Modelling the acclimation capacity of coral reefs to a warming ocean.

The symbiotic relationship between corals and photosynthetic algae is the foundation of coral reef ecosystems. This relationship breaks down, leading to coral death, when sea temperature exceeds the thermal tolerance of the coral-algae complex. While acclimation via phenotypic plasticity at the organismal level is an important mechanism for corals to cope with global warming, community-based shifts in response to acclimating capacities may give valuable indications about the future of corals at a regional scale. Reliable regional-scale predictions, however, are hampered by uncertainties on the speed with which coral communities will be able to acclimate. Here we present a trait-based, acclimation dynamics model, which we use in combination with observational data, to provide a first, crude estimate of the speed of coral acclimation at the community level and to investigate the effects of different global warming scenarios on three iconic reef ecosystems of the tropics: Great Barrier Reef, South East Asia, and Caribbean. The model predicts that coral acclimation may confer some level of protection by delaying the decline of some reefs such as the Great Barrier Reef. However, the current rates of acclimation will not be sufficient to rescue corals from global warming. Based on our estimates of coral acclimation capacities, the model results suggest substantial declines in coral abundances in all three regions, ranging from 12% to 55%, depending on the region and on the climate change scenario considered. Our results highlight the importance and urgency of precise assessments and quantitative estimates, for example through laboratory experiments, of the natural acclimation capacity of corals and of the speed with which corals may be able to acclimate to global warming.

Introduction

Shallow water coral reefs are marine limestone structures accreted by tiny organisms called polyps. They are characteristic of the tropical oceans, form habitats for a myriad of other organisms [1-3], and provide important ecological services, including food and coastal protection, for millions of people [4-6]. Coral polyps (corals henceforth) form a symbiotic relationship with unicellular photoautotrophs (the symbiont), called zooxanthellae [7, 8]. This association provides corals (the host) with photosynthetically fixed carbon [9, 10] and has thus contributed to their success in the nutrient-poor waters of the tropics [8, 11, 12]. Elevated sea temperature causes a breakdown of the coral-algae symbiosis [13-17]. In the worse cases, this breakdown leads to the expulsion of algae by the coral host, a process known as bleaching [13, 18, 19] because the loss of photosynthetic pigments makes the white skeleton of corals visible through the transparent tissue. Under the current rates of global warming [20, 21], a critically important aspect for the future of coral ecosystems is to determine whether corals will be able to respond at a sufficiently fast pace.

Corals can respond to global warming in different ways, including by moving to more favourable habitats, by genetic adaptation, or by acclimation. For sessile species like corals, range shifts are constrained by dispersal during their larval stage, the movements of which are strongly influenced by the prevailing currents [22]. Genetic adaptation is characterised by allele frequency changes between generations and is mediated by natural selection [23]. In contrast, acclimation is a response that does not involve genetic changes. It is characterised by phenotypic plasticity, whereby an alteration of the organism’s phenotype occurs in response to environmental change within the lifetime of the individual [23, 24]. Examples of phenotypic plasticity in corals include altered heterotrophic feeding during bleaching [25], increased retention of symbionts’ chlorophyll during heat-stress [26], enhanced photosynthetic rate [27], and induction of heat shock proteins [28] during light-stress, heat-stress, or both.

Previous modelling studies addressed coral adaptation either in a diagnostic fashion, as a threshold response mechanism [29-31], or by considering genetic responses of symbionts, encompassing an increase in thermal tolerance [32]. The thermal acclimation or adaptation capacity of coral reefs has been considered previously in two modelling studies [30, 31] and was based on empirical thermal bleaching thresholds, between 1°C-months and 6°C-months, derived from the most recent mean of maximal monthly temperatures, because these temperatures have shown damaging effects in coral reefs. However, the mechanisms underpinning thermal acclimation or adaptation, which depend on the physiological machinery of corals, are not considered in these previous modelling studies. In addition, little is known about the speed of coral acclimation, an aspect that is critical for producing reliable predictions about the fate of coral reefs in a changing climate.

Here we present a new model that captures a whole coral community by considering the average energy invested in the symbiotic relationship as a mean community trait fuelled by the physiological machinery of the corals. We then use this model in combination with observations of changes in coral cover over time to estimate the speed of coral acclimation at the community level. Finally, we investigate the effects that different global warming scenarios have on three coral reef systems of the tropics: the Great Barrier Reef, South East Asia, and the Caribbean (Fig 1). In our model (Fig 1a), coral growth is constrained by temperature-limited growth curves (Fig 1b) and corals respond to changing environmental temperature via acclimation (i.e. phenotypic plasticity). We make the distinction between “thermal acclimation and/or adaptation”, which is defined as an increase in bleaching thresholds [30, 31], and physiological acclimation, which we define as an increase in coral fitness under changing temperature. Physiological acclimation in nature encompasses phenotypic changes that individual corals can undergo in order to compensate for the growth deficiencies induced by thermal stress, these changes may include increased retention of chlorophyll [26], induction of heat shock proteins [28], and other physiological and immunological responses [33]. Our model does not resolve single species or individual organisms but it captures the effects that such changes may have at the community level through variations in the average trait.

Fig 1

Model schematic and studied regions.

(a) Schematic depicting the major interactions between the coral host and the symbiotic algae captured by the model; the coral host grows logistically as a function of symbiotic feedback and environmental temperature; corals invest energy in symbiosis (for example the energy necessary for providing CO2 to the algae [34–36]) and receives a symbiotic feedback (for example photosynthate); corals sustain symbiotic costs, which are associated to the maintenance of microenvironments for housing the algae [34] and to stress associated to photosynthesis (like the presence of reactive oxygen species [35]), and are subject to mortality; algae grow logistically as a function of environmental temperature and coral abundance; algae are expelled during bleaching events, which occur when environmental temperature exceeds the optimal regional temperature (i.e., T, panel b) for coral growth by a variable range of temperature increase reflecting the severity of bleaching (see subsection Bleaching). (b) Temperature-limited coral growth curves (Eq 7); dashed lines mark the regional temperature optima. (c) Studied regions: Great Barrier Reef (GBR), South East Asia (SEA), and Caribbean (CAR). The map is produced with the Python’s Matplotlib Basemap Toolkit available from https://matplotlib.org/basemap/api/basemap_api.html (© 2011, Jeffrey Whitaker).

The novelty of our work lays in the way we implement coral acclimation to changing temperature. In our model, community variations in physiological acclimation are captured by changes in an average physiological trait, which is defined as the mean energy that the coral community invests in the symbiotic relationship, and is proportional to the gradient of coral fitness. The constant of proportionality denotes the speed of coral acclimation, i.e. the speed with which the coral community moves towards an optimal trait value, one that maximises fitness, under changing environmental temperature. Future projections for bleaching, energy investment trait, and coral and symbiont abundances are produced under three Representative Concentration Pathways (RCPs) of future CO2 emissions: RCP 2.6, RCP 4.5 and RCP 8.5, respectively for low, moderate and high CO2 emissions.

To foster reproducibility, transparency, and flow of ideas, we provide the numerical code of our model as open-source software (https://github.com/systemsecologygroup/CoralZooxProjection) so that it can be used, modified, and redistributed freely.

Models and methods

We developed a trait-based mathematical model to investigate the acclimation dynamics of coral-algae symbiosis under different Representative Concentration Pathways (RCPs) and in different regions of the tropics. The model is based on evidence that corals are in control of the symbiotic relationship [37-39]. The model describes the temporal dynamics of the coral abundance (C), of the symbiotic algal abundance (S), and of the coral trait (U).

Since our study is focused on coral acclimation as a mechanism for counteracting global warming [40, 41], we choose to consider a coral trait (U) that is subject to plastic change over ecological time scales. This plastic trait is defined as the mean energy per coral abundance that a coral community invests per unit of time in the symbiotic relationship (for example, the energy necessary for providing CO2 to algae [34-36]).

The model is formulated as follows: where

The full set of model variables, parameters, units, and values are reported in Table 1. The different components and specific terms of the model are detailed in the following.

Table 1

State variables, functions, and parameters constituting our model.

