- All sources are known
- Source means are known
- TEFs are known
- Sources are distinct
20 April, 2023
Basic Mixing Model Assumptions
Additional Biological Assumptions
- Consumer tissue sampled at appropriate time relative to sources
- Consumer is at equilibrium with their food
- TEF is a fair reflection of consumer physiology
- fasting
- high carbon / nitrogen diets
- reproduction
- growth
- hibernation
- migration
Some (11) Dos and don’ts of mixing models
A priori questions - 1
- The general question “What does this/these animal(s) eat?” is commonplace
- can suffer from uncertainties
- especially if restricted to individual animals
- restricted to one point in time
- Might be more powerful to ask:
- do these animals differ in their diet of Source A?
- how does their diet vary over time?
Consider diet - 2
- Consider what is known about the animal’s diet
- you need to know all the food sources they eat
- A SIMM can then tell you what proportion of each occurs in their diet
- Provides a longer term average than say gut or faeces contents analysis
Sample collection - 3a
- tissue in the consumer takes time to made from the assimilated material
- some tissue has a fast turn-over, and some can be very slow
- may never actually be in equilrium with their food
- important therefore to sample sources at the time the tissue was laid down
- blood plasma is practically instantaneous (a few days)
- blood cells a week or two
- feathers and scales could be months old
- important to think about the biology of your organisms
Sample collection - 3b
- Sources may vary in isotopic concentrations over time
- Sources likely vary through space
- Getting a good picture of this variation, and including it in the modelling process is very important
- How many source samples will you take?
- particularly when you have hierarchically nested populations of consumers, the number of samples at each level can have a large effect on precision of estimated diets Semmens et al 2009.
Enrichment factors - 4a
- “you are what you eat plus a few per-mil”
- the plus represents what your physiology is doing to the isotopic ratios as they are processed into tissue
Enrichment factors - 4b
- Enrichment / Discrimination factors are best added to sources allowing differences depending on the source
- They vary a lot among tissues, individuals and species
- Some people worry about internal routing
- different nutrients are sent along different pathways depending on physiological state of the organism and anabolic processes (building of tissues)
- My own view that the uncertainty one includes encompasses all these concerns
- There are statistically phenomenological ways these can be predicted using phylogenetic regression using our package SIDER and people like Sebastien Lefebvre are working on more physiological mechanistic models that use body mass and metabolic rate to predict them.
Plot your data - 5a
Plot your data - Fry’s concerns - 5b
- Fry, B. 2013. Alternative approaches for solving underdetermined isotope mixing problems. MEPS.
- Brett, M. 2016. Resource polygon geometry predicts Bayesian stable isotope mixing model bias. MEPS.
- these are over-simplifications as we will see later in the course when we remember to look at the full posterior estimates and not just focus on the means
- Brett used simulations of only a single consumer to show that the prior dominates the solutions…
Include sources in an informed way - 6
Consider grouping sources - 7a
- Temptation might be to aggregate nearby sources (blue and green)
- Gain is to go from under- to fully-determined system (+/- the uncertainty)
- It falsely increases precision
- However in this case it could be justified as U. lactuca and Enteromorpha sp are actually the same species
Consider grouping sources - 7b
- better to aggregate after fitting a SIMM
- can gain remarkably increased precision about a less detailed question
Elemental concentration - 8a
- Not all sources have same concentration of elements
- Berries are nearly all carbon
- Flesh is mostly nitrogen
- Consuming equal proportions of each source by bulk mass can lead to more carbon influence from the carbon rich source
- Considering this concentration dependence can warp the mixing polygon
- Phillips & Koch. 2002. Incorporating concentration dependence in stable isotope mixing models
Isotope routing - 8b
- related to concentration dependence effects, once assimilated, different molecules get sent through different pathways en route to tissue formation.
- more of the assimilated carbon might go one route
- while more of the nitrogen might go elsewhere
- ultimately tissues can then end represented by up more or less of the carbon or nitrogen signal
- balance can be shifted by physiologicla state, such as reproduction, fasting or gorging.
- generally not well understood, so best advice is to pick appropriate discrimimation factor and add uncertainty
Incorporate uncertainty - 9
- Estimate mean consumer diet +/- error
- SIAR pushes this error to residual error
- MixSIR pushes it on the proportions
- Uncertainty on Sources
- specified as sd in SIAR / MixSIR
- can be estimated from data in MixSIAR
- Discrimination / Enrichment Factors
- specified as sd
- No errors on Concentrations in current formulations
Report distributions of results - 10a
- mode
- median
- mean
- credible intervals
Report distributions of results - 10a
- negative correlations imply inability to discern between sources
- consider a posteriori aggregation
- the negative correlation can shrink their combined variance
var(a+b) = var(a) + var(b) + 2*(cov(a,b))- positive correlations indicate solutions where increasing one source requires inclusion of another
- e.g. diametrically opposed sources
Limitations - 11
- Geometry of your data
- Biology
- The fitting algorithm
- convergence
- autocorrelation
- number of samples
New horizons - 12
- including other contraints
- p(1) > p(2) & p(1) > p(3)
- reconstruct entire food-webs: Kadoya, Osada & Takimoto. 2012. IsoWeb.
- amino acids
- better informed priors
- from e.g. DNA or abundance data
- detailed models of movement of elements through organisms: physiology & metabolism