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.
Examples of models in biology
Species distribution models (SDMs)
In essence, empirical SDMs are correlative and can map the potential range of species based on the combination of environmental conditions from locations where they are known to occur.
Image from Ragnvald
Examples of models in biology
Species distribution models (SDMs)
Higgins et al. 2023 Science use a semi-mechanistic SDM which uses a plant growth model to interpret how plant species should respond to different environmental conditions.
The relationships between parameters are defined mechanistically, based on known equations, but the parameters themselves are estimated statistically from empirical data based on known localities of the species.
Examples of models in biology
DNA nucleotide substitution models
The probability of mutations between different base pair combinations are not equal. We now understand some of the mechanism behind this, and can account for unequal transition frequencies in our models of DNA evolution. From Yang and Rannala 2012 Nat Rev Genet
Examples of models in biology
Mechanistic general ecosystem models (GEMs)
Data management and computation
The volume, variety and velocity of biological and related data are ever increasing.
Quantitative biology is more than just modeling. A large part is developing the necessary tools and skills for managing and manipulating large and varied datasets.