# Weather and topography regulate the benefit of a conditionally helpful parasite

Jonathan Monsinjon, Christopher Mcquaid, Katy Nicastro, Laurent Seuront, Mauricio Oróstica, Gerardo Zardi

► To cite this version:

Jonathan Monsinjon, Christopher Mcquaid, Katy Nicastro, Laurent Seuront, Mauricio Oróstica, et al. Weather and topography regulate the benefit of a conditionally helpful parasite. Functional Ecology, 2021, 10.1111/1365-2435.13939. hal-03453966

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<figure><img src="image_1.png" /></figure>
# Weather and topography regulate the benefit of a conditionally helpful parasite

Monsinjon Jonathan <fnref n="1" />,*, McQuaid Christopher D. <fnref n="1" />, Nicastro Katy R. <fnref n="1" />, <fnref n="2" />, <fnref n="3" />, Seuront Laurent <fnref n="1" />, <fnref n="2" />, <fnref n="3" />, <fnref n="4" />, Oróstica Mauricio H. <fnref n="1" />, Zardi Gerardo I. <fnref n="1" />

## Abstract :

1. Heat-induced mass mortalities involving ecosystem engineers may have long-lasting detrimental effects at the community level, eliminating the ecosystem services they provide.

2. Intertidal mussels are ecologically and economically valuable with some populations facing unprecedented heat-induced mass mortalities. Critically, mussels are also frequently infested by endolithic parasites that modify shell albedo, hence reducing overheating and mortality rates under heat stress.

3. Using a biophysical model, we explored the topographical and meteorological conditions under which endolithically driven thermal buffering becomes critical to survival. Based on meteorological data from a global climate analysis, we modelled body temperatures of infested and non-infested mussels over the last decade (2010–2020) at nine sites spread across c. 20° of latitude.

4. We show that thermal buffering is enhanced where and when heat stress is greatest, that is, on sun-exposed surfaces under high solar radiation and high air temperature.

5. These results suggest that new co-evolutionary pathways are likely to open for these symbiotic organisms as climate continues to change, potentially tipping the balance of the relationship from a parasitic to a more mutualistic one. However, endolithically driven reductions in body temperatures can also occur at or below optimal temperatures, thereby reducing the host's metabolic rates and making the interplay of positive and negative effects complex.

6. In parallel, we hindcasted body temperatures using empirical data from nearby weather stations and found that predictions were very similar with those obtained from two global climate reanalyses (i.e. NCEP-DOE Reanalysis 2 and ECMWF Reanalysis v5).

<footnote n="1">¹ Department of Zoology and Entomology Rhodes University Grahamstown, South Africa</footnote>

<footnote n="2">² CCMAR, CIMAR Associated Laboratory University of Algarve Faro, Portugal</footnote>

<footnote n="3">³ Laboratoire d'Océanologie et de Géosciences Univ. Lille CNR SUniv. Littoral Côte d'Opale UMR 8187 LOG Lille, France</footnote>

<footnote n="4">⁴ Department of Marine Resources and Energy Tokyo University of Marine Science and Technology Tokyo, Japan</footnote>

<footnote>* Corresponding author : Jonathan Monsinjon, email address : jonathan.monsinjon@gmail.com</footnote>
7. This result holds great promise for modelling the distribution of terrestrial ectotherms at ecologically relevant spatiotemporal scales, as it suggests we can reasonably bypass the practical issues associated with weather stations. For intertidal ectotherms, however, the challenge will be incorporating body temperatures over the full tidal cycle.

**Keywords** : biophysics, ectotherm, heatwave, microhabitat, mussel, mutualism, symbiotic relationship, temperature
37

**Introduction**

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Heat-induced mass mortalities are becoming more frequent, longer and more severe in

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both terrestrial (Meehl & Tebaldi 2004) and marine (Di Lorenzo & Mantua 2016; Oliver et al.

40

2018) environments as climate warming progresses. Heat-related mass mortalities have

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affected a wide variety of taxa including birds (McKechnie & Wolf 2010), mammals

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(Welbergen et al. 2008; Pruvot et al. 2019), kelps (Smale 2020), corals (Hughes et al. 2017;

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Le Nohaïc et al. 2017), and mussels (Harley 2008; Seuront et al. 2019). Such mass mortality

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events have potentially dramatic cascading effects when they involve ecosystem engineers

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that provide the biogenic habitat that supports high biodiversity (Smale et al. 2019).

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Invertebrate body temperatures largely depend on environmental drivers, mediated

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by body size, shape, positioning, and behaviour, plus intrinsic physical properties (Porter &

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Gates 1969; Helmuth 1998; Nicastro et al. 2012) that are potentially altered by parasitism

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(Zardi et al. 2016; Gehman & Harley 2019). Many marine invertebrates are infested by

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endolithic fungi, algae or cyanobacteria that bore into their hosts' outer layer and alter their

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physiology, colour, and morphology (Kaehler 1999; Golubic, Radtke & Campion-Alsumard

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2005; Zardi et al. 2009; Gleason et al. 2017). This is the case for intertidal mussels, which are

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critical ecosystem engineers (Arribas et al. 2014). In these species, endolithic microbes can

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cause considerable shell damage, reducing scope for growth by increasing metabolic

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maintenance costs (Ndhlovu, McQuaid & Monaco 2020), eventually leading to host death

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through shell collapse (Kaehler & McQuaid 1999). During extreme warming events,

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however, this symbiotic association can become advantageous (Zardi et al. 2016; Gehman &

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Harley 2019; Zardi et al. 2021) as discolouration of the shell caused by endolithic activity

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enhances solar reflectivity so that infested mussels can be 5°C cooler than non-infested
individuals, potentially increasing host survival rates during heat waves (Zardi *et al.* 2016; Gehman & Harley 2019).

