Estimation of Vital Rates: Use of Index Statistics? Relevance of Detection Probability

Count Statistics and Survival: Why Bother with p? Index approach to survival rate estimation: –Mark and release animals at time i, and then ask what fraction of these are caught 1 year later This kind of “estimator” will always be biased low

Count Statistics and Survival R i = number of marked animals released at time i m i+1 = number of R i caught at time i+1 m i+1 /R i = “return rate” φ i = survival probability, i to i+1 p i = detection/capture probability

Count Statistics and Movement: Why Bother with p? Index approach to movement estimation –Mark and release animals at location 1 at time i –Recapture or re-observe animals at time i+1 at locations 1 and 2 –“Estimate” movement rate as: Ratio of recaptures in location 2 to total recaptures in locations 1 + 2

M i+1 rs = number of marked animals released at location r in period i that are alive at location s in period i+1 (unknown when p ≠ 1) m i+1 rs = number of marked animals released at location r in period i and recaptured at location s in period i+1 ψ i rs = probability that an animal alive in location r at time i, and alive at time i+1, has moved to location s Count Statistics and Movement

If all marked animals caught (p=1): If marked animals are not all detected: # of animals that moved Total # of animals still alive at i+1 But this estimator is biased when

Count Statistics & Reproductive Rates: Why Bother with p? Index approach to age ratio estimation: Use ratio of raw counts of young to adults This “estimator” will be biased in the presence of any age-specific variation in p

Count Statistics & Reproductive Rates N i (0) = number of young at sample period i N i (1) = number of adults at sample period i n i (0) = number of young caught at i n i (1) = number of adults caught at i p i (0) = capture probability for young at i p i (1) = capture probability for adults at i

True age ratio, quantity of interest: Index “estimator” Biased whenever Count Statistics & Reproductive Rates

Estimation of Vital Rates: Use of Index Statistics? Conclusion: Don’t do that! Detection probability is relevant to estimation of abundance and change in abundance, but also vital rates (survival, reproduction, movement)