Nest Survival
Nest Survival
The nest survival data type is a slightly different model than the Known Fate data type included in MARK. The input data in the encounter histories file is specified with the Nest Survival Group=1 statement. Following this command are the data on the nests for this group. For each nest record, 5 values must be given. First is the day the nest(s) was/were found, labelled time i. Next is the last day the nest(s) was/were known to be present, labelled time j, which for successful nests should be the day the nest hatched. Then comes the last day that a nest(s) was checked or should have hatched, labelled time k, which for successful nests should be the day the nest hatched. However, for successful nests, all the information about survival is contained in times i and j. Time k is only used for unsuccessful nests to bracket the interval when the nest was destroyed. The fourth variable is the fate of the nest(s): 0 means successful, and 1 means destroyed or unsuccessful. The last (fifth) value is the number (frequency) of nests that had this history.Individual covariates are allowed after these 5 required variables. The following is an example input file for nest success data with 2 groups and 63 occasions, where one individual covariate (age of nest at time the nest was found) is included:
Nest survival group=1;
/*GGOO, 1995-076*/ 53 59 63 1 1 4;
/*OGDD, 1995-047*/ 18 36 36 0 1 11;
/*WGDD, 1995-003*/ 1 20 20 0 1 15;
/*OGDD, 1995-027*/ 14 26 26 0 1 17;
/*OGDY, 1995-032*/ 14 24 24 0 1 19;
/*OGYW, 1995-051*/ 23 30 30 0 1 22;
/*WGYY, 1995-054*/ 25 31 31 0 1 23;
/*WGOO, 1995-068*/ 39 40 40 0 1 28;
/*WGOB, 1995-069*/ 39 40 40 0 1 28;
/*YGDY, 1995-049*/ 22 23 23 0 1 29;
Nest survival group=2;
/*WGYB, 1995-014*/ 11 37 37 0 1 3;
/*GGDD, 1995-018*/ 12 38 38 0 1 3;
/*OGOO, 1995-055*/ 26 49 49 0 1 4;
/*YGDB, 1995-007*/ 10 34 34 0 1 5;
/*WGYG, 1995-044*/ 17 37 37 0 1 9;
/*OGDG, 1995-004*/ 6 25 25 0 1 10;
/*WGYD, 1995-045*/ 17 34 34 0 1 12;
/*WGOG, 1995-062*/ 30 30 36 1 1 12;
/*WGDB, 1995-020*/ 13 25 25 0 1 17;
/*YGBB, 1995-074*/ 44 55 55 0 1 18;
/*WGGW, 1995-078*/ 58 58 61 1 1 18;
/*YGDD, 1995-038*/ 16 26 26 0 1 19;
/*YGWY, 1995-072*/ 43 46 46 0 1 26;
The first nest for group 1 was found on day i = 53, checked and found still present on day j = 59, and found destroyed on day k = 63. The last variable (an individual covariate) in this example is the age of the nest at the time it was first found — 4 days old for the first nest. The second nest for group 1 was found on day i = 18, and found to successfully hatched on day j = 36. The age of this nest was 11 days when it was found on day 18.
The number of occasions for the nest survival model is the total number of days that nests are checked, with the first nest checked on day 1. Thus, if the last day a nest is checked is 70, then the number of occasions would be 70.
For successful nests, i.e., fate=0, the last time seen alive (j) and the last time (k) should always be the same and equal to the day the nest hatched. For unsuccessful nests, fate>0, j < k. In MARK, the cell probability is modeled as the product of the survival rates from time i to time j-1. For successful nests, time k is ignored. For situations where the date of hatch is not known exactly, none of the times should exceed the potential hatch date, because the nest should not be considered at risk of failure when it has already hatched. For unsuccessful nests, the cell probability for the nest is taken as the product of the survival rates from time i to time j-1, times 1 minus the product of survival from j to k-1.
The following series of examples for 5 occasions will clarify how to code nest survival data with the triplet i, j, and k.
i = 1 j = 3 k = 5 fate = 1 gives 1010100001, with cell probability S(1)S(2)[1 – S(3)S(4)].
i = 1 j = 3 k = 3 fate = 0 gives 1010100000, with cell probability S(1)S(2).
i = 1 j = 3 k = 3 fate = 1 is invalid because the nest was observed both present and destroyed on day 3.
i = 1 j = 1 k = 3 fate = 1 is gives 1000010000, with cell probability 1 – S(1)S(2).
i = 1 j = 1 k = 3 fate = 0 is invalid because the nest was observed present only on day i = 1. If the nest was still present on day 3, then j should have been coded as j = 3.
i = 1 j = 3 k = 5 fate = 0 is partially invalid because the nest was observed for the interval 1 to 5, when the nest was successful, but the coding shown will only use the data from 1 to 3, giving 1000100000, with cell probability S(1)S(2). For fate = 0, j = k.
i = 3 j = 3 k = 3 fate = 0 or 1 is invalid because the nest was not observed over an interval for either fate.
The key difference between Known Fate and Nest Survival data types is that with nest survival data, we don’t know exactly what day the nest was destroyed for cases where the nest was unsuccessful. Thus, consider the cell probability for the first nest described above. The cell probability would look like:
S(53) S(54) S(55) S(56) S(57) S(58) [1 – S(59) S(60) S(61) S(62)] .
The first portion of the expression models the survival of the nest from day i = 53 to day j = 59. The second portion of the expression, in brackets, models the failure of the nest during the interval from day j = 59 to day k = 63. That is, had the nest been successful during this interval, the probability would have been S(59) S(60) S(61) S(62). Because the nest was destroyed at some time during that interval, this quantity is substracted from 1. The encounter history for this example would consist of 52 pairs of ’00’, followed by the following string with blanks inserted to delimit occasions denoted on the second line:
10 00 00 00 00 00 10 00 00 01
53 54 55 56 57 58 59 60 61 62
Effective Sample Size
The effective sample size for AICc is computed somewhat differently for the nest survival model than other models in MARK. Typically, each binomial trial in a model provides one degree of freedom. For the nest survival model, each day that the nest is known to survive contributes 1 degree of freedom because each day is a binomial trial where the result is known. However, the interval in which a nest fails only contributes 1 degree of freedom also, because the exact day of failure is not known, but only that the nest failed during the interval. Thus, a record like
/*YGBB, 1995-074*/ 44 55 55 0 1 18;
contributes 10 degrees of freedom, because there are 10 binomial trials where the nest was known to succeed. However, the following record only contributes a single degree of freedom, because the nest failed somewhere in the interval 58-61.
/*WGGW, 1995-078*/ 58 58 61 1 1 18;