Feasibility of extending SeabORD to the entire breeding season: study

Appendix B: Interpretation of "baseline mean survival"

SeabORD currently estimates the intercept in the mass-survival model by using the "baseline mean survival rate", s₀, whose value is based (e.g. Table 3-3 of Searle et al., 2015, for the Forth-Tay SPAs) upon expert judgement or published literature.

In general, however, the mean baseline survival rate generated by SeabORD, using an intercept whose values has been estimated using s₀, will not be exactly equal to s₀. That is because s₀ actually corresponds to the survival rate associated with any bird having mean baseline mass, rather than to mean survival rate across birds with a distribution of masses calculated under baseline conditions. To illustrate this, assume that the baseline mean survival for the population of interest is 95% - within the current implementation of the mass-survival relationship within SeabORD this would be the survival rate for a bird whose mass is equal to the baseline mean mass. Across the entire colony, however, there would actually be more birds with 91% survival probability than with 99%, because of the properties of the logit function, so the average survival probability across the colony would be a bit less than 95%. It follows that, in order for the mean survival rate simulated by SeabORD to actually equal 95%, it would be necessary for the value used for s₀ to be a little bit higher than 95%.

To see this in more mathematical terms, we can re-arrange Equation 1 to obtain:

(Equation 3)

Combining Equations 1 and 3 then implies that:

(Equation 4)

If all m_ij = 0 it follows immediately from Equation 4 that p_j = s_0j; otherwise, however, p_j will not in general be equal to s_0j. It follows that the "baseline mean survival" value s_0j (e.g. as specified in Table 3-3 of Searle et al., 2015) is the survival corresponding to mean (baseline) mass, not the mean baseline survival.