What is the Pianka's Index?
- How does it work?
- How can one calculate this index?
- How often is it used?
- In what context do people usually use it?
- Can one infer any statistical significance with this index?
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$\begingroup$ Do you plan to apply it to a particular dataset or problem, or are you asking out of general curiosity? Have you looked at Pianka's paper? $\endgroup$– fileunderwaterNov 8, 2013 at 15:52
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$\begingroup$ No I haven't had a look to Pianka's paper! I might not have looked thoroughly but I haven't found a paper that only presents such equation. I found some equations without really knowing what was called the Pianka's Index. I might aime to apply it on a dataset but for the moment my question is not specific. I just want to know how it works and why do poeple usually use this index. $\endgroup$– Remi.bNov 8, 2013 at 17:11
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1 Answer
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Pianka's index of niche overlap is defined in his papers from 1973 and 1974, as:
$O_{kl}=\dfrac{\sum_i^n{p_{il} p_{ik}}}{\sqrt{\sum_i^n{p_{il}^2} \sum_i^n{p_{ik}^2}}}$
where $O_{kl}$ is the resource overlap between species $k$ and $l$, and since the index is symmetric $O_{kj} = O_{lk}$. $p_{ib}$ represents the proportion of resource $i$ that is used by species $b$. The index is a modification of one presented in MacArthur & Levins (1967).
As apparent from the formula, the only thing you need to calculate the index are estimates of resource use from the resources that both species depend on. The tricky part can be to determine how you calculate proportianal use of all resources.
I haven't used the index myself, and cannot really say anything about how common it is. I have seen references to it though. Pianka (1973) use it to study overlap between lizard species, and how the distribution of niche overlaps differ between habitat types. I haven't seen any statistical tests on it, but you should be able to use resampling or bootstrap to determine the uncertainty in the index.
answered Nov 8, 2013 at 20:47
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$\begingroup$ Thank you! Shouldn't $j$ be $l$ in your formula? Or where is $l$ in the right-hand-side and what does $j$ mean? $\endgroup$– Remi.bNov 9, 2013 at 7:17
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$\begingroup$ Just to make I understood it correctly. $p_{ij} + p_{ik}$ does not necessarily equal to 1 even if there are no other species (than $j$ and $k$) using the resource $i$ because one should take into account that not all resources are used at 100%. Is it correct? Thank you for your help! $\endgroup$– Remi.bNov 19, 2013 at 9:31
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$\begingroup$ If yes, do you think it would make sense to divide the index by n in order to have comparable indices? $\endgroup$– Remi.bNov 20, 2013 at 11:49