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| Titel |
Power-law intermittent ratio distributions in marine ecology |
| VerfasserIn |
Francois Schmitt, Sylvie B. Zongo |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250057620
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| Zusammenfassung |
| In marine ecology and biogeochemical marine studies, one can find quite often some studies using ratio statistics between two quantities. There are two main instances where this happens: stoichiometry studies concerning nutrient concentrations in biogeochemical studies and sex ratio statistics in population dynamics studies. In the first case, one considers e.g. N/P ratio of nitrogen and phosphat concentration, to detect possible limitation nutrients for phytoplankton growth. The sex ratio statistics is the study of the ratio M/F of male to female concentration.
There are results concerning ratio statistics in the mathematical literature, and several theorem are known. For example, if the variables X and Y are Gaussian, the ratio Z=X/Y is a Cauchy random variable with power-law tail and its variance does not exist. There are other results for more general cases and globally, the ratio Z is in many situations an intermittent random variable with a power-law tail of exponent 2 or 3.
In the light of these results, we consider some experimental ratio of nutrient concentrations or sex ratio of zooplankton. We show that these distributions have power-law tails. We also discuss the difference between the mean of X/Y and of Y/X. Finally we underline the fact that the ratio of the mean is not the mean of the ratio. Our general conclusion is that a random variable created as a ratio of two variables has a very peculiar statistical behaviour and can only be used in experimental studies with much caution. |
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