Calculating habitat richness and evenness

Diversity, Richness, and Evenness

In ecology, diversity is usually thought of as being composed of richness – the number of kinds of things, and evenness the relative abundance of things.  Most commonly these terms are used with reference to species diversity, a concept that includes species richness (the number of species) and species evenness (the relative abundances of the different species).  An area with 100 plant species (richness = 100) is considered to be more diverse than an area with only 10 species (richness = 100).  But an area with 100 species where each species is reasonably well-represented would also be considered more diverse than an area where 99% percent of the plants are a single species and the other species are all very rare. 

Similar concepts can be used with reference to the diversity of habitats.  Consider landcover in the following two made-up refuges, each of which contain the same four habitat types:

Smoky Pines Wildlife Refuge: 500 ha mud flats, 400 ha wetland, 600 ha deciduous forest, 500 ha scrubland.

Great Auk Wildlife Refuge: 5 ha mudflats, 5 ha wetland, 1960 ha deciduous forest, 20 ha scrubland.

Each of these refuges has a habitat richness of n=4 and each is exactly 2000 ha.  But the first refuge contains a roughly equal distribution of the four habitats, whereas the second is almost entirely deciduous forest with only small pieces of the other 3 habitats.  One can easily imagine that the first refuge would be more at risk from invasive species than would the second.  For this reason, it is important to think of habitat heterogeneity both in terms of the numbers of habitats and the equitability of those habitats.  Our analysis will attempt to separate the two.

Calculating Evenness

A number of different metrics are available for calculating evenness (and diversity).  We’ll use a common index of evenness called Simpson’s E.  Here’s the step-by-step recipe for Simpson’s E.

1) First determine the total number of habitats present.  For the Smoky Pines Refuge Above, there are 4 habitats.

2) Calculate the proportional representation of each habitat (p_i).  There are 2000 hectares total, so p_mudflats  = 500/2000 = 0.25; p_wetland  = 400/2000 = 0.20, p_forest  = 600/2000 = 0.30, p_scrubland  = 500/2000 = 0.25. 

3) Square all these proportions (p_i’s) and sum these squares, i.e.  ∑ p_i²

For the Smoky Pines refuge, that would be (0.25)²+(0.20)²+(0.30)²+(0.25)² = 0.255

4) Now take the reciprocal of this, i.e. 1/ ∑ p_i² .  Here that would be 1/0.255 = 3.92.

This quantity (1/ ∑ p_i²) is known as Simpson’s D, and is a measure of diversity.  Conceptually, ∑p_i² is an estimate of the probability that any two hectares chosen at random from the reserve will be the same habitat type.  So the more habitat types and the more even their distribution (i.e. the greater the diversity), the lower this probability becomes.  Taking the reciprocal flips this around so that more diverse areas have a higher value of the index. 

5) Now to get evenness (E), we just divide D by the total number of habitats present (which is the maximum possible value for D).  E = D/D_max = 3.92/4 = 0.98.  This index ranges from 1/D_max (in this case 0.25) to 1 (equal distribution of all habitats).  0.98 is very high evenness, which makes sense given that the amounts of each habitat are very similar.  For comparison, the evenness (E) of Great Auk refuge turns out to be only 0.26, very close to the minimum.

Using hierarchical data

The landcover data for the actual refuges look like the data above, except that the habitat classifications are hierarchical – that is, there are broader scale classifications and finer scale classifications.  To see which of these is more important for predicting plant invasion, we’ll calculate habitat richness and evenness at both levels of the hierarchy.  Here’s a real dataset from the survey. 

Refuge Cover Types 

Vegetation cover types (acres / hectares): acres

Forrest and Woodland: 

   Evergreen Upland: 0

   Evergreen Wetland: 0

   Evergreen Desert: 0

   Deciduous Upland: 200

   Deciduous Wetland: 20

   Deciduous Desert: 0

   Mixed Evergreen Deciduous Upland: 100

   Mixed Evergreen Deciduous Wetland: 0

   Mixed Evergreen Deciduous Desert: 0

   Plantations, Orchards, Groves: 2

Shrublands and Dwarf Shrublands: 

   Evergreen Upland: 0

   Evergreen Wetland: 0

   Evergreen Desert: 0

   Deciduous Upland: 0

   Deciduous Wetland: 0

   Deciduous Desert: 0

   Mixed Evergreen Deciduous Upland: 0

   Mixed Evergreen Deciduous Wetland: 0

   Mixed Evergreen Deciduous Desert: 0

   Fruit/Nut, Shrub and Vine: 0

Perennial Grassland: 

   Upland: 0

   Wetland: 0

   Desert: 0

Annual Grassland: 

   Upland: 75

   Wetland: 31

   Desert: 0

Perennial Forbes: 

   Upland: 50

   Wetland: 31

   Desert: 0

Annual Forbes: 

   Upland: 50

   Wetland: 25

   Desert: 0

Planted/cultivated grassland or forbes: 1753

Submersed aquatic vegetation: 100

Mud or sand flats: 0

Developed, Industrial, Urban: 5

Open water: 50

Note that the broad scale categories are aligned with the left margin, whereas the fine-scale (within habitat) classifications are indented.

