Submerged plants are influenced by multiple factors. The main focus is hereby directed toward surface water dissolved nitrogen (N) or phosporus (P) compounds. Nonetheless, N and P seem to have limited predictability from my perspective and Dissolved Inorganic Carbon (DIC) seems to be more predictable (i.e Demars et al, 2012, I repeated this with the TIM index from Schneider and Melzer (2003) on a dataset with similar results, see the appendix). Further, N and P are often 10 till 1000 times higher (often not limited) in the sediment compared to the dissolved amounts in the surface water. So, why would any plant spend large amounts of energy acquiring it solely from the surface water. Many others have shown the effects of Dissolved Inorganic Carbon (DIC) to be important (Iversen et al. 2019). Furthermore, results from studies using multivariate-analysis have very different results showing N and P are "important", or it are "unimportant". Yet, they never discuss any possible co-correlation (pseudo-correlation). It seems like N and P, besides the obvious effects on light restrictions (via phytoplanton), is less important than what is assumed. Moreover, often most of these studies never include DIC related parameters, even worse, when monitoring water quality (i.e. in light of the Water Frame Work directive) DIC as HCO3 or CO2 is often hardly included.
From my perspective only a few parameters other than N and P seem "important", Light/turbidity (obviously), flow velocity, DIC and salinity (Chambers et al., 1991; Demars et al., 2012; Haslam, 2014; Iversen et al., 2019; Poikane et al., 2018; Remane and Schlieper, 1972). It is not to say that N and P are not "important" since an decrease in CO2 or increase in HCO3 often goes paired with an higher concentration of N and P. Yet, perhaps the occurrence of species is in most cases only indirect related to N and P and causal effects are missing. Does anyone has/had any thoughts on this? Why is there such a (seemingly) reluctance in using DIC explaining macrophyte distribution patterns?
The proportion of the variance for your dependent variables that is explained by the independent variables is low, which means other factors are involved. This is shown by so few of your data points being close to your regression lines and low Rˆ2 values. Perhaps you could combine the data or add other factors to the regression equations :)
I agree with your, response. However, macrophyte indices are "sold" as a predictor for N or P compounds (Holmes et al., 1999; Schneider and Melzer, 2003). Which it clearly does not do. Additionally a bit of a negative point of this dataset is that it are all relative eutrophic systems. So, results might be be slightly limited since not a great portion of the gradient is probably not covered. Yet, the results here are quite variable (ranging to "good" or "bad" sort to say). Including, multiple parameters might improve the model, but R-squared or pseudo-R-squared are a bit of a bad usage of goodness-of-fit in this regard. Including any random parameter to a linear model or CCA for that matter improves your R-squared, pseudo-R-squared, explained variation (captured variation).
For example, I created created a 100 random datasets with first 15 predictor variables and secondly with 5 predictor variables, with n=200. I performed this for both a CCA and than with an LM and loc. A clearly visible your captured variation increases with the number of predictors (Figure 1). We might correct this with the adjusted-R-squared, which works relatively well. If we take the median value found by the CCA and LM (both 0.08) and apply the adjusted-R-squared 1 - (1 - 0.08) * ((200 - 1)/(200-15)) = the captured variation decreases to 0.01.
Now we know this I constructed an LM with both TN and TP assuming that TN and TP captures all N and P compounds. The result of this model is similar to the previous: Adjusted-R-squared = 0 (LCI = 0 and HCI = 0.02, n = 638, p-value = 0.04; Figure 2 for 3D plot). Additionally to the parameters TN and TP I constructed a second LM and included HCO3. The Adjusted-R-squared now increases to 0.13 (LCI = 0.08 and HCI = 0.19, n = 284, p-value = < 0.001).
Regarding co-correlation (multicorrelation); yes this indeed may be significant. There are accepted methods for dealing with multicorrelation, such as use of variance inflation factors (which increases the p value for any one independent variable to a more realistic/accurate value) to evaluate multi-linear model results. You may want to consider more sophisticated statistical model approaches, such as principal components analysis (and others).
Iam not the biggest fan of solely using p-values, (see https://www.researchgate.net/project/Because-I-can-not-write-articles, "AUC versus p-value"). Furthermore, a PCA will only elude the general direction (or principal components) of the parameters in the dataset. It will, not predict species occurrence. And, just as the LM, PCA and CCA's are linear approaches unable to capture non-linear interactions (?). Hence, the point is, TN and TP, depending on which approach or model is used, seem to have limited predicting "power" compared to HCO3. Even salinity (Cl or SO4) seemed to have a beter predictability. We can indeed discuss the biological relevance of TN or TP for macrophytes. However, this does not make them valuable predictors.
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