Populations change over time Changes in U.S. Bird Populations by habitat Science News 2009.

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Presentation transcript:

Populations change over time Changes in U.S. Bird Populations by habitat Science News 2009

Are Populations increasing? Decreasing? # breeding pairs Year

Easy to tell with long term data sets

What about short term data sets?

Exponential Growth Model Population size 2005 = 100 Population size 2006 = 200

Exponential Growth Model Assumption: all individuals are equal. Is this assumption is wrong???

Age in relative units Number of survivors (log scale)

Competing models Population size 2005 = 100 Population size 2006 = 200 Model #1Model #2 Not all individuals are equalAll individuals are equal Juvenile survival = 0.45 Adult survival = Juveniles become adults Adults produce 13 offspring each Population size 2005 = Juveniles, 10 adults Population size 2006 = 200

Year Population Size Year 2 = 200 for both

Year Population Size 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

Exponential growth model N t =30 individuals Age-structured model Nt =Nt = newborns 1-year olds 2-year olds

Exponential growth model N t =30 individuals Age-structured model 0 0 S0S0 F1F1 S1S1 0 F2F F1F1 F2F2 S0S0 S1S1

Exponential growth model N t =30 individuals Age-structured model N t+1 = 0 0 S0S0 F1F1 S1S1 0 F2F

Age vs. Stage or size Models 0 0 S0S0 F1F1 S1S1 0 F2F S S S FMFM S S FLFL S S SML

From Eby et al S S S FMFM S S FLFL S S SF

What about growth rate? R = Growth Rate, or λ (lambda) Luckily, λ is an intrinsic property of the matrix N t+1 = 0 0 S0S0 F1F1 S1S1 0 F2F Only one solution For Lambda for each matrix

Natural log of lambda Model output from paper There are many values, because – they varied hypoxia and effects on juvenile growth rate and calculated a lambda value for each simulation. Hypoxia No Hypoxia