Phenotypic Variance: Scientific Hypothesis- Statistical Inference in R- R Studio Assignment

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MAS7373
R Studio Assignment:

Task:

Read carefully! By far the most common way for students to lose marks is from not having read the question carefully, and so (for instance) testing a different scientific hypothesis than the one they were asked to
test.

You have now reported a sufficient number of statistical analyses that we are not going to tell you exactly what to report, with two exceptions: First, when a question tells you that you may assume an assumption is satisfied, you don’t need to check the assumption (so don't!). Second, follow the set up for answer from the Model Answer in the lab manual.

You may need to transform the data, or conduct a randomization test. You will not need to rearrange the data files. If you get an error message indicating that R can’t run the analysis you want to run, one possible explanation is that you’re trying to run the wrong analysis! (Although it is not true that the only analysis you can run is the analysis you should run. On many of the datasets, it is possible to run analyses other than the one you should run without R giving you an error message.)

The only R commands and statistical tests you need to use are the ones you learned in earlier labs this term. Like the other lab assigments, this assignment is to be completed individually.

1. [18 points] Closely-related species often share many attributes because of their shared evolutionary history. This makes it difficult to study the association between different attributes across species, because different but related species can’t be considered independent observations due to their shared evolutionary history.

One way to avoid this non-independence problem is to use what are known as phylogenetically independent contrasts. In this approach, you compare a species that possesses some attribute of interest to a closely related species that lacks that attribute. Any differences between them must have evolved since they last shared a common ancestor. Repeating the same comparison for many different pairs of species, each of which has their own last common ancestor, give you many independent observations with which to test whether the attribute of interest is
associated with any other attributes.

For instance, “dataset 1.txt” contains data on 16 pairs of small-bodied lizard species. Each row contains data for one of the 16 pairs. The two members of each pair are closely related (they’re two different species from the same genus), and each of the 16 pairs is from a different genus.

One member of each pair is common, the other is rare, as indicated by the column headings. You are interested in whether common species tend to be smaller than rare species, because they require less food per individual, thereby allowing more individuals to be supported on the same amount of food. To address this question, you’ve compiled data on the mean adult body mass (in g) of each species; those are the numbers in the data file. Check the assumptions of the test you choose, formally and graphically.

2. [34 points] The following question is based on a modified version of the work of Adler et al. 2011. These researchers were interested in the effect of primary productivity on plant species richness in grasslands. Two scientific hypotheses regarding the effect of primary productivity on plant species richness are as follows:

3.  Plant species richness will increase with increasing productivity because more productive plots are those located in places that support better plant growth (fertile soil, long growing season, etc.). More productive plots, measured as plant biomass, should be able to support more plants, and all else being equal the more plants you have the more species you should have (richness).

4.  Plant species richness will decrease with increasing productivity because when plant biomass is high competition for light and soil nutrients is intense and only the most competitive species can persist, the others being competitively excluded. ?To test these hypotheses Adler et al. sampled primary productivity (indexed by total aboveground plant biomass, g per m2) and plant species richness in 51 grassland sites from around the world.
Within each site, they measured primary productivity and plant species richness in each of 30 plots, each 1 m2 in area.

2a. The data are in “dataset 2.txt”. The column "biomass" gives total aboveground plant biomass in each plot, and the column “richness” gives the plant species richness of each plot. Analyze these data to
determine whether grassland plant species richness increases or decreases with productivity. Check the assumptions of the test you intend to use, formally and graphically.

2b. Why might you be concerned about non-independence of observations in your analysis for question 2? Briefly (1-2 sentences) describe a way in which your analysis could be modified to address the non-independence issue.

3. [16 points] Phenotypic variance measures the variability of a trait among the individuals comprising a biological population. Phenotypic variance can differ among populations of the same species, due to natural selection and other evolutionary forces. For instance, all else being equal, larger populations are expected to harbor more genetic variation, and thus more phenotypic variation, because rare genetic variants are less likely to be lost to genetic drift.

You decide to address this question by studying trichomes, which are small hairs on leaves. You identify four populations of wild Potentilla diversifolia plants, varying in population size. From each population, you randomly sample 10 plants, and count the number of leaf hairs in a 1cm2 area of one leaf.

Data from the forty plants from four populations are in file “dataset3.txt”. Each row gives data for one plant. The first column (population) indicates which population the data are from; populations are ordered from largest (pop1) to smallest (pop4). The second column (hairs) is the number of trichomes per square cm of leaf. Analyze these data to
determine if phenotypic variance varies among these four populations.

You may assume that trichome counts in each population were sampled from approximately-normal distributions.

4. [28 points] Spatial synchrony refers to spatially-separated populations of the same species exhibiting positively-correlated fluctuations in abundance (i.e. when any given population increases in abundance, others tend to do so as well, and similarly for declines in abundance).

Spatial synchrony is a common phenomenon in nature; even populations hundreds or thousands of km apart can exhibit synchronous fluctuations in abundance. One possible cause of spatial synchrony is dispersal: movement of individual organisms from one population to another partially mixes those populations and so tends to synchronize them. In the limit, if organisms move from one population to another quite often and quite quickly, the different populations effectively become a single big population.

One way to study the effects of dispersal on spatial synchrony is to compare synchrony among otherwise similar species that differ in their dispersal rates, for instance because they occupy different sorts of habitats. Imagine that you conduct such a study. From a long-term monitoring program, you have data on the average synchrony of 30
butterfly species. Ten of these species comprise populations located in large unfragmented grasslands, so there is no barrier preventing butterflies from moving among populations. You therefore assume that dispersal rates among populations are high. Ten different butterfly species occupy fragmented landscapes: populations live in small patches
of grassland, surrounded by forest through which it is thought butterflies move only very rarely, so that dispersal rates are low. The remaining ten butterfly species also occupy patches of grassland surrounded by forest, but these patches are connected by dispersal corridors—narrow strips of grassland through which butterflies are thought to move freely. Species occupying landscapes with corridors are thought to exhibit intermediate dispersal rates.

The datafile “dataset 4.txt” contains your data. The column “habitat.type” identifies the type of habitat occupied by each of your 30 species. The column "synchrony" gives the mean correlation in abundance between the populations comprising each species. As with any correlation coefficient, these mean correlations range from -1 to 1,
with values <0 indicating negative correlations on average, 0 indicating no correlation (i.e. populations fluctuate independently of one another), and 1 indicating a perfectly positive correlation (i.e. all populations fluctuate in perfect synchrony with one another).

Analyze these data to determine whether habitat type has the expected effect on mean spatial synchrony. Check the assumptions of your chosen test, formally and graphically.

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