1. Question 1: Rainforest species survey
   A team of researchers surveys the plant species at a number of sites within a rainforest. They also collect soil data and elevation data for these sites, as well as recording whether each site was in a valley, on a slope, or on a ridge. Their research question was whether soil characteristics, elevation and/or landscape position could predict the vegetation communities at different sites.
   How many sites were there?

1 points  

QUESTION 2

1. How many species were recorded?

1 points  

QUESTION 3

1. What distance function is most appropriate to calculate a distance matrix between the sites based on the log-transformed species count data?

1 points  

QUESTION 4

1. Now investigate whether there is a difference between sites in different landscape positions, in terms of their vegetation composition. Construct and plot a nmMDS of the sites. What is the stress for the MDS (to two decimal places)?

1 points  

QUESTION 5

1. Does this mean that the MDS is a reasonable representation of the differences between sites? YES/NO

1 points  

QUESTION 6

1. Which site out of sites 1,2 and 3 seems most different to all the other sites in terms of vegetation composition? 1/2/3

1 points  

QUESTION 7

1. Make the sites colour represent their position within the landscape (valley, slope or ridge) – is there a visual indication that the sites group by landscape position?

1 points  

QUESTION 8

1. Does an ANOSIM show that this grouping is significant?

1 points  

QUESTION 9

1. Does a PERMANOVA show that this grouping is significant?

1 points  

QUESTION 10

1. Now turn your attention to the environmental (soil and elevation) data, including measures of soil Ph, site elevation, and levels of soil P, Ca, Mg, K and N (in ppm) and percentage soil organic matter. Is there evidence of correlations in this data?

1 points  

QUESTION 11

1. Perform a principal components analysis on this environmental data. First do this without scaling the variables. Plot the resulting PCA biplot. Which variable(s) is/are dominating the results?

1 points  

QUESTION 12

1. Why?

1 points  

QUESTION 13

1. Now perform the principal components analysis on the environmental data with scaling, and plot the resulting PCA biplot. Which would be better if we want to give similar importance to all the environmental variables in our analysis?

1 points  

QUESTION 14

1. Consider the results of the PCA that gives similar importance to all the environmental variables. How much variance do the first two PCs explain (as a percent out of 100)?

____________________

1 points  

QUESTION 15

1. Does this mean that the 2-D biplot is a reasonable representation of the variation in the environmental data across the sites?

1 points  

QUESTION 16

1. Variation in which of the environmental variables is least well represented in the 2-D biplot?

1 points  

QUESTION 17

1. According to the biplot, which site looks like it has the highest levels of P? (enter just the number of the site)

________

1 points  

QUESTION 18

1. Which variables appear to be strongly positively correlated with Ca?

1 points  

QUESTION 19

1. Which variables appear to be strongly negatively correlated with elevation?

1 points  

QUESTION 20

1. Which variable seems to be positively correlated with soil N but negatively correlated with soil Ca?

1 points  

QUESTION 21

1. Which variables appear to vary independently of elevation?

1 points  

QUESTION 22

1. How does soil N seem to be related to soil Ca?

1 points  

QUESTION 23

1. PC1 is most strongly related to which variable?

K/soil organic mater/Ph/Mg/elevation/P/N/Ca

1. PC2 is most strongly related to which variable?

K/soil organic mater/Ph/Mg/elevation/P/N/Ca

1. PC3 is most strongly related to which variable?

K/soil organic mater/Ph/Mg/elevation/P/N/Ca/

3 points  

QUESTION 24

1. Is there a relationship between elevation and Shannon diversity index?

1 points  

QUESTION 25

1. Is there a relationship between PC1 and Shannon diversity index?

1 points  

QUESTION 26

1. Is there a relationship between PC2 and Shannon diversity index?

1 points  

QUESTION 27

1. Is there a relationship between PC3 and Shannon diversity index?

1 points  

QUESTION 28

1. Does the adonis function indicate a significant relationship between differences in soil P and differences in vegetation composition?

1 points  

QUESTION 29

1. Does the adonis function indicate a significant relationship between differences in soil K and differences in vegetation composition?

1 points  

QUESTION 30

1. Does the adonis function indicate a significant relationship between differences in soil N and differences in vegetation composition?

1 points  

QUESTION 31

1. Does the adonis function indicate a significant relationship between differences in soil Ca and differences in vegetation composition?

1 points  

QUESTION 32

1. Does the adonis function indicate a significant relationship between differences in elevation and differences in vegetation composition?

