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.

1) The data for this study is in the 'rainforest.xlsx' file. Convert it to csv and read it into R. You'll need the vegan library, so install it if needed, then import it, and have a look at it.

2) How many sites?

3) How many species?

4) We want to consider the differences between sites in terms of species composition, so extract the species count data from the data you've read in. Since some of the species are much more abundant than others, and we don't want to totally lose the rarer species in the analysis, log transform the count data before proceeding further (add one to all the counts to avoid zeros and then take the log).

5) Then calculate a distance matrix between the sites based on the log-transformed species count data. Use either Euclidean or Bray-Curtis distance, whichever is most appropriate for this kind of data.

6) 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, using the distance matrix. What is the stress for the MDS? Does this mean that the MDS is a reasonable representation of the differences between sites? Which site out of sites 1,2 and 3 seems most different to all the other sites in terms of vegetation composition? Make the sites colour represent their position within the landscape (valley, slope or ridge) and see if there is visual indication that the sites group by landscape position. Then use an ANOSIM to formally test whether this grouping is significant. Then use the adonis function (PERMANOVA) as an alternative formal test.

7) 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. Extract this data from the main data frame. Plot all these variables against each other to look for evidence of correlations (and calculate correlations directly).

8) Perform a principal components analysis on this environmental data. First do this without scaling the variables. Plot the resulting PCA biplot. Which variables are dominating the results? Why? 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?

9) Consider the results of the PCA that gives similar importance to all the environmental variables. How much variance do the first two PCs explain? Does this mean that the 2-D biplot is a reasonable representation of the variation in the environmental data across the sites? Variation in which of the environmental variables is least well represented in the 2-D biplot? According to the biplot, which site looks like it has the highest levels of P? Which variables appear to be strongly positively correlated with Ca? Which variables appear to be strongly negatively correlated with elevation? Which variables appear to vary independently of elevation? Which variable seems to be positively correlated with soil N but negatively correlated with soil Ca? How does soil N seem to be related to soil Ca? PC1 is most strongly related to which variable? PC2 is most strongly related to which variable? PC3 is most strongly related to which variable?

10) Now let's consider a univariate measure of diversity across the sites, and see if this is related to the environmental variables. Calculate the Shannon diversity index for all the sites. Plot this against elevation. Does it look like there is a relationship between elevation and diversity? Test the relationship with a linear model. Extract the first three PCs from the results of the PCA. In turn, pot each of these against the diversity. In each case, look to see whether it look like there is a relationship between the PC and diversity, and then test the relationship with a linear model.

11) Now let's look at the relationship between environmental variables and the overall differences in vegetation composition. First consider soil P. Use the same MDS we constructed before, but plot the sites with the size of the points representing the level of soil P. Scale the size of the points to get a good contrast in sizes. Does it look like there is a pattern? Test the pattern with the adonis function. Is there a significant relationship between differences in soil P and differences in vegetation composition?

12) Now do similar MDS plots and adonis tests for each of the following: soil K, soil N, soil Ca and elevation. In each case, is there a significant relationship between differences in the environmental variable and differences in vegetation composition?

13) Rather than doing all the soil variables separately, we can use the results of the PCA analysis instead. Do similar MDS plots for each of the first three PCs. Does it look like there is a significant relationship between differences in the PC and differences in vegetation composition? Does this match the results of the previous tests? Now use the adonis function with PC1, PC2 and PC3 as three explanatory variables, including all interactions between them. (Note fitting a model with several explanatory variables would not be valid for the original variables, since they are highly correlated, but is perfect for the PCs, since they are defined to be independent). Which PCs and interactions have a significant effect on composition? Does this match the results of the previous tests?

14) What are the overall conclusions you would draw from this analysis above, accounting for the correlations in environmental variables that you observed?