Because the balance between positive and negative effects in host-parasite systems can be context-dependent (e.g., Duncan *et al.* 2010; Bates *et al.* 2011; MacLeod & Poulin 2016), we can expect it to change over space and time. To address this in the context of the mussel-endolith system, we identified the topographical and meteorological conditions under which endolithic microbes effectively reduce exposure to heat stress. To achieve this, we predicted the body temperature of non-infested (Tb<sub>non-infested</sub>) and infested (Tb<sub>infested</sub>) mussels under a range of topographic orientations (i.e., combinations of aspect and inclination angle of the attachment surface) using a biophysical model. To ensure that a wide range of environmental conditions, including extreme weather events, was covered, we reconstructed mussel body temperatures over the last decade (2010-2020) at nine sites spread across ca. 20° of latitude along the north Atlantic coast (Fig. 1, see Table S1 in Supporting Information). Ideally, one would use empirical data from local weather stations to model body temperatures. However, such data are typically scarce, discontinuous, or simply not available during the full extent of the study period. To overcome these practical issues, we used environmental data from a global climate reanalysis. We assessed the validity of this approach by comparing body temperatures reconstructed using data from nearby weather stations and body temperatures recorded *in-situ* with biomimetic sensors (thereafter referred to as “robomussels” following Judge, Choi & Helmuth 2018). Then, we evaluated endolithically-driven thermal buffering by calculating the temperature difference between non-infested and infested mussels (Tb<sub>non-infested</sub> - Tb<sub>infested</sub>), categorizing these differences into two levels of thermal buffering: (1) neutral (Tb<sub>non-infested</sub> ≈ Tb<sub>infested</sub>) and (2) positive (Tb<sub>infested</sub> < Tb<sub>non-infested</sub>). Additionally, we calculated the time spent over two critical
84 thermal thresholds to assess under what circumstances endolithically-driven thermal

85 buffering is sufficient to spare infested mussels from heat-related stress or death.

<figure><img src="image_2.png" /></figure>

86

87 **Figure 1. Location of study sites.** Mussel body temperatures were predicted for several sites

88 in the United Kingdom (green), France (red), and Portugal (blue). Abbreviations: Nebogeo

89 (NEB), Bay of Skaill (SKA), Aberffraw (ABE), Wimereux (WIM), Locquémeau (LOC), Pointe

90 Saint-Gildas (GIL), Viana do Castelo (VIA), Monte Clerigo (MON), Vilamoura (VIL).

91

92 **Material and Methods**
93

Biophysical model

94

We modelled mussel body temperature using the microclimate model implemented in the R package NicheMapR v. 3.0.0 (Porter et al. 1973; Kearney & Porter 2017; Kearney 2021) with R v. 4.0.4 (R Core Team 2021). The model computes hourly temperatures at 10 user-specified depths based on the physical first principles of heat exchange (i.e., radiation, convection, conduction, and evaporation) and allows the setting of different types of layers.

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96

97

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99

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We set two types of layers: a “mussel” layer for the first 5 cm and a “rock” layer below. For the first layer, we used thermal properties (thermal conductivity = 0.5681 W.m⁻¹K⁻¹, specific heat capacity = 3496.3 J.kg⁻¹K⁻¹) derived from experiments on *Perna canaliculus* (Mateparae 2003) and other physical properties (density = 1.086 g.m⁻³, water content = 95%) derived from experiments on *Mytilus edulis* and *Mytilus trossulus* (Harbach & Palm 2018). For the second layer, we used thermal properties of a type of granite with high porosity in saturated conditions (thermal conductivity = 2.99 W.m⁻¹K⁻¹, specific heat capacity = 800 J.kg⁻¹K⁻¹)

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104

105

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derived from engineering geology studies (Cho, S. Kwon & Choi 2009; Cho & Kwon 2010)

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and other physical properties (density = 2.7 g.m⁻³, water content = 34%) derived from

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measurements on weathered granite (Kwon et al. 2011; Rouxel et al. 2012). Microclimate

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was computed at 5-cm height and temperature predictions were obtained at 2.5-cm depth,

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representing internal body temperatures (Tb) at the scale of a large mussel bed. Based on

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reflectance measurements for *Mytilus californianus* (Gehman & Harley 2019), we set

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reflectivity at 0.161 and 0.245, respectively for non-infested (darker) and infested (paler)

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mussels, to compute Tb<sub>non-infested</sub> and Tb<sub>infested</sub>. We calculated these values from 350 nm to

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1100 nm based on reflectance spectra of eroded and non-eroded shells (previously digitized

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from Fig. 4A in Gehman & Harley 2019) and the ASTM G-173 standard irradiance spectrum

116

for dry air derived from SMARTs v. 2.9.2 (Gueymard 2001) using the formula in Smith *et al.*
(2016). NicheMapR allows the user to predict temperatures of the substratum (or the organism) during periods of submergence, calculating heat balance via conduction and convection only (see parameter 'shore' in NicheMapR's help). We selected this option whenever mussels were expected to be submerged (i.e., when tidal levels were higher than the mussels' height on the shore). To distinguish between periods of submergence and aerial exposure, we calculated the Effective Shore Level (ESL), an estimate of intertidal height using temperature profiles and tidal heights (Harley & Helmuth 2003; Gilman et al. 2006). The method uses sudden drops in logger temperatures and the corresponding tidal height at this time to estimate when robomussels are first immersed by the returning tide.
We obtained hourly tidal predictions (using the XTide software; https://flaterco.com/xtide/) for nearby maritime ports (Table S2) and interpolated tidal levels at 30-min intervals (using na.approx function from the R package zoo; Zeileis & Grothendieck 2005) to match the time at which robomussels were set to record temperature (see Zardi et al. 2021). We retrieved all tidal levels that were associated with a temperature drop of > 8°C in 30 min during incoming tides. This corresponds to a drop of 5.33°C in 20 min, ensuring the reliability of ESL estimates and maximising the probability of correctly identifying the effects of tidal emersion (Gilman et al. 2006). For each study site, we then calculated the mean ESL (± standard deviation, SD) using temperature data from all robomussels pooled together (Table S3). Finally, we ran the model under most possible topographic orientations by varying the inclination angle ('slope' from 0° to 90° every 10°) and the direction that the surface faces ('aspect' in degrees North from 0° to 350° every 10°). We assumed moist air conditions with no shade, no moisture throughout the substratum, no vegetation and no organic matter or snow cover over the mussel layer. The other parameters were left as
140 default (see settings in NicheMapR's help for the following functions: microclimate,

141 micro_ncep and micro_era5).