1 points  

QUESTION 33

Which PCs and interactions have a significant effect on composition?
pc1                   yesno
pc2                   yesno
pc3                               yesno
pc1:pc2            yesno
pc1:pc3            yesno
pc2:pc3            yesno
pc1:pc2:pc3      yesno

7 points  

QUESTION 34

1. Does this match the results of the previous tests?

1 points  

QUESTION 35

Which of the following conclusions would you draw from this analysis above, accounting for the correlations in environmental variables that you observed?

• Elevation appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil N YES/NO
• Elevation appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil P YES/NO
• Elevation appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil Ph YES/NO
• K appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil N YES/NO
• K appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil P YES/NO
• K appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil Ph YES/NO
• P appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil N YES/NO
• P appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil elevation YES/NO
• P appears to have an effect on species composition, but this may actually be an indirect effect due to differences in soil Ph YES/NO

9 points  

QUESTION 36

1. The most common species is species number:
   ___________________

1 points  

QUESTION 37

This species prefers (relatively high/intermediate/relatively low) elevation sites with (relatively high/intermediate/relatively low) levels of P and (relatively high/intermediate/relatively) low Ph levels.

3 points  

QUESTION 38

1. The second most common species is species number:

___________________

1 points  

QUESTION 39

This species prefers (relatively high/intermediate/relatively) low elevation sites with (relatively high/intermediate/relatively low) levels of P and (relatively high/intermediate/relatively low) Ph levels.

3 points  

QUESTION 40

1. More guinea pigs
   My friend was so excited about the potential of testing his baby guinea pigs to predict their head hair length, number of rosettes and chance of show success, that he did the whole thing again the following year, but with a greater number of babies.
   The resulting data is in the file ‘guineapigs assignment.csv’. Open it up in Excel and have a look. Then get the data into R.
   Has he measured the same variables as last time?

1 points  

QUESTION 41

1. How many guinea pigs did he include in his study this time?
   ________________

1 points  

QUESTION 42

1. Fit a multiple regression model predicting adult head fur length with all the ‘baby’ variables as predictors, but no interactions (call this model fm for ‘full model’).
   How many variables show as significant (p<0.05) in the model summary?
   __________________

1 points  

QUESTION 43

1. How many variables show as very highly significant (p<0.001) in the model summary?

__________________

1 points  

QUESTION 44

1. Look at the correlation between the predictors visually and/or numerically. Do we see similar correlation patterns in the predictors to those we saw last time?

1 points  

QUESTION 45

1. Carefully do step-wise model selection based on dropping the least significant term until only significant terms are left (sm1 for ‘simplified model 1’). Are you left with the same significant variables as in the full model?

1 points  

QUESTION 46

1. Now do automated step-wise model reduction of the full model based on AIC (sm2). Are you left with any terms in simplified model 2 that were not retained in simplified model 1?

1 points  

QUESTION 47

1. Now try to fit a multiple regression model predicting adult head fur length with all the ‘baby’ variables as predictors, and also all second order interactions (fim for ‘full interactions model’). Why can we do that this time, while it didn’t work in the labs?

1 points  

QUESTION 48

1. Do automated step-wise model reduction of this model based on AIC (fims for ‘full interactions model, simplified’). Are you left with any terms in the simplified interactions model that were not retained in simplified model 2?

1 points  

QUESTION 49

1. Now fit a null model (fmn). Then use the step function to do automated ‘both directions’ model selection based on AIC, allowing all baby variables and up to second order interactions between them (call it fmbda1 with ‘bda’ for ‘both directions AIC’). Look at the summary of this model.
   Now try doing the same thing – automated ‘both directions’ model selection based on AIC, allowing all baby variables and up to second order interactions between them, but this time starting with sm1 instead of the null model (call it fmbda2). Look at the summary of this model.
   Now try automated ‘both directions’ model selection based on BIC, still allowing all baby variables and up to second order interactions between them – try starting first with the null model then with sm1 – call the resulting models fmbdb1 and fmbdb2. Look at the summary of these models.
   Look at the AIC of the seven models that we have fitted based on some kind of model/variable selection (ignore full models where no selection was applied – they must be worse).
   Look at the BIC of these seven models.
   Some of these models are actually the same model ie the different procedures have found the same ‘best model’. If we remove these duplicates, how many distinct different simplified models do we have left to consider?
   ____________________

1 points  

QUESTION 50

Which one has the best AIC? ____________________

And which the best BIC? ______________________

(Make sure you write the model abbreviation exactly for these – if more than one model had equal best AIC or BIC, either abbreviation will do.)
One of the models is clearly not a good model to consider, as it has the worst BIC and is also really complicated. Which one? ______________________

This model resulted from the automated selection procedure ‘getting stuck’ and not simplifying enough. Never trust an automated model simplification procedure!! :) So we can leave that one out.

3 points  

QUESTION 51

Look closely at the remaining models. We can conclude that the (more/less) hormone3 a baby has, the longer its head hair length is likely to be when adult.

