Overview
This is a 4week 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  Description  Notes 
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
 NewtonRaphson'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 densitydependent 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 sumofsquares
 Coefficient of Determination
 Comparing model fits with the adjusted Coefficient of Determination


Lectures 8 and 9
Agestructured models

 Cohorts
 New population dynamics equation
 Death process
 Birth process
 Ricker and BevertonHolt models
 Solving for maximum R and S
 Construct a hypothetical agestructured bass population


Lectures 10 and 11
Lifehistory tables

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


Lecture 12
Life cycle graphs

 Life cycle graphs for age and stagebased 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

 Ageaggregated vs agestructured 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 todate


Lectures 19 and 20
Examples

 Using all the model together, work through some examples to put the course into context.

No notes 
Week  Description  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 stockrecruitment model using Solver
 Construct and agestructured model, with a stockrecruit relationship for densitydependence, to a hypothetical bass population.
 Evaluating different model fits to data


Practical 2
Matrix models

 Construct and example of 1) and agebased, and 2) a stagebased Leslie matrix model.


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