Term of Award

Fall 2009

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Patricia Humphrey

Committee Member 1

Anna Oganyan

Committee Member 2

Charles Champ


Our primary question was the effect of departures from assumptions on population estimates obtained using three maximum likelihood population size estimators: M0 (all individuals have the same capture probability on all occasions), Mb (behavior is affected by prior capture) and Mt (all individuals have the same capture probability that varies by occasion). After examining the initial results and observing substantial negative bias (underestimates), we attempted to model the bias for M0 and Mb capture scenarios as these situations had consistent patterns. The Mt scenario with its erratic behaviors was not modeled. We noted that M0 and Mt performed equally well for the M0 and Mb captures. Mb did better as an estimator for the Mb capture scenario than for the M0 scenario. The Mt estimator for Mt captures did not perform well. Depending on actual capture probabilities, either of the other two estimators may give better, less biased results.

Research Data and Supplementary Material