142

143 **Meteorological data**

144 To predict mussel body temperatures during aerial exposure, we drove the NicheMapR

145 microclimate model using three sources of meteorological data. Air temperature, wind

146 speed, solar radiation, relative humidity, precipitation, and cloud cover were obtained from:

147 (i) nearby weather stations (Table S4), (ii) the NCEP-DOE Reanalysis 2 (Kanamitsu et al.

148 2002) hereafter referred to as NCEP, and (iii) the ECMWF Reanalysis v5 (Hersbach et al.

149 2019) hereafter referred to as ERA5. Weather station observations in the United Kingdom

150 (Met Office 2019a; Met Office 2019b; Met Office 2019c), France and Portugal were provided

151 by the Centre for Environmental Data Analysis (CEDA; http://data.ceda.ac.uk/badc/ukmo-

152 midas-open/data/), Météo-France (https://donneespubliques.meteofrance.fr/) and Instituto

153 Portugês do Mar e da Atmosfera (IPMA; https://www.ipma.pt/en/otempo/obs.superficie/),

154 respectively. Note that cloud cover was not available from weather stations and was

155 therefore calculated from the ratio of hourly clear sky solar radiation (previously computed

156 using NicheMapR's microclimate function) compared to the observed hourly global solar

157 radiation measured by weather stations (Kearney et al. 2014; Kearney & Porter 2017). In

158 addition, wind speed was measured at 10-metre height and downscaled to a height of 2 m

159 using the formula in Kearney et al. (2014) to match the model's reference height. We

160 computed aerosol attenuation using a global aerosol data set (Koepke et al. 1997) to

161 account for scatter from atmospheric particles (Kearney & Porter 2017). Occasional missing

162 data (see Fig. S1 in Supporting Information) were linearly interpolated using na.approx
function from the R package zoo (Zeileis & Grothendieck 2005). For three of our sites, we could not predict mussel body temperatures using observations from weather stations because solar radiation data were not available (Fig. S1, Table S4). Alternatively, NCEP and ERA5 global climate reanalyses provide all required data on a continuous time scale from 1979 onward (6-hourly and hourly, respectively) at different spatial resolution (2.5° × 2.5° and 0.25° × 0.25°, respectively). To compute mussel body temperatures from NCEP data, we used NicheMapR's micro_ncep function, which integrates some functions of the R packages microclima (Maclean, Mosedale & Bennie 2018; Mosedale, Bennie & Duffy 2021), elevatr (Hollister 2020), rnooa (Chamberlain 2021), and RNCEP (Kemp et al. 2012) to compute mesoclimate effects such as elevation-associated lapse rates, wind sheltering, coastal influences and cold air drainage (but see Kearney et al. 2020 for details). We used a similar function (micro_era5), which integrates a function of the R package mcera5 (Duffy in prep), to compute mussel body temperatures from ERA5 data. Here, we tested whether accounting for coastal influence due to exposure to the sea improved estimates of mussel body temperature during aerial exposure. To do so, we ran micro_ncep and micro_era5 with and without the coastal influence option and compared the output based on goodness-of-fit metrics (see section below). To predict mussel body temperatures during submergence, we drove the model using hourly sea surface temperatures extracted at our study sites from ERA5.

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## Model validation

To validate the approach and select the most suited source of meteorological data, we compared our predictions of Tb<sub>non-infested</sub> and Tb<sub>infested</sub> with temperature data recorded in-situ

185
using robomussels (Judge, Choi & Helmuth 2018) previously deployed at our nine study sites
in summer 2017 and 2018 (Fig. S2 and Table S1, but see Zardi et al. 2021 for details). At each
site, three to six pairs of robomussels (one infested and one non-infested using shells of
*Mytilus galloprovincialis*) were deployed within the mid mussel zone on a relatively flat
surface (< 20°) and equidistant from each other (ca. 10 cm). In the original study, Zardi et al.
(2021) did not measure the exact slope and aspect of the surface where robomussels were
placed. Therefore, we chose to infer their topographic orientation by searching for the
combination of aspect and inclination angle that best described temperatures recorded in-
situ by robomussels during aerial exposure. To do so, we computed Tbnon-infested and Tbinfested
for three possible inclination angles (0°, 10°, 20°) and every possible aspect (from 0° to 350°
every 10°), and we selected the topographic orientation individually for each pair of
robomussels based on the lowest Root Mean Square Error (RMSE). We also calculated
Pearson's correlation coefficient as an additional goodness-of-fit metric, with higher
correlation coefficients indicative of a better fit between observations and predictions. We
assessed the validity of our approach to predict mussel body temperatures during periods of
submergence using the same metrics. Note, however, that the method used here to
distinguish between periods of aerial exposure and submergence (i.e., when tidal levels are,
respectively, lower or higher than the estimated elevation of mussels on the shore) may
introduce some bias. In fact, the ESL is not meant to be fixed. Instead, ESLs can vary
between tidal cycles due to surge and wave exposure (Gilman et al. 2006). To overcome
this, we followed Lathlean, Ayre and Minchinton (2011) in ensuring that temperature data
were correctly attributed to periods of aerial exposure or submergence by applying a buffer
zone (mean ESL ± 0.3 m). We excluded all data that fell within this buffer zone when
calculating goodness-of-fit metrics.
210