To calculate richness for the broad-scale, look for all the habitat types that have some non-zero acreage.  I see this for 1) Forest and Woodlands, 2) Annual Grassland, 3) Perennial Forbes, 4) Annual Forbes, 5) Planted/cultivated grassland, 6) Submersed aquatic vegetation, 7) Developed, and 8) Open Water.  That makes 8 habitat types.

For fine-scale richness, count all the total number of habitat types that are represented by summing the indented types and the non-indented habitats which have no finer-scale classification (e.g. Open water and Developed).  So, now we count 1) Deciduous Upland Forest, 2) Deciduous Wetland Forest, 3) Mixed Evergreen Deciduous Upland Forest, 4) Plantations, 5) Annual Grassland Upland, 6) Annual Grassland Wetland, 7) Perennial Forbes Upland, 8) Perennial Forbes Wetland, 9) Annual Forbes Upland, 10) Annual Forbes Wetland, 11) Planted, 12) Submersed aquatic, 13) Developed, and 14) Open Water.  That makes 14 habitat types. 

Now for evenness.  If you add up the totals of all the habitat types, you get 2492 acres.  In this case, that matches the total refuge size entered by the manager (which is good).  But don’t necessarily assume this is the case: when calculating evenness, always use the total of all the habitat areas entered rather than the total area given by the manager. 

For the broad-scale classification, we’ll first calculate the p_i’s for each habitat

Forest and Woodlands = 200+20+100+2 = 322, 322/2492 = 0.13

Annual Grassland = 75+31= 106, 106/2492 = 0.043

Perennial Forbes = 50+31=81, 81/2492 = 0.033

Annual Forbes = 50+25 = 75, 75/2492 = 0.030

Planted/cultivated grassland = 1753, 1753/2492 = 0.703

Submersed aquatic vegetation = 100, 100/2492 = 0.040

Developed = 5, 5/2492 = 0.0020

Open Water = 50, 50/2492 = 0.020

Now, the sum of all the p_i² = (0.13)² + (0.043)² + (0.033)² + (0.030)²+ 0.703)²+ (0.040)²+ (0.002)²+ (0.020)² = 0.517. 

Take the reciprocal, to get D = 1/0.571 = 1.93

And evenness E = D/D_max or 1.93/8 = 0.24.  Most of the habitat is either cultivated grassland or forest, so this low value seems reasonable.

For the fine-scale classification, we use the same set of steps with the 14 habitats that are represented.

Deciduous Upland Forest = 200, 200/2492 = 0.080

Deciduous Wetland Forest = 20, 20/2492 = 0.0080

Mixed Evergreen Deciduous Upland Forest = 100, 100/2492 = 0.040

Plantations = 2, 2/2492 = 0.00080

Annual Grassland Upland = 75, 75/2492 = 0.030

Annual Grassland Wetland = 31, 31/2492 = 0.0124

Perennial Forbes Upland = 50, 50/2492 = 0.020

Perennial Forbes Wetland = 31, 31/2492 = 0.0124

Annual Forbes Upland = 50, 50/2492 = 0.020

Annual Forbes Wetland = 25, 24/2492 = 0.010

Planted/cultivated grassland = 1753, 1753/2492 = 0.703

Submersed aquatic vegetation = 100, 100/2492 = 0.040

Developed = 5, 5/2492 = 0.0020

Open Water = 50, 50/2492 = 0.020

Summing all the p_i² = (0.080)² + (0.008)²+(0.040)² + (0.0008)² + (0.030)² + (0.0124)² + (0.020)² + (0.0124)²+ (0.020)²+ (0.010)²+ (0.703)²+ (0.040)² + (0.0020)² + (0.020)² = 0.506

So D= 1/0.506 = 1.97 and E = 1.97/14 = 0.14

Comparing the values from the fine-scale to the values for the broad-scale you’ll see that the diversity is a little higher but the evenness is lower.  By breaking things up, we’ve added new habitats but generally in small amounts. 

Now that you understand all of this, here are some tools that will hopefully make your life much easier:

Excel spreadsheet for calculating habitat richness and evenness (directions are embedded)

And

Example spreadsheet (shows what everything should look like when you’ve used the spreadsheet successfully)