# Scottish Marine and Freshwater Science Volume 6 Number 10: At-Sea Turnover of Breeding Seabirds - Final Report to Marine Scotland Science

The aim of this project was to review the potential issue of "turnover‟ of individual seabirds at sea during the breeding season and to assess how this may lead abundance estimates derived from boat or aerial surveys to underestimate the total number of b

### Appendix A Algorithm for Simulating Foraging Locations

**Without Site Fidelity**

In the absence of site fidelity the foraging locations on each
of the
*d* days are simulated by splitting the study area into a
fine resolution regular grid (0.5 x 0.5 degrees) that contains
*n* grid cells. The expected foraging density
*f
_{i}* within each grid square

*i*is estimated from GPS data, and for each bird

*j*the foraging locations

*g*on days

_{jk}*k*= 1,...,

*d*are then simulated independently from a multinomial distribution with size one and probabilities (

*f*

_{1,...,}

*f*), so that

_{n}
*g
_{jk}*~ Multinomial(1, (

*f*

_{1},...,

*f*))

_{n}This is exactly the same approach as that used in Searle
*et al.*, 2014.

**With Site Fidelity**

We now assume that fidelity operates at the spatial scale of a
grid which is coarser than the fine grid (and which is based on
aggregating cells of the fine grid, so that the fine grid is nested
within the coarse), and that the level of fidelity is given by a
parameter that lies between zero (fidelity is the same as that
obtained under independence) and one (perfect fidelity). For each
bird
*j* we modify the original independently-generated locations
*g
_{jk}* so that they have site fidelity, in the
following way:

(1) Find the coarse grid cells
*c
_{j}*

_{1,...,}

*c*that are associated with

_{jd}*g*

_{j}_{1},...,

*g*;

_{jd}(2) Find the number of these coarse grid cells that are unique -
let this be
*u*(
*j*);

(3) Calculate the number of coarse grid cells that would be visited if fidelity were equal to to be;

*v*(
*j*) = round{1 + (1 - ) (
*u*(
*j*) - 1)};

(4) Randomly select
*v*(
*j*) from the set of
*u*(
*j*) unique coarse grid cells;

(5) Re-assign each day to lie within one of this set of coarse grid cells. Each coarse grid cell is allocated at least one day; the remaining days are allocated by simulating from a multinomial distribution in which the probability of being allocated to coarse grid cell 'x' on a particular day is proportional to the frequency with which days were allocated to 'x' in the original simulations.

(6) Then use the bird density
*p
_{i}* to simulate the grid cell for each bird on each
day, conditional on the coarse grid cell that they are contained in
on that day.

One potential problem at step (5) is that the random selection
may lead to less than
*v*(
*j*) unique coarse grid cells. We, therefore, begin by
assigning each of the unique coarse grid cells randomly to one day
each, guaranteeing that this does not happen; the coarse grid cells
for the remaining
*d* -
*v*(
*j*) days are then allocated in proportion to their
frequencies in the original selections made by each bird (before
site fidelity is imposed).

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