Symbol	Description	Units	Value	Reference
C	coral abundance	cm2	variable
S	algal abundance	cells	variable
U	coral plastic trait (energy investment)	energy ⋅ cm−2 ⋅ month−1	variable
t	time	month	variable
F	fitness	month−1	function
κ	fraction of coral growth dependent on S	dimensionless	function
E	fraction of coral growth dependent on U	dimensionless	function
μ	cost of symbiosis	month−1	function
G C	temperature-limited coral growth rate	month−1	function
G S	temperature-limited symbiont growth rate	month−1	function
G max	coral maximum growth rate	month−1	0.83	[42]
a	symbiont linear growth parameter	month−1	0.09	[10, 32]
b	symbiont exponential growth parameter	°C−1	0.063	[43, 44]
K C	coral carrying capacity	cm2	4.4 ⋅ 1015†, 1.2 ⋅ 1016‡, 1.9 ⋅ 1015§
K S	symbiont carrying capacity	cells	function
K smax	maximum symbiont carrying capacity per coral abundance	cells ⋅ cm−2	3 ⋅ 106	[45]
M C	coral mortality rate	month−1	0.83 ⋅ 10−3 *
G	coral growth function	dimensionless	function
T	environmental temperature (forcing)	°C	external input
T¯	mean of growth temperature G	°C	26.8†, 28.1‡, 27.1§	[46]
T opt	optimal temperature for coral growth	°C	26.8†, 28.5‡, 27.6§
σ	standard deviation of G	°C	1.0†, 0.8‡, 0.9§	[46]
s	skewness of G	°C	2 ⋅ 10−4†, 3.8‡, 1.1§	[46]
α	coral linear cost parameter	month−1	10−3 *
r	coral exponential cost parameter	(energy ⋅ cm−2 ⋅ month−1)−1	12 ⋅ 103 *
β	strength of symbiotic feedback	(energy ⋅ cm−2 ⋅ month−1)−1	12 ⋅ 102 *
Γh	symbiont to host ratio for which κ = 0.5	cells cm−2	1 ⋅ 106‖	[45]
N	speed of acclimation (estimated in this study)	(energy ⋅ cm−2 ⋅ month−1)2	5.54 ⋅ 10−13†, 2.65 ⋅ 10−13‡, 2.375 ⋅ 10−13§

* Parameter not quantified in the literature, its value was thus chosen to obtain a good model to data fit and to produce stable dynamics.

† Value for Great Barrier Reef;

‡ Value for South East Asia;

§ Value for the Caribbean.

‖ Minimal value for healthy corals.

Coral dynamics

In our model, net coral growth (Eq 4) is simulated as the difference between gross growth, G κE(1 − C/K), and losses due to symbiotic costs (Eq 6) and natural mortality, which is captured by the parameter M, which accounts for losses other than those related to the maintenance of the symbiotic relationship (e.g., due to senescence or physical damages).

Gross growth, G κE(1 − C/K), is the product between a temperature-dependent growth rate G, a symbiotic feedback κE (Eq 5), and a logistic term. The logistic term, which is defined by the carrying capacity K, is the most commonly used formulation for limited growth. We calculated the carrying capacities of a specific region by summing up the planar surface area of all the potential reef habitats estimated by a previous study [47] in that region, and we accounted for the shape of corals by multiplying these values with the mean of the conversion factors, 11.86 and 16.4 for, respectively, massive and branching corals [48]. This approach for calculating coral carrying capacities allows us to account for the contribution, in roughly equal proportions, of the two most common coral morphologies. In reality, these morphologies may not always occur in equal proportions. Albeit with this caveat, a previous study [48] determined that this approach produces more realistic estimates than simply considering planar habitat areas.

The symbiotic feedback κE (Eq 5) reflects the benefit that corals receive from algae. κ is the fraction of coral growth due to the translocation of photosynthate and thus dependent on symbiont abundance. κ tends to a maximum 1 as the symbiont abundance S increases, and half saturates as the symbiont abundance reaches a certain fraction Γ of coral abundance C. E is the fraction of coral growth dependent on the amount of energy U invested in symbiosis. E increases exponentially with U at a rate β and saturates to 1, reflecting the fact that benefits received by corals cannot increase indefinitely. It follows that the symbiotic feedback κE is 0 in the absence of symbionts and/or in the absence of energy investment U and is maximised when the symbiont abundance S and the energy investment U reach optimal values.

At minimum symbiotic feedback (i.e. when κE = 0), corals grow at rate 0; at maximum symbiotic feedback (i.e. when κE = 1), corals grow at rate G, which depends on environmental temperature T, as follows: where G(T)/max[G(T)] is the normalised coral growth function and G is the maximum possible coral growth rate. Fig 1b shows the temperature-limited growth rate curves G(T) of the different regions. If environmental temperature falls away from these tolerance ranges then coral growth will be zero and the abundance of the community will decline.

Given that the extension rates of corals range between 0.08 and 20 cm year−1, depending on the coral species and their location depth [42], we choose a coral maximum growth rate G equal to 10 year−1, i.e. 0.83 month−1, to reflect the maximum growth rate (in terms of fold change per unit of time) of coral communities composed of both massive and branching corals. Thus, G, represents the proportion of maximal growth that the coral can achieve given the environmental temperature and given the symbiotic association with the algae.

The global occurrence of coral reefs as a function of temperature, can be represented by a skewed normal distribution, with mean , standard deviation σ, and skewness s [46]. Thus we assumed where ϕ and Φ are, respectively, probability and cumulative distribution functions of a normal distribution with mean 0 and standard deviation 1. This formulation associates temperature-limited coral growth rates to fixed thermal tolerance distributions.

The costs incurred by the coral host for investing energy into the symbiotic relationship are represented by the term μ(U, S) (Eq 6). We distinguish between costs associated merely to the presence of the symbiont (thus depending on S) and costs related to the energy invested in the symbiotic relationship (thus depending on U). The costs associated to the presence of the symbiont (e.g. costs associated to the production of peri-algal vacuoles [8] are represented by a linear term (S/K). This formulation simulates the presence of a physiological limit on the size of the symbiont population that corals can sustain. The costs related to the energy invested in the symbiotic relationship, e.g. damages from reactive oxygen species [35], are non-saturating and increase exponentially at a rate r. α is a proportionality term bearing the unit of the symbiotic cost. It follows that when U = 0, then μ ≠ 0 if S ≠ 0, reflecting the fact that corals still bear costs related to the mere presence of symbionts even when no energy is invested in the symbiotic relationship. These can be considered as baseline operating costs for corals. When S = 0, then μ = 0, reflecting the lack of symbiotic costs in the absence of symbionts. In this case, corals do not receive any symbiotic benefit and die at a mortality rate M.

Symbiont dynamics

Since the growth of zooxanthellae is controlled by the coral host [37-39], we assumed that the symbiont population grows logistically (Eq 2) with a maximum growth rate G and a carrying capacity K that depends on coral abundance C. In analogy to other unicellular photoautotrophs, the maximum growth rate of the symbiont depends on temperature according to the following function: where T is environmental temperature, a = 1.0768 year−1, i.e. 0.09 month−1 [10, 32], and b = 0.063°C [43]. Eq 9 is an envelop function for temperature-dependent growth rates expressed by multiple phytoplankton species in different laboratory cultures [43].

The carrying capacity is defined as: where K is the amount of symbiont abundance per coral abundance found, on average, in healthy coral communities. K usually ranges between one and six millions cells per cm2 of coral surface, depending on the coral species [45, 49]. We, therefore, set K = 3 ⋅ 106 cells ⋅ cm−2.

The full control of algal growth by the corals is attained by preventing zooxanthellae to take up any photosynthate they produce and by assuming an infallible ability of the host to control the nutrient flux. The latter ensures that the symbiont population never exceeds the hosting capacity of the corals. In nature, eutrophication can concur with temperature to induce a breakdown of the symbiotic relationship through uncontrolled symbiont growth [50]. These synergistic effects, however, are beyond the scope of our study.

Bleaching

Bleaching is defined as the loss of zooxanthellae cells and/or zooxanthellae pigments [51, 52]. This phenomenon is caused by a variety of factors, the most important being increases in sea temperature and solar radiation [19, 53]. Evidence indicates that the loss of cells is driven by high temperature, whereas the loss of pigments is driven by high light [54]. Since our work mainly focuses on bleaching induced by thermal stress, we simulate this process as the loss of zooxanthellae cells.

