Natural nutrient subsidies alter demographic rates in a functionally important coral-reef fish

By improving resource quality, cross-ecosystem nutrient subsidies may boost demographic rates of consumers in recipient ecosystems, which in turn can affect population and community dynamics. However, empirical studies on how nutrient subsidies simultaneously affect multiple demographic rates are lacking, in part because humans have disrupted the majority of these natural flows. Here, we compare the demographics of a sex-changing parrotfish (Chlorurus sordidus) between reefs where cross-ecosystem nutrients provided by seabirds are available versus nearby reefs where invasive, predatory rats have removed seabird populations. For this functionally important species, we found evidence for a trade-off between investing in growth and fecundity, with parrotfish around rat-free islands with many seabirds exhibiting 35% faster growth, but 21% lower size-based fecundity, than those around rat-infested islands with few seabirds. Although there were no concurrent differences in population-level density or biomass, overall mean body size was 16% larger around rat-free islands. Because the functional significance of parrotfish as grazers and bioeroders increases non-linearly with size, the increased growth rates and body sizes around rat-free islands likely contributes to higher ecosystem function on coral reefs that receive natural nutrient subsidies. More broadly, these results demonstrate additional benefits, and potential trade-offs, of restoring natural nutrient pathways for recipient ecosystems.

∞~ Uniform(min(L), max(L) x 2) 0 ~ Uniform(0, min(L)) k ~ Uniform(0,2) kb ~ Normal(0,1) σ ~ Student(3,0,10) Priors for ∞ , 0 , k, and kb were set following Graham et al. (2018), which used the same VBGF specification to compare damselfish growth between rat-infested and rat-free islands. Default priors were used for σ. A log-log specification was used to improve model convergence. We compared the above model where k was allowed to vary by rat status to a model where both ∞ and k were allowed to vary by rat status. The estimated growth curves and difference in k between rat-free and rat-infested models were similar in the two models (k-only model: estimated k = 0.27, 95% HPDI = 0.16 to 0.41; estimated kb = 0.10, 95% HPDI = 0.02 to 0.20; both k and ∞ model: k = 0.26, 95% HPDI = 0.07 to 0.50; kb = 0.09, 95% HPDI = -0.17 to 0.31). There was also no evidence that ∞ differed between rat-free and rat-infested islands even when it was allowed to vary (estimated difference in ∞ = 0.06, 95% HPDI = -7.51 to 4.83). Furthermore, the model fit was best when only k was allowed to vary by rat status, compared to the model in which both ∞ and k were allowed to vary, as well as a null model in which neither were allowed to vary.
To test for a correlation between GSI and growth rate within individual parrotfish, we ran an additional VBGF model in which k was allowed to vary by individual rather than by rat status. We extracted these individual k estimates and conducted a Bayesian correlation analysis between measured GSI and model-estimated k using the R package correlation (Makowski et al. 2020).
Maximum length (Lmax) and age (Tmax) of female C. sordidus were modelled following normal distributions as: The priors for α were weakly informative based on the observed range of maximum age and length. The priors for β1 were weakly informative with means around zero, thus providing no indication about the direction of any potential rat versus seabird effect or effect.
Default priors were used for σ.
Population density (D) and biomass (B) of C. sordidus from visual surveys were modelled as: Dij ~ HurdleGamma(µi, shape, hu) Bij ~ HurdleGamma(µi, shape, hu) (1,1) Hurdle gamma distributions with log links were used because the data consisted of non-negative, continuous values and were zero-inflated. Weakly informative priors were used for α and β1, and default priors were used for σ, hu, and shape parameters.
The frequency distribution of C. sordidus size (length, L) around rat-free versus ratinfested islands was modelled as: Lij ~ ExGaussian(µi, beta, σ)   Table S2. Median difference and 95% highest posterior density interval (HPDI) of rat-free compared to rat-infested islands from Bayesian models. Where applicable, models were run for all study islands combined, collection islands only, and survey islands only. See also Table S1 and Figure S2. gonad weights. The prior for β2 was constrained to stay above zero because the relationship between length and gonad weight is always positive. The priors for β1 and σ were specified as in the models for nitrogen. We compared the above additive-only model to a model containing an interaction term (rat x length) using leave-one-out cross-validation. There was no improvement in model fit when an interaction term was included, and parameter estimates were nearly identical regardless of model choice, so the simpler additive-only model was used.

Supplementary Table S2: Model estimates of differences in island, reef, and environmental characteristics between rat-free versus rat-infested study islands.
We then estimated gonad weight, along with 95% highest posterior density (HPD) intervals, of each female from the population-level suveys based on its observed length. We summed these estimated gonad weights across all females observed on each transect to estimate total gonad weight. Total gonad weight was modelled as a function of rat presence, with the intercept allowed to vary by atoll, following a hurdle gamma model using a log link (similar to models for biomass and density, specified in Supplemental Material SM2). As for all other models, weakly informative priors were used for the intercept (α) and slope (β) parameters, and default priors were used for σ, hu, and shape parameters. In addition to modelling the estimated gonad weights, we re-ran the models using the upper and lower limits of the 95% HPD intervals, and obtained similar results in all cases.
Importantly, this analysis provides an approximate, instantaneous estimate of population-level gonad weight at one point in time, and therefore does not account for any potential differences in the timing and/or length of the spawning season around rat-free versus rat-infested islands. Despite the caveats, this analysis is useful in that it provides the first estimation of population-level potential relative reproductive output, around rat-free versus rat-infested islands, and serves as a comparison to the results for individual-level reproductive investment around these same islands.