1. Philosophy of science: the scientific method
How we understand the world
Science
A “method” for achieving this goal
Development of theory
Formulation of hypotheses - predictions
Tests of predictions
Design & Analysis
How we test predictions
of hypotheses
Statistics
Tool for quantitative tests

2. Definitions Theory: a set of ideas formulated to explain something
Hypothesis:
general – supposition or conjecture put forth in the form of a prediction according to a theory, observation, belief, or problem
specific – formulation of a general hypothesis for application to a specific test (observational OR experimental)
Null hypothesis: expected outcome if supposed mechanism
is not manifested (i.e. “no effect”)
Predictions: expected outcomes if both assumptions and conjecture are correct

3. Definitions (examples)
Theory: species distributions determined by dispersal of offspring
Hypothesis:
general – larval settlement of mussels determines adult distribution (i.e. is restricted to the area inhabited by adults)
specific – if we sample larval settlement of mussels in and out of adult distribution, then settlement will only occur within area inhabited by adults
Null hypothesis: if we sample larval settlement of mussels in and out of adult distribution, there will be no difference in settlement
Predictions: theory predicts that larval settlement will only occur where adults are

4. Definitions Induction (or inductive reasoning):
reasoning that general laws exist because particular
cases that seem to be examples of it exist
Deduction (or deductive reasoning):
reasoning that something must be true because it is a particular case of a general (universal) law known to be true
induction
specific
general
deduction
5 swans seen, all are white
all swans are white

5. Examples Induction (or inductive reasoning):
Every swan I have seen is white, therefore all swans are white
(if) (particular/observation), (then) (universal/ inference)
Deduction (or deductive reasoning):
All swans are white, therefore next swan I see will be white
(if) (universal/ theory), (then) (particular/observation)
“DIGS”: deductive is general to specific
Comparison:
1. Which is more testable? What if next swan is not white?
2. Which is normally used in everyday experience?
3. Which is more repeatable by different people?

6. Hypothetico-deductive reasoning
Deduction (or deductive reasoning):
formalized and popularized as basis of scientific method by Karl Popper (in readings)
Two phases: conception and assessment
Conception: how one comes up with a new idea or insight (“rules” of formulation are not obvious).
-- theory, observation, belief, problem
-- creative, difficult to teach, but often inductive!
Assessment: deductive phase, should be repeatable
Together, hypothetico-deductive reasoning

7. or experimental results
Hypothetico-deductive reasoning
Perceived Problem
I. Conception
Largely inductive reasoning
Previous Observations
Belief
*Note: General hypothesis
stated as alternative HA
to null HO
INSIGHT
Falsification
rejection
H rejected
H “supported (confirmed)” O A
Existing Theory
General hypothesis*
II. Assessment
Confirmation
H “supported (confirmed)”
H rejected O A
Specific hypotheses
Deductive reasoning
(and predictions)
Comparison with
new observations
or experimental results

8. Hypothetico-deductive reasoning Platt’s (1964) “Strong Inference”
Is there provision for “accepting” general hypothesis?
Why not?
Because it is easy to find confirmatory observations for almost any hypothesis, there is always the possibility of a negative result yet to be tested, and only one negative result refutes it absolutely
2) Propositions not subject to rejection (not falsifiable) are not “scientific”.
3) Progress made by repeated testing (rejection or confirmation) of alternative hypotheses until all reasonable ones have been tested (“last man standing”).

9. Example – Platt’s (1964) “Strong Inference”
Observation: discrete distributions of vegetation along elevation gradient (zonation) adjacent to Younger Lagoon
(S)
(R)
(A)
Anise (A)
100
percent
cover
Rush (R) 50
Salicornia (S) 2 4 6 8
elevation (m) above mean water level

10. Example – Platt’s (1964) “Strong Inference”
Observation: discrete distributions of vegetation along elevation gradient (zonation) adjacent to Younger Lagoon
Is there any existing theory to explain this pattern?
Limits of species distributions often set by their relative tolerance to physical factors:
-- water immersion
-- salinity
-- desiccation
-- soil characteristics
Insight: distribution limits set by tolerance to water immersion
General hypothesis: (HA) lower limit of rush set by tolerance to immersion
[alternatively, “null hypothesis” (Ho) of no effect of immersion on lower limit of rush distribution]

11. Example – Platt’s (1964) “Strong Inference”
General hypothesis: lower limit of rush set by tolerance to immersion
(alternatively, “null hypothesis” of no effect of immersion on lower limit of rush distribution)
Specific hypotheses:
Observational –
HA: average water level coincides with lower limit of rush;
Ho: no relationship between water level and lower limit.
Experimental –
HA rush plants transplanted to clearing below lower limit will die.
Ho: no difference in survival between transplants and controls

12. Example – Platt’s (1964) “Strong Inference”
4a) Test of prediction: repeatedly observe water levels and find that lower limit of rush coincides with mean water level ( confirm hypothesis that lower limit set by immersion).
Consider other tests (e.g., other species) of general hypothesis
4b) Test of prediction: repeatedly observe water levels and find that lower limit of rush does NOT coincide with mean water level ( reject hypothesis that lower limit set by immersion).
Consider other alternative hypotheses until you can’t reject one.
5a,b) Parallel results and conclusions from experimental tests of predictions – Why??
correlation vs. causation

13. Example – Platt’s (1964) “Strong Inference”
1) Observation (or theory)  Question
2) General hypothesis (question rephrased as testable statement)
3) Specific hypothesis (that state testable predictions that are directly related to how you would test the general hypothesis)
4) Test(s) of prediction(s)
confirm hypothesis  consider other tests of general hypothesis to possibly reject or further substantiate
reject hypothesis  consider other alternative hypotheses until you can’t reject one.

14. Problems
1) This process leads to “paradigms”, a way of thinking that has many followers, with great inertia. Contrary evidence considered an exception rather than evidence for falsification.
2) Some (e.g., Roughgarden) argue that this is not how we do science, but rather by building a convincing case of many different lines of evidence (i.e. inductive conception and assessment)
3) Others (e.g., Quinn & Dunham) argue that ecology, in particular, is too complex (many variables that interact with one another) to devise unequivocal tests.
Examples: importance of process (e.g., competition) is context dependent (e.g., environmental harshness or recruitment limitation)
4) In ecology, we’re often interested in relative effects and strengths of effects (rather than mere presence – absence of effects).

15. Rigorous Science Based on absolute or probability values
Rigorous Science Based on absolute or probability values? The linkage between Popperian science and statistical analysis

16. Absolute vs. measured differences
Philosophical underpinnings of Popperian Method is based on absolute differences
E.g., All swans are white, therefore the next swan I see will be white.
If the next
swan is not white, then the hypothesis is refuted absolutely. B)
Instead, most results are based on comparisons of measured variables
not really true vs. false but degree to which an effect exists (recall Quinn and Dunham)
Example
General or working hypothesis – larval settlement determines adult distribution -
Specific hypothesis – number of mussel larvae settling is higher in areas inside the adult distribution than in areas outside it
Observation 1:
Number outside 10 15 18 12 13
Mean
Observation 2:
Number outside
Number inside 3 10 5 7 2 9 8 12
Mean
9.2
Number inside
What counts as a difference?
Are these different?