How is emigration reflected when gamma = 0 in RD?

[Becca]

Hi there,

I am writing a manuscript on a capture-recapture study of a population of Harlequin frogs. We sampled 10 nights a month for 10 months over the course of a year and a half. I am using the closed-capture robust design model. I curious about how gamma and survival affect each other, because some of my best models have gamma set to zero. I would expect that when we set gamma to zero, survival values should be reflecting any potential emigration as deaths, as in both cases these are individuals that are "leaving" the population. However, when we compare models where gamma is 0 to those that are not (and nothing else is different), there does not appear to be a 1 to 1 relationship between changes in gamma and changes in survival. It appears that gamma is influencing population size rather than being "subtracted" from survival. We are most interested in estimates of survival and population size, so I am concerned that if there is not a linear relationship between changes in survival and emigration our estimates of survival when gamma is 0 will be overestimated. Does setting gamma to 0 create unrealistic survival and population size estimates?

The frogs appear to have high site fidelity, so I do think it is reasonable to expect emigration to be close to zero for the majority of the study. However, towards the end of the study, the habitat degraded, so elevated emigration during those months is a possibility.

Any insight would be appreciated. Thanks!
Becca

[cooch]

Hi there,

I am writing a manuscript on a capture-recapture study of a population of Harlequin frogs. We sampled 10 nights a month for 10 months over the course of a year and a half. I am using the closed-capture robust design model. I curious about how gamma and survival affect each other, because some of my best models have gamma set to zero. I would expect that when we set gamma to zero, survival values should be reflecting any potential emigration as deaths, as in both cases these are individuals that are "leaving" the population. However, when we compare models where gamma is 0 to those that are not (and nothing else is different), there does not appear to be a 1 to 1 relationship between changes in gamma and changes in survival. It appears that gamma is influencing population size rather than being "subtracted" from survival. We are most interested in estimates of survival and population size, so I am concerned that if there is not a linear relationship between changes in survival and emigration our estimates of survival when gamma is 0 will be overestimated. Does setting gamma to 0 create unrealistic survival and population size estimates?

The frogs appear to have high site fidelity, so I do think it is reasonable to expect emigration to be close to zero for the majority of the study. However, towards the end of the study, the habitat degraded, so elevated emigration during those months is a possibility.

Any insight would be appreciated. Thanks!
Becca

Gamma (prime, double-prime) refer to probability of *temporary* emigration (in some form - see Chapter 15 for specifics). Only permanent emigration will influence survival. Further, when you say 'gamma is equal to/set to zero, you need to be more specific. Which gamma (prime or double-prime)? If you haven't done so already, I'd suggest a careful read of Chapter 15.

[Becca]

I set both gamma prime and double prime to zero, as in the null emigration model. In the other model, gamma prime is set equal to gamma double prime (the random emigration model). For the first part of the study, before the habitat degraded, estimates of S are similar between the two models. However, estimates of survival at the end of the study period are higher in the null than the random emigration model. I am curious why this is so, if only permanent emigration affects survival. If I understand correctly, calculating emigration probabilities depends also on the estimated recapture probabilities (p). Considering that my p values are higher in the random emigration model, could this be how setting gamma to 0 affects apparent survival?