Temperature thresholds for bleaching are typically estimated as the level of thermal stress, which are known as Degree Heating Weeks (DHW) [15, 55, 56] (see also https://coralreefwatch.noaa.gov/satellite/index.php) or Degree Heating Months (DHM) [30]. These metrics represent different ways of measuring accumulated SSTs above a climatological maximum [30, 55]. They account for both magnitude and duration of thermal stress, which are the determining factors of the severity of bleaching events [8]. These metrics do not consider the amount of zooxanthellae abundance lost, but rather indicate the percentage of corals at risk of degradation due to bleaching [30, 55]. In addition, these metrics account only for the effect of temperature despite solar irradiance is also a decisive factor. New methods, that describe bleaching by the combined effect of solar irradiance and temperature, are being developed [57]. Here, we use a much simpler method. We implement bleaching as a reduction δ in symbiont abundance when, at a given time t, the environmental temperature T(t) exceeds the optimal temperature for coral growth T by some amount ϵ falling within the observed ranges of temperature increase ΔT (Table 2). Due to the high variability shown by the observations (S1 Appendix), the percent reduction of symbiont abundance δ corresponding to ΔT is randomly drawn from a uniform distribution constrained by the observed ranges of symbiont reduction ΔS (Table 2). In summary, a bleaching event at a time t is included in the symbiont dynamics by imposing the following condition on the symbiont abundance:

Table 2

Ranges of temperature increase (ΔT) and corresponding ranges of symbiont abundance reduction (ΔS) derived from observational data of temperature-induced bleaching (see S1 Appendix, for additional details).

Region	ΔTobs (°C)	ΔSobs (%)
GBR	2–4	10–95
	≥ 4	60–95
SEA	≥ 1	25–95
CAR	1–3	15–95
	3–6	35–95
	≥ 6	80–95

Being based on observations of symbiont abundance reduction following bleaching events, our method reflects the long-term evolutionary adaptation to local temperature.

Coral acclimation

In contrast to a previous work [58] that simulated the genetic adaptation of corals, a novel and crucial feature of our model is the focus on coral acclimation to changing temperature. In our model, corals can acclimate within fixed temperature-limited growth curves (Fig 1b), which are expressions of long-term evolutionary adaptations to local temperature variations. An approach based on genetic adaptation would involve, instead, shifts in thermal growth optima T, i.e. changes in the temperature-limited coral growth curves (Fig 1b). These temperature-limited growth curves reflect community-aggregate temperature dependencies consistently with the fact that our model captures acclimation at the community level through mean changes in the plastic trait U.

Eq 3 describes the temporal dynamics of the trait U. This trait is a physiological trait reflecting the energy that corals invest in the symbiotic relationship. By assuming that the temporal change of U is proportional to the fitness gradient of the coral, we capture the general feature of any adaptive process in which the trait of an organism moves towards values that increases fitness [59]. This is consistent with the “adaptive plasticity hypothesis” [60], which states that phenotypic plasticity maximises the fitness of a population in a variable environment (although in nature plastic responses do not always increase fitness and can actually be maladaptive). The constant of proportionality N (Eq 3) represents the speed with which corals move towards an optimal trait value, i.e. the one that maximises their fitness (Eq 4). Coral fitness, in our model, depends on many factors, including temperature (via coral growth, Eq 7). Thus corals acclimate to maximise energy gains under changing temperature conditions.

Speed of acclimation

We estimated the speed of acclimation, for each studied region for the period 1970–2007 (Fig 2), by comparing the simulated relative coral abundance (i.e. percentage of coral abundance with respect to regional carrying capacity) with observed relative coral abundance (i.e. the mean percentage of coral cover with respect to the potential reef habitat estimated visually by the person who collected the data). For the observational data, we used previously collected data of changes in coral cover over time [61], see S2 Appendix, and integrated this dataset with observations from the GBR [62]. Observations of percentage coral cover are usually collected without any specification of the size of the potential reef habitat from which it was estimated and therefore might not reflect the regional coral carrying capacity. However, given that a potential reef habitat represents a snapshot of the total area that could be covered by corals, we assumed that the mean of all observations of coral cover reflects, qualitatively, a measure of coral abundance in relation to a carrying capacity (i.e. in relation to the total amount of coral cover that the considered region can sustain), see section Coral dynamics. The estimates included the following steps: (1) the model parameters were fixed to reported literature values (see Table 1), (2) the model was run with historical environmental temperature forcing (i.e. the WOD13 data only from 1970 to 2010, see S3 Appendix), and (3) the speed of acclimation was adjusted to match model results with observations (Fig 2). The model results that compared best with observations were selected visually.

Fig 2

Model simulations at different speeds of acclimation.

Model simulations (purple lines) are qualitatively compared to observations [61, 62], expressed as yearly median of coral abundances (green dots). The selected speed of acclimation, in each region (panels a, b, and c, respectively), is the one that produces results (thick purple line) consistent with observations. The arrows indicate the direction of increase in speed of acclimation and the thin grey lines indicate, for each region, environmental temperatures relative to corresponding optimal growth temperatures T.

Study regions and temperature forcing

We apply our model to three distinct coral-reef locations (Fig 1c): the Great Barrier Reef (GBR), South East Asia (SEA), and the Caribbean (CAR). For the Great Barrier Reef, we considered the region between 145° East and 165° East and between 10° South and 28° South. For South East Asia, we considered the region between 100° East and 137° East, and between 13° North and 10° South. The Caribbean region is between 65° West and 80° West and between 10° North and 20° North.

We collected Sea Surface Temperature (SST) data from the World Ocean Database 2013 (WOD13, https://www.nodc.noaa.gov/OC5/WOD13/) and considered only the data flagged as acceptable in quality by the WOD13 curators. For the future temperature scenarios, we considered the Representative Concentration Pathways (RCP) designed for the Coupled Model Intercomparison Project Phase 5 (CMIP5) [63]. Thus, we collected the temperature data of the RCP scenarios generated by the Max Planck Institute Earth System Model (MPI–ESM), compiled and maintained by the German Climate Computing Centre (DKRZ https://esgf-data.dkrz.de/search/cmip5-dkrz/). We considered the low RCP 2.6, the moderate RCP 4.5 and the high RCP 8.5 CO2 emission scenarios at medium-resolution (MPI-ESM-MR). These scenarios predict that, relative to 1986–2005, temperatures can rise for the period 2081–2100 between 0.3 and 1.7°C under RCP 2.6; between 1.1 and 2.6°C under RCP 4.5, and between 2.6 and 4.8°C under RCP 8.5 [64]. The combined environmental temperature datasets (the WOD13 historical data from 1955 to 2010 and the future RCP scenarios from 2010 to 2100) used to force the model are presented in S3 Appendix.

In order to assess the effects of the long-term trend of global warming, we conducted model simulations under the hypothetical absence of short-term (monthly) temperature fluctuations, i.e. without bleaching. By visually comparing the model results obtained with bleaching and without bleaching, one can also evaluate, albeit qualitatively, the impact of bleaching events. The experiments without bleaching were performed by forcing the model with the annual averages of environmental temperatures for the period 1955–2100. The results of these experiments are presented in S4 Appendix.

Simulations and sensitivity analysis

The mathematical model is coded in Python. In the code, small terms are added to the variables in the denominators in order to prevent divisions by zero. The simulations are structured as follows. We first consider a spin-up phase of 2000 years during which we let the model dynamics evolve under fixed temperatures (equal to the average temperatures of the period 1955–2000 in the three regions, which are 25.90°C, 28.45°C, and 27.57°C for, respectively, the Great Barrier Reef, the South East Asia, and the Caribbean). This spin-up phase removes numerical artefacts typically occurring at the beginning of a simulation due to non-linearities in the model equations. After this phase, the model has reached an equilibrium and we then introduce the temperature forcing for the period 1955–2100 to produce the actual long-term model results.

