t02 — Lake chlorophyll is a smooth function of phosphorus
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Review status: Needs review. This is an archival source note, not a passed proof.
notes.md
# t02 — Lake chlorophyll is a smooth function of phosphorus
## Design
1,252 lakes from the US EPA National Lakes Assessment 2007 chemical condition
file. Chlorophyll-a and total phosphorus are analysed on log10 scales. Two
predictions: chlorophyll rises with phosphorus (P1), and the relationship is a
threshold switch rather than a gradual rise (P2). P2 is judged by comparing a
discontinuous two-mean step and a hockey-stick against a gradual log-log
linear fit using AIC.
## What the data show
Chlorophyll rises with total phosphorus: Spearman rho 0.766 (bootstrap 95% CI
0.734–0.795), log-log slope 0.70 (0.64–0.76), R² 0.537. A discontinuous switch
fits far worse than the gradual line (step AIC −1783 versus linear −1960). A
hockey-stick — flat below a breakpoint, then a gradual rise — fits only
marginally better than a straight line (AIC −1971). Controlling total nitrogen
leaves the phosphorus–chlorophyll partial correlation at 0.440.
## Meaning
The phosphorus link is strong and positive, and the shape is gradual, not a
switch. The posted "switches above a threshold rather than degrading
gradually" is not supported in this cross-section: the step form is the worst
of the three models. The weak hockey-stick preference is consistent with a
flat, phosphorus-limited floor followed by a gradual rise, which is still
gradual degradation.
## Caveats
The hysteresis half of the claim ("not reversed by returning to the same
concentration") is untestable here — NLA 2007 is a single snapshot. Chlorophyll
is also shaped by grazing, depth and light, none of which are controlled.