211

Thermal buffering

212 Using meteorological data from one of the global climate reanalyses, we reconstructed
213 Tbnon-infested and Tbinfested from 2010-01-01 to 2020-01-01 for a wide range of topographic
214 orientations at our nine study sites. Using these temperature time series, we evaluated
215 endolithically-driven thermal buffering by calculating the proportion of time spent within
216 two categories of thermal buffering, one defined as neutral (Tbnon-infested ≈ Tbinfested) and the
217 other as positive (Tbnon-infested < Tbinfested). We chose a 0.5°C cut-off to distinguish between
218 these two categories because such a difference in body temperature entails less than 50%
219 difference in survival when approaching critical thermal limits (Seuront et al. 2019; Ndhlovu,
220 McQuaid & Monaco 2020). In other words, thermal buffering is considered neutral if the
221 absolute difference between Tbnon-infested and Tbinfested is ≤ 0.5°C or positive if the difference is
222 > 0.5°C. We used these categories to identify where (topographic orientation) and when
223 (time of day) thermal buffering is enhanced. On the other hand, we aimed to identify the
224 meteorological conditions associated with the lowest and highest differences between
225 Tbnon-infested and Tbinfested. To do so, we used body temperatures predicted for mussels on a
226 horizontal surface during aerial exposure and retrieved the data on solar radiation, wind
227 speed, air temperature, and relative humidity (downscaled at 5-cm height with NicheMapR).

228

In this case, we categorized endolithically-driven temperature differences as follows:

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[minimum, 5th percentile] and [95th percentile, maximum], respectively for the lowest and highest ranges of body temperature differences.

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232

Critical thermal limits

Commenté [JM1]: Error: Tb<sub>infested</sub> < Tb<sub>non-infested</sub>

Commenté [JM2]: within intervals
To test whether the change in shell reflectance caused by endoliths provides an effective
defence against heat stress, we calculated the time spent over two critical thermal
thresholds independently for non-infested and infested mussels. The lethal temperature at
which approximately half of individuals are expected to die (LT₅₀) lies between 35°C and
38°C based on experiments on *Mytilus californianus* and *Mytilus galloprovincialis* (Denny *et al.* 2011; Sorte *et al.* 2019) and the lethal temperature at which almost all individuals are
expected to die (LT₁₀₀) is 41°C based on experiments on *Mytilus californianus* (Denny *et al.* 2011). Therefore, we chose LT₅₀ = 38°C and LT₁₀₀ = 41°C as critical thermal limits for survival.

On the other hand, it is possible that endolithically-driven thermal buffering reduces body
temperatures even within the optimal range of thermal performances, thus adding a
potential cost of endolith infestation if Tbₗnſſed falls below optimal temperatures, reducing
metabolic rate. To assess this, we retrieved Tb and Tbₗnſſed expected in sun-
sheltered and sun-exposed habitats (North-facing at 90° inclination and South-facing at 20°
inclination, respectively) and compared body temperatures with lethal and optimal thermal
ranges. Based on metabolic rate experiments, optimal thermal performances occur roughly
between 22°C and 32°C for *M. californianus* (Monaco, Wethey & Helmuth 2016) and the
optimal body temperature (Tbopt) lies around 30°C for *M. galloprovincialis* (Monaco &
McQuaid 2018).

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252

Results

253

Model validation

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255

Overall, using meteorological data from either nearby weather stations or global climate
reanalyses (NCEP and ERA5) yielded very similar results (Fig. 2, Table S5), albeit the mean
RMSE across all sites was slightly lower when using weather stations observations: RMSE < 3°C (Fig. 2a) vs RMSE ≈ 3°C (Fig. 2c,e,g,i). Note, however, that the mean RMSE and correlation coefficient calculated across all sites for weather station data (Fig. 2a-b) are not directly comparable to those calculated for climate reanalyses (Fig. 2c-j) because they do not include predictions from three sites (LOC, GIL, and VIA; Fig. 2a-b). At the site level, the fit was sometimes slightly better when using NCEP or ERA5 data instead of weather station observations (Fig. 2, Table S5). Some RMSEs were lower for ABE, MON and VIL (26% of our dataset) when using NCEP data, and for WIM and VIL (16% of our dataset) when using ERA5 data (Table S5). Some correlation coefficients were higher for MON and VIL (13% of our dataset) when using NCEP data, and for SKA, ABE, WIM, MON and VIL (32% of our dataset) when using ERA5 data (Table S5). On the other hand, accounting for coastal influences did not improve body temperature predictions during aerial exposure when using either NCEP (Fig. 2e-f) or ERA5 (Fig. 2i-j) data. During submergence, the fit was reasonably good (i.e., RMSE ≤ 3°C and correlation coefficient ≥ 0.5) for WIM only (Table S5). Given that the approaches tested here yielded similar outcomes (Fig. 2, Table S5), we selected the less computationally demanding one (i.e., NCEP with no coastal effects) to predict long-term mussel body temperatures and explore the effect of topographic orientation. With a few exceptions, this approach allowed us to reconstruct body temperature trajectories with reasonable accuracy (Fig. S2). During emergence, high robomussel temperatures were slightly underestimated and low temperatures slightly overestimated (Fig. S3), except for one pair of robomussels at one site (third pair of robomussel at LOC) which showed the worst fit. During submersion, high robomussel temperatures were strongly overestimated and low robomussel temperatures strongly underestimated (Fig. S3), with a few exceptions

Commenté [JM3]: weather station observations
279 showing the opposite relationship (NEB, SKA, and VIA) or a closer accordance between

280 predicted and recorded temperatures (MON, VIL, and the third pair of robomussel at LOC).

