This document summarizes a study that used Bayesian modeling to analyze the relationship between lifespan and reproductive investment in birds while accounting for phylogenetic relationships and data issues. The study developed a state-space model that estimates coefficients, phylogenetic signal, true responses, and error using MCMC. The model found lifespan is moderately associated with body weight and reproductive effort. It also found BTO data underestimates lifespan for many species and that the method of phylogenetic correction is important.

1. Death and uncertainty: Bayesian
modeling of the association between life
span and reproductive investment in
birds.
Photo: bramblejungle/flickr
Owen R. Jones* and Fernando Colchero
Max Planck Institute for Demographic Research, Rostock
*jones@demogr.mpg.de, website: owenjon.es
11th September 2012, GfÖ, Lüneburg, Germany

2. Grey partridge (Perdix perdix)
Fulmar (Fulmarus glacialis)

3. de Magalhaes & Costa 2009 J. Evol. Biol.
Robinson 2005 BTO Research Report 407

4. Data issues: sample size
30
25
Max. observed lifespan
• Maximum observed life
20
span increases with
sample size 15
• Species with small sample 10
sizes are problematic 5
0
0 20 40 60 80 100
Sample size

5. Data issues: truncation/censoring
Birth/hatching Death

6. Data issues: truncation/censoring
Birth/hatching Death
Truncation

7. Data issues: truncation/censoring
Birth/hatching Death
Truncation
Censoring

9. 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.

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

11. The data set
• 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
Robinson 2005 BTO Research Report 407

12. Bird illustrations: RSPB

13. Cuckoo (Cuculus canorus)

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

15. Bird illustrations: RSPB

16. Bird illustrations: RSPB

17. Bird illustrations: RSPB

18. Bird illustrations: RSPB

19. Phylogenetic signal measures the amount that
phylogeny influences trait (0 - 1).
Pagel’s Lambda for longevity ~ 0.73

20. Ordinary least squares regression
50
20
Life span (yrs)
10
5
2
5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods)

21. Ordinary least squares regression
50
20
Life span (yrs)
10
5
2
5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods)
R2 = 0.26 R2 = 0.27

22. Phylogenetic correction
Independent contrasts
Assumes Lambda = 1
50
20
Life span (yrs)
10
5
2
5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods)
R2 = 0.26 to <0.01 R2 = 0.27 to <0.01

23. Phylogenetic correction
Independent contrasts Optimised PGLS
Assumes Lambda = 1 Lambda = 0.73
50 50
20 20
Life span (yrs)
Life span (yrs)
10 10
5 5
2 2
5 50 500 5000 1 2 5 10 20 5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods) Weight (g) Effort (clutch size * broods)
R2 = 0.26 to <0.01 R2 = 0.27 to <0.01 R2 = 0.26 to 0.06 R2 = 0.27 to 0.07

24. Phylogenetic correction
Independent contrasts Optimised PGLS
Assumes Lambda = 1 Lambda = 0.73
50 50
20 20
Life span (yrs)
Life span (yrs)
10 10
5 5
2 2
5 50 500 5000 1 2 5 10 20 5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods) Weight (g) Effort (clutch size * broods)
R2 = 0.26 to <0.01 R2 = 0.27 to <0.01 R2 = 0.26 to 0.06 R2 = 0.27 to 0.07
Can we improve the fit by accounting
for data problems?

25. Bayesian state-space model
Process model
Predictor Observed Response
X Y
Phylogeny

26. Bayesian state-space model
Process model
Predictor Observed Response
X Y
Phylogeny
Data model
•Sample size
•Censoring True Response
•Truncation Y*

27. Bayesian state-space model
Maximise likelihood of both
Process model
• MCMC framework
Predictor Observed Response
• Simultaneously estimates:
X Y • Coefficients of process model
Phylogeny • Phylogenetic signal
• True response
Data model • Error in process model
• Error in data model
•Sample size • -> Degree of censoring,
•Censoring True Response truncation and sample size
•Truncation Y* effects.

28. State-space regression
models
50
20
Life span (yrs)
10
5
2
5 50 500 5000 1 2 5 10 20
Weight (g) Effort (clutch size * broods)
R2 = 0.06 to 0.10 R2 = 0.07 to 0.12

29. BTO data underestimates lifespan for
many species
1000
800
% difference in life span
600
400
200
0
0 5 10 15 20
Effort

30. BTO data underestimates lifespan for
many species
1000
800
% difference in life span
600
400
200
0
0 5 10 15 20
Effort

31. 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!

32. We have a new R package!!
To estimate survival/mortality
trajectories from capture-mark-
recapture data.
http://basta.r-forge.r-project.org