Beta-Dispersion
Beta-dispersion tests if the dispersion, variance, of two or more
groups are significantly different or not. First, an item named “groups”
must be made that contains lists of the location and number of isolates
from that location used in the analysis. We will then check to make sure
the lists in “groups” adds up to the number of isolated used in
analysis.
First, make a list of the locations for each pathotype. Note that
when you are using two or more locations you will need to make a list
for each location with a length of isolates used.
groups <- factor(c(rep("Michigan_1", 11), rep("Michigan_2", 10)))
# this number shows how many isolates are in all "groups" lists combined
length(groups)
## [1] 21
# this shows the number of isolates within your data set, these numbers should
# match for downstream analyses to work!!
length(unique(P_sojae_survey$Isolate))
## [1] 21
Next, beta-dispersion will be calculated using the Jaccard distance
matrix made previously. An ANOVA is then performed to identify
significance within the dataset. Post-hoc tests can be used to identify
significant interactions between specific locations within the dataset.
This can then be plotted to visualize how the beta-dispersion is
different between groups.
# calculates the beta-dispersion for each group, when comparing 2 or more
pathotype.disp <-
betadisper(P_sojae_survey.matrix.jaccard, groups)
# tests if centroid distances are significantly different from each other
pathotype.disp.anova <- anova(pathotype.disp)
pathotype.disp.anova
## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 1 0.008375 0.0083752 0.9672 0.3377
## Residuals 19 0.164523 0.0086591
# test significance between each group
pathotype.disp.TukeyHSD <- TukeyHSD(pathotype.disp)
pathotype.disp.TukeyHSD
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = distances ~ group, data = df)
##
## $group
## diff lwr upr p adj
## Michigan_2-Michigan_1 -0.03998626 -0.1250853 0.04511275 0.3377355
# plot showing the dispersion for each group
plot(pathotype.disp, hull = FALSE, ellipse = TRUE)
The ANOVA identified no significant differences between groups
dispersion (p = 0.3377355). This means that the groups dispersion, or
variance, is not significantly different from each other and the groups
dispersion is likely homogeneous between groups. At this point, a Tukey
HSD test is not warranted, but we use it as an example here. Again, a
p-value of 0.3377355 is reported from the Tukey HSD tests and we reject
the hypothesis that these groups may have different dispersion. We can
plot the dispersion for each group using the plot()
function. As expected, since we have identified no significant
differences, the two groups dispersion overlap a great deal and are not
distinct from each other. Again this shows that pathotype dispersion
between the groups is homogeneous and not different in this
instance.
If we were working with a data set that had groups with significantly
different dispersion we would expect to see a significant ANOVA p-value
(p < 0.05) as well as significance when using the Tukey HSD test.
Lastly, the plotted dispersion will form distinct, separate, groups
which can be observed.
Differences in beta-dispersion may indicate separate pathotype groups
which should be further investigated with Permutation Based Analysis of
Variance (PERMANOVA) and Analysis of Similarity (ANOSIM) analysis.
Groups which have similar dispersion may still be significantly
different in regards to their centroids, which will be tested using a
PERMANOVA.
Permutation Based Analysis of Variance (PERMANOVA)
PERMANOVA tests if the centroids, similar to means, of each group are
significantly different from each other. Likewise, an \(R^2\) statistic is calculated, showing the
percentage of the variance explained by the groups.
pathotype.adonis <- adonis2(P_sojae_survey.matrix.jaccard ~ groups)
pathotype.adonis
## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
##
## adonis2(formula = P_sojae_survey.matrix.jaccard ~ groups)
## Df SumOfSqs R2 F Pr(>F)
## groups 1 0.11358 0.07869 1.6229 0.191
## Residual 19 1.32976 0.92131
## Total 20 1.44335 1.00000
The PERMANOVA identified no significant differences between the
groups centroids, or means (p = 0.191). In addition to
identifying significance between group centroids, the PERMANOVA also
calculates how much of the variance can be explained by the specified
groups (see the \(R^2\) column in the
PERMANOVA output). In this case, the \(R^2\) is 0.0786944, so 7.9% of the variance
is explained by the groups used in analysis. Based on the PERMANOVA
results we can conclude that these two groups are not different from
each other and likely have similar pathotypes to each other.
Analysis of Similarity (ANOSIM)
ANOSIM statistic (R) ranges from between -1 and 1. Positive numbers
suggest that there is more similarity within groups than there is
between groups. Values close to zero indicate no difference between
groups (i.e., similarities are the same between groups).
pathotype.anosim <- anosim(P_sojae_survey.matrix.jaccard, groups)
pathotype.anosim
##
## Call:
## anosim(x = P_sojae_survey.matrix.jaccard, grouping = groups)
## Dissimilarity: jaccard
##
## ANOSIM statistic R: 0.06882
## Significance: 0.159
##
## Permutation: free
## Number of permutations: 999
ANOSIM statistic (R) was 0.0688182, so there are more similarities
between groups than there are within groups. This is evidence that the
groups are not different from one another. Likewise the significance is
>0.05 so there is no significant difference between groups’
similarities.
