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.

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