Temperature sensitivity of detrital photosynthesis

Abstract Background and Aims Kelp forests are increasingly considered blue carbon habitats for ocean-based biological carbon dioxide removal, but knowledge gaps remain in our understanding of their carbon cycle. Of particular interest is the remineralization of detritus, which can remain photosynthetically active. Here, we study a widespread, thermotolerant kelp (Ecklonia radiata) to explore detrital photosynthesis as a mechanism underlying temperature and light as two key drivers of remineralization. Methods We used meta-analysis to constrain the thermal optimum (Topt) of E. radiata. Temperature and light were subsequently controlled over a 119-day ex situ decomposition experiment. Flow-through experimental tanks were kept in darkness at 15 °C or under a subcompensating maximal irradiance of 8 µmol photons m−2 s−1 at 15, 20 or 25 °C. Photosynthesis of laterals (analogues to leaves) was estimated using closed-chamber oxygen evolution in darkness and under a saturating irradiance of 420 µmol photons m−2 s−1. Key Results T opt of E. radiata is 18 °C across performance variables (photosynthesis, growth, abundance, size, mass and fertility), life stages (gametophyte and sporophyte) and populations. Our models predict that a temperature of >15 °C reduces the potential for E. radiata detritus to be photosynthetically viable, hence detrital Topt ≤ 15 °C. Detritus is viable under subcompensating irradiance, where it performs better than in darkness. Comparison of net and gross photosynthesis indicates that elevated temperature primarily decreases detrital photosynthesis, whereas darkness primarily increases detrital respiration compared with optimal experimental conditions, in which detrital photosynthesis can persist for ≥119 days. Conclusions T opt of kelp detritus is ≥3 °C colder than that of the intact plant. Given that E. radiata is one of the most temperature-tolerant kelps, this suggests that photosynthesis is generally more thermosensitive in the detrital phase, which partly explains the enhancing effect of temperature on remineralization. In contrast to darkness, even subcompensating irradiance maintains detrital viability, elucidating the accelerating effect of depth and its concomitant light reduction on remineralization to some extent. Detrital photosynthesis is a meaningful mechanism underlying at least two drivers of remineralization, even below the photoenvironment inhabited by the attached alga.

