Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Question 2: Drought experiments Find and open the 'drought' excel file. This data shows the results from a drought experiment for four different species. There

Question 2: Drought experiments

Find and open the 'drought' excel file. This data shows the results from a drought experiment for four different species. There were ten big pots for each species. In each case, about the same amount of seed was sown in each pot, but due to variability in germination, the number of plants in each pot was quite variable.

The number of plants in each pot was counted and then a six week drought was applied. After six weeks the pots were watered again. The number of plants that survived the drought was then counted in each of the pots.

The research question was whether there were differences between species in drought tolerance (ie survival).

First put the data into an appropriate format within Excel for entry into R (a separate row for each rep, or pot in this case), convert to .csv and read it in.

(Or convert within R if you prefer)

Next calculate the percentage survival for each pot in R.

Use a boxplot to plot the percentage survival by species - what does this show?

Use a standard linear ANOVA to test for differences between species. What do you find?

There are several major problems with using a standard linear ANOVA in this case. Binomial data, like survival data, is not likely to be normally distributed, especially if there are values close to 0% or 100%. Traditionally this was dealt with by arcsin transformation. You could do this to the data easily in R, then try the ANOVA again. However, we have another problem because there are different numbers of plants in each pot. We should therefore give the pots with more plants more weight in the analysis. This can be done using the 'lm' function and you can look up how to do it, but it is much easier to use the 'glm' function with binomial error distribution, which will handle all these issues automatically.

Use a binomial glm analysis to test whether there are differences between species. Don't forget to check whether there is evidence of overdispersion in the data, and account for it if needed.

If you find a significant effect of species overall, then how to do pair-wise comparisons is always a good question... there is not really any super easy approach with a binomial glm. One possibility in this case to test whether two similar species are significantly different is to do a glm on a subset of the data containing only these species. You can get the subset by using the R function 'subset'.

Another approach might be to relabel the two most similar species with one name (so they are then the same level for the species factor), then fit another model (give it another name), then test whether the two models are different. (This is like what we did in labs for the germination example). If they are not significantly different, then the relabelling is ok, which means the species are not significantly different. You can continue trying to group species in this way until you know that all ungrouped combinations are significantly different.

Test for differences between species using either of these two methods above.

Another issue in this case is the fact that plant density may have had an effect on survival, and that this effect could have depended on species as well. Fit another glm with pre-drought plant number as a covariate, and determine whether there is evidence for whether plant density may have had an effect on survival, and whether this effect could have depended on species. If you find evidence that plant density has had an effect on survival then you will need to test for differences between species again, while also accounting for this affect of plant density. In this case, plotting percentage survival against initial plant density with different colours/characters for different species will help a lot, especially if you then plot the model predictions for the different species as well.

Write down your conclusions about this experiment based on your full analysis.

show on R using library(tidyr)

table {mso-displayed-decimal-separator:"\."; mso-displayed-thousand-separator:"\,";} tr {mso-height-source:auto;} col {mso-width-source:auto;} td {padding-top:1px; padding-right:1px; padding-left:1px; mso-ignore:padding; color:windowtext; font-size:10.0pt; font-weight:400; font-style:normal; text-decoration:none; font-family:Arial; mso-generic-font-family:auto; mso-font-charset:0; text-align:general; vertical-align:bottom; border:none; white-space:nowrap; mso-rotate:0;}

species P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
1 before drought 54 49 53 49 52 50 46 53 51 58
1 after drought 7 9 9 8 10 8 10 14 4 10
2 before drought 63 65 56 54 54 60 59 61 53 58
2 after drought 44 41 35 32 40 35 34 45 32 36
3 before drought 72 70 69 69 60 72 73 72 73 66
3 after drought 63 53 52 60 51 53 52 62 61 61
4 before drought 77 77 73 86 78 75 84 76 81 82
4 after drought 15 17 9 16 13 9 20 15 16 17

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Essential Calculus Early Transcendental Functions

Authors: Ron Larson, Robert P. Hostetler, Bruce H. Edwards

1st Edition

618879188, 618879182, 978-0618879182

More Books

Students also viewed these Mathematics questions

Question

1. Which is the most abundant gas presented in the atmosphere?

Answered: 1 week ago