The initial conditions were chosen as follows: C(t = 0) = 0.75 ⋅ K cm2; U(t = 0) = 5 ⋅ 10−7 energy cm−2 month−1; S(t = 0) = 10−3 cells. These initial conditions refer to the beginning of the spin-up phase, 2000 years prior 1955. Not knowing the abundances of corals and symbionts in the regions of interest at this initial time, we adopted a conservative approach by setting the initial coral abundance to 75% of the coral regional carrying capacities (K), which we estimated from suitable coral reef habitats (see subsection Coral dynamics). The initial conditions for U and S were chosen based on technical constraints in order to ensure that the model results are at equilibrium throughout the simulations and to avoid numerical crashes. However, the functional relationships between corals and symbionts in our model (e.g., the amount of symbiont abundance per coral abundance, K, used to calculate the symbiont carrying capacity, see subsection Symbiont dynamics) are based on observational data. Therefore, despite the caveats, we are confident that, during the spin-up phase, the model results evolve towards realistic abundance levels for both symbionts and corals.

Given the uncertainties involved in modelling studies like this one, we conducted an in-depth analysis to explore the sensitivity of the model results to specific assumptions and to variations in the speed of acclimation and the other parameters. With respect to specific assumptions, we tested the model results in the absence of bleaching, as explained at the end of subsection Study regions and temperature forcing, and in the absence of acclimation (i.e. with N = 0 in Eq 3, which implies for corals a constant investment of energy into the symbiotic relationship). The results of these sensitivity analyses are presented in the next section and in S5 Appendix.

Results

It is currently unknown whether the rate of coral acclimation, i.e. the speed with which corals acclimate to changing environmental conditions, is fast enough to match, and possibly offset, the current and future rates of warming. We do not have any information on the speed of coral acclimation and the physiological and ecological mechanisms with which coral reef communities may be able to acclimate are only poorly understood. Therefore, we provide a first, qualitative estimate of the speed of coral acclimation N using our model in combination with observations on coral cover. Although coral cover data are influenced by a blend of processes and factors (e.g. multiple co-occurring environmental disturbances, ecological competition, etc.), they provide a preliminary workbench and a comparable metric across different reefs for first qualitative estimates. The observations show an overall decreasing trend in relative coral abundance, for the period 1970–2010 (Fig 2, green dots). In all regions, the simulated relative coral abundance (Fig 2, thin purple lines) increases with increasing speed of coral acclimation (Fig 2, upward arrow). We estimated speeds of acclimation N = 5.54 ⋅ 10−13, N = 2.65 ⋅ 10−13 and N = 2.375 ⋅ 10−13 for, respectively, the Great Barrier Reef, the South East Asia and the Caribbean. These numbers are very small because, according to the units of the model, the speed of coral acclimation reflects the amount of energy that the equivalent of 1 cm2 of coral cover (i.e., an extremely small portion of a coral colony) invests into the symbiotic relationship every month (see Table 1).

In our model, the speed of acclimation depends on several factors, including (1) the equilibrium of the abundance levels reached during the spin-up phase, (2) the temperature-limited growth formulation, and (3) the observed relative coral abundances. Thus, corals exhibit different speeds of acclimation in the three regions (Table 1). This reflects the different acclimation capacities that coral communities with varying species compositions can have in different regions. The estimated speeds of acclimation allowed us to produce predictions for the dynamics of coral trait and coral and algal abundances under increasing bleaching events resulting from different emission scenarios.

Future projections

Our model indicates that the cumulative number of bleaching events increases with increasing emissions in all regions (Fig 3a–3c). However, the rate of increase in bleaching events is less pronounced in the Great Barrier Reef (Fig 3a) than in the other regions (Fig 3b and 3c). This allows corals of the Great Barrier Reef to better acclimate to the increasing temperature by increasing energy investments U (Fig 3d–3f). The capacity of corals to acclimate, and thus to counteract bleaching, is lowest under scenario RCP 8.5 (Fig 3d–3f).

Fig 3

Simulated trait and abundance dynamics in the three regions and under different RCPs.

(a-c) Cumulative number of bleaching assuming that these events occur whenever environmental temperature exceeds by 2°C the optimal temperature for coral growth. (d-f) Coral energy investment trait. (g-i) Coral abundance and (j-l) symbiont abundance, relative to the period 1986–2005. Note that in South East Asia and in the Caribbean, the dynamics of coral trait and coral abundance under RCP 4.5 overlap with those under RCP 8.5. In the year 2010, the coloured lines and the black lines are at different levels because, in the runs with acclimation (coloured lines), corals are able to reach higher abundances during the spin-up phase and between 1955 and 2010, thus increasing the overall performance of the coral-algae complex.

The increasing number of bleaching events is associated with declines in coral abundance in all regions, albeit the decline is least severe in the Great Barrier Reef (Fig 3g–3i). Bleaching events (Fig 3a–3c) are also characterised by fluctuations in symbiont abundance (Fig 3j–3l). Under RCP 4.5 and RCP 8.5, the symbiont populations of South East Asia and the Caribbean collapse by the year 2060 due to the high number of bleaching events in those regions. In our model, corals die at a fixed mortality rate of 0.83 ⋅ 10−3 month−1, implying that when symbionts are fully expelled corals will decline slowly. This is why neither fluctuations in symbiont abundance nor a full expulsion of symbionts produces a complete collapse of the coral communities (Fig 3g–3i).

Corals invest energy into the symbiotic relationship in order to “harvest” photosynthetic products from the symbionts. The benefits of investing energy into the symbiotic relationship (represented by the coral gross growth, the positive term in Eq 4) manifest themselves in pluses following heat waves (see S6 Appendix). The benefits of the symbiotic relationship for corals change when the physiological responses that bolster the symbionts are activated by the corals during heat waves. However, benefits and costs are nearly anti-reciprocal (because of the nature of our modelling approach, according to which the trait evolves towards values that optimise fitness) and thus cancel each other out, producing a continuous, smooth dynamics in the coral trait (Fig 3d–3f).

The model runs conducted without acclimation confirms that the capacity of corals to respond to increasing temperatures is generally low (Fig 3d–3i). The acclimation capacity of corals is among the lowest under RCP 8.5 because, under this scenario, environmental temperature T moves away from the thermal optima T and even reach values that are outside the temperature-limited coral growth curves (Fig 4). The acclimation capacity of corals is higher in the Great Barrier Reef, as compared to other regions, because in the Great Barrier Reef the temperature trend remains within the temperature-limited coral growth curves, at least under RCP 2.6 and RCP 4.5 (Fig 4).

Fig 4

Monthly temperature forcing scenarios and thermal-limited coral growth curves.

Low emissions (RCP 2.6) produce temperature trends (grey lines) that fall within the thermal-limited coral growth curves (coloured lines in the right side of each panel) in all regions (a-c). As emissions increase (RCP 4.5), the trends in environmental temperatures move away from the temperature optima T (marked by dashed lines), especially in the South East Asia and in the Caribbean (d-f) and even fall outside the thermal tolerance curves under RCP 8.5 (g-i). The dotted lines mark the limits of the coral thermal tolerances.

Overall, for the period 2081–2100 relative to 1986–2005, our model predicts percentage declines in coral abundances by 15%, 12%, and 18% under, respectively, RCP 2.6, RCP 4.5, and RCP 8.5 in the Great Barrier Reef; by 47%, 55%, and 53% under, respectively, RCP 2.6, RCP 4.5, and RCP 8.5 in South East Asia; and by more than 42%, 49%, and 52% under, respectively, RCP 2.6, RCP 4.5, and RCP 8.5 in the Caribbean.

Model sensitivity to speed of acclimation

We performed simulations over a range of speeds of acclimation with and without bleaching. We scaled the resulting coral mean abundances in order to highlight the effects produced by ±25% change in the value of each parameter at a corresponding speed of acclimation. In all regions, coral abundances increase with increasing speeds of acclimation, regardless of the percent change in any of the model parameter considered and independently of the presence of bleaching (see Figs 5 and 6, for the case with bleaching, and S5 Appendix, for the case without bleaching).

Fig 5

Sensitivity to speed of acclimation N for +25% change in each parameter.

Simulations with bleaching. Vertical lines mark the speed of acclimation we estimated from coral cover data (see S2 Appendix).

Fig 6

Sensitivity to speed of acclimation N for −25% change in each parameter.

Simulations with bleaching. Vertical lines mark the speed of acclimation we estimated from coral cover data (see S2 Appendix).

