Richness Measurements and Null Models: Mid-Domain Effect

I. Some conventional diversity statistics.

a. Total apparent richness

b. What is the problem with reporting these values?

c. Fundamental problem quantifying community structure because it is a complex phenomenon:

i. Factors determining community structure:

1. Number of species

2. Relative abundances of each

3. Number of individuals

4. Size of area sampled

ii. No single statistic can adequately capture these components.

II. Better methods:

a. Fits relative abundances of species from one sample to a parametric distribution (not discussed today)

b. Species accumulation and rarefaction curves

i. Species per sampled unit (area) is really species density, not richness - need for consideration of sampled area and effort.

ii. These methods are good for determining an expected richness for subsamples of individuals or smaller areas for comparison.

iii. Rarefaction

1. Estimates expected richness in a random sample of individuals from a large collection.

2. Allows for meaningful comparisons among samples/collections of different sizes.

3. Three Assumptions of rarefaction

- sample is a statistically adequate representative of the community

- conspecifics are uniform-randomly dispersed

- species are dispersed independently

THESE CONDITIONS RARELY HOLD IN ECOLOGY

NONRANDOM SPATIAL DISPERSION PATTERNS ARE TYPICAL IN ECOLOGY

ex - sample from one location may likely have many individuals from one species (a grove of trees)

- Rarefaction selects individuals randomly, selecting the clump of conspecifics is unlikely.

4. Likely perform poorly for small areas and small samples

5. Good when comparing sites of equal area, but different numbers of individuals.

iv. Species accumulation curves

1. Created by adding individuals and species in the order in which they are observed.

2. Use of means and confidence intervals good for comparing different-sized areas.

iii. Examples

1. McCabe & Gotelli (2000)

- sample-based rarefaction and individual-based methods with different answers.

2. Collins and Simberloff (2007)

- comparisons of accumulation curves to rarefaction.

3. Considerations from Gotelli and Colwell (2001)

c. Non-parametric estimators - Incidence (presence/absence) & abundance-based (accumulation curves).

i. These methods are good for extrapolating to an asymptotic richness from a smaller area or sample.

ii. Incidence-based methods

1. Incidence-based can be good when relative abundances of each species are unknown, or sampling methods do not count individuals encountered once the species had been recorded.

2. Two methods -

- Chao 2 - Q1 & Q2 - unique to one or two quadrats

- Incidence-based coverage estimator (ICE) - based on species found in 10 or fewer sampling units.

iii. Common relative abundance methods

1. Chao 1 - as singletons and doubletons increase, the greater the difference in the observed and estimated richness.

2. Abundance-based coverage estimator (ACE) - based on species with 10 or fewer individuals in sample.

iv. Incidence-based coverage estimator (ICE) used by Longino et al. (2002)

1. EstimateS - a few things it will do for you.

III. Null models and the more specific Neutral Models

a. Null Model - a pattern-generating model that is based on randomization of ecological data and deliberately excludes a mechanism being tested.

i. A null hypothesis is NOT that communities are entirely random, or have no structure.

1. Structure is only random with respect to the mechanism being tested.

ii. Provide specificity and flexibility in analysis that is impossible with conventional statistical methods using techniques like reshuffling, bootstrapping, or resampling from an observed data set, or Monte Carlo techniques that sample from a specified parent distribution.

1. allow to reflect limitations from the scale at which sampling was conducted, or limited sampling effort.

b. Historical controversy over null models:

i. Began with the analysis of species co-occurrence.

1. Essentially centered around whether particular models were predisposed to Type II errors (incorrectly accepting a false null hypothesis) & Type I errors (incorrectly rejecting a true null hypothesis).

ii. Connor and Simberloff (1979) attack on Diamond's assembly rules.

1. Examined co-occurrence patterns in the absence of competitive interactions using presence-absence matrices.

2. Long controversy kept many ecologists from using null models so that they would not become involved in the debate.

- as an interesting side-note, Gotelli and McCabe (2002) found communities to have non-random co-occurrence patterns, consistent with Diamond's (1975) model.