281
<figure><img src="image_3.png" /></figure>
**Figure 2. Model validation.** Goodness-of-fit metrics for the prediction of mussel body temperature (Tb) during aerial exposure using either weather station observations (a, b) or global climate reanalyses: NCEP with and without coastal influence (respectively c, d, and e, f) and ERA5 with and without coastal influence (respectively g, h, and i, j). Histograms represent mean RMSEs (left panels) and mean correlation coefficients (right panels) for every site, and error bars are 2.5th and 97.5th percentiles. Red lines represent the mean across all sites, and red shaded areas are 2.5th and 97.5th percentiles. Predictions of Tb were compared with temperatures recorded *in-situ* using pairs of robomussels (i.e., biomimetic sensors built with shells of either infested or non-infested mussels). Tb was predicted for specific combinations of aspect and inclination angle for each pair of robomussels (Table S5). Tb was not predicted for LOC, GIL, and VIA because solar radiation was not available from nearby weather stations. From left to right, sites are given north to south (for abbreviations: see Fig. 1).

296

297 **Under what topographic orientations is thermal buffering enhanced?**

298 Thermal buffering was essentially neutral under most topographic orientations (Fig. 3a,c,e).
299 Thermal buffering was, however, sometimes positive (roughly within 5-25% of the time for
300 most locations; Fig. 3b,d,f) on horizontal and inclined surfaces with angles increasing from
301 10° up to 90° as the aspect shifts from 90° to 180° (i.e., clockwise from East to South) or
302 from 270° to 180° (i.e., anticlockwise from West to South). This general pattern whereby
303 endolithically-driven thermal buffering can be positive on sun-exposed surfaces was
304 consistent across study sites, albeit with important variations in the maximum proportion of
305 time spent under each category of thermal buffering (Fig. 3, Fig. S4). For instance, thermal
buffering was almost never positive at two high-latitude sites (NEB and SKA; Fig. S4) but also rarely positive (roughly within 5-10% of the time) at two low-latitude sites (MON and VIL; Fig. S4). Under the same range of topographic orientations, and especially on South-facing surfaces at 20-30° inclination, thermal buffering was positive up to 35% of the time at two distant sites (LOC and VIA) while it did not exceed 20% of the time at relatively closer sites (e.g., GIL and MON, respectively for comparison with LOC and VIA; Fig. S4).

During the day, we can expect thermal buffering to be positive at any time but mostly between 08:00 and 21:00 (i.e., when exposed to sunlight) with a peak in frequency occurring between 12:00 and 14:00 (Fig. 4). At this time of day, thermal buffering was most frequently positive on Southeast- and South-facing surfaces as compared to Northwest- and North-facing ones, albeit the difference was invariably minimal at 20° inclination (Fig. S5a).

At 90° inclination, however, thermal buffering was almost never positive on surfaces that are sheltered from sunlight during a large part of the day (i.e., Northwest, North, and Northeast) while it was most frequently positive in other cases (Fig. S5b). In these latter cases, thermal buffering can be positive only between 08:00 and 21:00, with a peak in frequency occurring at different times depending on the aspect (Fig. S5b). In fact, the peak occurred at 11:00 and 12:00 on surfaces exposed to morning sunlight and shifted progressively to 15:00 and 16:00 on surfaces exposed to afternoon sunlight (Fig. S5b).

324
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Topographic orientation and endolithically-driven thermal buffering. Proportion of time (% time in colour scale) spent under two categories of thermal buffering: neutral (left panels) if Tb<sub>non-infested</sub> ≈ Tb<sub>infested</sub> and positive (right panels) if Tb<sub>infested</sub> < Tb<sub>non-infested</sub> based on body temperatures predicted between 2010-01-01 and 2020-01-01 for sites in the United Kingdom (a, b), France (c, d), and Portugal (e, f). Letters in bold indicate cardinal directions.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Time of day and endolithically-driven thermal buffering. Colours indicate the proportion of time spent under two categories of thermal buffering: neutral (grey) if Tb<sub>non-infested</sub> ≈ Tb<sub>infested</sub> and positive (red) if Tb<sub>infested</sub> < Tb<sub>non-infested</sub> based on body temperatures predicted between 2010-01-01 and 2020-01-01 on a horizontal surface (all study sites pooled together). Triangles indicate the time of day when body temperature exceeded 38°C (grey) or 41°C (black) at least once.</figcaption></figure>

**Under what meteorological conditions is thermal buffering enhanced?**

Considering a horizontal surface, the lowest differences between Tb<sub>non-infested</sub> and Tb<sub>infested</sub> ranged from -0.52°C to 0.01°C and the highest from 1.36°C to 3.23°C (Fig. 5a). The lowest differences occurred under extremely low solar irradiance, low to high wind speed, low air temperature, and high relative humidity (Fig. 5b-e). Under such conditions, both non-infested and infested mussels experienced similar body temperatures (i.e., Tb<sub>non-infested</sub> = Tb<sub>infested</sub> = 9.34°C ± 3.06°C; mean ± SD). In contrast, the greatest differences between Tb<sub>non-infested</sub> and Tb<sub>infested</sub> occurred under moderate to high solar irradiance, mostly low wind
speed, high air temperature, and moderate relative humidity (Fig. 5b-e). Under these conditions, non-infested mussels were on average warmer ($T_{bnon-infested} = 31.64^{\circ}C \pm 4.37^{\circ}C$) than infested ones ($T_{binfested} = 29.89^{\circ}C \pm 4.14^{\circ}C$).

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<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
Figure 5. Differences in body temperature and associated meteorological conditions.

