# Standardized Selection Ratio (SSR)

In this article the athors used the Standardized Selection Ratio (SSR) in order to infer what is the preferred host (anemone) of anemonefish.

Here is a quotation coming from their methods:

  The “preferred host” of anemonefish was assessed calculating the “Standardized
Selection Ratio (SSR)” (values between 0 and 1) (Manly et al. 1993). Manly’s standardized
selection ratio represents the probability that an individual will use a particular habitat
type, taking into account the different resource availability. For each anemonefish species (i) inhabiting an anemone species (j), SSR was calculated as:


$$SSR = \frac{wi}{\sum{}{wj}}$$

where $wi = \frac{oi}{pj}$

    Oi is the relative frequency of the anemonefish species i and pj the relative frequency
of the anemone species j. Higher values of SSR indicate a strong preference for the
selected resource. The Log- Likelihood statistic (χ2L) (Manly et al. 1993) was used to
check the significance of the observed distribution under a null hypothesis of a random
host choice.


Here is the book they cite (Manly et al. 1993).

Can you help me understanding basically what they did and how they calculated their SSR and p.values. If $wi = \frac{oi}{pj}$ what does wj equals to?

I can see why you might be confused! The authors chose bad notation, since the way they wrote it $w_i$ clearly depends not just on the choice of anenomefish species $i$ but also on the choice of anenome species $j$. And it is not clear how exactly they are performing their sum in the definition of SSR: sum over all possible anenome-anenomefish species pairs or only over all anenomefish species? The former makes sense but is extremely unclear, and the latter doesn't make sense because there's no way to interpret that as a probability that an anenomefish will choose a particular anenome because the sum of the SSR for all the different anenome species would not necessarily be 1, so the probability of an anenomefish species choosing some species of anenome would not be 1!