MATH $401$ Week $5$ Homework Assignment $(10$ points$)$

In this week$$s homework assignment, you$$ll use the Rcapture R package to evaluate aspects of a mark$-$recapture dataset and estimate abundance for a population of a rare mouse species inhabiting a small island. Mice were captured in traps baited with seed over three consecutive nights per week for four weeks. Each time a mouse was captured for the first time, it was $$marked$$ by attaching a tag with a unique code to its ear, making individuals identifiable if recaptured. Use the R script file $$MATH $401$ Week $5$ example R script$$ as a guide for completing this assignment, which will require you to install and load the Rcapture package and import the $$hare$$ dataset that$$s included with this package. However, you$$ll use the $$MATH $401$ Week $5$ assignment dataset$.$csv file to answer the following questions. Please form your responses using complete sentences $(1$ point$).$

How many sampling occasions are there? $(1$ point$)$

How many individual mice were captured overall? $(1$ point$)$

How many mice were captured in the fourth sampling occasion? Hint: Use the $$ni$$ column in the frequency statistics table that you generate. $(1$ point$)$

How many individual mice were captured three times? Hint: Use the $$fi$$ column in the frequency statistics table that you generate. $(1$ point$)$

How many mice were captured on the first trap night? Hint: Use the $$ui$$ column in the frequency statistics table that you generate. $(1$ point$)$

Run a closed capture model on these data. Using the $$M$0($first listed$)$ model from the abundance estimations table you generate, what is the estimated abundance for this mouse population? $(2$ points$)$

Supporting your answer with at least one specific example from the abundance estimations table you generate, is there any evidence suggesting some models have poor fit? $(2$ points$)$

data set: c$1$ c$2$ c$3$ c$4$ c$5$ c$6$ c$7$ c$8$ c$9$ c$10$ c$11$ c$12$

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$010100100000$

$010000000000$

$010001001000$

$011000000000$

$010000011000$

$010000000000$

$010000000000$

$000100000000$

$000100000000$

$000010000000$

$000010000000$

$000010000000$

$000010000000$

$000000100000$

$000000100000$

$000000100000$

$000000100000$

$000000100000$

$000000100000$

$000000010000$

$000000010000$

$000000010000$

$100000010000$

$000000001000$

$000000000100$

$000000000100$

$000000000100$

$000000000100$

$000000000100$

$000000000001$

$000000000001$

$000000000100$

$000000000010$