### 2.18.6.2. Response of C expenditure to plant C:N ratios[¶](#response-of-c-expenditure-to-plant-c-n-ratios "Permalink to this headline")

We first calculate a \\(\\delta\_{CN}\\), which is the difference between the target C:N (\\(target\_{CN}\\)) a model parameter, and the existing C:N ratio (\\(CN\_{plant}\\))

> \\\[CN\_{plant} = \\frac{C\_{leaf} + C\_{leaf,storage}}{N\_{leaf} + N\_{leaf,storage})}\\\]

and

\\\[\\delta\_{CN} = CN\_{plant} - target\_{CN}\\\]

We then increase \\(\\gamma\_{FUN}\\) to account for situations where (even if N is expensive) plant C:N ratios have increased too far from the target. Where \\(\\delta\_{CN}\\) is negative, we reduce C spent on N uptake and retain more C for growth

> \\\[\\begin{split}\\gamma\_{FUN} = \\left\\{\\begin{array}{lr} \\gamma\_{FUN}+ 0.5.(delta\_{CN}/c\_{flexcn})& delta\_{CN} > 0\\\\ \\gamma\_{FUN}+(1-\\gamma\_{FUN}).min(1,\\delta\_{CN}/c\_{flexcn}) & delta\_{CN} < 0 \\end{array}\\right\\}\\end{split}\\\]

We then restrict the degree to which C expenditure can be reduced (to prevent unrealistically high C:N ratios) as

> \\\[\\gamma\_{FUN} = max(min(1.0,\\gamma\_{FUN}),0.5)\\\]