Where more than one mean or standard deviation are provided, the values refer to light and dark sample and blank incubations in that order.σ is assigned a non-negative exponential prior with rate = 1 by default (McElreath, 2019).A Gaussian prior with mean = 228 µM and standard deviation = 20 µM was chosen for the intercept (α) based on known regional i.e., South Indian Central Water (Woo and Pattiaratchi, 2008) and local (Rose et al., 2012) dissolved O2.Different slope (β) priors were selected for each incubation type by centring on zero (blanks) or back-transforming rates from similar O2 evolution experiments on E. radiata laterals from our study site (cf.15-20°C incubation temperature, 120-mL chambers, ~0.22 g dry mass, Fig. 1D, Staehr and Wernberg, 2009;Wernberg et al., 2016).Prior rates of O2 change (βp, µM min -1 ) were back-calculated as where r is the given mean rate of photosynthesis or respiration (mg O2 g -1 dry mass h -1 ) for temperatures 15 and 20°C (Fig. 1D), m is the given mean dry mass (0.22 g), V is the given incubation volume (0.12 L), Δt is the reported period (60 min), M is the molar mass of O2 and 10 3 is the conversion from mM to µM.
For each of the 160 resulting models, prior and posterior probability distributions for β (Fig. S1A) and α (Fig. S1B) were visually compared and means and 98% percentile intervals of µ as well as 98% percentile prediction intervals for predicted observations calculated and visualised over the range of t (Fig. S1C).Posterior probability distributions of both α and β are of interest downstream since α + β × -t ̅ is an estimate of the initial incubation O2 (µM) which may affect photosynthesis and respiration.β (µM min -1 ) posteriors were converted to Pn, R, Pg (mmol O2 g -1 dry mass h -1 ) and Pd (mmol O2 g -1 dry mass d -1 ) as where subscript l, d and b denote light and dark sample and blank incubations from the same measurement group, V is the posterior probability distribution of the mean of empirically derived incubation volume (mean = 175 mL), m is the sample dry mass (g), 10 3 is the conversion from µmol to mmol and Δt is the desired period (1 = 60 min, 2 = 12 h).We converted blotted mass to dry mass by multiplying by sample-specific dry-blotted mass ratios to make our rates comparable with the literature.Note the reversed signs in the last two equations since βd and therefore R are given as negative values.Importantly, by performing calculations on entire probability distributions rather than central tendencies, all measurement error is propagated.For instance, Pg inherits error from βl, βd, βb and V (Fig. S2, S3).The resulting 57 probability distributions for P were summarised as mean and standard deviation to enable propagation of measurement error to the next series of models (Equation S5).
Confounders were included using multiple linear regression to avoid biased inference.Photosynthesis may be sensitive to a variety of variables, including O2, temperature, pressure, salinity and resource availability (carbon and nutrients), the latter being a function of the available seawater volume per tissue mass.The O2 meter automatically corrects for temperature, pressure and salinity, and we normalised by sample mass (Equation S3) and attempted to control temperature using a 20°C controlled temperature room.However, this does not remove the confounding effect of these variables and they deserve incorporation.The posterior probability distribution of initial incubation O2 for each measurement is readily estimated by α + β × -t ̅ (Equation S1) and summarised as mean and standard deviation for each value of P (Equation S3).Standardised incubation temperature across each ~5-min measurement (T, °C) was additionally estimated using a simple intercept model as where the first line is the Gaussian likelihood function describing the response variable, the second describes µ, and the last two are regularising prior probability distributions for the remaining parameters.µ from this model was summarised as mean and standard deviation for each observation of P (Equation S3).Pressure, salinity and sample mass had little to no variability within measurement series, so they were simply summarised as mean for each value of P (Equation S3).Therefore, of the five confounders we identified, only initial incubation O2 and mean incubation temperature had modellable measurement error, requiring incorporation into the model (McElreath, 2019).
Each of the four tanks assigned to each treatment varied slightly in size, position, water level, sediment depth etc. Partial pooling was employed to incorporate such variation by explicitly modelling the standard deviation across tank slopes.As such, this method estimates a parameter based on other parameters and is therefore called multilevel or hierarchical modelling.Partial pooling is the default for any type of categorical variable (McElreath, 2019) but after fitting a full multilevel model, we chose not to have pooling between treatments because (1) as opposed to tanks, we are not aiming to predict the response for new, unknown treatments and (2) data missingness (see main manuscript for a discussion of this issue) causes the light 15°C treatment to have most observations and skew the slopes of all other treatments towards its value.Under other circumstances this regularisation would be desired, but in our case it just exacerbates the underestimation of the treatment effect caused by non-random missing data.The five initial measurements from 29 th June were randomly assigned a tank and treatment prior to the next modelling stage.The uneven number of replicates resulted in an additional observation in the dark 15°C treatment, causing the maximal sample size to be n = 26 rather than n = 25.
Taking all of the above into account, P (mmol O2 g -1 dry mass h -1 or mmol O2 g -1 dry mass d -1 ), inferred from observed P with measurement error (Pobs ± sP), was modelled as a function of detrital age (A, d), numerically coded versions of the four-level treatment variable (Tr, dark 15°C, light 15°C, light 20°C and light 25°C) and the 16-level tank variable (Ta) and standardised versions of the incubation confounders initial O2 with measurement error (Oobs ± sO, µM), mean incubation temperature with measurement error (Tobs ± sT, °C), mean pressure (Pr, hPa), salinity (S, ‰) and sample dry mass (M, g) as Pobs ~ normal(mean = P, standard deviation = sP ) Oobs ~ normal(mean = O, standard deviation = sO) Tobs ~ normal(mean = T, standard deviation = sT) O, T ~ normal(mean = 0, standard deviation = 1) α ~ normal(mean = 0.05, 0.07, 0.27, standard deviation = 0.02, 0.02, 0.2) βTr ~ normal(mean = -0.001,-0.001, -0.01, standard deviation = 0.001, 0.001, 0.02) βO, βT, βP, βS, βM ~ normal(mean = 0, standard deviation = 0.01, 0.01, 0.2) z ~ normal(mean = 0, standard deviation = 1) σ, τ ~ exponential(rate = 1) where the first line is the Gaussian likelihood function describing the response variable, the second is the linear model describing µ, the third enables partial pooling of tank slopes without the hierarchical priors typical of multilevel models by estimating their z-score, the next four are priors for every observation in variables with measurable error, and the last five are priors for all parameters.Where more than one mean or standard deviation are provided, the values refer to net, gross and daily net photosynthesis in that order.Intercept priors were selected from previous E. radiata photosynthesis rates at 15-20°C (Fig. 1D, Staehr and Wernberg, 2009;Wernberg et al., 2016), and converted using dry to blotted mass ratios from our study.Slope priors were derived by averaging the only similar parameters available in the literature across species (Wright et al., 2022).
To complete the picture, we incorporated additional information contained in the unmeasurable disintegrated samples by calculating three binomial variables (see Data analysis and visualisation in main manuscript).Each probability (P, 0 or 1) was modelled as a function of detrital age (A, d), numerically coded versions of the four-level treatment variable (Tr) and the 16-level tank variable (Ta) as P ~ binomial(number = 1, probability = p) (6) logit(p) = α + (βTr + βTa) × A βTa = z × τ α ~ normal(mean = 5, standard deviation = 2.5) βTr ~ normal(mean = -0.1,standard deviation = 0.2) z ~ normal(mean = 0, standard deviation = 1) τ ~ exponential(rate = 1) where the first line is the Bernoulli likelihood function describing the response variable, the second is the linear model describing logit-transformed p, i.e., log odds, the third enables partial pooling of tank slopes without the hierarchical priors typical of multilevel models by estimating their z-score and the last four are priors.The above priors were chosen since α = 5 on the log odds scale translates to almost near certainty of survival, which is sensible for A = 0, and βTr = -0.1, which corresponds to the logistic rate k (log odds d -1 ) in this case, provides an indication of the expected negative slope, i.e., logistic decay.Since the intercept is already known to lie near 1 on the probability scale, time at which p = 0.5 is more meaningful to our model interpretation.This is given by the inflection point of the sigmoid curve on the probability scale (µ), the probability distributions of which was calculated as µ = ɑ β .Note that µ (d) is a quotient distribution and therefore does not have a defined mean or standard deviation, so the quotient of the means of ɑ and β was used as a close proxy for the mean of µ.

