on the analysis of relative abundances in ecogenomics - david lovell

… in ecogenomics

On the analysisof relative abundances

David Lovell, Vera Pawlowsky-Glahn and Juan José EgozcueEcogenomics from Data to Knowledge| Canberra | 14 February 2014

CSIRO COMPUTATIONAL INFORMATICS

…but perhaps “too much” if you don’t like maths Logarithms Variances Slope of a regression line Goodness-of-fit of a regression line

This presentation is meant for everyone: stop me if I’ve lost you!

Warning!There will be a little maths… not a lot…

On the analysis of relative abundances | David Lovell |

Logarithms… turn multiplication into addition of exponents



Variance… measures how far a set of numbers is spread out


less variance more variance


Slope and goodness of fit…What line best fits the points? And how close are the points to it?



…conclusions that are about the Universe …not artefacts of the way we have observed it

MotivationWant to draw sound conclusions from our observations


How can you tell if you’re measuring relative information? “Would doubling the amount of starting material double my measurements?”

Different steps in measurement can render data relative Sample preparation– obtaining a fixed mass and concentration of nucleic acid for further analysis– “We typically request that users provide us with 11 μg of total

RNA/sample (at a concentration of 1.25 μg/uL)”– “This protocol is optimized for 0.1–4 μg of total RNA…”

Measurement platform– “How many reads in a typical DNA/RNA-seq experiment?

A typical read count… may have hundreds of millions”http://www.vlsci.org.au/lscc/rna-seq

– A large, but finite amount… what would doubling the starting material do?

Motivation – more specificA lot of bioscience data carry only relative information


http://www.vlsci.org.au/lscc/rna-seq

Question to the audience: How often is about absolute microbial abundance observed or estimated?– Microbes per gram of soil?– Microbes per litre of seawater?

Motivation – more specificA lot of bioscience data carry only relative information


Relative data needs to be analysed and interpreteddifferently to absolute data Forget that, and you can easily draw the wrong conclusions from your data

A lot of bioscience data are relativeSo what?


I will Show you why correlation is not appropriate for relative data Give you an alternative measure of association that can be used confidently

The focus of this talk: correlationA workhorse of bioinformatics and quantitative bioscience


1. Spurious correlation

2. Geometry of relative data

3. Real-life examples of yeasty goodness from the Bähler Lab

Correlation for relative data?Three nails in its coffin


Ingredients Three (3) statistically independent variables x, y and z– Note that the correlation between x and y should be about zero

Method Form the ratios x/z and y/z Plot the ratios against each other Watch correlation magically appear

Serves… This recipe has served entire research disciplines for some years,

despite Karl Pearson’s warning in 1896

For a demonstration… See http://en.wikipedia.org/wiki/Spurious_correlation

Nail #1: Spurious correlationA recipe for disaster


http://en.wikipedia.org/wiki/Spurious_correlation

Spurious correlation in actionCooking the books

Have you got things in proportion? | David Lovell |

Imagine we’ve measured the relative abundance of some microbes We have made measurements in seven different samples Let’s focus in on the relationship between microbe1 and microbe2

Nail #2: Geometry of relative data



40%

30%

Sample #1


37.5%

35%

Sample #2


35%

40%

Sample #3


32.5%

45%

Sample #4


30%

50%

Sample #5


27.5%

55%

Sample #6


25%

60%

Sample #7


What do these pairs of relative abundancestell us about the relationship between

the absolute numbersof microbe1 and microbe2

in the seven environments sampled?


If the numbers of microbe1 increase,what are the numbers of microbe2

likely to do?


Hint:each pair of relative values

comes from a pair of absolute valuesthat lie on the ray from the origin


Correlations between relative values tell us nothing about the relationships betweenthe absolute values that gave rise to them



…unless total abundance is constant



…unless total abundance is constantOR

the pairs of relative values are proportional

ProportionalityA meaningful measure of association for relative data

yxt

y

t

x



When pairs of relative valuesstay in proportion across samples

so do their corresponding absolute values


When pairs of relative valuesstay in proportion across samples

so do their corresponding absolute values

…when we work with relative valueswe lose the ability to infer correlations,but we can still infer proportionalities

Q: How do we measure proportionality?A: Use a log-log plot

natural scale log-log scale

Pairs of values that behave proportionallyfit a line of slope 1

(i.e., 45°)on a log-log scale


slope ( ) in degrees

proportion of variance explained (r2 )



rxyx 21 2 )var(log)/var(log

() r21 2

The data: expression levels of over 3000 yeast genes over a 16-point time course …ok, so this is not ecogenomic data– But imagine this is about the abundance of 3000 OTUs

in 16 different samples

Total abundance is anything but constant

Nail #3: Real-life examplesYeasty goodness from the Bähler Lab



145 i.e.,1 at

of minimum2 r

y)xφ(

),(

log,log

Let’s not.

Instead, let’s bin the values of slope and r2

for all 30313030/2 pairs of mRNA

and show the counts on a heatmap

How does this look for yeast?…let’s plot the slope and r2 for 4.5 million pairs of mRNAs… yay!



)log,(log yxof contours 0.05 and 0.025

We have been working with Human Microbiome Data this summer Dang! There’s a lot of zeros– Zeros… the natural enemy of the logarithm

Also there are a lot of small counts: 1, 2, 3…– Counts (integers ≥ 0) do not carry only relative information– Expected counts do (reals ≥ 0)

Yes there are measures of association or dissimilarity that “handle” these data– Bray-Curtis, UniFrac…– But what reliable inferences can you make when OTUs play hide and seek?

Also this summer I have been become deeply suspicious of the practical value of null hypothesis

significance testing (p-values)– Esp., “statistically significant correlation coefficients”

Challenges with ecogenomic dataCan we make sense of microbial relative abundance?


Jürg Bähler and Sam Marguerat for data and wisdom on yeast The Spanish Government for supporting VP-G and JJE’s collaboration with DL Jack Simpson and Lauren Bragg for helping to make sense of microbes this summer Karoline Faust and co-authors for graciously providing the data matrices from– Faust, Karoline, J. Fah Sathirapongsasuti, Jacques Izard, Nicola Segata, Dirk Gevers, Jeroen Raes,

and Curtis Huttenhower. “Microbial Co-Occurrence Relationships in the Human Microbiome.” PLoS Comput Biol 8(7) (2012)

David Warton and co-authors for an excellent paper on Standardised Major Axis fitting– Warton, David I., Ian J. Wright, Daniel S. Falster, and Mark Westoby. 2006. “Bivariate Line-fitting

Methods for Allometry.” Biological Reviews 81 (2): 259–291. The R Core Team and developers of R packages including– Daniel Adler, Duncan Murdoch, Yihui Xie, Hadley Wickham,

Gerald van den Boogaart and Raimon Tolosano-Delgado Rachel, Felix and Ava (my wife and kids) for putting up with me on 5 hours sleep for

weeks on end

Thanks and acknowledgements


Thank youCSIRO Transformational BiologyDavid LovellBioinformatics and Analytics Leader t +61 2 6216 7042e [email protected] www.csiro.au/people/David.Lovell

CSIRO MATHEMATICS, INFORMATICS AND STATISTICS

on the analysis of relative abundances in ecogenomics - david lovell

Science

relative information

pairs of relative abundances

geometry of relative

relative data needs

spurious correlation

lot of bioscience data

absolute data

correlation nail