No evidence of fish biodiversity effects on coral reef ecosystem functioning across scales

We demonstrate that the conclusions drawn by Lefcheck et al. (2019) regarding the positive effects of fish diversity on coral reef ecosystem functioning across scales are flawed because of a series of conceptual and statistical issues that include spurious correlations, the conflation of population size and species diversity effects and a failure to recognize that observing a biodiversity effect at multiple sites is not equivalent to observing it at multiple scales.


Introduction
sought to show the beneficial effects of tropical fish biodiversity on coral reef ecosystem functioning at multiple scales. To do so, they collected data from video and transect surveys at ten sites to determine whether α and β species diversity of fish led to an increase in ecosystem functioning in the form of higher grazing rates at multiple scales and whether grazing rates enhanced ecosystem structure by reducing turf abundance and promoting coral abundance. Below, we describe a number of major conceptual and statistical flaws in their study that undermine their results and conclusions.

Conceptual and statistical flaws
Grazing rate is an inappropriate measure of ecosystem functioning The first conceptual issue lies in the use of the grazing rate (bite rate) as a measure of ecosystem functioning. Increased grazing of turf can promote ecosystem functioning if it reduces turf abundance and thus leads to an increase in reef-building corals via competitive release. Ecosystem functioning should thus be measured in terms of the impact of grazing on turf or coral rather than its rate. Grazing rate, on its own, is merely one of an infinite number of community or system-level properties that could also be arbitrarily designated as an "ecosystem function". Its relevance arises only due to its potential impact on an ecosystem property of interest. Showing a significant positive relationship between various diversity metrics and grazing rate is thus necessary but not sufficient to demonstrate greater ecosystem functioning.
However, the mixed-effects model in Lefcheck et al. showed no relationship between mass-standardized bite rate and either turf cover or coral cover in the video dataset ( Fig.  1A,B). The lack of a relationship suggests that changes in the mass-standardized bite rate do not translate into changes in turf or coral cover. Additionally, no relationship emerges when the mass-standardized bite rate is regressed against turf cover rather than turf height in the transect dataset (Fig. 1C). Similarly, no relationship exists when regressing juvenile coral recruitment against turf cover (Fig.  1D). This means that the entire case for a meaningful effect of bite rate on ecosystem functioning emerges only when turf height (not cover) is used in one of the two datasets. The results that link mass-standardized bite rate and ecosystem functioning are thus not robust.
No evidence that diversity promotes ecosystem functioning across scales The second conceptual issue stems from the claim that diversity promotes ecosystem functioning across scales and the suggestion that the results presented in Lefcheck et al. are consistent with the spatial insurance hypothesis. Spatial insurance effects occur when ecosystem functioning is enhanced and more stable at the regional scale as a result of local sites undergoing favorable conditions rescuing those undergoing unfavorable ones (Loreau et al., 2003). Because spatial insurance effects emerge at the regional scale, they cannot be detected by regressing local ecosystem functioning against local factors such as diversity and biomass at all sites. Although the results presented in Lefcheck et al. show that localized measures of diversity promote local ecosystem functioning, this local-scale effect of diversity was misinterpreted as evidence of a multi-scale effect because it arose at multiple sites. However, observing a biodiversity 1/5 arXiv:1904.02049v1 [q-bio.PE] 3 Apr 2019 No evidence of fish biodiversity effects on coral reef ecosystem functioning effect at multiple sites is not the same as observing it at multiple scales. Here, the suggestion that diversity enhances ecosystem functioning across multiple scales is simply not supported by the data. Additionally, the conceptual link drawn to the spatial insurance hypothesis does not make sense given that the analyses were all performed at the local scale.

Inevitable relationships between biomass, diversity and bite rate
The mixed-effects model presented in Lefcheck et al. showed a significant positive relationship between mass-standardized bite rate and biomass. However, this relationship is at least partially attributable to a spurious correlation because the response variable is the bite rate scaled by the explanatory variable (biomass). Monte Carlo simulations show that this leads to spurious correlations between mass-standardized bite rate and biomass when biomass and bite rate are inde-pendent random variables drawn from a uniform distribution ( Fig. 2A). When the spurious correlation issue is fixed by using the non mass-standardized bite rate as a response variable, the positive effect of biomass remains significant but that is because biomass is acting as a surrogate for the number of fish observed at each site (correlation = 0.97, p-value < 0.0001). Hence, a significant positive relationship between biomass and bite rate was to be expected since increasing the number of fish leads to both greater total biomass and a larger number of total bites.
A similar issue arises with α diversity (local species richness), which was also positively associated with bite rate. This was interpreted as a local diversity effect, with more species yielding a higher total bite rate, perhaps because of complementarity in resource use between fish species. However, the relationship between total bite rate and α diversity was bound to be positive since increasing α diversity is largely tantamount to increasing the total number 2/5 No evidence of fish biodiversity effects on coral reef ecosystem functioning Collinearity between diversity metrics shown via a significant positive relationship between β rich observed andβ rich predicted from a multiple regression of β rich against α and β rich explaining 83% of the variance. (C) Significant negative partial effect of the three-way interaction between α, β rich and β repl diversity on the mass-normalized bite rate. (D) The independent effect of each explanatory variable as a percentage of the variance explained in the mass-normalized bite rate. The model explains 89% of the total variance. Asterisks indicate statistically significant variables (p-value < 0.05).
of fish as long as the community is not saturated (i.e., no zero-sum game whereby the addition of an individual from one species leads to the loss of an individual from another species). Because increasing species richness leads to an increase in the number of fish (correlation = 0.54, p-value = 0.007), and adding individual fish will increase the total number of bites, the relationship between total bite rate and α diversity essentially has to be positive. Hence, since α diversity is at least partially acting as a surrogate for the total number of fish, it is not surprising to see a positive relationship emerge between total bite rate and α diversity. However, this is likely due to a population size effect rather than a true species diversity effect.

