Jolly (1965) and Seber (1965) submitted idea separately.
Marked population (Mi) is unknown because some may have died or emigrated. The basic problem is to estimate the unknown parameter Mi .
Use information obtained later in a study to improve estimates obtained early in the study.
This works for open populations to estimate number still alive in the marked population.
Si = a discrete sample (i) is taken at point Si in time.
Ø(phi)i = death + emigration rate = probability that an individual alive at time Si is still there at Si + 1.
Bi = birth + immigration rate = number of individuals in the population at Si + 1 that were not there at Si.
Ni = size of the population at Si.
Mi = subpopulation marked by the experimenter previous to S (generally the Mis are subject to Øis).
Pi = probability of any individual in Ni occurring in the sample at Si.
ni = number in the sample at Si (all ni returned).
mi = number of the marked subpopulation in sample at Si.
zi = number of marked individuals that were not in sample at Si (=Mi - mi) that were recaptured in samples after Si.
ri = number of ni recaptured after Si.
Capture history for groundsquirrels:
Time (i) | # Captured (ni) | # Recaptured (mi) | # Released w/marks (Ri) |
1 | 54 | 0 | 54 |
2 | 146 | 10 | 143 |
3 | 169 | 37 | 164 |
4 | 209 | 56 | 202 |
5 | 220 | 53 | 214 |
6 | 209 | 77 | 207 |
Matrix summary of individual captures:
Time of Last Capture | Time of Capture | |||||
#1 | #2 | #3 | #4 | #5 | #6 | |
#1 | . | 10 | 3 | 5 | 2 | 2 |
#2 | . | . | 34 | 18 | 8 | 4 |
#3 | . | . | . | 33 | 13 | 8 |
#4 | . | . | . | . | 30 | 20 |
#5 | . | . | . | . | . | 43 |
Z3 = [5 + 2 + 2] + [18 + 8 + 4] = 39
r3 = 33 + 13 + 8
so:
^M3 = [(Zi * Ri) / ri ] + mi = [(39 * 164) /54] + 37 = 155.4
and
^N3 = (n3 * ^M3) / m3 = (169 * 155.4) / 37 = 709.8
Z4 = [2 + 2] + [8 + 4] + [13 + 8] = 37
r4 = 30 + 20 = 50
^M4 = [(38 * 202) /50] + 56 = 205.5
^N4 = (209 * 205.5) / 56 = 767
^Ø3 = M4 / (M3 + n3 - m3) = 205.5 / (155.4 + 169 - 37) = 0.72
^B3 = ^N4 - ( ^N4 * ^Ø3) = 767 - (709.8 * 0.72) = 250.5
Population is geographically closed.
Every animal present in the population (marked and unmarked) has the same probability of capture (pi) in the ith sample.
Every marked animal present in the population immediately after the ith sample has the same probability of survival (Øi) until the (i + 1)th sampling time.
Marks are not lost or overlooked.
All samples are instantaneous (i.e., demographic closure is satisfied during each sampling occasion) and each release is made immediately after the sample.
Updated 31 July 1996