Known fate analysis for elk calf survival???

[sixtystrat]

We monitored radiocollared elk cows and caught and radiotagged calves shortly after birth. We estimated fecundity rates (whether a female gives birth or not) by monitoring radiocollared cows and estimated that as a simple binomial, and we probably counted some cows as never having had a calf when they in-fact gave birth but the calf died before we knew about it. We used known-fate analysis to estimate annual calf survival. The data will be used in a population projection model that incorporates fecundity and calf survival rates. My question is, does known fate analysis simply account for different numbers of animals at risk at any one time interval (i.e., different monthly survival rates during the year) or does it also adjust for calves that were presumably lost before they could be found (ala Mayfield)? If the latter is also the case, then the estimate of calf survival would count some events as calf mortalities whereas we counted those as cows that never gave birth, resulting in double counting that event. In other words, would mixing known-fate for calf survival and a binomial proportion for fecundity result in double counting some calves and result in a low biased recruitment rate? Should I be using a simple binomial for calf survival as well? My contention is that it is okay if both fecundity and calf survival are biased as long as their product (calf recruitment) is correct, as it would be if all cows are accounted for at the end of the year as either recruiting a calf or not. But if that bias is accounted for in one estimator and not the other, then the product would be wrong. I hope this makes sense. Thanks!!
Joe

[ganghis]

Hi Joe,

You need to be a little careful here. In essence what you have estimated is 1) the probability that an elk gives birth and the calf survives to the time of sampling, and 2) the probability of calf survival conditional on being sampled to start with. So you're right that that the probability of early calf survival is balled up into the fecundity.

Where you need to be careful is in setting up the population model. If you are on average only making contact with does a month after they have given birth, you'd only want to include 11 months of calf survival in the population model since the first month would be implicitly included in the fecundity estimate. You'd also want to be careful in examining sensitivities of projections to calf survival and fecundity rates because these are sort of tied together. Finally, there's bound to be some 'slop' in there because of the continuous nature of sampling and mortality processes (I'm guessing).

Chad Bishop and others have some recent stuff in JWM on estimating various components of fecundity/early survival in mule deer which might be worth taking a look at.

Hope this helps, Paul

[sixtystrat]

We were working with a small population and virtually all the cows were radiocollared. Would I be better off just using the binomial proportions of fecundity and survival in the population model?

[sixtystrat]

Oh now I get what you are saying. I need to use known fate for calves but be aware that it is not the "true" annual survival rate because some calves died before we could sample them.

[ganghis]

Yes, that's right. The only reason to use known fate here is to deal with right censoring... if you can always find a collar when you look for it, the binomial model should work just fine.

Apologies for confusing doe/fawn with cow/calf. Gary is undoubtedly shaking his head in disapproval.

Paul