15) Finally let's look more closely at the species that are driving these differences. Which are the two most common species (the species with the highest total counts)? What elevations do these two species prefer? What P levels do they prefer? And what Ph do they prefer? You could use GAMs or polynomial models to look at these questions in a statistically rigorous way, but you can also just use appropriate plots. These might include plotting abundance for the species against the relevant variable, or plotting one variable against another, with the circle size representing the abundance.

show and explain in R

Site	Ph	elevation	P	Ca	Mg	K	N	soil.organic.matter	sp1	sp2	sp3	sp4	sp5	sp6	sp7	sp8	sp9	sp10	sp11	sp12	sp13	sp14	sp15	sp16	sp17	sp18	sp19	sp20	sp21	sp22	sp23	sp24	sp25	sp26	sp27	sp28	sp29	sp30	sp31	sp32	sp33	sp34	sp35	sp36	sp37	sp38	sp39	sp40	sp41	sp42	sp43	sp44	sp45	sp46	sp47	sp48	sp49	sp50	sp51	sp52	sp53	sp54	sp55	sp56	sp57	sp58	sp59	sp60	sp61	sp62	sp63	sp64	sp65	sp66	sp67	sp68	sp69	sp70	sp71	sp72	sp73	sp74	sp75	sp76	sp77	sp78	sp79	sp80	sp81	sp82	sp83	sp84	sp85	sp86	sp87	sp88	sp89	sp90	sp91	sp92	sp93	sp94	sp95	sp96	sp97	sp98	sp99	sp100	sp101	sp102	sp103	sp104	sp105	sp106	sp107	sp108	sp109	sp110	sp111	sp112	sp113	sp114	location
1	4.9	305	24.8	1328	101	133	50	4.044611	1	7	0	0	0	2	1	2	4	17	0	6	0	0	0	2	0	0	0	1	94	0	16	2	119	38	0	2	0	0	1	9	0	0	0	10	4	0	8	0	0	0	4	1	0	1	1	0	12	0	78	16	0	2	0	0	0	0	0	3	1	2	12	0	2	2	0	5	0	0	0	0	1	0	0	0	42	0	0	1	0	3	1	2	0	1	4	2	0	0	20	3	0	23	4	1	0	0	6	3	0	1	0	0	0	0	3	4	0	17	5	0	4	0	slope
2	4.7	433	22.6	1309	106	194	46	3.708241	0	0	0	0	0	0	0	0	0	9	0	2	0	0	1	0	0	0	0	0	4	0	8	0	1	0	0	0	0	0	0	4	0	0	0	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	5	2	1	0	0	0	0	1	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	1	1	0	0	0	1	0	0	0	0	0	1	4	2	5	2	0	1	0	0	0	0	2	0	0	0	0	0	0	3	0	0	1	0	2	0	ridge
3	4	483	23.3	1200	90	154	45	3.575042	0	0	0	0	0	0	1	0	1	5	0	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	3	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	ridge
4	6.1	454	13	1463	117	176	45	3.517811	0	2	0	0	0	4	0	0	2	3	2	23	0	0	4	1	0	0	2	0	0	1	0	0	0	2	0	1	3	0	0	0	4	0	1	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	3	5	0	0	0	0	11	8	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	10	1	4	2	0	0	1	0	4	14	0	0	5	2	1	2	0	3	0	0	0	0	0	0	0	0	0	0	3	1	0	0	5	0	6	0	ridge
