20 April, 2023

Lecture Topics

  • Why use a Stable Isotope Mixing Model
  • Introduction to Bayesian statistics
  • Regression models and SIMMS
  • Dos and Donts of using SIMMS
  • Statistical model behind SIAR / simmr / MixSIAR
  • Stable Isotope Bayesian Ellipses (SIBER)
  • Estimating Trophic Discrimination Factors with SIDER
  • SIAR Vs simmr Vs MixSIAR
  • SIMMS for complex data
  • Source grouping
  • Building your own SIMM with jags

Practicals

  • R revision
  • simmr (not SIAR)
  • SIBER
  • SIDER
  • MixSIAR and jags

Questions ecologists often ask

  • What is this animal eating?
  • Are these animals specialists or generalists?
  • Why are these populations of animals eating different things?
  • How is this community functioning?

Isotopes can provide insights

Idealised Community

Moving heavy isotopes is hard work

heavy isotopes fractionate

Heavy isotopes are chemically sticky

chemical reactions fractionate

Observe the states and infer the process

infer the process by observing the state

Ecological process inferred by isotopes

  • Newsome, Martinez del Rio, Bearhop & Phillips. 2007. A Niche for Isotopic Ecology. Frontiers in Ecology and the Environment.
  • d-space and p-space moving from d-space to p-space

Mixing Models move from d- to p-space

  • Direct measure of trophic interactions via consumption

siar output example

Determined system - 2 sources 1 tracer

  • How much of black and blue is the red dot made of?
  • consumer = (1/3)*(-10) + (2/3)*(5) = 0

Determined system - 3 sources 2 tracers

  • How much of black, blue and magenta is the red dot made of?
  • p = c(0.2, 0.4, 0.4)

Under-determined - 3 sources 1 tracers

  • problems arise
  • 1/3 black + 2/3 blue
  • 1/6 black + 5/6 magenta
  • 1/3 black + 1/6 magenta + 3/5 blue

Under-determined - 4 sources 2 tracers

  • similar issue but more nuanced

IsoSource

histogram output from isosource

  • took a brute force approach
  • try every possible combination of sources in 1% increments
  • accept if within some treshold of the mixture (consumer)
  • reject if outside treshold

SIAR / MixSIR / MixSIAR

histogram output from siar

  • uses Bayesian Inference to assign probabilities to the estimates
  • frequency of occurrence, and proximity of estimate to the observed value increases the probability of a solution
  • can also include prior information that weights the probability of a solution

Comparing dietary proportions

  • Proportion of terrestrial grass in the diet of Brent geese geese eat grass in different proportions

Diet over time

  • Diet can be linked to covariates such as time swallow diets change over time

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 question is key

  • as with all science, your question will determine which analysis you require
  • formulating a clear question at the start will inform your study design
  • If you need to know what an animal is eating, then you require a SIMM
  • if you want to compare the niche widths of populations then you probably want the ellipse functions in SIBER
  • if you want to compare entire communities for niche structure, then you probably want the hull-based metrics in SIBER