Discussion

The potential for coral communities to acclimate to global warming is critically important for the future of reef ecosystems. Yet, and despite major scientific efforts devoted to this aspect, we still know surprising little about it. The rate with which corals can acclimate to increasing temperatures is also a subject of controversy [65], perhaps unsurprisingly given the many different physiological and ecological mechanisms potentially involved (see [26, 28, 33]). Using our model in combination with coral cover data [61, 62], we produce first-order estimates of the speeds of coral acclimation (N) for the three different regions considered in this study. Physiological acclimation in nature involves phenotypic variations that could be brought about by plastic changes in the physiology of the different populations composing the coral community or by shifts in species compositions. Our model does not resolve single species but it captures the effects that such shifts may have at the community level through changes in the average trait.

Being based on qualitative comparisons between model results and coral cover data and since most of coral cover data are not well resolved in terms of spatial and temporal coverages, these estimates remain somewhat crude. However, to our knowledge, the coral cover data we used constitute the best time-series currently available for attempting such preliminary estimates.

With our estimated speeds of acclimation and for the period 2081–2100 relative to 1986–2005, the model predicts up to 2% increase in energy investment U (e.g. in the Great Barrier Reef under RCP 2.6, Fig 3d) and up to 55% decrease in coral abundance (e.g. in South East Asia, under RCP 8. 5, Fig 3h). We should point out that the decreases in coral abundances shown by our results are rather conservative predictions because, for example, our model does not include coral starvation mechanisms under heat stress events [66]. Nonetheless, our results indicate that the current rate of coral acclimation may not be sufficient to preserve coral reefs in the future, unless rapid genetic changes allow corals to shift their temperature-limited growth to a higher temperature optimum (see Fig 4 showing projected temperatures moving outside current temperature-limited coral growth curves under increasing emissions). Transplant experiments suggest that both genetic adaptation and acclimation can operate in some populations of fast-growing corals [26].

We also found that, under the hypothetical absence of short-term (monthly) temperature fluctuations, a substantial decline in coral abundance will occur in South East Asia and in the Caribbean (e.g. 27% and 37% decrease in coral abundance under, respectively, moderate RCP 4.5 and high RCP 8.5 emission scenarios, see S4 Appendix). Previous model projections [30, 31] showed that even if coral reefs had high thermal acclimation or adaptation capacities, they would still undergo long-term degradation. Consistently, our model indicates that, even if the conditions causing bleaching were to be mitigated, coral abundance would still decline due to the long-term trend component of global warming (see S4 Appendix). Although recent observations showed that coral reefs have already acclimated to an increase in temperature of 0.5°C [67], the physiological mechanisms behind this change are not clear. A possibility is that changes in symbiont composition (towards more thermally tolerant symbionts) could have increased the thermal tolerance of the coral-algae complex [52] and thereby their thermal bleaching threshold.

Our sensitivity analysis shows that higher speed of acclimation N would lead to higher coral abundance (Figs 5 and 6, and S5 Appendix). This indicates that our acclimation formulation is robust with respect to specific choices of parameter values because coral abundance always increases with increasing speed of acclimation, as expected, given that faster acclimation should lead to higher abundance yield. The model results are sensitive to parameters such as maximum coral growth rate G (see S5 Appendix). This suggests that local management policies aiming at reducing nutrient runoff and pollution could be an effective strategy for mitigating anthropogenic impacts on coral growth [68] and, thus, for buffering the decline of coral communities. Additionally, the parameter G, corresponding to overall coral community growth, depends on the community composition because different coral species display different growth rates [42]. Shifts in species compositions (not captured by our model) might contribute to increase the value of G and, consequently, mitigate the decline of coral-algae abundances. The endeavour of capturing inter-specific responses of corals to climate change is relevant but it would require a different modelling approach than that used here, for example, Agent-Based Modelling [65].

Our modelling approach is based on a generalised theory of acclimation and thus we conceptualised the coral trait as the energy that corals invest in the symbiotic relationship. This approach allows us to derive only a qualitative understanding of what might occur to corals under global warming. Laboratory data would be needed to equip the model with a less abstract formulation of the energy investment trait for example based on carbon and nitrogen fluxes. Alternatively, our model could be further developed to include a more detailed treatment of the phyisological and biogeochemical processes involved in energy investment by following, for example, the principles of Dynamic Energy Budget theory [69, 70]. Additionally, our modelling approach considers coral and algal communities as single entities, despite evidence shows that the thermal acclimation of symbionts could be species-specific and that harbouring mixed algal populations could constitute an ecological advantage for corals [52]. The effects of different combinations of symbiont species and their shuffling under changing environmental temperature are thus promising avenues for future research.

Temperature increase is not the only problem faced by corals. Many anthropogenic stressors, such as eutrophication, ocean acidification and deoxygenation, concur to reduce coral abundance over time [16, 71, 72]. In this respect, our results are quite conservative given our focus on temperature-related disturbances. However, we hope that our modelling study can foster research on the rates of coral acclimation, which is a key natural determinant of coral survival under global warming. Gobal solutions for reducing emissions, management policies for minimising local anthropogenic threats, and human-assisted evolution remain the ultimate strategies for protecting coral reefs because, according to our model results, their natural acclimation capacity alone will not be sufficient to offset the effects of global warming.

Levels of bleaching.

(PDF)

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Speed of acclimation.

(PDF)

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Forcing data.

(PDF)

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Simulations without bleaching.

(PDF)

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Sensitivity analysis.

(PDF)

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Symbiotic relationship: Benefits versus costs for corals.

(PDF)

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14 Nov 2021

Dear Prof Merico,

Thank you very much for submitting your manuscript "Modelling the acclimation capacity of coral reefs to a warming ocean" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

Thank you for submitting your work to PLOS Computational Biology, overall, the paper is interesting and provides fresh insights on modeling for coral reef populations an important and understudied topic. The reviewers have provided ample feedback that is bound to make this manuscript better in the next revision. Key issues such as the assumptions of the model, distinction between acclimatization and genetic adaptation must be addressed. Please make the changes requested by the reviewers address them with a point-by-point response. In addition, the manuscript can benefit from a round of proof-reading to eliminate some of the lingering grammar mistakes and improve the overall readability. I will be looking forward to reading the revised manuscript.

Best,

Bishoy

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Thank you for submitting your work to PLOS Computational Biology, overall, the paper is interesting and provides fresh insights on modeling for coral reef populations an important and understudied topic. The reviewers have provided ample feedback that is bound to make this manuscript better in the next revision. Key issues such as the assumptions of the model, distinction between acclimatization and genetic adaptation must be addressed. Please make the changes requested by the reviewers address them with a point-by-point response. In addition, the manuscript can benefit from a round of proof-reading to eliminate some of the lingering grammar mistakes and improve the overall readability. I will be looking forward to reading the revised manuscript.

Best,

Bishoy

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: In this paper, the authors develop a computational model of coral-symbiont dynamics in the context of rising sea surface temperatures to estimate the extent to which phenotypic plasticity can keep pace with global warming projections in three distinct coral reef systems: the GBR, SE Asia, and the Caribbean. The authors first formulated a general dynamical population model and then visually fitted predictions of this model to multi-decadal time series of coral cover in each of the three focal reef systems. This fitting provided system-specific estimates for rates of adaptation in a coral trait that translates to energetic investment in symbiotic zooxanthellae, estimates then used in future projections of long-term coral cover in each system under each of three region-specific future climatic warming projections. The authors find that the ability of coral communities to acclimate to future warming is generally limited but varies by region, with the GBR showing the greatest and the Caribbean the least capacity to adapt to keep pace with climatic projections. This work contributes a novel, empirically rooted computational modeling framework that provides important initial insights on the capacity for reef forming corals to use phenotypic plasticity to counter warming - a poorly understood phenomenon that is fundamental to our understanding of the ecology and conservation of coral reefs globally in the face of unprecedented anthropogenic threats.

I really enjoyed reading this paper. Aside from very minor grammatical issues throughout, it was easy to follow and was well motivated, methods and results clearly presented, and conclusions well justified by the findings. I also think that this type of global scale, data-motivated projection modeling is exactly the kind of work that is needed to set the stage to establish realistic, empirically rooted estimates for what the future will hold for critically threatened ecosystems. I commend the authors on the novelty and practicality of the work. I believe that a revised version of this work could be a highly cited addition to this journal. To this end, below I offer some comments and suggestions (with line number, where applicable) that I hope held improve the final version of the ms.

