Death and uncertainty: Bayesian modeling of the association between life span and reproductive investment in birds.

Owen R. Jones* and Fernando ColcheroMax Planck Institute for Demographic Research, Rostock*jones@demogr.mpg.de, website: owenjon.es

11th September 2012, GfÖ, Lüneburg, Germany

Phot

o: b

ram

blej

ungl

e/fli

ckr

Fulmar (Fulmarus glacialis)

Grey partridge (Perdix perdix)

de Magalhaes & Costa 2009 J. Evol. Biol.

Robinson 2005 BTO Research Report 407

Sample size

Max

. obs

erve

d life

span

0 20 40 60 80 100

0

5

10

15

20

25

30

Data issues: sample size

• Maximum observed life span increases with sample size

• Species with small sample sizes are problematic

Birth/hatching Death

Data issues: truncation/censoring

DeathBirth/hatching

Data issues: truncation/censoring

Truncation

Death

Censoring

DeathBirth/hatching

Truncation

Data issues: truncation/censoring

Trait evolution‣ Closely related species tend to share

similar trait values by inheritance (phylogenetic signal)

‣ Traits can also be similar due to similar life style (convergent evolution)

‣ Life history correlation can be due to influence of the trait in question, or simply an inherited characteristic.

• To develop and test a statistical modelling framework that accounts for these data issues while using phylogenic information.

Aim

• British Trust for Ornithology has carried out mark-capture-recovery since 1933

• Maximum recorded life span for >200 species• Clutch size, number of broods, body mass

The data set

Robinson 2005 BTO Research Report 407

Bird illustrations: RSPB

Cuckoo (Cuculus canorus)

Phylogeny: Thomas, GH 2008 Proc. R. Soc. B

Bird illustrations: RSPB

Bird illustrations: RSPB

Bird illustrations: RSPB

Bird illustrations: RSPB

Pagel’s Lambda for longevity ~ 0.73

Phylogenetic signal measures the amount that phylogeny influences trait (0 - 1).

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

Ordinary least squares regression

R2 = 0.27R2 = 0.26

Ordinary least squares regression

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

R2 = 0.27 to <0.01R2 = 0.26 to <0.01

Phylogenetic correction

Independent contrastsAssumes Lambda = 1

Independent contrasts

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

R2 = 0.27 to <0.01R2 = 0.26 to <0.01

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

Optimised PGLS

R2 = 0.27 to 0.07R2 = 0.26 to 0.06

Phylogenetic correction

Assumes Lambda = 1 Lambda = 0.73

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

R2 = 0.27 to <0.01R2 = 0.26 to <0.01

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

R2 = 0.27 to 0.07R2 = 0.26 to 0.06

Phylogenetic correction

Can we improve the fit by accounting for data problems?

Independent contrasts Optimised PGLSAssumes Lambda = 1 Lambda = 0.73

Process model

X YPredictor Observed Response

Bayesian state-space model

Phylogeny

Process model

True Response

Y*

X YPredictor Observed Response

•Sample size•Censoring•Truncation

Data model

Bayesian state-space model

Phylogeny

Process model

True Response

Y*

X YPredictor Observed Response

•Sample size•Censoring•Truncation

Data model

Maximise likelihood of both

Phylogeny

• MCMC framework• Simultaneously estimates:• Coefficients of process model• Phylogenetic signal• True response• Error in process model• Error in data model• -> Degree of censoring,

truncation and sample size effects.

Bayesian state-space model

R2 = 0.07 to 0.12R2 = 0.06 to 0.10

State-space regression models

Weight (g)

Life

spa

n (y

rs)

5 50 500 5000

2

5

10

20

50

Effort (clutch size * broods)

1 2 5 10 20

BTO data underestimates lifespan for many species

Effort

% d

iffer

ence

in li

fe s

pan

0 5 10 15 20

020

040

060

080

010

00

BTO data underestimates lifespan for many species

Effort

% d

iffer

ence

in li

fe s

pan

0 5 10 15 20

020

040

060

080

010

00

Conclusions

• Life history patterns are moderated by phylogeny - we can use this information

• Method of correction is fundamentally important (i.e. evolutionary model assumed)

• Data issues can be solved

• Further analyses are in the pipeline!

We have a new R package!!

http://basta.r-forge.r-project.org

To estimate survival/mortality trajectories from capture-mark-recapture data.