Niche Comparisons

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Requirements

• Decision regarding which space (G or E) will be the arena for testing

• Careful elaboration of what is the null hypothesis and what are critical values for rejecting it

• Measure observed similarity• Assess similarity expected at random• Compare observed versus expected similarities• Make conclusions about the null hypothesis

Which Space?

• Geographic (e.g., Warren et al. 2008)– Original niche comparisons were developed here– Topology and such are easy to visualize and quite simple

to comprehend– Representation of the niche and its full dimensions is

less clear• Environmental (e.g., Broennimann et al. 2012)– Corresponds more closely to the niche– Topology, density, etc., are less well understood and less

easily visualized– Correspondence to geographic space is not always easy

to understand

Null Hypothesis• Null hypothesis will generally be “these two

niches are not more different than would be expected by chance”

• As such, critical value will be the lower 5% of similarity in the null distribution

SimilarityLow High

Freq

uenc

y

5% 95%

REJECT ACCEPT

Similarity Metric• D, I, or any other metric of matching or

similarity between two 2-dimensional areas (G space) or multidimensional forms (E space)

• Simply must respond to the question of how similar or different are the two entities in the chosen space

Warren et al. “Background” Similarity

• Cast random points within M of one species• Build model based on the random “background”

points• Measure similarity to the model of the other species

based on occurrence points• Repeat many times to develop a distribution

summarizing “background similarity”• Repeat entire process but switching the two species• Implemented within ENMTools and in R• Disadvantage: requires models to be transferred to

the same area in order for comparisons to be developed (consequence of G space choice)

IdentityTestWarren et al.(2008)

BackgroundSimilarityTestWarren et al.(2008)

Escobar-Qiao Squirrel Test• Driven by desire to avoid model transfers• Identify geographic areas of overlap in

environments between the two M areas• These areas represent environments common to

the two accessible areas• Any differences in use of environments within

those areas can be interpreted directly as niche difference– Can use between-group inertia– Or could use randomization tests like Warren et al.

2008 test for identity

Figure 3. Top: visualization of similar overlapping environments in native (blue) and invasive (red) areas. Note the many unshared environments across the native range (gray points). Axes are the first three principal components derived from the original climate layers. Bottom: geographic areas with similar environments in the native (blue) and invaded (red) ranges. Note the many unshared environments across the native range (gray areas).

Figure 4. Gray Squirrel (Sciurus carolinensis) occurrences (yellow points) in invaded (red) areas (A) and display of occurrences in corresponding environmental space (B). Occurrences (green points) in overlapping-environment (red) between native and invaded ranges (C) were compared in the environmental space (D). Notice the occurrences from native areas (green ellipsoid) nested within the ellipsoid corresponding to occurrences from the invaded areas (yellow ellipsoid) in the environmental space. Background values are show as gray.

Broennimann et al. E-space Similarity

• Echoes Warren et al. in terms of testing identity versus testing similarity of pairs of niches

• Moves the question and the analyses to environmental space

• Uses kernel densities to take into account the weird and uneven distribution of environmental spaces

• Uses randomization tests to assess identity and similarity

Europe North America

Identity test

Similarity tests

Fire Ants

Conclusions

• Several options are available to researchers for testing niche similarity and niche identity

• Niche-oriented questions MUST consider M in some sense or in some way

• Crucial decisions: G versus E space, model transfer, etc.