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Interaction
•
"The whole is
other than the sum of its parts" (Aristotle, Metaphysics).
In the realm of applied mathematics and statistics, we would
regard the whole as a non-additive combination of its parts.
•
Interaction in
statistics
—
Consider Y= aX1+
bX2 versus Y= aX1+ bX2 + c(X1X2)
—
X1 and
X2 are two parts that determine the whole, Y, and a,
b and c determine the magnitudes of the effects of X1,
X2, and their non-additive interaction, X1X2,
respectively.
In statistics, this interaction is approximated
multiplicatively.
—
In the first
equation, the whole is determined by the sum of its parts (c = 0);
whereas, in the second equation, the whole is other than the sum
of its parts (c ≠ 0).
What's Science?
•
An attempt to
explain how the universe works
•
These explanations
(hypotheses) must be testable empirically
Scientific Method
•
Phenomenon:
something in nature that we wish to explain
•
Hypotheses:
educated guesses of cause and effect
•
Theory:
the conceptual framework within which our hypotheses are framed
•
Predictions:
logical deductions of our hypotheses (predictions must be
independent of the data or knowledge that went into formulating
our hypotheses)
•
Tests:
empirical falsification or verification of our predictions
Tinbergen's Four
Levels of Analyzing a Phenotypic Trait
·
Causation:
mechanisms. An analysis of the physiological mechanisms and
environmental mechanisms that give rise to a phenotype.
·
Ontogeny:
development. An analysis of all of the processes between genes and
the environment that go into the development of the phenotype.
Includes learning.
·
Survival
Value: An
analysis of how natural selection acts on the trait in question.
·
Evolution: phylogenetic
history. For example, do two species share a trait through common
ancestry or through convergent evolution?
Darwin's
Natural Selection
Natural
Selection: Directional,
Stabilizing and Disruptive Selection
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