# Biology

Population Growth

Lecture 12 ∙ October 11, 2018

1

Announcements

Exam Tuesday

Bring scantron, #2 pencil

No other tools/notes allowed

Review session Monday 6-8pm, HH 320

Peer Reviews due Tuesday at start of class

2

Study tips

Review the objectives from each lecture, make sure you can meet each objective

Practice interpreting life tables, survivorship curves, and population growth curves

Go over the problem sets

today’s objectives

Interpret population growth rate from a life table

Infer life history traits from a population growth curve

Predict population growth patterns based on life history traits

4

Previous population size (Nt-1)

Number of births (B)

Number of deaths (D)

Number of immigrants/joiners(I)

Number that emigrate/leave (E)

What processes determine current population size (Nt)?

Population dynamics

Nt = Nt-1 + (B-D) + (I-E)

5

Previous population size (Nt-1)

Number of births (B)

Number of deaths (D)

Number of immigrants/joiners(I)

Number that emigrate/leave (E)

What processes determine current population size (Nt)?

Population dynamics

Nt = Nt-1 + (B-D) + (I-E)

What effects the rate of change?

6

The answers to this questions help us:

Protect biodiversity through conservation efforts

Mitigate harmful effects of human population growth

Understand why certain populations are declining

Understand how organisms interact with each other and their environments to predict the impact of environmental change

What processes determine future population size?

Population dynamics

7

Two kinds of life table are useful

Cohort (dynamic) life table – good for plants and other

sessile organisms

Survivorship patterns

You fill in these, calculate the rest

Survivorship from one period to the next: 0.625/0.857 = 0.729

Mortality from one period to the next: 1 – 0.857 = 0.729

mx

8

Two kinds of life table are useful

Cohort (dynamic) life table – good for plants and other

sessile organisms

Survivorship patterns

You fill in these, calculate the rest

Survivorship from one period to the next: 0.064/0.171 = 0.374

Mortality from one period to the next: 1 – 0.456 = 0.544

# alive / # started in cohort

527/843 = 0.625

mx

9

Two kinds of life table are useful

Cohort (dynamic) life table – good for plants and other

sessile organisms

Survivorship patterns

You fill in these, calculate the rest

Survivorship from one period to the next: 0.064/0.171 = 0.374

Mortality from one period to the next: 1 – 0.456 = 0.544

# alive / # started in cohort

527/843 = 0.625

This comes in when we talk about growth rate

mx

10

Two kinds of life table are useful

Cohort (dynamic) life table – good for plants and other

sessile organisms

Survivorship patterns

Based on direct observation

Fecundity schedule = age-specific birth rates over lifespan

mx

11

Net reproductive rate (R0) = average number of offspring produced by an individual organism over lifespan

Sum (∑) of the average number of offspring produced by each individual in each age class(mx), weighted by the proportion surviving in each age class (Lx)

How does net birth rate interact with survivorship to influence population growth?

Net reproductive rate

R0 = ∑ Lxmx

Fecundity schedule = age-specific birth rates over lifespan; called mx DO NOT confuse this with mortality!

12

How does net birth rate interact with survivorship to influence population growth?

Net reproductive rate

R0 = ∑ Lxmx=2.4177

13

R0 > 1  population is growing

R0 < 1  population is declining

R0 = 1  population is stable

How does net birth rate interact with survivorship to influence population growth?

Net reproductive rate

R0 = ∑ Lxmx

14

The answers to this questions help us:

Protect biodiversity through conservation efforts

Mitigate harmful effects of human population growth

Understand why certain populations are declining

Understand how organisms interact with each other and their environments to predict the impact of environmental change

What processes determine future population size?

Population dynamics

15

Geometric rate of increase () is the future population size (Nt+1) divided by the current population size (Nt)

200 / 100 = 2  the population is doubling

This equation applies to populations with non-overlapping generations

How do we calculate Nt+1?

If each individual leaves an average of R0 offspring, then Nt+1 is NtR0

What is the population growth rate based on population size (Nt) and reproductive rate (R0)?

Geometric growth rate

 = Nt+1 / Nt

How do we calculate Nt+1?

If each individual leaves an average of R0 offspring, then Nt+1 is NtR0

Nt = 124

Each individual leaves an average of 2 offspring over the course of lifespan

What is R0?

What is Nt+1?

What is ?

What is the population growth rate based on population size (Nt) and reproductive rate (R0)?

Geometric growth rate

 = Nt+1 / Nt

How do we calculate Nt+1?

If each individual leaves an average of R0 offspring, then Nt+1 is NtR0

Nt = 124

Each individual leaves an average of 2 offspring over the course of lifespan

What is R0?  2

What is Nt+1?  248

What is ?  2

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