Week 2 Equations

What type of growth equation is this?

discrete time Geometric population growth

What does this mean?

Population size at time t

What does this mean?

Population size at the next time step

What does this mean?

Lambda = finite rate of increase

How do you calculate Lambda?

N + birth rate - death rate

What type of growth equation is this?

Geometric

What does this mean?

Population at time zero

What does this mean?

y = lambda = finite growth rate

t = number of time intervals that have passed

What does this equation tell you?

Population size at time t

Using the previous equation if

What type of growth equation is this?

Continuous Exponential growth

What does r stand for?

Instantaneous growth rate

How do you calculate r ?

birth rate - death rate

At what value of r is the population stable at the initial population size (neither growing or declining).

r = 0 for stable population growth

What does this mean?

The rate of change of the population over time

What is this equation saying?

The rate at which the population grows is proportional to the size of the population

Using the previous equation

What do discrete time models look at?

population size in discrete time steps

Discrete growth shows population size changes after?

A specific event eg seasonal births or annual events

Continuous growth shows population size?

Continuously changing

What type of growth equation is this?

Exponential

so?

we have a higher growth rate

r is constant

Using this equation - Let’s say my ground squirrel population has 50 individuals this year (which we will call year 0) and we want to know how many individuals there will be next year, if we think the finite rate of increase will be 1.5, how many will we project there will be?

In reality, when I go back to the population in year 1, I find the population size to be

different from that I projected. I actually have 65 individuals when I return. What was the

finite rate of increase actually between year 0 and year 1?

65/50 = 1.3

Using the new finite rate of increase, without using the spreadsheet can

you think of a way to project my squirrel population from 50 individuals in year 0 to the

population size in year 50?

I set up a test tube with lots of food with 20 protists and wait 22.5 minutes. I think the intrinsic rate of

increase will be around 0.4 per minute. How many protists should I have in my test tube? First try with the

equations then check your answer on the spreadsheet