Properties of Community Data

in Ecology

Adapted from Ecological Statistical Workshop, FLC, Daniel Laughlin

Community Data Summary

• Community data matrices

• Species on gradients

• Problems with community data

• Normality assumptions

Key questions to keep in the back of your mind:1. How do species abundances relate to each other?2. How do species relate to environmental gradients?

Community data matrices

or Molecular marker

(abundance orpresence/absenceused as a measure ofspecies performance)

Independentsample units

Traits

SPARSE

Full Community Dataset

n = # of sampleunits (plots)

p = # of species

t = # of traits

e = # of environmentalvariables orfactors

d = # of dimensions

n x p n x e n x t n x d

t x p t x e

e x p

plots inspecies space plots in envir

spaceplots intrait space

plots inreducedspeciesspace

traits in species space

used for species inenvironmental space (A’E) traits in envir

space

d x pspecies in reducedplot space

Ordination can address more questions than how plots differ in composition…

Species on environmental gradients

Gaussian ideal - peak abundances, nonlinear - this is challenging to analyze

Linear responses to gradients - okay for short gradients

Major Problems with Community Data

1. Species responses have the “zero truncation problem”

2. Curves are “solid” due to the action of many other factors

3. Response curves can be complex

4. High beta diversity

5. Nonnormal species distributions

Major Problems with Community Data

• species responses truncated at zero • only zeros are possible beyond limits• no info on how unfavorable the environment is for a species

• “curves” are typically solid envelopes rather than curves• species is usually less abundant than its potential (even zeros are possible)

1. Zero truncation 2. “Solid” curves

Major Problems with Community Data

3. Complex curves-polymodal, asymmetric, discontinuous

Average lichen cover on twigs in shore pine bogs in SE Alaska.

High beta diversity

• Beta diversity = the difference in community composition between communities along an environmental gradient or among communities within a landscape

Whittaker’s (1972) Beta Diversity

γ = number of species in composite sample (total number of species)ά = average species richness in the sample units

No formal units, but can be thought of as ‘number of distinct communities”

The one is subtracted to make zero beta diversity correspond to zero variation in species turnover.

Rule of thumb:βw < 1 are low, βw > 5 are high

Are species distributions normal?

• Univariate normality (it’s what we’re used to)

• Bivariate normality (it’s easy to visualize)

– Idealized community data– Real community data

• Multivariate normality (straightforward extension of bivariate normality to multiple dimensions)

Univariate normality

Normality can be assessed by:skewness (asymmetry), andkurtosis (peakiness)

Skew = 0Kurtosis = 0

Skewness

• Community data will nearly always be positively skewed due to lots of zeroes

• Linear models require |skew| < 1

• Assess skewness of data in PCORD (Row and Column Summary)

Positively skewed distribution typical of community data

PLHE

-0.1 0 .1 .2 .3 .4 .5 .6 .7

HYVI

0 .05 .1 .15

HYIN

-0.2 0 .2 .4 .6 .8 1

Bivariate Normality

Viewsfromabove

Bivariate Species Distributions

Idealized Gaussian species response curves

positive association negative association

bivariate distribution is non-linear dust bunny distribution-plotting one species against another (lots of points near orgin and along axes)

Bivariate Species Distributions

Realistic data with “solid” response curves

positive association negative association

dust bunny distributiondust bunny distribution

Bi- and Tri-variate DistributionsBivariate normal distribution forms elliptical cloud

Bivariate distribution with most points lying near one or two axes

Multivariate normal distribution (hyperellipsoid)

Multivariate dust bunny distribution

Dust bunny in 3-D species space

Environmental gradients form strong non-linear shape in species space

A: cluster within the cloud of points (stands) occupying vegetation space.

B: 3 dimensional abstract vegetation space: each dimension represents an element (e.g. proportion of a certain species) in the analysis (X Y Z axes).

A, the results of a classification approach (here attempted after ordination) in which similar individuals are grouped and considered as a single cell or unit.

B, the results of an ordination approach in which similar stands nevertheless retain their unique properties and thus no information is lost (X1 Y1 Z1 axes).

Key Point: Abstract space has no connection with real space from which the records were initially collected.

Multivariate Normality

• Linear algebra easily extends these concepts into multiple dimensions

• Most multivariate methods assume multivariate normality (linear ordination methods)

• Ecological data are seriously abnormal• Thus, we will often require different

methods