updates to MARK & MARK book...
Posted: Wed Jul 23, 2025 11:14 amGreetings --
Wanted to announce several things related to program MARK in current form -- several new an important 'tweaks and updates', especially as relates to 'unequal intervals':
1\ The transition parameters of the robust design, Barker, and Barker robust design models are now corrected for time interval length. Although the robust design model can be equivalent to the multi-state model, correction for unequal time intervals is handled differently. Robust design models assume survival is the same regardless of whether the animal is available or not available for capture. Thus, an animal can move between these 2 states and survival is not affected. This assumption of identical survival is required to get parameter identifiability in the model. In contrast, the multi-state models only allow movement at the end of the time interval because survival is usually different between the 2 states, and thus movement during the interval would require a model with a weighted product of survival rates depending on timing of when movement occurred. Therefore the psi parameters of the multi-state models do not need correction for the length of the time interval because they are in theory instantaneous, whereas the gamma'' and gamma' parameters of the robust design models should be corrected for the length of the time interval because you would expect move movement occurring during longer intervals.
In the robust design models, survival (S) is corrected for time interval length (L) as S^L. The gamma' parameter is corrected as gamma'^L and the gamma'' parameter is corrected as 1 - (1 - gamma'')^L. The reason for this difference is that gamma' is the probability of remaining unavailable for capture, and so is the probability of remaining off site. This scenario is like survival, where S is corrected as S^L. In contrast, gamma'' is the probability of becoming unavailable, so that 1 - gamma'' is the probability of remaining on site. Thus 1 - gamma'' is the quantity needing correcting.
In the Barker model, survival (S) is corrected for time interval length (L) as S^L. The R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L, which puts each of these parameters on a 1-unit time scale. The F parameter is corrected as F^L and the F' parameter is corrected as 1 - (1 - F')^L. The r parameter does not need a time correction because it only applies when the animal dies, which can only happen once no matter how long the time interval. Likewise, the p parameter does not need a time interval correction.
In the Barker robust design model, survival (S) is corrected for time interval length (L) as S^L. The R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L, which puts each of these parameters on a 1-unit time scale. The F parameter is also corrected as F^L. The a'' parameter is corrected as a''^L and the a' parameter is corrected as 1 - (1 - a')^L. The r parameter does not need a time correction because it only applies when the animal dies, which can only happen once no matter how long the time interval.
All of this is covered in expanded detail in the relevant chapters in the MARK book.
2\ A new model, Hidden Markov Multi-state Jolly-Seber, data type 185, has been added. This model is a combination of the Hidden Markov model and the Multi-state Jolly-Seber model. It is not documented in the book at the moment.
3\ speaking of the book, to honour the 'silver anniversary' of the thing (currently in its 25th revision), the book has been updated in several areas (unequal intervals, Delta method, etc, etc). Individual chapters posted on the website are most current. For those of you who like things in a single volume (well, two volumes actually -- at >1,200 pages, the book is well beyond single-volume-length), the printed and bound versions of the book have also been updated (links on the MARK website).
Wanted to announce several things related to program MARK in current form -- several new an important 'tweaks and updates', especially as relates to 'unequal intervals':
1\ The transition parameters of the robust design, Barker, and Barker robust design models are now corrected for time interval length. Although the robust design model can be equivalent to the multi-state model, correction for unequal time intervals is handled differently. Robust design models assume survival is the same regardless of whether the animal is available or not available for capture. Thus, an animal can move between these 2 states and survival is not affected. This assumption of identical survival is required to get parameter identifiability in the model. In contrast, the multi-state models only allow movement at the end of the time interval because survival is usually different between the 2 states, and thus movement during the interval would require a model with a weighted product of survival rates depending on timing of when movement occurred. Therefore the psi parameters of the multi-state models do not need correction for the length of the time interval because they are in theory instantaneous, whereas the gamma'' and gamma' parameters of the robust design models should be corrected for the length of the time interval because you would expect move movement occurring during longer intervals.
In the robust design models, survival (S) is corrected for time interval length (L) as S^L. The gamma' parameter is corrected as gamma'^L and the gamma'' parameter is corrected as 1 - (1 - gamma'')^L. The reason for this difference is that gamma' is the probability of remaining unavailable for capture, and so is the probability of remaining off site. This scenario is like survival, where S is corrected as S^L. In contrast, gamma'' is the probability of becoming unavailable, so that 1 - gamma'' is the probability of remaining on site. Thus 1 - gamma'' is the quantity needing correcting.
In the Barker model, survival (S) is corrected for time interval length (L) as S^L. The R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L, which puts each of these parameters on a 1-unit time scale. The F parameter is corrected as F^L and the F' parameter is corrected as 1 - (1 - F')^L. The r parameter does not need a time correction because it only applies when the animal dies, which can only happen once no matter how long the time interval. Likewise, the p parameter does not need a time interval correction.
In the Barker robust design model, survival (S) is corrected for time interval length (L) as S^L. The R and R' parameters are corrected as 1 - (1 - R)^L and 1 - (1 - R')^L, which puts each of these parameters on a 1-unit time scale. The F parameter is also corrected as F^L. The a'' parameter is corrected as a''^L and the a' parameter is corrected as 1 - (1 - a')^L. The r parameter does not need a time correction because it only applies when the animal dies, which can only happen once no matter how long the time interval.
All of this is covered in expanded detail in the relevant chapters in the MARK book.
2\ A new model, Hidden Markov Multi-state Jolly-Seber, data type 185, has been added. This model is a combination of the Hidden Markov model and the Multi-state Jolly-Seber model. It is not documented in the book at the moment.
3\ speaking of the book, to honour the 'silver anniversary' of the thing (currently in its 25th revision), the book has been updated in several areas (unequal intervals, Delta method, etc, etc). Individual chapters posted on the website are most current. For those of you who like things in a single volume (well, two volumes actually -- at >1,200 pages, the book is well beyond single-volume-length), the printed and bound versions of the book have also been updated (links on the MARK website).