Introductions

I can start this off. Then we can go around the room, thinking about


Syllabus

Work through syllabus, clarify structure, etc.


Course website

Go through the course website and make sure everyone has easy access and is clear on how to get the lecture notes, readings, and homeworks.


Notes


What is theoretical ecology?

Ecology: study of species interactions

Theory: Body of evidence linking a general explanation to a commonly observed phenomenon

Theoretical ecology attempts to explain patterns observed in nature through generalized models


Models

Statistical model: A model exploring the statistical relationships between a response and some set of predictor variables.

e.g., linear regression


What is the relationship betwen sepal length and sepal length in irises?

data(iris)
mod <- glm(iris$Sepal.Length ~ iris$Sepal.Width)
plot(iris$Sepal.Length ~ iris$Sepal.Width, 
  col=1:3[as.numeric(iris$Species)])
abline(mod)


Phenomenological model: A model describing some phenomenon, often independent of any data.

e.g., exponential growth


Population dynamics with exponential growth

\[ N_{t+1} = N_t \lambda \]

expoGrowth <- function(n, lambda=1.25, times=100){
  nt <- c(n)
  for(i in 1:times){
    nt[i+1] <- nt[i] * lambda
  }
  return(nt)
}

plot(expoGrowth(10), type='l', ylab='Population size', 
  xlab='Time', lwd=2)
lines(expoGrowth(10, lambda=2), col='dodgerblue', lwd=2)


This course will focus pretty much entirely on phenomenological models (as I have defined them)

Also, evolutionary models do not really get emphasized in this book, but this could be good fodder for your paper summaries or final projects if you are interested


Why theoretical ecology?

Observation: some set of ecological processes is causing this population to cycle

Conclusion: this population is cycling

Theory: which of the cycle-generating processes could cause cycles?

Generation of novel question: can models create cycles under processes with different ‘strengths’?


Why theoretical ecology?

Population model: Ricker model to explore population dynamics and the role of demographic/environmental stochasticity

Experiment: fit models to experimental data and find demographic stochasticity important in controlled laboratory experiments

Observation: fit models to empirical time series to explore the relative importance of demographic and environmental stochasticity in natural systems


Why theoretical ecology?


Why theoretical ecology?


Barriers to a more theory-rich discipline

https://www.cell.com/trends/ecology-evolution/fulltext/S0169-5347(19)30171-5


The promise of theory in ecology

‘To do science is to search for repeated patterns… The best person to do this [in ecology] is the naturalist who loves to note changes in bird life up a mountainside, or changes in plant life from mainland to island, or changes in butterflies from temperate to tropics’ - Robert MacArthur

note: I 100% disagree with the assertion that there is a ‘best’ type of ecologist, and that the ‘best’ type would be a naturalist


Patterns without theory can be deceiving

distribution of birds in Bismarck Archipelago
distribution of birds in Bismarck Archipelago

https://esajournals.onlinelibrary.wiley.com/doi/10.1890/14-1848.1

Where did Diamond go wrong?


Theory requires tests

There is an inherent feedback in developing some conceptual theory based on observations, and then testing this theory in different locations or in experimental trials.


Breaking the training divide

https://www.cell.com/trends/ecology-evolution/fulltext/S0169-5347(19)30171-5


So, you’re like a ‘modeler’?

https://royalsocietypublishing.org/doi/10.1098/rsfs.2012.0008

https://www.journals.uchicago.edu/doi/pdfplus/10.1086/717206


Discussion

Codling and Dumbrell. 2012. Mathematical and theoretical ecology:linking models with ecological processes. Interface doi:10.1098/rsfs.2012.0008

Note:


The paper was written over a decade ago. In what ways do you think things have changed in the field?


What were your reactions when you read this?

“Without ecological theory, collecting data is a futile and meaningless endeavour. Likewise, producing elegantand beautiful mathematical models of ecological systems without validation against real data is an empty achievement”.


Simplifying assumptions and the mean-field approximation


Generating testable predictions


Lines in the sand

Broadly speaking, ecological models can be split into two separate categories; simplistic mathematical models, which offer analytically tractable solutions and the examination of the underlying model properties, and more complex simulation-based models (cannot be solved analytically)


Role of stochastic processes

Ecological systems are very different from physical and chemical systems, notably containing more uncertainty and chaotic dynamics, and are often influenced by stochastic processes.

To what extent can models incorporate either/or of these processes, allowing theory to easily bridge this data-model divide the authors try to emphasize?


Ecology in the absence of theory

After all, without theory providing testable hypotheses, ecology could become nothing more than data collection for its own sake