12 April, 2024

Inference from d-space

  • Isotopes are like naturally occurring PCA analyses
  • They are two axes, behind which lie multiple biotic and physical factors
  • d15N tells us a lot about trophic level for example
  • d13C can tell us about marine Vs terrestrial among other scenopoetic factors
  • Idea is that isotopic niche correlates in some way with ecological niche

Specialists Vs generalists

specialists vs generalists in isotope d-space

Bearhop, Adam, Waldron, Fuller & MacLeod. 2004. Determining trophic niche width: a novel approach using stable isotope analysis. J Anim Ecol.

Drivers of niche width

niche width shrinks with fragmentation

Layman et al. 2007. Niche width collapse in a resilient top predator following ecosystem fragmentation.

Invasive species

niche width of native species affected by invasive species

Jackson, M.C. et al. 2012. Population-Level Metrics of Trophic Structure Based on Stable Isotopes and Their Application to Invasion Ecology. PLoSONE.

The problem with convex hulls

They can only get bigger.

SIBER

headline from SIBER paper

The standard ellipse

illustration of a standard bivariate ellipse

  • a = semi-major axis length
  • b = semi-minor axis length
  • Area = pi*a*b
  • contains ~= 40% of the data
  • located by the means of X and Y
  • shape and size determined by covariance matrix Sigma

Uncertainty of the ellipse

comparison of ellipses and hulls

Sample size, ellipses and hulls

effect of sample size on fitted hulls and ellipses

a = Hulls & b = Ellipses

Sample size and bias in ellipse estimation

effect of sample size on fitted hulls and ellipses

a = SEA, b = SEAc and c = SEA_B

SIBER has two quite different routines

  • Question is: do you want to compare populations within a community, or make comparisons across entire communities?

Comparisons of populations

four ellipses fit to data

SIBER output

estimates of ellipse size for community 1

Other ways one might compare populations

four ellipses fit to data