Overview
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 | Description | Notes |
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Lecture 1
Introduction to Population ecology and modelling
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Lecture 1 |
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Lectures 2 and 3
Mathematics revision
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- 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
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Lectures 2 and 3 |
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Lectures 4 and 5
Laws of population growth
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- Difference vs differential equations
- Deriving geometric and exponential models
- Doubling times
- Deriving density-dependent models – Logistic model
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Lectures 4 and 5 |
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Monday 6th October
Cancelled for a fieldtrip
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Lectures 6 and 7
Fitting models to data
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- The modelling process
- Introducing a generic loss function - the sum-of-squares
- Coefficient of Determination
- Comparing model fits with the adjusted Coefficient of Determination
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Lectures 8 and 9
Age-structured models
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- Cohorts
- New population dynamics equation
- Death process
- Birth process
- Ricker and Beverton-Holt models
- Solving for maximum R and S
- Construct a hypothetical age-structured bass population
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Lectures 10 and 11
Life-history tables
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- 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
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Lecture 12
Life cycle graphs
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- Life cycle graphs for age- and stage-based models with their mathematics
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Lecture 13
Linear algebra
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- An introduction to linear algebra
- Vectors and matrices
- Additon, multiplication and inverses
- Simultaneous equations
- Linear regression
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Lectures 14 and 15
Age- and stage structured matrix models
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- Leslie models
- Lefkovich models
- Estimating λ and stable age distribution
- Projecting over time
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Lectures 16 and 17
Harvesting populations
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- 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
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Lecture 18
Course synopsis
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- A quick overview of all the models in the course to-date
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Lectures 19 and 20
Examples
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- Using all the model together, work through some examples to put the course into context.
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No notes |
| Week | Description | Notes |
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Practical 1
Growth models
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- 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
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Practical 2
Matrix models
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- Construct and example of 1) and age-based, and 2) a stage-based Leslie matrix model.
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Last Modified: Fri, 05 Jun 2015 15:37:24 SAST