5	6.3	244	20	1496	122	126	49	4.059763	9	1	1	0	0	6	0	0	31	5	0	44	1	0	2	1	0	0	0	2	15	2	7	8	5	74	3	3	37	1	0	0	0	0	3	282	30	7	32	5	0	4	22	12	0	0	0	12	13	0	5	14	0	2	25	1	1	6	0	29	2	6	68	0	1	32	11	0	0	0	0	0	0	0	0	1	1	0	0	0	16	9	13	3	18	7	42	103	0	0	65	1	0	10	1	2	3	0	24	2	1	11	3	0	0	0	19	1	0	9	8	0	7	5	valley
6	4.2	461	20.8	1268	94	132	49	3.809331	0	0	0	0	0	0	0	0	0	9	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	3	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	ridge
7	4.1	398	20.5	1264	84	142	49	3.96484	0	1	0	0	0	0	1	0	0	36	0	1	0	0	1	0	2	0	0	0	3	0	2	0	0	1	0	0	0	0	0	12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	1	1	5	0	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0	2	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	3	1	0	1	4	0	0	1	2	0	0	0	0	0	0	1	0	1	0	0	1	0	0	0	slope
8	6.5	297	18	1458	130	128	50	4.022525	15	3	0	0	0	2	0	0	58	5	0	17	1	0	3	3	0	0	3	11	2	2	4	1	3	41	2	0	42	0	0	0	3	0	2	60	8	15	7	9	0	18	32	14	0	0	0	0	4	0	2	14	0	0	32	0	0	0	5	32	0	5	144	1	0	59	0	0	0	0	0	0	0	1	0	0	0	3	1	0	5	14	5	0	5	18	140	44	0	0	18	0	0	1	1	10	0	0	31	0	0	22	1	0	0	0	15	1	0	12	3	0	5	1	valley
9	4.4	484	20.7	1339	99	151	46	3.637626	0	0	0	0	0	1	0	0	0	5	0	2	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0	1	0	2	1	0	0	0	0	0	1	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	2	0	0	0	2	0	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	ridge
10	4.7	219	27.2	1242	96	170	53	4.381196	0	2	1	0	0	1	21	0	1	17	0	17	0	0	0	7	0	0	0	0	292	0	20	5	40	21	0	0	1	0	0	9	0	1	0	72	38	1	65	0	0	0	5	1	0	0	1	1	92	12	39	5	1	2	0	1	0	0	0	1	0	0	4	1	0	2	18	25	15	0	16	0	0	0	0	0	24	0	0	1	2	2	0	18	3	0	1	3	0	0	37	0	0	27	28	0	0	0	5	25	2	2	1	0	0	0	2	2	0	10	3	0	2	2	valley
11	5.5	272	21.6	1384	116	136	50	3.875909	6	12	0	0	0	5	2	0	2	4	0	28	0	1	8	20	0	0	1	1	28	0	29	36	37	139	0	2	2	0	1	0	0	0	1	76	7	1	15	1	0	1	10	5	0	3	0	11	19	1	21	18	0	5	1	2	0	2	2	8	1	1	19	0	0	5	29	5	0	0	4	0	0	0	0	0	10	0	0	2	5	7	1	2	2	2	6	6	0	0	115	1	1	92	5	1	0	0	18	0	20	5	4	0	0	0	5	1	0	100	28	0	10	8	valley
12	5.9	279	22.2	1426	119	113	52	4.252464	8	13	0	0	1	15	0	0	11	8	0	66	0	0	3	10	0	0	1	1	9	0	15	5	17	164	2	5	9	1	1	0	0	0	4	97	12	3	11	6	0	4	32	6	0	1	0	5	4	0	6	24	2	0	4	0	0	1	0	12	1	3	57	0	0	28	10	1	0	0	0	0	0	0	0	0	2	1	4	0	7	32	5	2	5	8	14	29	1	0	88	8	0	19	1	2	0	0	14	1	6	7	5	0	0	1	22	0	0	34	28	0	13	7	valley
13	7.5	320	19.8	1728	142	160	51	4.092801	3	1	0	0	0	0	0	0	3	4	0	3	0	0	3	1	0	1	7	13	1	1	2	0	0	5	0	0	2	0	2	1	0	1	0	7	1	0	2	1	0	3	3	16	0	0	0	0	2	0	2	3	1	0	1	0	0	1	0	6	0	2	7	0	3	4	0	0	0	0	0	0	4	0	0	0	1	11	0	0	0	2	3	0	2	14	8	5	8	0	3	1	0	1	0	2	20	0	50	0	0	20	0	0	0	7	4	0	0	4	0	3	1	0	slope