Distribution of (a) differences in body temperature (Tb<sub>non-infested</sub> - Tb<sub>infested</sub>) during aerial exposure and considering a horizontal surface (all study sites pooled together), (b) solar irradiance, (c) wind speed, (d) air temperature, and (e) relative humidity. Coloured areas in panel a encompass the lowest (blue) and highest (red) ranges of differences between Tb<sub>non-infested</sub> and Tb<sub>infested</sub>. Colours in the other panels display the distribution of each meteorological variable when Tb<sub>non-infested</sub> - Tb<sub>infested</sub> fell within either the lowest (blue) or the highest (red) range.

361

Do endoliths effectively protect their host from overheating?

On surfaces sheltered from the sun most of the time (i.e., steep inclination angles and aspects shifting away from the South), neither Tb<sub>infested</sub> nor Tb<sub>non-infested</sub> exceeded 38°C (Fig. 6, Fig. S6). In contrast, on more exposed surfaces, Tb<sub>non-infested</sub> often exceeded 38°C while Tb<sub>infested</sub> remained below this critical threshold. A similar pattern emerged when considering a higher thermal threshold (i.e., 41°C), albeit with a more marked difference between infested and non-infested mussels (Fig. 7, Fig. S7). At sites in the United Kingdom, Tb<sub>infested</sub> never exceeded 41°C while Tb<sub>non-infested</sub> exceeded this threshold for a few hours (Fig. 7a-b) at one site (ABE; Fig. S7). At the other sites in France and Portugal, Tb<sub>infested</sub> sometimes exceeded 41°C but less often and under a much narrower range of topographic orientations (i.e., essentially South-facing surfaces with a slight inclination) than values for Tb<sub>non-infested</sub> (Fig. 7c-f, Fig. S7). On a horizontal surface (or for any aspect with a slight inclination) lethal body temperatures were exceeded between 11:00 and 19:00 (Fig. 4, Fig. S5a). On the other hand, lethal body temperatures were never reached on any vertical surfaces (Fig. S5b).

363

364

365

366

367

368

369

370

371

372

373

374

375
376 fact, when considering a fully sun-sheltered surface, where body temperatures never
377 reached any critical threshold, endolithically-driven thermal buffering remained minimal
378 (Fig. 8a). In contrast, when considering a fully sun-exposed surface, endolithically-driven
379 thermal buffering was progressively enhanced while approaching and exceeding lethal
380 temperatures (Fig. 8b). Note that, in such cases, infested mussels could be up to 2°C cooler
381 than non-infested ones while Tbnon-infested was at the lower limit of optimal body
382 temperatures (Fig. 8b).

383
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

384

385

386

387

388

<caption>Figure 6. Topographic orientation and time spent over 38°C. Number of hours (in colour scale) spent over 38°C for Tb<sub>infested</sub> (left panels) and Tb<sub>non-infested</sub> (right panels) based on body temperatures predicted between 2010-01-01 and 2020-01-01 for sites in the United Kingdom (a, b), France (c, d), and Portugal (e, f). Letters in bold indicate cardinal directions.</caption>

389
<figure><img src="image_17.png" /><figcaption>**Figure 7.** Topographic orientation and time spent over 41°C. Number of hours (in colour scale) spent over 41°C for Tb<sub>infested</sub> (left panels) and Tb<sub>non-infested</sub> (right panels) based on body temperatures predicted between 2010-01-01 and 2020-01-01 for sites in the United Kingdom (**a**, **b**), France (**c**, **d**), and Portugal (**e**, **f**). Letters in bold indicate cardinal directions.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 8. Efficiency of endolithically-driven thermal buffering under two distinct topographic orientations.** Temperature difference ($T_{\text{non-infested}} - T_{\text{infested}}$) vs $T_{\text{non-infested}}$</figcaption></figure>

based on body temperatures predicted between 2010-01-01 and 2020-01-01 (all study sites pooled together) on a surface sheltered from the sun, i.e., North-facing at 90° inclination (a) and an exposed one, i.e., South-facing at 20° inclination (b). Coloured areas cover optimal (blue) and lethal (red) ranges of body temperature (the area in light red covers temperatures at which some individuals may still survive). White circles indicate the optimal temperature ($T_{\text{obt}}$), and grey and black triangles indicate lethal temperatures ($LT_{50}$ and $LT_{100}$, respectively).
407 Discussion

408 Our study demonstrates that the thermal buffering effect conferred by parasitic endoliths is
409 mostly neutral for most topographic orientations. Thermal buffering is, however,
410 advantageous when heat stress is greatest, that is, on sun-exposed surfaces, between
411 midday and late afternoon, during hot weather, with clear skies and light winds. The
412 context-dependent protection against harmful temperatures can make a difference during
413 heat waves by giving infested mussels a higher chance of survival (Gehman & Harley 2019;
414 Zardi et al. 2021). This result is particularly relevant for populations of intertidal mussels,
415 which, like most intertidal ectotherms, live at or near the upper limits of their thermal
416 tolerances (Somero 2010). As climate changes, with an increase in solar radiation due to
417 decreased cloud cover (Schneider, Kaul & Pressel 2019), endolithically-driven thermal
418 buffering could prevent the extirpation of important mussel populations and potentially
419 redirect these partners toward a novel co-evolutionary pathway. Such mutualistic
420 relationships may open new ecological opportunities (Wellborn & Langerhans 2015) as they
421 can allow the host to experience less thermal stress at the hottest edges of their small- and
422 large-scale distributional ranges (i.e., the intertidal zone and biogeographic regions,
423 respectively). Our results further suggest, however, that mussels living in sun-sheltered
424 microhabitats (or during mild weather) are not (or much less) exposed to stressful
425 temperatures, in which case infested mussels are clearly at a competitive disadvantage
426 because they suffer only the costs imposed by endoliths, namely considerable shell damage
427 leading to increased metabolic maintenance costs (Ndhlovu, McQuaid & Monaco 2020) and
428 eventually death through shell collapse (Kaehler & McQuaid 1999).

