicinity of the head to the base of the tail) as it does not change in A. triostegus during metamorphosis (Supplementary Fig. 9).
    Thyroid hormone quantification
    TH was extracted from frozen fish, following an extraction protocol adapted from previous studies70,71,72, including on coral-reef fishes11. Fish were individually crushed in 500 µl of methanol using a Minilys and glass beads (3*30 s, 5.000 rpm), centrifuged at 4 °C (10 min, 12.000 rpm), and supernatant reserved. These operations were performed twice, then fish were crushed one last time with 400 µl of methanol, 100 µl of chloroform, and 100 µl of barbital buffer (3*30 s, 5.000 rpm, RT), centrifuged at 4 °C (10 min, 12.000 rpm), and supernatant reserved. Pooled supernatants were then dried at 70 °C for 2 h. Dried pellets were re-suspended in 400 µl of methanol, 100 µl of chloroform, and 100 µl of barbital buffer, centrifuged at 4 °C (20 min, 12.000 rpm), and supernatant reserved. The same operation was again performed on the pellets. Pooled supernatants were once again dried out at 70 °C for 2 h with the final extract reconstituted in 2 ml of PBS 1× for quantification (Roche Elica kit on a Cobas analyzer, following the manufacturer’s standardized method). TH levels in pg g−1 of fish were then transformed into relative levels by selecting the respective control fish as standards in the increased temperature and CPF exposure treatment experiments.
    Behavioral tests
    A two-channel chemical choice flume73,74,75 was used to assess the responses of A. triostegus towards chemical predator cues (Supplementary Fig. 10). Each trial presented an individual fish with two water sources: control seawater (Ø = UV-sterilized and 1-µm filtered seawater from the collection site) vs “seawater containing chemical cues from predator” (P = UV-sterilized and 1-µm filtered seawater from the collection site in which five Lutjanus fulvus predators were soaked, into a 125-L tank, for 2 h prior to the experiment). Water was fed into the flume through two water inlets, with equivalent flow rates of 100 ml min−1 maintained using flow meters (MM Minimaster, Admi-France). This rate ensured laminar flow of each water source was maintained in parallel while allowing fish to swim naturally between the two water sources. Fine mesh and collimators also helped to ensure laminar flow of each water source was maintained75. Preliminary experiments were conducted to ensure the absence of unanticipated biased behavior within the two-channel flume (e.g., preference for one side of the flume over the other, irrespectively of the water sources, or preference for the drain area over the choice area). Prior to each trial, dye tests were conducted to confirm laminar flow, without eddies or areas of water mixing, within the choice area. After releasing the fish in the middle of the choice area, a 2-min acclimation period was observed, then fish position (left or right part of the choice area, or drain area) was recorded every 2 s for 5 min (Supplementary Fig. 10), using a camera (GoPro Hero 2) located above the edge of the flume tank. Water inlets were then switched (to account for any side preference due to fish’s immobility) followed by another 2-min acclimation period. A second 5-min test period followed, during which fish position was again assessed every 2 s. Preference or avoidance of water sources, and the absence of a side preference, were confirmed by comparing responses during the first and second 5-min test periods. These experiments were performed in the dark with red light, to limit potential visual perturbations such as the presence of an observer and to allow comparison between d2 and d0 fish, as d0 fish were tested immediately after collection (i.e., at night) as this is when they are actively moving from the ocean to the reef, and is thus the most biologically relevant time to do so. Fish that did not swim actively during the first acclimation period were removed from the analysis (n = 3) to prevent side preference bias. However, all remaining fish swam actively between the two water sources after water inlets were switched (either during the second acclimation period or during the second test period), ensuring no continuous side bias due to immobility. Fish that spent more than 50% of the test time in the drain area (i.e., where the two water sources mix) were also removed from the analysis (n = 4) as we considered that they did not show any particular preference or avoidance for any of the two water sources. Fish that did not make a clear choice between the two water sources but spent more than 50% of the time in the choice area were included in the analysis. This was done as we wanted to assess fish preference as well as the absence of preference.
