代写STATS 776 Estimating Animal Abundance Assignment 1, Semester 1, 2024代写数据结构语言程序

日期：2024-03-25 04:07

STATS 776 Estimating Animal Abundance

Assignment 1, Semester 1, 2024

Due: 10pm Thursday 28th  March

Notes:

?   This assignment is worth 33% of your final mark and requires a substantial amount of work. Do not leave it until the last few days.

?   Late     assignments     are      not     accepted     unless     an      extension     has     been      granted (https://canvas.auckland.ac.nz/courses/106002/pages/extensions).

?   It is your responsibility to back up your computer files. If you are using your own computer, it is your responsibility to ensure that you can access the data and run R and R Studio well ahead of the assignment due date.

Data are available from Fish & Game for a three-year mark-recapture study carried out over a weekend (Saturday and Sunday) in January 2022, 2023 and 2024 on mallard ducks on the Kaipara Harbour. The data are stored in kaipara.csv containing the capture history of each individual.

Question 1.   [40 Marks]

Treating each year as a closed capture-recapture population study only for the bands applied that weekend, answer the following questions.

1.   How many ducks were caught on Saturday and Sunday each year? What mark- recapture parameters are these? [5 marks]

2.   How many ducks were recaptured each year? What mark-recapture parameter is this? [5 marks]

3.   How many unique ducks were captured each year? What is the equation to derive this using capture-recapture parameters? [5 marks]

4.   For each year calculate the unbiased estimators N* and v*. [6 marks]

5.   Are any of these estimates likely to be biased? Why? [6 marks]

6.   For each year calculate the empirical coefficient of variation for the unbiased estimators. [3 marks]

7.   What do you conclude about the population size estimates of mallard ducks on the Kaipara Harbour? [5 marks]

8.   What recommendations in data collection do you make for future studies of mallard ducks on the Kaipara Harbour? [5 marks]

Question 2.   [20 Marks]

In 2023 many storms occurred in Auckland and this has been hypothesised to explain the results.

1.   If the  storms  caused a high mortality of the ducks in the traps on  Saturday, what assumption has been violated and how would this affect our population estimate? [4 marks]

2. If the storms caused a high mortality of the ducks on Saturday night, what assumption has been violated and how would this affect our population estimate? [4 marks]

3.   If the  storms caused ducks to fly away and leave the study area on Saturday night, what assumption has been violated and how would this affect our population estimate? [4 marks]

4.   If the storms stopped some ducks from being caught over the weekend, what

assumption has been violated and how would this affect our population estimate? [4 marks]

5.   If the storms changed the re-catchability of ducks on Sunday, what assumption has been violated and how would this affect our population estimate? [4 marks]

Question 3.   [20 Marks]

We are now interested in mallard duck annual  survival on the Kaipara Harbour. The R object kaipara.data contains the sex and age of ducks (note the closed capture sessions are now collapsed to one annual session).

1.   Tabulate the observed unique histories and calculate their frequencies. [4 marks]

2.   Using the R package openCR and the function openCR.fit()construct the Cormack-Jolly-Seber survival null model for ? and p and report the estimates. [3 marks]

3.   To investigate the effects of each of sex, age and time, construct the three respective Cormack-Jolly-Seber survival models (both ? and p depend on the covariate) and report the estimates.            [4 marks]

4.   Do any of the models have issues? What are these issues and what are possible explanations? [6 marks]

5.   Use AICc model selection to calculate which model has the most support. Summarise your model selection results with a table and in plain English. [3 marks]

Question 4.   [20 Marks]

We are interested in determining if there is a sex bias in the adult ducks captured over the course of the three-year study.

1.   What proportion of adult ducks that were captured were male? What number of ducks would be male if we assumed an equal sex-ratio as our null hypothesis? [2 marks]

2.   Present the code for a bootstrap randomisation test with 999 permutations to determine if the observed proportion of male ducks is different (or equal to) what would be expected under the null hypothesis (i.e. a two-tailed test). Calculate the p-value. [6 marks]

3.   Plot a histogram of your bootstrap randomisation null distribution indicating the true observed proportion of male ducks.      [2 marks]

4.   In general, why might we undertake randomisation tests on a dataset? [2 marks]

5.   Repeat the bootstrap randomisation 100 times and plot a histogram of the distribution of p-values, and report the minimum, maximum and mean of this distribution. [4 marks]

6.   Does increasing the number of permutations change the consistency of our test?

What does this tell you about the number of permutations in our randomisation test? [4 marks]