Preliminaries: Our lexicon for the quarter

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Preliminaries Our lexicon for the quarter

• Models of science and hypothesis testing

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Ecology

• Ecology the relationship between organisms and
  the environment
• System (such as ecosystem) components tied
  together by regular interactions
• Structure measurable conditions of the system a
  single point in time
• Function processes that drive the system
• Environment the abiotic and biotic conditions
  under which interactions occur

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Models of Science

• Descriptive natural history
• Predictive modeling
• Hypothesis testing
• Bayesian likelihood models

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Descriptive Science

• Describing new species as we discovered new land
  masses
• The Human Genome Project
• Deep Space telescopes
• Voyages of Discovery

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Another model is Predictive modeling

• Examples Climate change, Astronomy
• When controlled experiments are impossible
• Observe pattern and infer
• Model systems and see if known parameters predict
  observed values

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Testing Hypotheses

• Observation and description
• Pattern analysis
• Natural experiments
• Manipulative experiments
• These progress from weak to strong inference
• And, generally, from specific to broad

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The phases of hypotheses

• The descriptive phase
• If herons prefer to eat fish, then we would
  expect herons to be more prevalent near water
  than far from water
• The functional phase
• If herons prefer fish to other types of prey than
  they should select these prey when offered a
  choice

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Types of hypotheses

• Simple qualitative propositions A is/has B
• Herons are strictly piscivores
• Consequence If A, then B
• If fed, herons will consume invertebrates
• Correlational The more A, the more/less B
• The higher the density of invertebrates, the
  higher the fraction of the heron diet
• Null A and B are unrelated / independent
• The abundance of fish is independent of the
  biomass of invertebrates consumed by heron

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The null hypothesis

• H0 Herons do not prefer habitats with fish over
  other habitats
• Ha herons are more frequent on habitats with
  fish (wetlands) than those without (uplands)
• Ha2 herons are more frequent on upland habitats
  than wetland habitats

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Introducing variability

• Testing hypotheses requires collecting data
• Data points have associated error
• Sampling error
• Natural variation
• Rejecting the null hypothesis requires asking
  whether the sets of observations differ by more
  than we would expect by chance
• This requires estimating variation and statistics

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The Popperian model of hypothesis testing

• We do not prove hypotheses true
• We only can collect data to reject hypotheses
• Rejecting all other plausible hypotheses leads us
  to infer that a particular hypothesis is true
• BUT, we cant know it is true because we may find
  that another plausible hypothesis exists, we just
  didnt think of it, or think it possible
• This insight is thanks to Karl Popper (1968)

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Bayesian model testing

• Relies on assessing the maximum likelihood model
  across a number of competing models
• Suggests that hypothesis testing casts science
  incorrectly by
• Implying that much of what we want to know is
  either black or white
• That truth is knowable
• That interactions are simple

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Experimental Design

• Experimental Units the entity to be manipulated
  (eg, the organism)
• Response variables unit to detect response of
  experimental treatment
• Treatments the amount of manipulation
• Control the unmanipulated treatment

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Attributes of the Experiment

• Replication number of repeated independent
  trials
• Independence How we determine whether replicates
  are really replicates (vs pseudo-replicates).
• Randomization A generally accepted means of
  insuring independence
• Variability The measure of how large the
  differences in response variables are within
  treatment groups.

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Error
Our test
F
T
Correct Type I Error Type II
Error Correct
T
Reality
F
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Lets try it out