429
430 Modulation of thermal buffering

431 Under solar radiation, low-reflectance individuals gain heat faster and reach higher
432 equilibrium temperatures than their higher-reflectance counterparts (Porter & Gates 1969),
433 so that one could expect the evolution of light body pigmentation in hot climates (Gibert et
434 al. 1998). In climates where it is important to gain solar heat as rapidly as possible in order
435 to maximise the time available for foraging or mate-finding, darker ectothermic animals can
436 show better survival and reproductive success than their paler counterparts (Clusella Trullas,
437 van Wyk & Spotila 2007; Clusella-Trullas et al. 2008; Smith et al. 2016). However, reflectance
438 also affects the rate of cooling, with dark ectotherms loosing heat faster (Geen & Johnston
439 2014). All else being equal, the rate of solar heat gain depends on more than just colour
440 (Walsberg, Campbell & King 1978; Walsberg 1983; Turner & Lombard 1990; Helmuth 1998;
441 Umbers, Herberstein & Madin 2013). For instance, the heat budget of small animals is more
442 dependent on convective cooling than radiative heating (Turner & Lombard 1990; Helmuth
443 et al. 2011; Umbers, Herberstein & Madin 2013) and this effect can be amplified in dark
444 animals under thin boundary layer conditions (Walsberg, Campbell & King 1978; Walsberg
445 1983). This explains why non-infested mussels were sometimes slightly cooler than infested
446 ones and reinforces the importance of both wind speed and the microhabitat in thermal
447 buffering (Seabra et al. 2011; Zardi et al. 2021). In intertidal mussels, orientation relative to
448 the substratum can result in large temperature differences among individuals lying close
449 together; such microscale differences can even exceed seasonal variation depending on
450 whether they are sheltered from the sun (e.g., North-facing vertical surfaces in the northern
451 hemisphere) or exposed to direct sunlight during a large part of the day (Harley 2008;
452 Seabra et al. 2011; Choi et al. 2019). Here, we show that topographic orientation and
453 exposure to sunlight regulate the thermal buffering effect of endoliths, with infested
mussels expected to (i) be more frequently cooler, and (ii) avoid overheating more often than non-infested ones on sun-exposed surfaces (e.g., South-facing at 20° inclination) between roughly midday and late afternoon. These are precisely the times and places when mussels are most likely to be exposed to high air temperatures and direct sunlight, so that non-infested mussels warm up faster and to higher temperatures than infested ones. We predicted that, on a horizontal surface, the lowest differences in body temperature between infested and non-infested mussels would occur under very low solar irradiance and cool air temperature. Such conditions are likely to occur at night or during cloudy days, that is, when overheating is unlikely. Conversely, endolithically-driven thermal buffering is greatest and most likely to enhance survival during heat waves under clear sky conditions, when mussels may come dangerously close to lethal temperatures. Here we show that thermal buffering does indeed allow infested mussels to remain below 38°C or 41°C more often than non-infested ones and under a wider range of topographic orientations, with some variation in the maximum time spent over these critical thresholds across study sites due to differences in latitude but also factors influencing at small scales such as tidal amplitude and time spent under aerial exposure (Helmuth et al. 2006). For instance, our predictions of body temperatures suggest that both infested and non-infested mussels never reached 38°C at two sites in the North of the United Kingdom (at least during our study period) while they reached 41°C more than once on sun-exposed surfaces at other sites. This suggests that endolithically-driven thermal buffering does not necessarily provide an advantage at the coldest edges of the large-scale distributional range of mussels (at least for *Mytilus* spp. in our case). It is also important to note that thermal preferences and critical thermal thresholds can vary at different levels, from individuals (e.g., via acclimatization) to populations (e.g., via local adaptation; Sanford & Kelly 2011; Thyrring, Tremblay & Sejr
2019). Here, for a more general approach, we used data obtained from the literature for two distinct species: *Mytilus californianus* and *Mytilus galloprovincialis* (Monaco & McQuaid 2018; Sorte *et al.* 2019). Future studies would be needed to further highlight any potential intraspecific variation by incorporating population-specific and inter-individual variation in critical temperatures.

483

## Balance between parasitism and mutualism

In line with previous studies (Zardi *et al.* 2016; Gehman & Harley 2019), we highlight an example of a symbiotic relationship that switches between parasitism and mutualism, whereby the host mostly suffers from the damage caused by endoliths but sometimes benefits from the thermal buffering they provide. On sun-exposed surfaces in most of our study sites, we predicted that non-infested mussels would have experienced lethal temperatures while infested individuals were exposed less often or not at all to stressful or lethal body temperatures. This should allow infested mussels to show higher fitness and better survival than non-infested individuals in places where body temperatures approach or reach the species' upper thermal tolerances. In other words, endolithic infestation is potentially increasing the width of the realized thermal niche. However, we also showed that the cost of endolithic infestation is not outweighed by any thermal advantage in sun-sheltered microhabitats, and that thermal buffering can sometimes reduce body temperatures when the animals are already within their optimum thermal range. Rocky shores are often topographically complex, and thus provide their inhabitants with a huge diversity of thermal microhabitats (Helmuth *et al.* 2006; Harley 2008; Denny *et al.* 2011; Seabra *et al.* 2011). In such situations, it is unlikely that all infested individuals will exhibit
higher fitness than non-infested ones at the same shore level. In turn, in environments where intertidal mussel beds are located on relatively flat reefs, such as along the French coast of the eastern English Channel, endolithic infestation may provide hosts with much higher fitness than non-infested mussels. In fact, following a mass mortality event during a relatively moderate heat wave (Seuront et al. 2019), the great majority (96% to 100%) of empty mussel shells found on the shore had no sign of endolithic infestation (Seuront, unpublished data). Therefore, in environments lacking topographic complexity, the sustainability of intertidal mussel beds may increasingly depend on the thermal buffering provided by endoliths. On the other hand, endolithic infestation comes with a series of costs which can strongly reduce mussel fitness (e.g., weakening and fracturing of the shell, and reduction of growth and reproductive output due to a shift in resources allocation for shell repair) and can be responsible for a high proportion (> 50%) of total mortality, depending on the severity of infestation (Kaehler & McQuaid 1999; Zardi et al. 2009; Marquet et al. 2013; Ndhlovu, McQuaid & Monaco 2020). Given the costs imposed by endoliths, it seems unlikely that these partners will enter a novel co-evolutionary pathway toward an entirely mutualistic relationship. Nevertheless, most mutualistic relationships may have arisen from successive evolutionary transitions which originated from an interaction with damaging parasites that turned out to be beneficial under certain circumstances (Fellous & Salvaudon 2009). Although rare, other examples of parasites providing context-dependent advantages do exist: some parasitic trematodes make marine snails more heat- and acidification-tolerant (Bates et al. 2011; MacLeod & Poulin 2016) and some parasitic bacteria provide a paramecium with protection against osmotic stress (Duncan et al. 2010). Particularly important for further studies would be the evaluation of the fitness of infested individuals relative to non-infested ones across all environments and whether endoliths modify their
hosts' thermal tolerances, for instance by reducing the expression of heat-shock proteins
due to altered resource allocation. The resolution of this specific issue, though of ecological
relevance, lies well beyond the scope of the present study, and warrants the need for
further work to further decipher the role of endolithic infestation on the thermal ecology of
mussels.