14	6.1	347	20	1560	127	171	48	3.903581	3	14	0	0	2	9	0	0	10	3	0	33	0	0	16	8	0	0	3	5	0	0	7	0	0	25	1	3	8	0	0	3	2	0	9	13	2	12	1	6	0	14	29	3	0	2	0	0	2	0	4	68	2	0	9	0	0	15	1	28	2	36	5	0	3	10	1	0	0	0	0	0	4	0	0	0	1	0	7	0	7	23	2	0	0	1	18	51	0	0	24	6	0	7	1	4	3	0	8	0	2	2	9	0	0	0	85	0	1	5	7	0	22	0	slope
15	6.3	440	18.9	1584	123	174	47	3.600511	0	2	0	0	0	6	0	0	13	0	2	18	0	0	1	5	0	0	1	0	0	0	1	0	0	0	0	0	2	1	0	0	1	0	0	3	0	6	0	1	0	0	1	0	0	0	0	0	0	0	0	1	0	1	8	0	0	0	0	21	4	2	2	0	1	1	0	0	0	0	0	0	0	0	0	0	0	1	5	0	2	2	0	0	0	2	10	24	0	0	3	0	0	2	0	11	3	0	0	0	4	0	0	0	0	3	1	1	0	1	2	0	0	0	ridge
16	4.3	463	20.6	1276	88	174	48	3.920291	0	0	0	0	0	0	0	0	0	5	0	3	0	0	0	0	0	0	0	0	2	0	2	0	0	0	0	0	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0	1	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	ridge
17	6.2	201	20.2	1561	128	185	55	4.573508	5	3	3	0	0	2	2	0	28	7	0	61	0	0	9	13	0	0	1	3	24	0	11	14	3	38	2	6	27	1	2	2	0	1	1	217	192	4	106	4	0	7	12	10	0	3	0	17	30	0	3	18	0	1	19	1	0	6	0	23	2	6	30	0	2	16	60	1	0	0	1	1	0	1	0	0	0	0	4	1	26	15	8	2	29	7	42	90	1	0	102	3	0	19	1	4	1	0	29	0	4	4	2	0	0	2	20	0	0	20	7	0	3	4	valley
18	6.9	401	15.8	1565	135	179	48	3.855405	1	3	0	1	0	0	0	0	14	0	2	2	0	0	1	1	0	0	10	9	0	4	0	0	0	2	0	1	2	0	2	0	1	2	1	4	1	0	0	2	0	2	2	2	0	0	0	0	0	0	0	2	0	0	6	0	0	0	0	25	3	0	3	0	6	0	0	0	0	0	0	0	1	1	0	0	0	3	0	1	0	1	0	0	1	7	23	8	3	0	4	1	0	1	0	42	9	0	4	0	2	0	1	0	0	9	0	0	0	0	1	0	0	0	ridge
19	5.5	309	22.9	1409	116	103	54	4.437547	1	36	0	0	0	11	0	0	3	13	0	31	0	0	7	15	0	0	0	1	18	0	16	11	33	85	0	3	5	0	0	3	0	0	2	28	4	0	5	2	0	1	22	2	1	6	0	0	8	0	22	36	2	0	2	0	0	0	0	9	1	5	14	0	2	18	5	1	0	0	0	0	0	0	0	0	12	0	3	2	5	7	0	4	1	1	6	8	0	0	77	4	0	73	1	2	1	0	5	0	25	6	5	0	0	0	12	1	0	80	31	0	4	2	slope
20	5.7	429	17.4	1409	119	172	48	3.870581	0	9	0	0	0	11	0	0	1	6	0	28	0	0	4	7	0	2	1	0	0	0	5	0	0	7	0	0	1	1	1	0	0	0	2	2	0	0	2	0	0	0	2	1	0	1	0	0	0	0	0	0	2	1	0	0	1	1	0	12	10	1	0	0	0	0	2	0	0	0	0	0	0	0	0	0	1	0	3	1	3	0	0	0	0	0	3	5	0	0	11	2	0	11	0	4	0	0	2	0	7	0	2	0	0	3	2	0	0	3	13	0	10	0	ridge
21	6.4	457	15.4	1542	128	130	45	3.393849	0	0	0	0	0	0	0	0	15	2	5	10	0	0	0	0	0	0	0	0	0	4	1	0	0	2	0	0	3	1	0	0	1	0	0	1	0	0	0	1	0	0	0	0	0	1	0	0	0	0	0	2	0	0	7	0	0	0	0	15	5	1	0	0	0	1	0	1	0	1	0	0	0	2	0	0	0	1	5	0	3	0	0	0	0	0	10	18	0	0	2	0	0	1	0	6	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	ridge
22	6.3	351	23.3	1554	130	133	54	4.483217	3	6	0	0	0	6	0	1	46	4	1	19	0	0	10	1	0	0	0	9	2	3	3	0	2	21	2	0	18	0	0	1	1	0	9	14	2	25	0	16	0	12	26	1	0	1	0	0	0	0	0	49	0	0	22	0	0	11	1	38	1	21	8	1	4	17	0	0	0	1	0	0	1	0	0	1	2	1	2	1	2	10	0	0	1	1	46	68	1	0	17	4	0	5	0	6	0	0	7	0	2	1	10	0	0	4	29	0	0	3	3	0	7	0	slope