Spurious relationship between β rich and bite rate
Lefcheck et al. found a positive relationship between local bite rate and β rich diversity-a measure of the uniqueness of the community at a given site-and claimed that it represented evidence of a spatial insurance effect. As mentioned above, this local relationship between β rich diversity and bite rate cannot represent evidence of a regional spatial insurance effect. Additionally, there is no clear mechanism by which higher β rich diversity can lead to a higher bite rate at the local scale, as the positive effects of β rich diversity on bite rate can only emerge when sites are aggregated at larger spatial scales. Any positive effect of a site's compositional uniqueness expressed via β rich diversity on local bite 3/5 rate would be captured by local factors such as α diversity and biomass. It is more likely that the positive effect of β rich diversity on local bite rate reported in Lefcheck et al. is due to multicollinearity between the explanatory variables α, β repl and β rich diversity included in their mixed-effects model (Fig. 2B).
Furthermore, perhaps under the mistaken impression that the additive partitions of total β diversity-namely β repl and β rich -had to be orthogonal, the authors verified that all possible two-way interactions between α diversity and the components of β diversity were not significant but failed to test and include the significant three-way interaction between α, β repl and β rich diversity in their model (p-value = 0.03). The coefficient associated with this significant three-way interaction is negative, so an increase in any of the three diversity metrics will lead to a reduction in the mass-standardized bite rate (Fig. 2C). Standard statistical practice dictates that in the presence of such a significant negative three-way interaction, the positive main effects of α and β rich diversity should not be interpreted because their independent effects on mass-standardized bite rate are not consistent (Whitlock and Schluter, 2008;Quinn and Keough, 2002;Sokal and Rohlf, 2011;Zar, 1999). Hence, the positive main effects of α and β rich diversity that constitute the backbone of Lefcheck et al.'s conclusions are suspect at best. To verify this claim, we used hierarchical partitioning (Chevan and Sutherland, 1991;Mac Nally, 2000) to determine the independent effect of each explanatory variable on mass-standardized bite rate and found that only biomass and α diversity were significant and collectively represented 72% of the variance explained, whereas β rich and β repl diversity were not significant and collectively represented only 12% of the variance explained (Fig. 2D). This is not surprising since the positive effects of β diversity cannot emerge at the local scale.

Misinterpreted evidence for complementary
Multiple regression was used to relate mass-standardized bite rate at each site to the proportional biomass of each species in order to determine whether there was 'complementarity' between species in terms of their contributions to bite rate. However, there seems to be some confusion about how to interpret these results. Significant positive relationships between proportional abundance and massstandardized bite rates across sites cannot be interpreted as evidence of 'complementarity' without ensuring that the bite rates observed in multi-species communities at the very least exceed those expected based on the bite rates observed in their constituent single-species populations. Otherwise, significant relationships between proportional biomass and bite rates could just as likely arise because of redundancy between species that equally contribute to the bite rate at all sites.
If anything, these significant relationships provide poten-tial evidence for a lack of 'complementarity' at the regional scale. Indeed, a significant relationship between bite rate and a focal species' proportional biomass means that the focal species contributes significantly to the bite rate across all sites. Hence, fewer significant relationships indicates fewer species 'dominating' or contributing consistently to the local bite rate across all sites and suggests greater spatial 'complementarity', with some species contributing more to the local bite rate at a subset of sites. In this case, the proportional biomass of four of the nine species was significantly related to bite rate across all sites, which suggests that about 56% (5/9) of species are spatially 'dominant' and about 44% (4/9) of species either contribute differentially ('complementarily') or not at all to the local bite rate across sites.

Conclusion
Overall, we believe that the conceptual and statistical issues outlined above demonstrate that there is no evidence that fish diversity promotes ecosystem functioning across scales. Establishing this important result would require linking α and β diversity to greater ecosystem functioning in the form of higher coral cover or lower turf cover beyond the local scale by aggregating the data across sites as other researchers have done in terrestrial systems (Winfree et al., 2018).