### Population ecology

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.

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.

LectureDescriptionNotes

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
• 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

Examples

• 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.