Distance-based ordination

16 important questions on Distance-based ordination

What are multivariate analyses (MVA's)?

Simultaneously analysing multiple response variables.
  • ecological phenomena are inherently complex
  • often with many response variables

Why would you not do seperate univariates analyses?

  • Many independent tests: not efficient
  • Multiple testing: loose statistical power
  • Multicollinearity: several species may response similarly to predictors (redundancy)

What are the 3 types of ordination plots?

  1. Scatterplot (sites)
  2. Biplot (sites + species)
  3. Triplot (sites + species + predictors)
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How are euclidean distances calculated?

By using Pythagoras' theorem.

What are the steps of polar ordination: axis 2?

  1. Calculate distance between sites in terms of species composition
  2. Select the two most different sites: these are placed on opposite ends (poles) of axis 1
  3. Order the remaining sites between these poles
  4. Choose sites for axis 2 perpendicular to axis 1: select 2 other sites which are close together on axis 1, but very dissimilar
  5. Order all sites between these poles on axis 2

What is an ordination diagram?

The diagram is a composite of the 2 axis scores.

What is a short gradient?

Approximates linear response.

What is the abundace paradox?

Two locations not sharing any species could appear more similar (thus lower distance) than two locations which share species but with different abundances!

Two locations sharing all species could appear more different (thus higher distance) than two locations which do not share any species but which have low abundances!

What are the solutions for double zeros?

Transformations
  • log(1+x) (reducing the influence of large values)
  • sqrt(x) (reducing the influence of large values)
  • Hellinger’ (computing sqrt of relative abundances per location)

And/or use an asymmetric distance measure
  • measures that treat double zeros and double presences asymmetrically

What is Hellinger distance?

Hellinger transformation = Eucledean distance
  • less senstive to abundance paradox and double-zero problem

What are the disadvantages of Polar ordination?

  • Heuristic rules rather than a formal model
  • Axes are not statistically independent by design
  • Different people will end up with different ordinations

What is the Principal Coordinates Analysis (PCoA)?

  • Based on robust mathematics
  • Axes are statistically independent by design
  • The same solution every time (on the same dataset)

What is the aim of nonmetric multidimensional scaling?

Locate samples in reduced ordination space (2 or 3 axes) so that the Euclidean distances between these samples correspond to the dissimilarities in the original distance matrix.

Why can/will multiple people performing polar ordination on the same dataset arrive at different ordinations, especially if the dataset becomes larger and more complex?

Since it is based on heuristic rules rather than on an explicit underlying model.

What can the Manhattan distance on presence-absence data be interpreted as?

The number of species that are not shared between the two sites.

What are Hellinger distances?

Euclidean distances computed on Hellinger-transformed data.

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