Class Notes (1,100,000)

CA (620,000)

UTSG (50,000)

BIO (2,000)

BIO220H1 (200)

John Stinchcombe (70)

Lecture 5

# BIO220H1 Lecture Notes - Lecture 5: Exponential Growth, Logistic Function, Inflection Point

by OC307239

Department

BiologyCourse Code

BIO220H1Professor

John StinchcombeLecture

5This

**preview**shows pages 1-2. to view the full**7 pages of the document.**Lecture 5: Ecology and Evolution of Harvested Population

Humans harvesting biodiversity

We need to acquire energy from natural/man systems

Some of the energy from these systems are being diverted from us (for our

consumption)

Taking energy out of naturally occurring energy ows

In agriculture completely modify environment

oSet it up to suit us

oEnergy from sun converted into crops/domesticated animals for food

We need to consume for energy so some harvesting is inevitable for living

organisms to survive

What does this do to ecology and evolution of harvested species?

And because it’s inevitable can we prevent bad results

Outline

1. Simple models of species growth and harvesting strategies

a. Apply population growth models to understand optimal harvesting

strategies

2. How harvesting a*ects demographic of harvested species

3. Next lecture: How harvesting a*ects evolution of species that we manage and

we depend on

(1) The general rule

Aim is to harvest out the recruitment and leave the stock alone

oImagine population of species we want to manage

oThat population will be growing at some rate per year

oOnly want to harvest out growth and leave population to regenerate

oRecruitment = new additions to populations

O*spring

Maturing o*spring

Stock:

oCurrent population

So if can take out new additions only and leave stock (current population) the

way it is have potential to have self-perpetuating resources

Simple model for how populations grow

Logistic growth equation

oChange in number of individuals per unit time (dN/dt) is equal to product

to 3 terms:

R: Intrinsic population growth rate

How fast species can begin reproducing and regenerate

N: Number of individuals currently in population

Term in brackets

odN = change in abundance

odt = change in time

oso dN/dt is a rate (rate of change of population over time)

oK is the carrying capacity

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Graph of equation:

oCurrent population size as function of time

oEarly phases: Exponential growth

oAs more and more individuals = reach asymptote at K

oHave inection point

Below K/2, have exponential growth

Above K, have slowing of growth rate = fewer individuals produced

per unit time

Clicker Question

Which of statements are correct?

(1) As N → K, dN/dt →0 (correct)

(2) As N→0, dN/dt → exponential growth (As N is close to 0, then get rN which is

exponential growth) (correct)

(3) If r<0, dN/dt < 0 (correct)

Density-dependent growth rate can limit population size

Graph shows number of birds against time

As islands are colonized by terns

oTern carrying capacity on islands limited by nesting space

At >rst have exponential growth, then levels o* (Bird Island)

Ram island has highest carrying capacity

oStill in exponential growth phase

Using logistic curves to predict response of harvesting

Time of harvest on horizontal axis

Size of population in terms of K on vertical axis

Each vertical line represents a harvest season

At top arrows, if harvest up to there, then next generation population will grow

back to where it was

oHarvest down a bit, then it regrows

oBut since population close to K, overall rate of population growth is not

high

Don’t harvest a lot, it recovers but not a lot of recruitment because already close

to K

Same at bottom arrows

oRate of growth is quick but staggers up

How much we should harvest down to get maximum rate of growth?

oAt 50% of K slope of graph is the steepest (inection point)

If solve equation for maximum growth rate, will get K/2

So ideal situation:

oIf population is at K

oHarvest it down to K/2

Brings population down to density where it’s rate of growth is

maximized

Keeps population at region where rate of population growth is the

maximum

Bene>cial to us:

###### You're Reading a Preview

Unlock to view full version