Figure S2. Blank correction of slopes (Equation S3
). Posterior probability distributions of β (Equation S1) are shown for blanks (black), samples (blue) and samples after subtraction of the blank by measurement round (orange).Note that variation is added by blank subtraction.Incubations are stratified by their position on the four-position magnetic stirrer (counting row-wise from left to right), the measurement round (n) and the timepoint (t).S3).Posterior probability distributions of β after blank correction (Fig. S2) and normalisation by volume and sample dry mass (Equation S3) are shown for respiration (black), net photosynthesis (blue) and gross photosynthesis (orange).Note that variation is added by subtracting respiration.Incubations are stratified by their position on the fourposition magnetic stirrer (counting row-wise from left to right), the measurement round (n) and the timepoint (t).S3) and α + β × -t ̅ (Equation S1) or μ (Equation S4) for initial O2 and temperature respectively.Violins (last three panels) are posterior probability distributions for each observation, derived from β (Equation S1) via conversion (Equation S3).Lines and intervals are means and 50, 80 and 90% posterior probability intervals for µ (Equation S5) at mean detrital age A " .

Figure S3 .
Figure S3.Calculation of gross photosynthesis (EquationS3).Posterior probability distributions of β after blank correction (Fig.S2) and normalisation by volume and sample dry mass (EquationS3) are shown for respiration (black), net photosynthesis (blue) and gross photosynthesis (orange).Note that variation is added by subtracting respiration.Incubations are stratified by their position on the fourposition magnetic stirrer (counting row-wise from left to right), the measurement round (n) and the timepoint (t).

Figure S4 .
Figure S4.Effect of confounding variables associated with incubation on net (A), gross (B) and daily (24-h) net (C) detrital photosynthesis of Ecklonia radiata, given per gram of dry mass.Ellipses (first two panels) are bivariate posterior probability distributions for each observation, derived from β (Equation S1) via conversion (EquationS3) and α + β × -t ̅ (Equation S1) or μ (EquationS4) for initial O2 and temperature respectively.Violins (last three panels) are posterior probability distributions for each observation, derived from β (Equation S1) via conversion (EquationS3).Lines and intervals are means and 50, 80 and 90% posterior probability intervals for µ (Equation S5) at mean detrital age A " .