Ecological Detective

Preface: Beyond the Null hypothesis

Tools of an Ecological Detective

Classic Hypothesis Testing

  • M~1~: Boom and bust (complete extinction between colonizations) hypothesis

  • M~2~: Constant prevalance of population but only is detected when certain conditions arise

  • H~0~: Model M1 is true
  • H~A~: Some other model is true

Outcome:

  1. M~2~ is rejected but M~1~ is not
  2. M~1~ is rejected but M~2~ is not
  3. M~1~ and M~2~ are rejected
  4. M~1~ and M~2~ are not rejected

What if 1 and 2 happen?

  • then you can move forward

What if 3 or 4 happen?

  • new hypothesis
  • collect more data
  • cry

Likelihood approach

  • You can begin directly comparing models together

  1. construct a measure of the probability of the observed data, given the model is true

    • $Pr{data|M_i}$

  2. Likelihood is a measure of the chance that the model is true given the data

    • $L_i{M_i|data}$

  3. Directly compare the likelihoods among competing models

    • $L_i{M_1|data} \gg L_i{M_2|data}$ . Model 1 is better supported than Model 2
    • $L_i{M_2|data} \gg L_i{M_1|data}$ . Model 2 is better supported than Model 1
    • $L_i{M_2|data} \approx L_i{M_1|data}$ . Models are equally supported or not supported given the data

Bayesian approach

  • Allows for the incorporation of prior knowledge into your models
    • “prior probability that M~i~ is true” - $p_i$
    • ‘You are not so smart’ podcast 073: Bayes Theorom

Tools for Ecological Detection

  1. Hypotheses: possible explanation of mechanics underlying your observations
  2. Data: your analyses and predictions are only as good as the data you collect
  3. Goodness of fit (gof): How well does your model predict the data. Comparison of models does not necessarily mean that they fit the data well
  4. Numerical procedures: Need to assess gof rapidly and efficiently

Chapter 2: The Scientific Method and Modelling

What are some attributes of ecological data, that make classical hypothesis testing difficult?

  • Non-normal: data comes from different distributions
  • Adequate sample size is difficult to collect
  • Hard to replicate
  • Hard to control the environment. Environment changes.
  • Long time scales: ecology and evolution operate at larger time frames

Distinguish between models and hypotheses

  • Hypothesis: “an unproved theory, proposition, supposition tentatively accepted to explain certain facts or to provide the basis for further investigation”
  • Theory: “a systematic statement of principles involved” or “a formulation of apparent relationships of certain observed phenomena”
  • Model: “a stylized representation or a general description used in analyzing or explaining something”

Hypothesis that birds forage more efficiently in flocks than individually

  • Model A: Consumption is proportional to flock size $C = \alpha S$
  • Model B: Consumption saturates as flock size increases $$
  • Model C: Consumption increases and then decreases with increasing flock size $$