Statistical Models for Biology BIO 415 and BIO 514
Lecturer: TAs: ,
What is this class about?
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The application of statistical analysis to biological data
Introduction to statistical inference
• A deduction is any statement about nature that derives from a theory (often via mathematical reasoning).
• An induction is any statement coming from observations that could change our theories about how nature works.
The structure of scientific reasoning
Theories about the (unknown) real world
Induction (or Inference)
Observations (data)
Deduction and induction applied to senescence
The Rate of Living theory predicts inverse relation between metabolic rate and lifespan.
Observation
Large animals live longer, and they also have lower metabolic rates.
When separated from size, metabolic rate is a poor predictor of lifespan.
This theory can be tested by comparing populations of the
same species living in different environments.
Evolutionary Senescence Theory predicts that animals with high predation threat senesce faster.
Deduction: Opossums under higher predation threat senesce faster
Virginia opossum
Mainland opossums have many predators
Sapelo island opossums have few predators
This conclusion is deduced from Evolutionary Senescence Theory.
Induction: Measure average lifespan of 30 island and 30 mainland opossums.
Mainland average Island average lifespan is 48 months lifespan is 54 months
Question 1
On the mainland (many predators) average lifespan is 48 months.
On the island (few predators) average lifespan is 54 months.
Based on these data, is lifespan shorter when predation threat is high ?
A. Yes B. No
Randomness in observations makes induction difficult
A deterministic process always produces the same outcome (rare to non-existent in nature)
A random process is not perfectly predictable (typical in nature).
The average lifespan of a sample of opossums results from a random process
• Even if Evolutionary Senescence Theory is incorrect, average lifespan will not always be the same.
• Even if Evolutionary Senescence Theory is correct, average lifespan will not always differ.
Question 1
On the mainland (many predators) average lifespan is 48 months.
On the island (few predators) average lifespan is 54 months.
Based on these data, is lifespan shorter when predation threat is high ?
A good answer can only be given using
B. No statistics, to be taught in this class.
the methods of probability and
In the presence of randomness…
Deductions are statements about probability: i.e., quantitative measures of our certainty that an event will occur.
In the presence of randomness…
Induction relies on statistics: the method of saying something about the real world based on observations influenced by randomness.
The structure of scientific reasoning
Theories about the (unknown) real world
(Probability)
Induction (or Inference)
(Statistics)
Observations (data)
Outline of statistical reasoning
Two hypotheses:
Hypothesis 1: Predation has no effect on senescence
Hypothesis 2: Higher predation leads to faster senescence
Should we reject Hypothesis 1 in favor of Hypothesis 2?
Do animals that experience high levels of predation evolve shorter lifespans than animals that do not?
Answer by studying effect of predation on opossum lifespan.
To find out, measure the difference in average lifespan for 30 mainland and 30 island opossums.
Mainland opossums have many predators
Sapelo island opossums have few predators
Before gathering data, make a deduction
• Step 1: Assume (temporarily) that the simple hypothesis (no effect of predation on senescence) is true.
• Step 2: Under this simple hypothesis, calculate the probabilities of all possible outcomes for the data.
Results of probability calculations (assuming no difference in lifespan)
Mainland opossums Island opossums live longer live longer
We gather data: island lifespan is 6 months longer than mainland lifespan
Observed lifespan difference
Mainland opossums Island opossums live longer live longer
If there is no difference in senescence, what is the probability of seeing a difference this great or greater?
The shaded area gives the probability
Observed lifespan difference
If there is no difference in senescence, what is the probability of seeing a difference this great or greater?
The shaded area gives the probability
Observed lifespan difference
The probability is quite low: only 2.9%
A difference of 6 months is a surprising result, if there is no true difference in senescence
• How surprising? Only a 2.9% chance of a difference this great or greater.
• If this is too surprising, you can reject the hypothesis of no difference in favor of the hypothesis of longer island lifespans.
• You might be wrong!
Two key points
• Statistical inference is not possible without first carrying out a deductive probability calculation.
• No statistical inference is completely certain. Randomness might lead us to a wrong conclusion.
The structure of scientific reasoning
Theories about the (unknown) real world
(Probability)
Induction (or Inference)
(Statistics)
Observations (data)
• Statistics is about inference from random phenomena to say something about the real world.
• Statistics requires first deducing probabilities on the basis of some theory about the real world.
• No statistical inference is 100% correct.
Course objectives and administration
Learning goals
• Useprobabilityandstatisticstoreasonaboutthenaturalworld.
• PerformstatisticalanalysesusingthesoftwareenvironmentR.
• Usedatatoestimateparametersthatcharacterizebiological phenomena of interest.
• Performrigoroustestsofhypothesesaboutparameters.
• Choosethemostappropriatestatisticalmethodforadata
analysis problem.
• Writecompleteandconcisereportsoftheresultsofstatistical analyses.
• Recognizeandavoidpracticesthatleadtoinaccuratestatistical claims.
Course components
• Lectures: STPV 324; Recordings will be posted on Canvas
• Labs: LSE 236
Class communication
• Email questions to me or TAs
• Office hours in-person or via Zoom
• Receive and turn in assignments
• Take quizzes and final exam
• View lecture slides and recordings
Exams and quizzes
• Five online quizzes throughout the semester. • One online final exam.
• Two take-home exams (only one for BIO 514).
Independent project (BIO 514 only)
• Statistically analyze data of your choice to answer a biological question.
• Apply the skills learned in class.
• Mostly done in the latter half of the semester.
Recommended textbook
• The Analysis of Biological Data, Whitlock & Schluter.
• Reading assignments posted on Canvas.
• Two copies on reserve in Noble.
Any edition is OK (1st, 2nd, or 3rd)
Assessment: BIO 415
Lab reports
400 (40 per report)
200 (40 per quiz)
Take-home exam 1
Take-home exam 2
Final exam
50 (~0.5 per question)
Assessment: BIO 514
Lab reports
400 (40 per report)
200 (40 per quiz)
Take-home exam 1
Independent project
Final exam
50 (~0.5 per question)
R: A software environment for statistics and graphics
• Advantages of R
• Works on all platforms (Mac, Windows, Linux…).
• Can do virtually any statistical procedure.
• Powerful graphics.
• Script-based: Easy to save, edit, and re-use analyses.
• Challenges of R
• Script-based: Must learn the R language.
Office hours
• Can attend in person (ISTB1 304)…
• …or via Zoom (link on Canvas site)
• See Canvas for specific dates and times
• TAs will also hold regular office hours
Things to do by next week
• Read the syllabus (and take the quiz). • Register for iClicker.
• Download and install R and RStudio.
• Complete the first day survey.
• Labs start next week.
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