First, since coral cover is the only metric used in the time series that the model is being fitted to, I find myself wondering how much a signal of acclimation could be falsely attributed to a shift in coral species assemblage. For example, if temperatures increase over, say, 5 years in one of the study regions, and coral cover initially dips but then rebounds, this may fit the results of a model with acclimation and no species turnover when it is actually species turnover in this case that is driving the pattern. I appreciate that the authors qualify their findings in several instances by acknowledging both that this work is essentially a ‘first pass’ at estimating a very difficult, but crucial (from a conservation perspective) empirical metric (acclimation rate) and that other, not-modeled factors could be playing a significant role in the time series to which the model was fitted. But I think the authors could go a bit deeper here (e.g., discussing leading alternative drivers for the patterns observed and the likelihood that these would quantitatively or qualitatively affect the paper’s conclusions), to better contextualize their findings and the extent to which it seems likely that the model’s estimates for acclimation rate would be anywhere near reality. This additional content would also help paint a clearer picture for future work, by helping to prioritize the most timely extensions of this modeling framework.

Second, I think it would be helpful to have a bit more motivation for the mechanism of acclimation - how realistic is it for trait-dependent increases in coral energetic investment in symbionts to prevent bleaching? And what occurs physiologically to allow this to happen? A deeper foray into why this approach is realistic would help, I think, give credence to the overall paper results, which stem from these fundamental assumptions.

More specific / minor commoners:

Fig. 2 shows data juxtaposed to simulations for different acclimation rates, but it would be helpful to contextualize these plots a bit more by also showing SST over this same time period, perhaps absolute temps with a reference to each study region’s optimum value from Fig. 1b.

171: “We implement bleaching as a reduction in symbiont abundance when environmental temperature exceeds Topt, i.e. the optimal temperature for coral growth.” Table 2 then mentions that once the threshold temperature is exceeded, bleaching is determined by a draw from a uniform distribution. But isn’t bleaching severity correlated with temperature? Thus, I’m wondering: why not make bleaching a monotonic function of temperature, after the threshold is crossed, or, to maintain the stochastic element, make it a draw from a skewed distribution that reflects the bias of greater bleaching with greater temperatures? This seems reasonable, and so could be worth using, even as an alternative formulation to test the robustness of findings.

85: “…means that we always assume that the reef habitat has a maximal capacity of hosting an equal proportion of massive and branching corals.” Could you please unpack this statement a bit more? It’s not clear to me how the conversion factors mentioned in the preceding sentence ensure equal proportions of the two coral growth morphologies. I also wonder whether this assumption of equal proportions is also one that could be relaxed (perhaps based on region-specific relative species abundance data) to test the robustness of findings.

110: missing ‘cm’ after 10 and 0.83

152: “…host to control the nutrient flux. The latter ensures that the symbiont population never exceeds the hosting capacity of the corals.”

The authors later mention eutrophication as a potentially important additional factor to consider in the Discussion, but it could be useful to point out here how this assumption can be violated: data suggest that eutrophication can elicit a breakdown in the coral-zooxanthellae mutualism, whereby uncontrolled symbiont growth can actually depress coral growth (e.g., Gil, MA. “Unity through nonlinearity: A unimodal coral-nutrient interaction”. Ecology 2013). It’s outside the scope of this paper to speculate too much on potential indirect environmental effects that could interact with coral acclimation to rising temperatures, but it is also interesting to consider that eutrophication is often driven by runoff events that can increase in magnitude and frequency with warming, but in a region-specific manner - perhaps a cool future extension of this model.

201: ‘a shifts’ should be ‘an increase’

221: “However, given that a potential reef habitat represents a snapshot of the total area that could be covered by corals, we assumed that the mean of all observations of coral cover reflects, qualitatively, a measure of coral abundance in relation to a carrying capacity (i.e. in relation to the total amount of coral cover that the considered region can sustain).” From this statement, it’s not clear to me how the region-specific coral carrying capacity was determined. Is the carrying capacity the mean of all observations of coral cover? This would seem biased in favor of a lower carrying capacity than reality, given the high disturbance frequencies and magnitudes of these systems. Please provide further detail.

261: “…we conducted model simulations without bleaching.”

It would be helpful to describe the motivation for the modeling without bleaching.

266: “After this phase, we introduced the temperature forcing described in the previous section (for the period 1955–2100) in order to produce…”

Should 1955 be 2000, since this would be after the previously mentioned phase of 1955-2000?

Reviewer #2: This paper presents a model to explore a crucial topic in coral reef population ecology: the capacity for acclimatization in response to climate change. I was particularly impressed by the careful approach to model parameterization while maintaining generality.

My most substantive concern is that, to truly quantify the role of acclimatization, the paper needs to compare the results Fig. 3 to the case without any acclimatization (N=0). Without this comparison to isolate the effect of acclimatization, the authors cannot make conclusions about the specific role of acclimatization in their outcomes (e.g., lines 307-308), which is the primary goal of this paper. This should be a relatively straightforward comparison to do with the existing model.

For the model structure, it took me a while to understand why the benefit of the plastic trait U, the energy investment in symbiosis, appears in the coral growth function (in dC/dt) rather than the symbiont dynamics (dS/dt). If one interprets this trait as physiological responses that bolster the symbionts during marine heat waves (e.g., heat shock protein up-regulation; as described on lines 198-201), then one would expect the benefit of greater U to come in through lower symbiont mortality during marine heat waves. I think the reason why the authors chose the approach they did is because they needed both the costs and benefits of U to be in the same function in order to have one function for taking the derivative to calculate the selection differential that determines the trait change dynamics (dU/dt); the costs do belong in the coral dynamics due to energy investment effects, so then the authors put in the benefit in terms of coral benefits from symbionts. Which I can understand from a tractability standpoint, but irregardless of whether this or another explanation is the right one, the authors need to clarify why they're taking the approach they do when they first develop the model (in the Coral dynamics section of the Methods), and discuss the potential effects of this assumption (e.g., the effect of benefits occurring continuously rather than in pulses during marine heat waves, and what types of acclimatization that does and doesn't represent) in the Discussion (somewhere around lines 402-405 where they're discussing phenomenological vs. mechanistic modeling approaches might make sense). If at all possible, it'd also be great to see a functional sensitivity analysis comparison to a model structure where the benefits accrue in the symbionts rather than the coral, but I understand that this might not be mathematically tractable.

For the model analyses, in addition to adding an analysis without acclimatization for comparison, the paper would be stronger if the authors had the sensitivity analysis (currently in the appendix, Figs. S6-S9) in the main text, as it recognizes uncertainty in the parameterization and leads to some of the more interesting conclusions about what most influences acclimatization potential. This doesn't have to be all four sensitivity analysis figures; the ones with bleaching are more relevant than the ones without, and the results were pretty consistent across climate scenarios so the authors could chose one climate scenario to illustrate the sensitivity analysis in the main text and put the remaining RCPs in the appendix. This would be even better, and the results presented more simply, if the authors took a more formal approach to sensitivity analysis, whether as a local sensitivity analysis or global sensitivity analysis as described in:

Cariboni, J., Gatelli, D., Liska, R., & Saltelli, A. (2007). The role of sensitivity analysis in ecological modelling. Ecological modelling, 203(1-2), 167-182.

plus see:

Harper, Elizabeth B., John C. Stella, and Alexander K. Fremier. "Global sensitivity analysis for complex ecological models: a case study of riparian cottonwood population dynamics." Ecological Applications 21.4 (2011): 1225-1240.

for some different ways to visualize global sensitivity analysis outputs.

Three points on the motivation for this modeling exercise in the Introduction:

1. While the Abstract and Author summary both start with establishing the threat that climate change poses to tropical coral reefs before getting into responses to climate change via acclimatization and adaptation, the Introduction launches straight into those responses. Before this, at the onset of the Introduction, the authors should have a short paragraph that sets up the impact climate change has on corals (with relevant references) before getting to acclimatization and adaptation potential.

