# Abundance of Species in Ordination

### SOME BASIC TERMS with respect to species abundance in ordination

Species richness - The number of species in a given, defined unit such as a trap, quadrat, lake, county, etc. Species richness is always an integer.

Abundance - Some measure of the amount of a species in a sample. Sometimes called "performance".  Examples: density, number of breeding pairs, biomass, basal area, frequency, cover, territorial area, presence.

Density: number of individuals per unit area or volume. For example , if 11 phoebes were found in 5 ha, the density would be 2.2/ha.

Frequency: The proportion or percentage of subsamples which contain the species. If phoebes were found in 5 out of 8 observation points, their frequency would be 5/8 = 0.625

Basal Area: Commonly used for woody plants. The cross- sectional area of all trees of a given species combined. If three sycamore trees were found in a 10 ha quadrat, and the trees measured 1 cm, 2cm, and 10cm in diameter, then the basal area would be:

[p(1 cm)2/4 +p(2 cm)2/4 + p(10 cm)2/4]/10ha
= 82.5cm2/10ha
= 8.25cm2/ha

(Remember, the equation for the area of a circle is [p*r2] or [p*d2]/4, where p is approximately 3.1415927, r is the radius, and d is the diameter)

Cover: A measure of the vertical projection onto the ground. It can include overlaps or not. If based on pin samples, cover usually does include overlaps, but if based on visual estimates, it usually does not.  For visual estimates, some count "empty space" within a clump and others do not.

Cover is often summarized by broad "cover-abundance scales". This is often sufficient if one is only interested in spatial variation in a very heterogeneous environment, or in long-term temporal variation. However, it would be better to be much more precise if you are interested in monitoring fine-scale patterns.

Biomass: Usually dry biomass, but sometimes extrapolated from wet biomass. Biomass is sometimes estimated through "dimension analysis", which is based on regression equations.

Take a shrub example:
Biomass = ß0 +ß1(height) + ß2(number of stems) + ß3(basal area of stems) + ß4(longest diameter) + ß5(diameter perpendicular to longest) + e

b0, b1, b2, etc. are determined based on a modest number of shrubs.

Presence: Conceptually easy, but there are some subtleties:

• Rooted or Cover?
• fertile or not?
• nesting or accidental?

Relative abundance: The abundance of a species (by any measure), divided by the total abundance of all species combined. If there are 2.2 phoebes/ha, 3.6 flickers/ha, and 3.2 red-eyed vireos/ha, and not any other species, the relative density of the birds would be

phoebes: (2.2/ha)/(9/ha) = 0.244
flickers: (3.6/ha)/(9/ha) = 0.400
vireos: (3.2/ha)/(9/ha) = 0.356

If the frequency of phoebes is 0.625, the frequency of flickers is 0.500, and the frequency of vireos is
1.000, then the RELATIVE FREQUENCY of the birds would be

phoebes: (0.625)/(2.125) = 0.294
flickers: (0.500)/(2.125) = 0.235
vireos: (1.000)/(2.125) = 0.471

If the basal area of sycamores is 8.25cm2/ha, the basal area of cottonwoods is 105.32cm2/ha, the basal area of redbuds is 10.25cm2/ha, and the basal area of slippery elms is 89.20cm2/ha, and there are no other trees, then the relative basal area (more commonly known as relative dominance) of each species is:

sycamore: ( 8.25000cm2/ha)/(213.02cm2/ha) = 0.03873
cottonwood: (105.32000cm2/ha)/(213.02cm2/ha) = 0.49441
redbud: ( 10.25000cm2/ha)/(213.02cm2/ha) = 0.04812
slippery elm:( 89.20000cm2/ha)/(213.02cm2/ha) = 0.41874

Relative abundances must add to unity (save perhaps for some rounding error). Note that relative abundance has no units (it is dimensionless). Alternatively, relative abundances can be expressed as a percentage.

Species composition - A list of all the species in this defined unit, along with some measure of the abundance (often the relative abundance).

Species composition can be considered a vector - i.e. a column of numbers. If it is based on relative abundance, the numbers must sum to 1 or 100%.

Ordination, classification, and direct gradient analysis all attempt to reveal patterns of species composition.

What if you have more than one measure of abundance or performance for each species? You can:
1) analyze them all separately - this can yield new insights
2) figure out which one is the "best" for your purposes
3) create a synthetic importance value.

Importance values (IV) are usually either the sum or the average of measures of relative abundance. The most commonly used importance value in forests is the sum of relative density, relative frequency, and relative dominance, each expressed as a percentage.

 `Species` `Relative``density` `Relative``frequency` `Relative``dominance` `IV` `sycamore:` ` 2.100` ` 16.013` ` 3.873` ` 21.986` `cottonwood:` `12.231` ` 23.194` `49.441` ` 84.866` `redbud:` `67.021` ` 35.771` ` 4.812` ` 107.604` `slippery elm:` `18.648` ` 25.022` `41.874` ` 85.544`

In this case, the minimum possible IV is 0, and the maximum possible is 300.

For the purposes of analysis, it makes no difference whether you take the sum or the average, or whether you use relative values expressed as a proportion or as a percentage. This is because the different methods are linear combinations of each other.

Note that "Relative Frequency" requires some sort of subsamples within a sample. Since many studies do not include subsamples, IV is often calculated as the average of relative density and dominance.

One advantage of using IV is that it dampens the effects of single large individuals, or infrequent species which, when present, are very abundant (e.g. cedar waxwings, multi-stemmed shrubs).

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