1 points  

QUESTION 52

1. In addition, the more of what hormone number would result in the the baby most likely having shorter head hair length as an adult?

_____________

1 points  

QUESTION 53

1. The other variable that seems to be a strong predictor is: (Write all variable names exactly as they appear in the spreadsheets).
   _________________

1 points  

QUESTION 54

1. This strong predictor variable has a (positive/negative) relationship with adult head fur length.

1 points  

QUESTION 55

1. There is some indication that the effect of hormone 3 might depend on:  (Write all variable names exactly as they appear in the spreadsheets).
   _____________

1 points  

QUESTION 56

Higher levels of this variable (reduced/increased) the effect of hormone 3.

1 points  

QUESTION 57

1. Of these significant predictors, the one most likely to be confounded with other predictors is: (Write all variable names exactly as they appear in the spreadsheets).
   ____________

1 points  

QUESTION 58

1. Do the results agree exactly with the first analysis conducted in the lab?

1 points  

QUESTION 59

1. Which variable seemed maybe important then but not here? (Write all variable names exactly as they appear in the spreadsheets).
   ______________________

1 points  

QUESTION 60

1. Which variable seems important here but not then? (Write all variable names exactly as they appear in the spreadsheets).
   _____________________________

1 points  

QUESTION 61

1. Now, rosettes!
   Create a new TRUE/FALSE variable regarding whether the adult pig had 8 rosettes, like we did in the lab.
   Try to find the best model predicting whether an adult guinea pig will have rosettes, based on BIC. Include up to second order interactions in the possible model terms considered. Try a few different starting points to make sure you haven’t got stuck somewhere far from the best model (To make it a bit simpler, don’t worry about AIC this time.)
   What would you conclude from this best model?
   There seem to be two variables useful in predicting whether an adult pig will have 8 rosettes: one is hormone number:
   ____________________________

1 points  

QUESTION 62

1. and the other is a ‘fur variable’ i.e.:

1 points  

QUESTION 63

1. There (is/is not) a significant interaction between these two variables.

1 points  

QUESTION 64

1. This indicates that the effect of one (does/does not) depend on the level of the other.

1 points  

QUESTION 65

1. When the fur variable is relatively low, the hormone has a (strong positive/strong negative/medium positive/medium negative/weak positive/weak negative) effect on the chance that a pig will have 8 rosettes, while when the fur variable is relatively high, the hormone has a (strong positive/strong negative/medium positive/medium negative/weak positive/weak negative) effect the chance that a pig will have 8 rosettes.

2 points  

QUESTION 66

1. There is a 90%+ chance that a pig will have 8 rosettes. This is when the fur variable is at the lowest level it was measured at, and the significant hormone level is higher than about:

1 points  

QUESTION 67

1. When the fur variable is at the highest level it was measured at, the chance that a pig will have 8 rosettes (increases/decreases) as the significant hormone level increases.

1 points  

QUESTION 68

1. When the hormone is at very low levels the percentage chance is about:

______________

1 points  

QUESTION 69

1. When the hormone is at very high levels the percentage chance is about:
   _______________

1 points  

QUESTION 70

1. Now, my friend has five new guinea pig babies. Is it going to be a pampered life of indulgences to prepare for the show, or…. The BBQ?!?
   He has measured all the predictors on them. The data is in the file ‘guineapigs asignment year3.csv’.
   Based on the model that had the lowest BIC, predict the adult head fur length of each of these five babies? Write down the five predictions (note these lengths are cm! long haired guinea pigs! but just enter the numbers). Remember the ‘predict’ function!
   Predictions are:
   Guinea pig baby 1:

_______________

1 points  

QUESTION 71

1. Guinea pig baby 2:

____________________

1 points  

QUESTION 72

1. Guinea pig baby 3:

______________________

1 points  

QUESTION 73

1. Guinea pig baby 4:

______________________

1 points  

QUESTION 74

1. Guinea pig baby 5:

_________________________

1 points  

QUESTION 75

1. Based on the model that had the lowest BIC, what is the probability of having exactly eight rosettes for each of these five babies? Rank the babies from highest to lowest chance. The baby with the highest chance is number: (1,2,3,4,5) and the baby with the lowest chance is number: (1,2,3,4,5).

2 points  

QUESTION 76

1. Which baby is safest from the BBQ? Guinea pig baby number: (1,2,3,4,5)

1 points  

QUESTION 77

1. Which two are most likely to feel the heat? Guinea pig baby number: (1,2,3,4,5) and guinea pig baby number: (1,2,3,4,5).
2.  (Make sure you enter these in numerical order, so if it was 1 and 5, then enter 1 then 5, NOT 5 then 1).