    A double-choice tank was used to assess the responses of A. triostegus in the presence of a visual predator cues. Each trial presented an individual fish with a choice of two visual stimuli, each contained in a separate aquarium placed at the end of the central rectangular choice tank. These were an aquarium, containing a 10-cm (standard length) L. fulvus (P condition) vs an empty aquarium, equipped with an air stone (Ø condition) (Supplementary Fig. 11). Fish were first placed into the central “no choice” area of the choice tank for a 2-min acclimation period. During this time, fish were not able to see the contents of either adjacent aquaria or access the “choice” areas of the choice tank as opaque panels were positioned at the edges of the “no choice” area (see the dotted lines in Supplementary Fig. 11). Following the acclimation period, the opaque panels were removed, allowing fish to observe the visual stimuli in the adjacent aquaria through the transparent walls of the choice tank and to access the choice areas. Fish position (i.e., choice area 1, no choice area, choice area 2; Supplementary Fig. 11) was then assessed every 2 s over a 10 min, using a camera (GoPro Hero 2) to limit any external visual disturbances such as an observer’s presence. The camera was located above the choice tank. Location of visual stimulus (left or right side of the double-choice tank) was switched between each fish to ensure the absence of a side preference. Fish that remained immobile and spent >50% of the test time in the “no choice” area were removed from the analysis (n = 11), as we considered that they did not show any particular preference or avoidance for any of the two visual stimuli.
    Survival arena
    The survival tests presented in Figs. 2c, 3f were conducted in an arena set up in situ in a nursery lagoon area of the north coast (S17°29’7.0272″, W149°49’51.1166″). The arena consisted of a 1-m3 cage with a hard bottom covered with sand and coral rubble and four lateral walls made from 5-mm fine mesh (Supplementary Fig. 12). Each trial consisted of 45 fishes, with 15 from each treatment group. Fish from each treatment group were tagged with a specific color using visible implant fluorescent filament (Northwest Marine Technology) 2 h prior being released into the arena. For each trial, all fishes were released simultaneously and allowed to acclimate for 30 min before the introduction of six L. fulvus (15–20 cm SL). After 2 h, predators were removed, and surviving A. triostegus was identified to treatment using their color tag. Color tags attributed to each fish group were randomly switched between each replicate to ensure no predation bias based on tag color. Differences in survival during this predation test cannot be attributed to variation in fish size or condition between treatments, as these did not differ significantly between groups (Supplementary Fig. 13).
    Statistical analyses
    All statistical analyses were conducted using R version 3.5.376. Conway–Maxwell–Poisson (COM-Poisson) generalized linear models (GLM) were used to assess if pharmacological and anthropogenic stressor treatments influenced the number of lamellae, the number of trunk canal pores, and the number of survivors to the predation experiment77. COM-Poisson GLM were also used to assess if pharmacological treatments influenced the number of photoreceptor external segments. Linear models (LM) were used to assess if pharmacological treatments influenced the bipolar cell, ganglion cell, and photoreceptor nuclei densities, and if pharmacological and anthropogenic stressor treatments influenced fish Fulton’s K condition factor. LM were also used to assess if the trunk canal length varied with age. Gamma generalized linear mixed-effect models (GLMEM) were used to assess if anthropogenic stressor exposures influenced TH levels and T3/T4 ratios78. TH level or T3/T4 ratios were used as the dependent variable, and replicate was included as a random factor to account for differences in TH levels only due to the two different Cobas analyzers that were used in the two different years. As preliminary experiments provided no evidence that season and lunar phase affected T3 levels in metamorphosing A. triostegus, we did not include them in our analyses (Gamma GLMEM, Supplementary Fig. 14). For each model, diagnostic plots were examined and outputs compared with raw data to confirm goodness-of-fit and residual homoscedasticity, and, when applicable, residual normality was assessed using Shapiro–Wilk normality test. Paired t tests or Wilcoxon signed-rank tests were used to assess whether fish spent more time in the no cue choice area vs predator-cue choice area, depending on residual normality (Shapiro–Wilk normality test).
    Reporting summary
    Further information on research design is available in the Nature Research Reporting Summary linked to this article. More