Ecological Alpha Diversity

Compute common measures of ecological α-diversity on a dataset of species abundance by site

In ecology, alpha diversity (α-diversity) refers to biodiversity on a local scale. In this example, we will compute common diversity metrics from a dataset of tree counts in 50 1-hectare plots on Barro Colorado Island from the vegan R library (Oksanen et al., 2022).

Define ecological observation and environmental data (or import the data from a CSV file):

In[1]:=

BCITrees=

;BCIEnv=

;

Preview the observation data as a

Dataset

In[2]:=

(Dataset[#1,MaxItems6]&)[Transpose[Dataset[AssociationThread[First[#1]Transpose[Rest[#1]]]]]]&@BCITrees

Out[2]=

Convert the environmental data into a

Dataset

, and view the data:

In[3]:=

BCIEnv=(Dataset[#1,MaxItems6]&)[Transpose[Dataset[AssociationThread[First[#1]Transpose[Rest[#1]]]]]]&@BCIEnv

Out[3]=

Calculate the observed species richness at each site:

In[4]:=

richness=Length/@DeleteCases[Rest[BCITrees],0,∞]

Out[4]=

{93,84,90,94,101,85,82,88,90,94,87,84,93,98,93,93,93,89,109,100,99,91,99,95,105,91,99,85,86,97,77,88,86,92,83,92,88,82,84,80,102,87,86,81,81,86,102,91,91,93}

Recall the definitions of the Shannon-Weaver, Simpson and inverse Simpson diversity indices:

Shannon-Weaver diversity:

H=-

∑

i=1

log

Simpson's diversity:

=1-

∑

i=1

Inverse Simpson diversity:

∑

i=1

Here,

is the proportion of species

(in a list summing to 1),

is the number of species, and

is the base of the logarithm. When

b=

, we mark the Shannon-Weaver index as

. Other common bases are 2 and 10.

Define a function to compute the Shannon–Weaver diversity:

In[5]:=

ClearAll[ShannonWeaverDiversity]ShannonWeaverDiversity[proportions_List,logBase_:]:=-Sum[proportions〚i〛*Log[logBase,proportions〚i〛],{i,1,Length[proportions]}]

Define a function to compute Simpson's diversity:

In[6]:=

ClearAll[SimpsonDiversity]SimpsonDiversity[proportions_List]:=1-Sum

proportions〚i〛

,{i,1,Length[proportions]}

Define a function to compute the inverse Simpson's diversity:

In[7]:=

ClearAll[InverseSimpsonDiversity]InverseSimpsonDiversity[proportions_List]:=1Sum

proportions〚i〛

,{i,1,Length[proportions]}

Calculate the proportions of species in each site:

In[8]:=

proportionsBySite=

Total[#]

&@DeleteCases[#,0]&/@Rest[BCITrees]//N;

Compute measures of diversity for each site in the BCITrees dataset:

In[9]:=

H=ShannonWeaverDiversity/@proportionsBySite;D1=SimpsonDiversity/@proportionsBySite;D2=InverseSimpsonDiversity/@proportionsBySite;

Calculate Pielou's evenness

for each site:

In[10]:=

evenness=H/Log[richness];

Summarize these calculations in a

Dataset

In[11]:=

alphaDiversity=Dataset[#,MaxItems10]&@Transpose@Dataset@"Site"Range[Length[Rest[BCITrees]]],"Richness"richness,"Shannon"H,"Simpson"D1,"Inverse Simpson"D2,"Pielou's Evenness"evenness;

Preview the dataset and create histograms of α-diversity indices:

In[12]:=

Row[{alphaDiversity,Query[All,Histogram]@KeyDrop["Site"][Transpose[alphaDiversity]]},Spacer[10]]//Rasterize

Out[12]=

Convert the UTM coordinates from the environmental data table to

GeoPosition

, and append the Position and Habitat columns to the diversity table:

In[13]:=

BCIDiversityAndEnv=Dataset[#,MaxItems6]&@JoinAcross[alphaDiversity,BCIEnv[All,KeyTake[#,{"Site","Habitat"}],"Position"GeoPosition[GeoGridPosition[{#["UTM.EW"],#["UTM.NS"]},"UTMZone17"]]&],Key["Site"]]

Out[13]=

Plot heat maps of species richness and Shannon diversity over the studied area:

In[14]:=

Row@TableGeoDensityPlot#,

&@Normal[BCIDiversityAndEnv[All,#Position#[dependentVar]&]],{dependentVar,{"Richness","Shannon"}}

Out[14]=

Plot bubble charts of species richness and Shannon diversity, colored by habitat category:

In[15]:=

dataByHabitat=BCIDiversityAndEnv[GroupBy["Habitat"]];LegendedRow[#,Spacer[5]]&@TableGeoBubbleChart#,

&@Normal[Values[dataByHabitat][All,All,#Position#[dependentVar]&]],{dependentVar,{"Richness","Shannon"}},SwatchLegend

,Keys[Normal[dataByHabitat]]

Out[15]=

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Citation:
- Gotelli, N. J., & Ellison, A. M. (2012). A Primer of Ecological Statistics (Second Edition). Oxford University Press.
- Oksanen, J., Simpson, G. L., Blanchet, F. G., Kindt, R., Legendre, P., Minchin, P. R., O'Hara, R. B., Solymos, P., Stevens, M. H. H., Szoecs, E., Wagner, H., Barbour, M., Bedward, M., Bolker, B., Borcard, D., Carvalho, G., Chirico, M., Caceres, M. D., Durand, S., … Weedon, J. (2022). vegan: Community Ecology Package. https://CRAN.R-project.org/package=vegan

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Contributed by: Phileas Dazeley-Gaist

Ecological Alpha Diversity

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