3. Debate has abated a bit, but controversies persist, mainly due to challenges in developing algorithms that treat all samples with presence-absence matrices equally.

- Progress hampered by focus on competition with null models, much like with ideas about niches... there is more than competition among closely related species!

iii. No single "correct" null model.

1. Metabolic Theory of Ecology (MTE) is a null model.

2. MDE is also a null model.

c. Neutral models: A specialized form of a null model. It posit that random variation in extinction and speciation events, coupled with limited dispersal, can account for many community properties, including abundance distributions.

IV. Mid-domain effect (MDE) discussion and examples from sampling efforts and geographical barriers.

a. The mechanism these null models test, and therefore exclude, is the effect of spatial gradients (climatic, topographic, historical) on species range distribution across a landscape

b. Assumptions (factors that are not excluded from MDE models)

i. Populations are coherent, retain their natural spatial structure (range size and shape)

ii. Random placement of species ranges within a geographic area for a snapshot in time

-polygons (2D) or line segments (1D, with segment ends representing range boundaries)

c. Range size frequency distributions (RSFD)

i. Important when comparing MDE studies

ii. Ratio of size of ranges vs. size of geographic area greatly determines amount of overlap, and therefore the degree to which a dataset shows the MDE pattern (Colwell and Hurtt 1994, Dunn et al. 2007)

iii. It is important that the RSFD used in the model matches the true RSFD of the dataset

- If this is not corrected, the differences caused by spatial gradients between your empirical dataset and the model will be confounded by the differences in RFSD

- Using the true RSFD also gives your model inherent natural history "knowledge"

d. Yet another matter of scale...

i. Range size frequency distributions issue

- If ranges do not vary great

ii. Process vs. patterns

- Ecological and evolutionary drivers act at one level as the processes that determine richness patterns

- Statistically, the compound effects of these drivers demonstrate the MDE pattern at a higher level

~ requires multivariate analyses for proper testing

e. Comparing MDE models to empirical patterns can lead to better understanding of factors affecting species richness

i. Assuming MDE pattern is the norm, unexpected deviations can indicate speciation, extinction, historic range limit changes, or variation in sampling efforts

f. Criticism of MDE models

i. Most criticisms are process-level, not pattern-level

- The pattern can be observed in many systems...it's the process creating the pattern that is controversial

ii. Random geographic shuffling of ranges

- Range size and shape vs. range spatial location

- MDE models test climatic and historical determination of the spatial placement of ranges, not the size or shape of those ranges

iii. Absence of climatic gradients in models

- Should ranges consequently spread throughout the geographic area?

iv. Speciation and extinction events are spatially random

- Models assume random placement of ranges only for a snapshot in time, do not assume randomness for species origins or extinctions

V. Just gotta know more about these topics? Here are some other useful papers and sources of information

a. MDE

i. Colwell, R. K. and G. C. Hurtt. 1994. Nonbiological gradients in species richness and a spurious Rapoport effect. American Naturalist 144:570-595.

ii. Colwell, R. K. and D. C. Lees. 2000. The mid-domain effect: geometric constraints on the geography of species richness. Trends in Ecology & Evolution 15:70-76.

iii. Dunn, R. R., McCain, C. M., and Sanders, N. J. 2007. When does diversity fit null model predictions? Scale and range size mediate the mid-domain effect. Global Ecology and Biogeography 16:305–312.

iv. Laurie, H. and J. A. Silander, Jr. 2002. Geometric constraints and spatial patterns of species richness: critique of range-based models. Diversity and Distributions 8:351-364.

v. Christy has also created a program for testing the mid-domain effect. It is called Mid-Domain Null, and can be found on her website: http://spot.colorado.edu/~mccainc

vi. Colwell has a MDE program as well, not including replacement, called Range Model, which can be found at http://viceroy.eeb.uconn.edu/RangeModel