Population ecology


This is a 4-week module for the Ichthyology 302 course.  It comprises of 19 lectures and 2 practical sessions.

Formative assessment will be via the practical assignments and summative assessment will be from a final exam in November. As the module is 2/3rd of the fourth term, it will count 2/3rd of Paper 2 in the November examination.

Reading and references

These lectures are based on the following texts that are all in the library.

  • Begon, M., Mortimer, M. & Thompson, D.J. 1996. Population ecology: a unified study of animals an plants. 3rd edition. Blackwell Science.
  • Neal, D. 2004. Introduction to population biology. Cambridge University Press
  • Quinn, T.J. & Deriso, R.B. 1999. Quantitative fish dynamics. Oxford University Press
  • Rockwood, L.L. 2006. Introduction to population ecology. Blackwell Publishing.
  • Vandermeer, J.H. & Goldberg, D.E. 2003. Population ecology : first principles. Princeton University Press.




Lecture 1

Introduction to Population ecology and modelling

  Lecture 1

Lectures 2 and 3

Mathematics revision

  • Logarithms and exponents
  • Basic differential and integral calculus (incl. logs and exps)
  • Finding the maximum/minimum value(s) of a funcion
  • Newton-Raphson's method finding roots
Lectures 2 and 3

Lectures 4  and 5

Laws of population growth

  • Difference vs differential equations
  • Deriving geometric and exponential models
  • Doubling times
  • Deriving density-dependent models – Logistic model
Lectures 4 and 5

Monday 6th October 

Cancelled for a fieldtrip


Lectures 6 and 7 

Fitting models to data

  • The modelling process
  • Introducing a generic loss function - the sum-of-squares
  • Coefficient of Determination
  • Comparing model fits with the adjusted Coefficient of Determination

Lectures 8 and 9

Age-structured models

  • Cohorts
  • New population dynamics equation
  • Death process
    • Exponential decay model
  • Birth process
    • Ricker and Beverton-Holt models
    • Solving for maximum R and S
  • Construct a hypothetical age-structured bass population

Lectures 10 and 11

Life-history tables

  • Cohort-based life history tables
  • Survivorship curves - Type 1,2 and 3
  • Fecundity schedules
  • Information obtained:
    • Intrinsic rate of increase – Euler-Lotka equation
    • Mean generation time
    • Expected lifespan
    • Net reproductive output
    • Stable age structure 

Lecture 12

Life cycle graphs

  • Life cycle graphs for age- and stage-based models with their mathematics 

Lecture 13

Linear algebra

  • An introduction to linear algebra
  • Vectors and matrices
  • Additon, multiplication and inverses
  • Simultaneous equations
  • Linear regression

Lectures 14 and 15

Age- and stage structured matrix models

  • Leslie models
  • Lefkovich models
  • Estimating λ and stable age distribution
  • Projecting over time

Lectures 16 and 17

Harvesting populations

  • Age-aggregated vs age-structured models
  • Replacement vs equilibrium yield
  • General method for determining maximum harvest under equilibrium conditions
  • Baranov’s catch equation
  • Estimating yield from a cohort

Lecture 18

Course synopsis

  • A quick overview of all the models in the course to-date

Lectures 19 and 20


  • Using all the model together, work through some examples to put the course into context.
No notes



WeekDescription Notes

Practical 1

Growth models

  • Fitting linear regression to data via Solver 
  • Fit a logistic model to a paramecium dataset using Solver 
  • Fit a Ricker stock-recruitment model using Solver 
  • Construct and age-structured model, with a stock-recruit relationship for density-dependence, to a hypothetical bass population.
  • Evaluating different model fits to data


Practical 2

Matrix models

  • Construct and example of 1) and age-based, and 2) a stage-based Leslie matrix model.




Last Modified: Fri, 05 Jun 2015 15:37:24 SAST