530

531 Improving body temperature predictions

532 Our predictions of body temperature using meteorological data from a global climate
533 reanalysis were comparable to those obtained with data from nearby weather stations. This
534 holds great promises for the prediction of body temperatures of terrestrial ectotherms (or
535 intertidal ones during emersion) at ecologically relevant spatiotemporal scales, as we may
536 reasonably bypass the practical issues associated with weather stations (e.g., data gaps).
537 Nevertheless, although we could predict mussel body temperature during aerial exposure
538 with reasonable accuracy (roughly within 2-3.5°C in most cases; Table S5), there is scope for
539 improvement. For example, further experiments are needed to assess how body
540 temperature is affected by smaller-scale topographical effects (e.g., the shapes of the
541 mussel itself or nearby boulders). Future research may also be able to account for the
542 effects of mussel aggregation on microclimates, such as evaporative cooling due to gaping
543 behaviour (Nicastro et al. 2012) or conductive heat transfer within multi-layer mussel beds
544 (Mislan & Wethey 2015). Likewise, enhanced evaporative cooling in infested mussels due to
545 higher water retention potential of eroded shells (Gehman & Harley 2019) may be
546 important. Here, we calculated shell reflectivity based on measurements of reflectance
547 within 350-1100 nm of the solar spectrum while the radiation reaching the Earth's surface is
non-negligible until at least 2000 nm (Smith et al. 2016). Measuring shell reflectance of both infested and non-infested mussels using a full-spectrum reflectometer (at least within 350-2100 nm) could help to improve body temperature predictions during aerial exposure.

Fully characterising the physiological, ecological, and evolutionary consequences of endolithic infestation in natural mussel populations will require accurate estimates of submerged body temperatures and the prediction of body temperatures during complete tidal cycles (i.e., including during high tides when mussels are submerged). There are two reasons that could explain why we could not predict body temperatures during submergence with reasonable accuracy. First, we drove the biophysical model with water temperatures extracted from a climate reanalysis whereas temperatures recorded *in-situ* with buoys placed at our study sites could have provided better results (Lathlean, Ayre & Minchinton 2011). To overcome this, we must rely on future improvements of climate models that will capture the complexity of near-shore environments better and thus provide estimates more biologically meaningful for subtidal and intertidal organisms. Second, we used predictions of tidal heights obtained from XTide at locations sometimes quite distant from our study sites (within 2.34-72.2 km; Table S2), to distinguish between periods of submergence or aerial exposure. This can be problematic because the actual tidal height can vary locally due to the geomorphology of the coast, the influence of wind, waves, and atmospheric pressure. Not accounting for such sources of variation between predicted and realized tidal levels could have led us to misidentify the times when mussels were emerged or submerged. To overcome this, one could follow (i) Gilman et al. (2006) in accounting for wave action when estimating mussel height on the shore and (ii) Mislan et al. (2011) in tracing periods of emergence and submergence or exposure to surge and splash with water-level loggers combined with temperature loggers.
Nevertheless, our main focus here was to evaluate thermal buffering due to differences in shell reflectance, and this is mostly driven by solar radiation (Zardi *et al.* 2021), that is, when mussels are exposed to terrestrial conditions. Our main conclusion that the moderating effects of endoliths on body temperatures are greatest when and where temperatures are most extreme will not be affected by predictions of body temperatures during submergence.

578

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807 Acknowledgements

808 This work is based upon research supported by the National Research Foundation of South

809 Africa (Grant number 64801). The work was also financially supported by a Pierre Hubert

810 Curien PESSOA Program, projects UIDB/04326/2020 from the Fundação para a Ciência e

811 Tecnologia (FCT-MEC, Portugal), and by Rhodes University.

812 Conflict of interest

813 The authors declare no conflict of interest.

814 Authors' contributions

815 JRM initiated the project and conducted the data analysis. JRM conceived the manuscript

816 with contributions from CDM, GIZ and KRN. GIZ, KRN, MO, and LS collected field data. JRM

817 wrote the manuscript with contributions from all authors.

818 Data availability

819 Robomussel data are available from the Dryad Digital Repository:

820 https://doi.org/10.5061/dryad.79cnp5hwg (Monsinjon et al. 2021).

821 Code availability

822 The modelling code used in the present study is available upon reasonable request from the

823 corresponding author.

824 Supporting information

825 Additional supporting information may be found in the online version of this article.