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New Methods in Ecology

New Methods in Ecology. Complex statistical tests, and why we should be cautious!. Complex tests. Logistic Regression Principal Components Analysis Cluster Analysis. Multivariate. Multi variate tests mean you have a single explanatory variable, but multiple response variables.

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New Methods in Ecology

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  1. New Methods in Ecology Complexstatistical tests, and why we should be cautious!

  2. Complextests • Logistic Regression • Principal Components Analysis • Cluster Analysis Multivariate • Multivariatetests mean you have a single explanatory variable, but multiple response variables.

  3. Logistic Regression

  4. Logistic Regression Insects were exposed to a pesticide to determine the effectiveness of the treatment. The response is dead individuals from a sample

  5. Linear regression on the proportions killed vs dose P(kill) = ax + b dose At dose 0, Proportion killed is less than 0 (negative deaths?) and greater than dose 4, get > 100% mortality!

  6. Need to ensure the model is bounded by 0 and 1, build a new equation P(kill) dose No longer have impossible predictions, and the model fits better

  7. Can now look at what proportion would be killed at a particular dosage P(kill) dose

  8. Logistic regression issues… • Implementing and coding the model can be difficult • Can be tough to work through the equation • Is it easier to design around the issue? • Use the same number in each batch, use “number dead” as the response variable?

  9. Multivariate Statistics • Single explanatory variable, multiple response variables • Multivariate tests can be useful and insightful • Can be deeply confusing • Very often misused • Difficult to explain the results • Used to mask bad designs, confuse/impress stupid people.

  10. Parrots in Bonaire Sam Williams www.parrotwatch.org Sam collected a load of data on different aspects of the birds’ biology

  11. Parrots in Bonaire • What to do with all this? • 1 descriptive variable (nest) • Multiple response variables • Principal component analysis…

  12. Principal Component Analysis • Obtains values for as many principle components as there are response variables • Each PC accounts for some more of the total variation • Each nest has a PC value for each PC • Each response variable has a rotation value for each PC • What do these PC values and rotation values relate to? • God knows

  13. Principal Component Output Principle Component Scree plot, first few Principal components account for much of the variation

  14. Principal Component Output Biplot of the first 2 principle components Can be used to look for correlations Some significance tests(redundancy analysis) Lots of noise!

  15. Other use of PCA • each nest/individual/replicate has a value of each Principal component • Can use these values as a response variable, and subject to other tests • Called “Dimensionality Reduction”

  16. Salmon Genomics and Survival • Gene expression data for ~16000 genes, from ~300 fish. • Each fish is a replicate, each gene is a response variable

  17. Salmon Genomics and Survival • 16000 genes is lot of data, and a lot of variation. • Do a PCA on the genes, use the PC values as a response variable • Reduces the dimension of the data, rather than 16000 response variables, now have 1 (PC1, or PC2) • Can then use this in other tests.

  18. Salmon Genomics and Survival Principle component • Related value of PC1 to survival of the fish, showed a correlation for one stock

  19. Salmon Genomics and Survival Scotch Chilko Adams Proportion surviving days • Condensed the gene expression data into something useable • Method insanely complex and computer intensive • Still don’t really know what PC1 is!

  20. Cluster Analysis • Like PCA, a multivariate method • Unlike PCA, looks for patterns within the data • Produces a hierarchical cluster • Groups similar individuals together • Unsupervised • Have to then decide where groups lie • Try and relate the grouping to something else?

  21. Cluster Analysis

  22. Multivariate Summary • Multivariate statistics are useful for data mining • Often used when data collection was done improperly/you’ve been given data sets • Can indicate how to proceed • Can be very messy • Totally opposite to the a priori “carry out an experiment to test a hypothesis” idea.

  23. Complex stats Summary • Can be very useful and insightful if used properly • More complex doesn’t necessarily mean better • Can be difficult to interpret • Remember the golden rule – know how to analyse the type of data you will collect, before you collect it!

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