2. For the motivation of focusing on acclimatization vs. genetic adaptation, I disagree with the authors' claim that that the long generation times of corals make evolution less relevant (lines 12-14, and repeated elsewhere: 3rd sentence of the Abstract, lines 67-69, 193-195, and 370-371), as evidence has now been mounting for decades that evolution can occur on ecological time scales (this body of research even now has its own field, eco-evo dynamics; see, e.g. Schoener 2011, Science 331:426-429). Even though corals are long-lived as the authors say, a selective sweep takes only one extreme event, such as a bleaching event, for gene frequencies to shift, and the symbionts within corals, which can also evolve, have very high turnover rates. Really, acclimatization vs. genetic genetic adaptation is a false dichotomy: rather than either/or, both have the potential to play a role in future coral dynamics under climate change, and there's no need to claim one as unimportant to say the other is important. Instead, the authors could just make the point that both acclimatization and genetic adaptation might play a role in future coral persistence, and while a few models have quantified evolutionary capacity, quantifying acclimatization capacity as well can help further understand overall coral adaptive potential. Note that, once the authors have established the motivation for why one might look to quantifying acclimatization capacity in the Introduction, there's no need to repeat the motivation elsewhere in the manuscript (e.g., lines 66-69, 193-195).

3. In both the Introduction and Discussion, I think there's a missed opportunity here to connect to the idea of "pre-exposure" (also called pre-conditioning, stress-hardening, and induced acclimatization, among other names) that is gaining interest in the field of coral reef restoration as a way to promote the likelihood of outplanted corals persisting under future climate change. See Chapter 3 on Physiological Interventions of the 2018 National Academies report on "A Research Review of Interventions to Increase the Persistence and Resilience of Coral Reefs", available at:

https://www.nationalacademies.org/our-work/interventions-to-increase-the-resilience-of-coral-reefs

for a review of this approach. Quantification of acclimatization potential, as is done in this paper, can help inform the capacity for this management intervention to affect coral persistence under future climate change. In addition, might the model developed here provide a framework for the types of decision-support tools described in the second report linked above (on "A Decision Framework for Interventions to Increase the Persistence and Resilience of Coral Reefs"), which can help managers navigate whether and how to implement interventions like pre-exposure?

The model could use greater clarity in presentation in a few places. In particular, somewhere in the Bleaching subsection of the Methods, it'd be helpful to have a mathematical expression for the implementation of bleaching with relevant parameters defined. Are the authors essentially having discrete bleaching events within the continuous-time model, such that this is a pulse-impulsive or semi-discrete model as described in:

Mailleret, L., & Lemesle, V. (2009). A note on semi-discrete modelling in the life sciences. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367(1908), 4779-4799

? In addition, equations (1)-(6) would be clearer if all state variable dependencies were consistently specified for all functions, e.g. F(U,S,C) instead of F(I, kappa*E,C) in eq. 1, K_S(C) instead of K_S in eq. 2, and kappa(S)E(U) instead of kappa*E in eq. 4 (with these state-variable-dependency specifications elsewhere in the text wherever relevant), perhaps with temperature T dependency specified where relevant as well.

Additional comments:

First sentence of the Introduction on line 1: in addition to adaptation and acclimatization, there is a third commonly-invoked response that organisms might have to climate change, range shifts, which tend to get discussed less in the context of coral reefs but are one of the most frequently-observed responses to climate change across systems:

Parmesan, C. (2006). Ecological and evolutionary responses to recent climate change. Annu. Rev. Ecol. Evol. Syst., 37, 637-669.

Line 60: "adaptive dynamics" invokes a specific invasion analysis approach to modeling evolutionary change, please use a different phrase here.

Line 65: "plastic trait" would be a more precise label than "adaptive trait".

Lines 161-171 are repetitive to the Introduction, and spending this amount of space on DHMs in the Methods might mislead a reader into thinking that the authors are going to take a DHM approach. I would start with the approach taken here, then briefly justify it.

Line 209: this could be more clearly framed as an assumption that plasticity is adaptive in the case of this model, as in reality plasticity is not always adaptive, especially when human-driven environmental change leads to "evolutionary traps".

Section on "Simulations and sensitivity analysis": what are the initial conditions for the simulations?

Lines 275-285: this text is repetitive to the Introduction.

Line 333: typo in "important".

Line 349-350: this sentence is a fragment.

Lines 400-401: "theory of adaptation" should be "theory of acclimatization"; a generalized theory of adaptation would have both genetic and plastic responses.

In addition, this discussion of mechanistic vs. phenomenological approaches to modeling might benefit from the example of dynamic energy budget models as a mechanistic approach in contrast to the phenomenological approach here; note that DEB models have been applied to corals:

Cunning, R., Muller, E. B., Gates, R. D., & Nisbet, R. M. (2017). A dynamic bioenergetic model for coral-Symbiodinium symbioses and coral bleaching as an alternate stable state. Journal of Theoretical Biology, 431, 49-62.

Muller, E. B., Kooijman, S. A., Edmunds, P. J., Doyle, F. J., & Nisbet, R. M. (2009). Dynamic energy budgets in syntrophic symbiotic relationships between heterotrophic hosts and photoautotrophic symbionts. Journal of Theoretical Biology, 259(1), 44-57.

For the discussion of the sensitivity analysis, note that a potential implication of the high sensitivity to coral growth (lines 406-414) could be that local management approaches that might buffer coral growth, such as control of the runoff of pollutants that affect coral growth as reviewed in:

Fabricius, K. E. (2005). Effects of terrestrial runoff on the ecology of corals and coral reefs: review and synthesis. Marine pollution bulletin, 50(2), 125-146.

might then increase acclimatization potential to global climate change.

I appreciate that the authors discussed a few of the model assumptions throughout the Discussion. Another assumption to consider discussing is whether and how the model represents the potential for constraints to plasticity or acclimatization potential.

Reviewer #3: The authors model corals acclimating to increasing temperatures, where corals acclimate by changing the amount of energy they invest in the symbiosis. Energy investment can potentially make up for symbionts lost due to bleaching, by increasing the per-symbiont benefit of the symbiosis to the coral. The authors build a differential equation model that tracks the growth and energy investment of a single coral and symbiont. They investigate corals from three regions (the Great Barrier Reef, South East Asia, and the Caribbean) under three different temperature scenarios, and find that corals on the Great Barrier Reef are best able to use acclimation to survive, but none of the three regions' corals could survive via acclimation alone in the hottest warming scenario.

Coral acclimation is a topic of great interest for conservation, and the authors' focus on using incorporating real warming and trait data to understand the ability of coral acclimation to preserve reefs is likely to be of interest to many readers. The model and results are presented very clearly, and the authors do an excellent job of explaining the model's purpose and future uses.

There is a potential issue in the function for the temperature-dependent growth rate of the symbiont. The authors model the maximum symbiont growth rate as increasing exponentially with temperature. This relationship comes from studies across multiple species, where the maximum growth rate over all species at a particular temperature follows this pattern. However, individual species's growth rates probably do not follow this pattern (the Baskett et al. paper they cite models them as decreasing sharply after a certain temperature). For the model, this seems to imply that the coral is swapping out its symbionts every time the temperature changes, to always have a species that has the ability to achieve the maximum growth rate a particular temperature. I know the model is intended to provide information about populations, but since the differential equations so closely resemble the interaction between a single coral and symbiont, I think there are probably some consequences of modeling symbiont growth this way. In particular, the symbiont growth rate may be lower than is modeled (because most symbionts will not actually be growing at this rate). I think this decision and its consequences should be discussed.

Other comments:

I think it would be really helpful for gaining an intuitive understanding of the model to be able to see how the benefit of energy investment changes with temperature. A plot of the optimal investment for one of the warming scenarios would be nice, if that is possible to make.

The authors refer to the model as an adaptive dynamics model, which I think might be confusing to readers. To me adaptive dynamics is a technique for modeling evolution, and this model is important because it does not include evolution. Also, adaptive dynamics seems to me to require selection and some kind of inheritance mechanism. Possibly there is an argument that some sort of selection is present (maybe between polyps?). I think it would also be reasonable to say that this is a sensible acclimation rate to assume for other reasons. (It seems like a pretty sensible way to try to match your environment!)

