FW Laboratory Exercise. Survival Estimation from Banded/Tagged Animals. Year No. i Tagged

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1 FW66 -- Laboatoy Execise uvival Estimation fom Banded/Tagged Animals Conside a geogaphically closed population of tout (Youngs and Robson 97). The adults ae tagged duing fall spawning, and subsequently epoted caught (i.e., killed) by angles. You ae to estimate the suvival ate of the adults. The population was maked on k = 0 occasions. The times between banding peiods ae of equal length, one yea apat. The obseved data follow. Recoveies R ij Yea No. i Tagged Analyze these data with Pogam MARK, available on the CNR micocompute netwok. The pogam allows inteactive input to build models. The numbe of e-encounte occasions is 0, and the data type is dead ecoveies. The banding totals and ecovey matix fo input to MARK ae in the file J:\CLAE\FW66\EXERCIE.0\YOUNG.INP. While you cannot know the undelying pocess, descibed by specifying the E(R ij ), you can conside an aay of altenatives. Fo a given N i, each fish conceptually expeiences binomial outcomes.

2 FW66 -- uvival Estimation fom Banded/Tagged Animals Page uvives N i - Dead R ij Repoted - Not Repoted Of couse, if an animal suvives, it continues in the population the following yea. This pocess leads to a seies of connected binomial outcomes: N N N N N N N N N N N N N N N Yea Yea Yea Yea Yea Individual paametes ae shown as,...,, and,...,. This doesn't ule out =... =, o =... =. Thus, potential models come to mind:

3 FW66 -- uvival Estimation fom Banded/Tagged Animals Page Model Paametes {(.) (.)} =... = and =... = {(t) (.)}... and =... = {(.) (t)} =... = and... {(t) (t)}... and... Now is a good time to eview the exact definition of, the suvival pobability, and, the pobability that the band fom a dead animal is epoted (i.e., etuned to the banding laboatoy). The paamete index matices fo model {(t) (t)} look like this: uvival Recoveies Fo model {(t) (t)}, the paametes k and k ae confounded fo k equal to the numbe of occasions. That is, the last and the last ae confounded, and only the poduct can be estimated. Thus, instead of k paametes, only k - ae actually estimated. In the above case 0 and 0 ae confounded, with only the poduct ( - 0 ) 0 estimatable. The paamete index matices fo model {(.) (.)} ae much simple:

4 FW66 -- uvival Estimation fom Banded/Tagged Animals Page uvival Recoveies Fo Youngs and Robson s data, constuct a figue that demonstates the elationship between the models, and includes the paamete space fo each model. Which model is selected by AICc? In you figue, include the likelihood atio tests, df, and P value between the models. Pogam MARK will constuct these tests once you have geneated estimates fo all models. If you have completed the above, constuct a model coesponding to Model 0 of Bownie et al. (98). Hint: Model 0 equies the epoting ate fo animals thei fist yea afte making to be diffeent fom the est of the epoting ates fo that yea. Bownie et al. (98) use a diffeent notation fo band ecovey models, whee f i ' ( & i ) i. Questions fo Discussion. Which model might epesent the best appoximating model fo use in making infeences fom these data? Why?. What othe models might have been easonable to conside pio to the analysis?. Conside the issues of unde- and ove-fitting in this example. Compae the estimates of pecision fo estimates unde model {(.) (.)} vesus model {(t) (t)}.

5 FW66 -- uvival Estimation fom Banded/Tagged Animals Page. Is thee evidence fom the data that suvival ates vay with time? What do you conclude given that the likelihood atio test between model {(.) (.)} and model {(t) (.)} is significant (P < 0.0)? Be specific.. Is thee evidence fom the data that fishing ates vay with time? What is the distinction between fishing ate and epoting pobability? What do you conclude given that the likelihood atio test between model {(.) (.)} and model {(.) (t)} is significant (P < 0.0)? 6. What is the coespondence between the models you constucted, and Models,, and of Bownie et al. 98? 7. What is the meaning of the goodness-of-fit test fo these models? Which models fit the data? Which do not? What is meant by the expession the model fits the data.? 8. Why model at all? Conside both the philosophy and pacticalities of this question. 9. What if two diffeent models have essentially the same AIC value? Liteatue Cited Bownie, C., D. R. Andeson, K. P. Bunham, and D.. Robson. 98. tatistical infeence fom band ecovey data - a handbook, nd ed. U.. Fish Wildl. ev. Res. Publ. Num., Washington, D.C. 0pp. Youngs, W. D., and D.. Robson. 97. Estimating suvival ate fom tag etuns: model tests and sample size detemination. J. Fish. Res. Boad Can. :6-7. Youngs and Robson (97) Book Tout Recovey Data -- Results Model AICc Delta AICc AICc Weights Num. Pa Deviance {(t) (.)} {(.) (t)} {(t) (t)} {(.) (.)}

6 FW66 -- uvival Estimation fom Banded/Tagged Animals Page 6 Likelihood Ratio Test Results Reduced Model Geneal Model Chi-sq. df Pob {(.) (.)} {(t) (.)}.09 9 <0.000 {(.) (.)} {(.) (t)} <0.000 {(.) (.)} {(t) (t)} <0.000 {(t) (.)} {(t) (t)} {(.) (t)} {(t) (t)}