23	4.7	400	19.7	1291	104	162	50	4.002141	0	2	0	0	0	2	0	0	0	15	0	3	0	0	2	1	0	0	1	0	8	0	5	0	3	2	0	1	0	0	0	25	0	0	0	1	0	0	1	1	0	0	0	0	0	0	1	0	1	0	7	2	1	2	1	0	2	0	0	1	0	0	2	1	0	0	0	1	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	5	0	0	2	0	3	4	1	1	1	0	1	0	3	0	1	0	0	0	0	6	0	1	2	0	3	0	slope
24	5.3	472	17.8	1433	110	211	47	3.619773	0	2	0	1	0	1	0	0	0	3	0	7	0	0	1	1	0	0	0	0	0	0	4	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	10	10	0	0	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	3	2	1	2	9	0	0	2	0	0	0	9	0	0	0	0	0	0	0	0	3	8	0	0	0	ridge
25	6.4	389	18.4	1548	118	203	50	4.023358	1	7	0	0	0	3	0	0	31	4	1	13	0	0	13	1	0	0	5	8	0	6	5	0	0	6	0	2	9	1	0	1	2	0	2	6	1	10	1	8	0	5	3	0	0	0	0	0	0	0	0	9	1	1	20	0	0	3	0	65	0	11	5	0	2	4	0	0	0	1	0	0	0	0	0	0	0	1	5	1	1	3	0	0	2	2	37	56	0	0	9	4	0	0	0	17	4	0	1	0	3	1	9	0	0	4	12	0	0	1	4	0	9	0	slope
26	4.9	242	21.7	1358	111	150	56	4.55892	1	2	0	0	0	2	5	0	0	21	1	22	0	0	1	8	0	0	1	2	263	0	15	10	121	32	1	0	1	1	1	7	0	0	0	90	12	0	21	0	0	0	1	1	0	2	0	5	51	6	28	6	1	5	1	6	0	1	1	1	0	0	4	0	0	5	13	11	1	0	10	0	0	0	0	0	57	0	0	1	0	0	0	10	3	0	2	3	0	1	43	1	0	31	14	0	0	0	8	16	5	1	1	0	3	1	1	6	0	39	13	1	2	1	valley
27	4.8	235	22	1323	107	170	54	4.468916	0	3	2	0	0	2	11	0	0	16	0	12	0	0	0	6	0	0	0	0	307	0	10	14	75	36	0	3	1	0	0	5	1	0	0	74	27	1	36	0	0	1	5	1	0	0	0	7	68	4	37	6	0	2	0	1	0	0	0	1	0	0	6	0	0	1	17	14	7	0	4	0	0	0	0	0	42	0	0	2	1	1	4	7	3	0	3	4	0	0	38	0	3	32	20	0	0	0	1	21	3	1	1	2	1	0	0	6	0	29	5	0	1	0	valley
28	5.6	253	23.2	1431	110	177	51	4.162059	1	24	0	0	0	12	1	0	8	5	0	56	0	0	1	30	0	0	1	1	38	0	21	42	23	135	0	3	4	0	0	1	0	1	0	167	30	0	28	2	0	2	15	2	0	10	0	29	15	1	9	20	0	4	0	1	0	0	1	4	0	2	29	0	0	7	68	7	0	0	0	0	0	0	0	0	7	0	2	2	5	9	5	4	2	2	6	17	0	0	158	3	0	71	4	1	0	0	15	2	14	1	3	0	1	1	5	1	0	87	34	0	9	11	valley
29	5.4	229	21.8	1385	112	152	54	4.504727	4	12	3	0	1	4	7	0	2	13	0	35	0	1	3	22	0	0	1	1	84	1	27	58	29	87	1	0	1	0	1	1	0	0	1	156	35	0	43	0	0	1	4	3	0	2	0	26	51	3	16	12	2	7	1	2	0	0	1	5	0	0	7	0	0	1	71	1	0	0	6	0	0	1	1	0	14	0	2	3	6	4	3	3	4	1	4	9	0	0	147	2	0	144	6	0	0	0	9	2	28	4	3	0	0	0	1	3	0	81	22	0	4	6	valley
30	7.5	470	14.8	1813	142	170	48	3.760023	0	0	0	0	0	0	0	0	0	1	0	5	0	0	0	0	0	0	2	2	1	1	0	0	0	0	0	0	1	0	5	0	1	10	0	0	1	0	0	0	2	0	0	1	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	5	0	0	0	7	4	0	0	0	0	0	1	0	1	0	0	0	1	0	0	1	0	1	10	0	0	0	0	1	0	0	0	6	0	0	0	0	0	0	0	0	ridge