It seems to me that by changing the strength of the symbiotic feedback (beta) and and the coral exponential cost parameter (r), it is possible to scale energy (and thus rate of acclimation) values. I don't think this is a problem for the model, but I do think this means it would be helpful to give some intuition for what an energy investment of a particular amount means to the model coral (maybe something like how much of its growth is it investing in the symbiont?), and why the beta and r values were chosen.

The temperature-dependent host growth rate is derived from coral distribution data. Intuitively, it makes sense that if no corals can grow at a temperature, their growth rate at that temperature is zero. I think a sentence or two explaining how to get from the coral distribution to the growth rate function in the nonzero growth rate case would be nice.

I just skimmed the code, but it looks like some small terms are being added to the denominators of some functions to prevent division by 0. If so, it would be good to mention that in the methods section.

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3 Mar 2022

Submitted filename: Responses20220303.pdf

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5 Apr 2022

Dear Prof Merico,

Thank you very much for submitting your manuscript "Modelling the acclimation capacity of coral reefs to a warming ocean" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Dear Dr. Merico and Co-authors,

Thanks for re-submitting the manuscript and addressing all the reviewer comments. Overall, I think the manuscript has improved and is shaping up to be an important contribution to the field. Before accepting it for final publication, there are few minor issues that still need to be addressed. Please see the attached feedback from the reviewers and provide a new modified draft with the requested edits.

As the reviewers mention there is some ambiguity regarding the use of “acclimation at the community level” and “plasticity” in some of the contexts in the manuscript, which warrants more clarification and discussion of these terms or their intended use in the text.

Thanks,

Bishoy

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[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out

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Sincerely,

Bishoy Kamel

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PLOS Computational Biology

James O'Dwyer

Deputy Editor

PLOS Computational Biology

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Dear Dr. Merico and Co-authors,

Thanks for re-submitting the manuscript and addressing all the reviewer comments. Overall, I think the manuscript has improved and is shaping up to be an important contribution to the field. Before accepting it for final publication, there are few minor issues that still need to be addressed. Please see the attached feedback from the reviewers and provide a new modified draft with the requested edits.

As the reviewers mention there is some ambiguity regarding the use of “acclimation at the community level” and “plasticity” in some of the contexts in the manuscript, which warrants more clarification and discussion of these terms or their intended use in the text.

Thanks,

Bishoy

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: I appreciate the efforts the authors put into their revisions in response to my and the other reviewers’ comments. I believe the manuscript is clearly improved. The issue I have with this version is that I think the authors can and should be more up front about the fact that while they motivate this work around the need to understand ‘coral acclimation’, their model - as they acknowledge in the first paragraph of the discussion - deals with changes in phenotypes at the community level, something one could define as ‘acclimation at the community level’, I suppose. I struggle with this, because - again, as the authors acknowledge - species turnover is unavoidably a potential major mechanism underlying such ‘acclimation at the community level’, though this is not a mechanism one would think of as falling into the category of ‘acclimation’, since we (and the authors, in the Intro), tend to define acclimation at the organismal/species (not community) level. I think it would be better to be much more up front about this modeling study’s limitations with respect to assessing the capacity for ‘coral acclimation’ to respond to climate change. I’d recommend clarifying in the Abstract and Intro that this study focuses on the community level (and, thus, cannot isolate the effects of organismal adaptation), at which species turnover can (and, according to recent studies by Terry Hughes and colleagues working in the GBR, likely does) play a substantial role in shaping community phenotypic shifts in coral responding to environmental changes over time. For example, in the Abstract and Intro, the authors discuss the capacity for corals to acclimate via phenotypic plasticity, but to not confuse readers about the scale of inquiry for the actual study, I’d argue it would be more appreciate to discuss ‘coral community acclimation’, or some other term, and clarify that what we traditionally think of as acclimation or adaptation cannot be explicitly examined with the proposed model and that species turnover could be a critical driver.

Reviewer #2: The reviewers have mostly addressed my previous comments, especially with the added simulations without plasticity as a baseline for comparison, as well as the added figure S6 to illustrate the benefit and cost dynamics. However, some lingering issues remain from the new changes and unresolved previous comments (all line numbers refer to the revised manuscript without tracked changes):

1. While I agree with Reviewer #1's point about shifts in community composition, I disagree with the changes made in response: with the model setup, a shift in community composition would change parameters related to coral type, such as Topt and Gmax (as mentioned on line 452-453), perhaps with some changes in N too if different coral species had different plasticity levels, but I expect that this is swamped by the other differences. Therefore, instead of adding the claim that the model captures changes in community composition (lines 345 and 403-404), I support the original reviewer feedback of adding this as a caveat, i.e. recognizing that the acclimatization rates might be over-estimated because the model doesn't capture the effects community shifts on coral cover dynamics. I also support Reviewer #1's suggesting to include sensitivity to a couple of different values for the percent of each coral type present among the sensitivity analyses, which the authors had declined to do.

2. With moving some of the sensitivity analysis results to the main text in Figs. 5-6 as I had suggested, the authors also need to add Results text about these figures in the main text, which is currently missing.

3. While the authors indicate their agreement with my previous point about acclimation and genetic adaptation both playing a role in coral dynamics, and the false dichotomy inherent to presenting these as an either/or, the changes to the text do not reflect this: the framing language of "however", "alternately", and "although", as well as the continued mention of generation times (which, as I mentioned before, do not necessarily mean evolution is slow given the capacity for selective sweeps) and ecological vs. evolutionary time scales (which applies to macroevolutionary processes of speciation, not microevolutionary process of changes in gene frequency), on lines 29-31, 424-426, and in the abstract third sentence still imply that these are alternate, not co-occurring dynamics, and discounts the potential role of evolution. Please rephrase to recognize that both have the potential to occur, which can still motivate this study, as some studies have explored the role of genetic adaptation, but a mechanistic investigation into the role of acclimation is less well understood (with an eventual goal, hopefully, of including both to understanding their interaction, but understanding each in turn is a reasonable starting point and important to establishing their potential relative contributions before such integration). Also, in lines 36-38, note that the rolling-window approach to approximating adaptive and acclimation potential in these papers does not have an assumed-in bleaching threshold as implied here, but rather derives the threshold from the climatology, in particular the most recent mean of maximal monthly temperatures.

4. The added text about stress-hardening on lines 465-468, a point that I had raised in my previous review, is too vague to be useful. Please either (a) be specific about stress hardening (using that term and defining what it involves) as a potential management application, including citations on this approach, and how this model might inform that approach, or (b) delete this addition. For option (a), note that the addition is out of place: it is a sentence about management implications in the midst of a paragraph about model assumptions. Therefore, if included, it should be moved to a more appropriate place in the discussion.

5. For the data-based bleaching simulations: even if the parameters were estimated empirically, those parameters were somehow used in a mathematical expression (represented by code) to translate into their effect on coral dynamics. Please provide this information for full methods clarity.

6. To clarify my earlier comment about adaptive plasticity: what this text (lines 225-236) needs clarity on is the idea that plasticity is always perfectly adaptive, as represented in the model, is an assumption and does not always occur in reality, as, in reality, plasticity can sometimes decrease fitness, such as in the case of evolutionary traps. The current text could be misinterpreted to mean that the idea that plasticity is always adaptive is a biological truth.

7. For the addition about nutrient runoff and pollution effects on coral growth stemming from my previous feedback (lines 449), "controlling" doesn't make sense here; something like "buffering", "protecting", or (my preference) "mitigating anthropogenic impacts on" would work better (and why is this in quotes?).

8. On line 394, do you mean "acclimate" instead of "adapt"?

Reviewer #3: The authors addressed my comments, and there is just a small thing that I think should be added: I think in the methods the authors should say that the symbiont growth function comes from a curve of multiple species' thermal optima. The authors talk about modeling symbiont communities in the discussion, but I think it would be good to have this information about the function in the methods where the function is first described. Because the model partly has the purpose of being the "parent" of future models, it's likely that future readers will spend a lot of time with the methods section and would benefit from having all the information together.

I really liked the supplementary plots of the costs and benefits of the symbiosis. Figure S10 and all of section S6 helped me gain a better understanding of the model.

* line 49: "coral's" should possibly be "corals'"?

* line 386: "because of the acclimation dynamics nature of our modeling approach." I think removing "acclimation dynamics" from this phrase would make it clearer.

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Figure Files:

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Data Requirements:

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Reproducibility: