Populations change over time

Changes in U.S. Bird Populations by habitat

Science News 2009

Are Populations increasing? Decreasing?#

bree

ding

pai

rs

Year

Easy to tell with long term data sets

What about short term data sets?

tt RNN 1

Exponential Growth Model

Population size 2005 = 100

Population size 2006 = 200

R100

200100200 R

2R

tt RNN 1

Exponential Growth Model

Assumption: all individuals are equal.

Is this assumption is wrong???

Age in relative unitsNum

ber o

f sur

vivo

rs (l

og s

cale

)

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Competing models

Population size 2005 = 100

Population size 2006 = 200

2R

Model #1 Model #2

Not all individuals are equalAll individuals are equal

Juvenile survival = 0.45Adult survival = 0.9

0.33 Juveniles become adultsAdults produce 13 offspring each

Population size 2005 = 10090 Juveniles, 10 adults

Population size 2006 = 200

???2R

1 2 30

100

200

300

400

500

600

700Original DataNew Data

Year

Popu

latio

n Si

ze

Year 2 = 200 for both

Year

Popu

latio

n Si

ze

1 2 3 4 5 6 7 8 9 10 110

200000400000600000800000

100000012000001400000160000018000002000000

Original DataNew Data

Huge difference!

Stage and Size predict survival and fecundity

Plants- seed, seedling, adult

Invertebrates- number of molts, larva-pupa-adult

Fish- size predicts sex and number of eggs produced

Amphibians- egg-tadpole-adult

Birds- egg-chick-adult

Mammals- newborn, juvenile, adult

In fish, fecundity > with size

tt RNN 1

Exponential growth model

Nt=30 individuals

Age-structured model

Nt = 2082

newborns

1-year olds

2-year olds

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Exponential growth model

Nt=30 individuals

Age-structured model

0

0

S0

F1

S1

0

F2

0

00 1 2

F1 F2

S0 S1

tt RNN 1

Exponential growth model

Nt=30 individuals

Age-structured model

Nt+1=0

0

S0

F1

S1

0

F2

0

0

20

8

2

Age vs. Stage or size Models

0

0

S0

F1

S1

0

F2

0

0

0 1 2

S

S

S

FM

S

S

FL

S

S

S M L

From Eby et al. 2005

S

S

S

FM

S

S

FL

S

S

S F

tt RNN 1

What about growth rate?

R = Growth Rate, or λ (lambda)

Luckily, λ is an intrinsic property of the matrix

Nt+1=0

0

S0

F1

S1

0

F2

0

0

20

8

2

Only one solution For Lambda for

each matrix

Natural log of lambda

Model output from paperThere are many values, because – they varied hypoxia and effects on

juvenile growth rate and calculated a lambda value for each simulation.

Hypoxia No Hypoxia