3 April 2026
Goals for today
- Identify features of data that drive analyses
- Think critically about what the data could tell you
General approach
Question \(\rightarrow\) Data \(\rightarrow\) Model \(\rightarrow\) Inference \(\rightarrow\) Prediction
General approach
Question \(\rightarrow\) Data \(\rightarrow\) Model \(\rightarrow\) Inference \(\rightarrow\) Prediction
Common questions in ecology
At the individual level
Sex?
Fecundity?
Growth?
Survival?
Movement?
Common questions in ecology
At the population level
Abundance?
Survival?
Spatial distribution?
Movement/migration?
General approach
Question \(\rightarrow\) Data \(\rightarrow\) Model \(\rightarrow\) Inference \(\rightarrow\) Prediction
Ecological data
At the individual level
1 Detection \(\rightarrow\) presence/absence
2+ Detections \(\rightarrow\) survival, movement
Ecological data
At the individual level
1 Detection \(\rightarrow\) presence/absence
2+ Detections \(\rightarrow\) survival, movement
1 Measurement \(\rightarrow\) fecundity, age, size
2+ Measurements \(\rightarrow\) growth
Ecological data
At the population level
Detections \(\rightarrow\) presence/absence
Counts \(\rightarrow\) density or survival/movement
Data collection methods
Nonexhaustive counts
Data collection methods
Exhaustive counts
Data collection methods
(Non)exhaustive surveys
Depletions
Data collection methods
(Non)exhaustive surveys
Depletions
Capture/Tag/Recapture
Data types
Discrete values
Sex
Age
Fecundity
Counts/Census
Survival (individual)
Data types
Continuous
Size (length, mass)
Density
Survival (population)
A note on continuous variables
Approximating rational numbers with real numbers
Survival (7 of 9 survived \(\approx\) 0.78)
Composition (4 age-3, 18 age-4, 11 age-5 \(\rightarrow\) ~55% age-4)
Density (3 animals in 21 ha plot \(\approx\) 0.14 per ha)
A note on continuous variables
Approximating rational numbers with real numbers
Which of these give you more confidence?
A) 3 / 9 \(\approx\) 0.33
B) 300 / 900 \(\approx\) 0.33
The importance of raw data cannot be overstated
Distributions of data
Discrete distributions
Binary (0,1) \(\rightarrow\) Bernoulli
Discrete distributions
Binary (0,1) \(\rightarrow\) Bernoulli
Count (non-negative integers) \(\rightarrow\) Poisson or Negative-Binomial
Discrete distributions
Binary (0,1) \(\rightarrow\) Bernoulli
Count (non-negative integers) \(\rightarrow\) Poisson or Negative-Binomial
Composition (length-D counts) \(\rightarrow\) Binomial (D = 2) or Multinomial (D > 2)
Continuous distributions
Density (non-negative real values) \(\rightarrow\) log-Normal or Gamma
Continuous distributions
Density (non-negative real values) \(\rightarrow\) log-Normal or Gamma
Proportion (length-D simplex) \(\rightarrow\) Beta (D = 2) or Dirichlet (D > 2)
Continuous distributions
Density \(\left(\mathbb{R}^{\geq}\right)\) \(\rightarrow\) log-Normal or Gamma
Proportion (simplex\(^D\)) \(\rightarrow\) Beta (D = 2) or Dirichlet (D > 2)
Transformations (real values) \(\rightarrow\) Normal