seeking a consultation

[lepidoptera]

Hello,

I have conducted a mark-recapture study in a butterfly conservatory and would like to use MARK to estimate species lifespan. I have set up my encounter history and know that I need to run Burnham's model because I have both live captures and dead recoveries.
I have RTFM (really, I have) and still have too many questions before I confidently trust myself to use MARK. I have searched extensively and have been unable to find anyone at the University of Guelph, Ontario, Canada with experience with MARK. So - I am hoping that someone would be willing to consult with me (even if for a fee). I don't want to bore this forum with my many simple questions.
PLEASE contact me if you can help. I live in Toronto, Ontario. Could probably ask most questions over phone or e-mail. Could travel for consultation too, within reason.
Hope you can help,

Adrienne Brewster
MSc student
Department of Environmental Biology
University of Guelph
Guelph, ON, CANADA N1G 2W1
phone: (647) 438-7352
email: adriennebrewster@gmail.com

[cschwarz@stat.sfu.ca]

First have you read the papers on stop-over duration. The problem is similar - how long do birds "stop over" while migrating past a spot. In you case, the problem reduces to estimating length of stay. Similarly, this is also known as residence-time in the fisheries literature.

Some relevant papers are:

Schaub M., Pradel R., Jenni L. and Lebreton J.-. (2001) Migrating birds stop over longer than usually thought: an improved capture-recapture analysis. Ecology, 82, 852-859.

Manske M. and Schwarz C.J. (2000) Estimates of stream residence time and escapement based on capture-recapture data. Canadian Journal of Fisheries and Aquatic Sciences, 57, 241-246.

Lady J.M. and Skalski J.R. (1998) Estimators of stream residence time of Pacific salmon (Oncorhynchus spp.) based on release-recapture data. Canadian Journal of Fisheries and Aquatic Sciences, 55, 2580-2587.


Before getting too far into the analysis phase, you describe carefully how the data were collected, i.e. the study protocol so that the assumptions required and limitations of your data will be understood.

[cooch]

Hello,

I have conducted a mark-recapture study in a butterfly conservatory and would like to use MARK to estimate species lifespan.

I believe Carl's suggestions assume uncertainty about both time of entry, and exit, into the population - in such cases, the turnover statistic is a good measurement of 'realized lifetime' in the population.

If, on the other hand, you're looking for measure of life expectancy for individuals marked as offspring (such that there is certainty about the time/age) of entry into the population, then the standard 'pop bio 101' approach to estimate lifespan would be

1. take your age-specific estimates of survival - which you can derive using your favourite software application

2. calculate l(x) as the product of survival from age 0 -> age x, for all ages x -> oldest possible age class A (where l(0)=1, and l(A)=0).

3. estimate of life expectancy is then simply the area under the l(x) versus x curve. You can estimate the area numerically using a numerical intergation approach - the fastest, reasonably accurate method (given that l(x) is typically monotonic) is Simpson's rule or something analogous. Any intro calculus book will likely describe Simpson's rule (or similar approaches). This would give you an estimate of life-expectancy for a given cohort. You could modify if you want expectancy for some other partition.

Estimating the SE for life expectancy is non-trivial - but can be done.

[B.K. Sandercock]

MarkList:

The duration of a flight period for a butterfly or life expectancy (E-hat) can also be estimated from transition rates as follows (Page 208 of Brownie et al. 1985. Statistical inference from band recovery data - a handbook, USFWS, Res. Publ. 156, Washington DC):
E-hat = -1/ln(theta-hat)
where ln is the natural log and theta-hat is a transition rate over some time period. E.g., if daily apparent survival is 0.95, then the estimated flight period would be 19.5 days.

This formula only works if there is no time-dependence in the minimum AICc model, and if you have an overall estimate. If time-dependence is pronounced, then the bootstrapping procedures of Program Soda are a better option. The formula above would estimate for life expectancy for the period that individuals are observed and would not account for uncertainty regarding entry or exit. I have been unable to locate this formula in the Williams et al. text, so there may be other caveats.

I have tried to estimate flight period for regal fritillaries. Two issues that came up in the analyses were that the regals were not active on cold, wet days, which precluded sampling on a regular schedule. Mark allows you to specify unequal intervals between sampling occasions when you import the encounter histories, which proved to be a valuable feature for modeling this species. The second problem was that few individuals were recaptured (males: ~10%, females ~5%) and the probability of encounter from CJS models was dismal (p<0.03). This affected the model selection and confidence intervals of the parameter estimates. No problems with time-dependence if your model collapses to phi(.), p(.)

Good luck, Brett.

[cooch]

MarkList:

The duration of a flight period for a butterfly or life expectancy (E-hat) can also be estimated from transition rates as follows (Page 208 of Brownie et al. 1985. Statistical inference from band recovery data - a handbook, USFWS, Res. Publ. 156, Washington DC):
E-hat = -1/ln(theta-hat)
where ln is the natural log and theta-hat is a transition rate over some time period. E.g., if daily apparent survival is 0.95, then the estimated flight period would be 19.5 days.

This formula only works if there is no time-dependence in the minimum AICc model, and if you have an overall estimate.

Thats the key - Brett is correct that if survival is a constant, you can use this approximation (actually, if S is truly constant, its exact). But, there is no system I've ever seen for which this is true - if you mark individuals as 'babies', then even the most minimal model is typically 2 age classes, no time-dependence in either.

Either way, the formal approach would be integrate the probability function (which is what the l(x) function is, essentially), but Brett's suggestion of using LSODA where entry times are known with certainty would likely suffice for a numerical approach. And, it probably has the advantage of yielding the SE directly (if I recall LSODA correctly).

[lepidoptera]

Thanks for the many replies

To clarify my protocol - I marked all individuals right after they emerged from their chrysalides as adults - therefore entry is known - it is always day 1 of their adult life (and I am looking to estimate ADULT lifespan only). Although, not all were marked on the same day. I sampled about every 2-3 days for about 30-35 encounters in total (thank goodness you can specify interval spacing in MARK)

One more thing - I marked 75 different species, so I want to make sure I do the data analysis correctly the first time before I carry mistakes over 75 times.

I will work through the suggestions made, thanks.

Adrienne Brewster