Swan
Distribution Simulator
This
simulator is being developed as a queuing model. There are four life cycle
events (seasons): breeding, post-breeding, wintering, and pre-breeding.
The number of birds is known during September, and this will be used as
the number entering the queue for post-breeding. Then, that number will
be distributed throughout the network of areas based on the probability
of a bird moving from one area to every other in the subsequent season.
The probabilities upon which this is built are found at: http://swan.msu.montana.edu/cygnet/doc_migration_kb_tables.html.
The number of birds in a queue (at an area during a particular time period)
is the number of birds in that queue at the end of that time period.
Although the percentages as gathered from the experts do not provide information
regarding the amount of movement among areas (queues) within a season,
it is assumed that birds will be found generally in the same proportions
at the end of the season as represented by the probabilities of movement
from one area/season combination to another.
-
=
Probability of movement from area
to
area
obtained
from the tables.These probabilities are weighted values calculated as follows:
-
=
raw percentage value in column 1, row 1
-
=
confidence value in column 1, row 1
-
those cells having the
value, "X", are converted to a percentage of 5 with a confidence of .75
-
Inputs:
1.
# birds entering the post-breeding queue at starting time, :
-
name of file to be used
as database
-
year of data to use
as starting point, with latest year being the default
-
value for any particular
area(s), overriding that number from the database
2.
value for any probability of movement from/to any pair of areas, overriding
the value(s) in the database
3.
# years (steps in the loop)
-
default value is 1 (year)
-
provide options for
5 and 10 (years)
-
Outputs:
1. # birds
at each area entering the post-breeding queue at time 
-
Queue = a particular
area during a particular season for a particular year;
,
where: 
=
area, 
=
season, 
=
year.E.g.:
-
=
number of swans in area 1 during the post-breeding season during year 1
-
=
number of swans in area 1 during the wintering season during year 1
-
Birds wait in each queue
for the next time step (season), then are distributed to the next set of
queues.
-
Each yearly loop,
,
consists of four steps, or seasonal distributions. The final condition
of
is
represented as a set of the numbers of birds in each of 26 queues.
-
The output from
is
the input for
-
The total number of
birds for year one, post-breeding season:
-
The number of birds
in a queue, in this case: area 1, winter, and year 1:
