What is quanitative biology?
- models (maths and stats)
- data
- computation
Models
Models are simplified reconstructions of reality
How realistic do models need to be?
It depends on your question/objective…
Empirical vs mechanistic model continuum
Many models are intermediate on the continuum, incorporating mechanistic understanding, but still relying on statistical approaches and data.
Empirical approach
How does the speed of a car (or animal) affect the distance needed to stop?
Some data collected earlier…
Empirical approach
How does the speed of a car (or animal) affect the distance needed to stop?
Data showing a linear model of \(d_i = \beta_0 + \beta_1 \times v_i + \epsilon_i, \epsilon_i \sim N(0, \sigma)\), where \(d\) is the distance and \(v\) is the velocity.
Empirical approach
How does the speed of a car (or animal) affect the distance needed to stop?
Data showing a linear model of \(d_i = \beta_0 + \beta_1 \times v_i + \epsilon_i, \epsilon_i \sim N(0, \sigma)\), where \(d\) is the distance and \(v\) is the velocity.
Empirical approach
How does the speed of a car (or animal) affect the distance needed to stop?
Data showing a quadratic model of \(d_i = \frac{v_i^2}{2a} + \epsilon_i, \epsilon_i \sim N(0, \sigma)\), where \(d\) is the distance, \(v\) is the velocity and \(a\) is the friction coefficient multiplied by acceleration.
Mechanistic approach
How does the speed of a car (or animal) affect the distance needed to stop?
From physics first principles we know the stopping distance formula: \(d = \frac{v^2}{2a}\), where \(d\) is distance, \(v\) is velocity and \(a\) is the friction coefficient multiplied by acceleration.