my talk at euring 2013 on individual variability in capture-recapture models

1. All equal, really? Individual variability in capture-recapture models from biological and methodological perspectives Olivier Gimenez (Montpellier) Emmanuelle Cam (Toulouse) Jean-Michel Gaillard (Lyon)

2. Process in the wild Investigating process in natural populations Long-term individual monitoring datasets Methodological issues when moving from lab to natural conditions

3. Process in the wild Investigating process in natural populations Long-term individual monitoring datasets Methodological issues when moving from lab to natural conditions Issue 1: detectability < 1 Issue 2: individual heterogeneity (IH)

4. Issue 2: individual heterogeneity Simple capture-recapture models assume homogeneity From a statistical point of view, IH can cause bias in parameter estimates See also L. Cordes talk: Band reporting rates of waterfowl: Does individual heterogeneity bias estimated survival rates?

5. Issue of individual heterogeneity Simple CR models assume homogeneity From a statistical point of view, IH can cause bias in parameter estimates From a biological point of view, IH is of interest individual quality 2010

6. Accounting for individual heterogeneity Biologists rely on empirical measures (mass, gender, age, experience, etc.) Statistician attempt to filter out the signal from noisy observations? Focus shifting from mean to variance? How to account for IH?

7. How to account for IH Case study 1: detecting trade-offs Case study 2: describing senescence Does IH have a genetic basis? Case study 3: quantifying heritability How to determine the amount of IH? Case study 4: non parametric Bayesian approach Perspectives Outline of the talk

8. Outline of the talk How to account for variation in IH Case study 1: detecting trade-offs Case study 2: describing senescence Does IH have a genetic basis? Case study 3: quantifying heritability How to determine the amount of IH? Case study 4: non parametric Bayesian approach Perspectives

9. Natural selection favors individuals that maximize their fitness Limited energy budget: strategy of resource allocation Trade-off between traits related to fitness IH may mask trade-offs (Van Noordwijk & de Jong 1986 Am Nat) Assessing trade-offs in the wild

10. IH as covariates If IH is measurable, then use it! Often, continuous individual covariate changing over time: issue of missing data Work by S. Bonner and R. King on how to handle with continuous covariate

11. IH as covariates If IH is measurable, then use it! Often, continuous individual covariate changing over time: issue of missing data Work by S. Bonner and R. King on how to handle with continuous covariate Use states instead of sites in multisite models (categorical covariate)

12. Use breeders / non-breeders states (Nichols et al. 1994 Ecology) State-dependent survival Sstate : reproduction vs future survival State-dependent transitions ij : present vs. future reproduction Numerous applications Trade-offs and multistate models

13. Kittiwakes (Cam et al. 1998 Ecology) B NB S B 0.79 NB 0.65 0.90 0.10 0.67 0.33

15. Outline of the talk How to account for IH Case study 1: detecting trade-offs Case study 2: describing senescence Does IH have a genetic basis? Case study 3: quantifying heritability How to determine the amount of IH? Case study 4: non parametric Bayesian approach Perspectives

16. Over time, the observed hazard rate will approach the hazard rate of the more robust subcohort Vaupel and Yashin 1985 Am Stat Suggest that analyses conducted at the population vs. individual level should differ (Cam et al. 2002 Am Nat) What if detection p < 1 ? Impact of IH on age-varying survival

17. Finite mixture of individuals Use mixture models (Pledger et al. 2003 Biometrics) Latent variable for the class to which an individual belongs (Pradel 2009 EES) 2 classes of individuals (low vs. high quality)

18. Probabilities in a mixture model Under homogeneity is survival p is detection pp 1101Pr

19. Under heterogeneity is the probability that the individual belongs to state L L is survival for low quality individuals H is survival for high quality individuals Probabilities in a mixture model

20. Under heterogeneity is the probability that the individual belongs to state L L is survival for low quality individuals H is survival for high quality individuals pppp HHLL 111101Pr Probabilities in a mixture model

21. Finite mixture of individuals Use mixture models (Pledger et al. 2003) A model with a hidden structure, with a latent variable for the class to which an individual belong to (HMM; Pradel 2009) Mimic examples in Vaupel and Yashin (1985 Am Stat) with p < 1 using simulated data

22. 0 2 4 6 8 10 12 14 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sub-cohort 1 400 individuals (the most fragile) Sub-cohort 2 100 individuals (the most robust) Survival Age

23. 0 2 4 6 8 10 12 14 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fit at the population level Sub-cohort 2 100 individuals (the most robust) Sub-cohort 1 400 individuals (the most fragile) Survival Age

24. 0 2 4 6 8 10 12 14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fit at the individual level using a 2-class mixture Fit at the population level Sub-cohort 1 400 individuals (the most fragile) Sub-cohort 2 100 individuals (the most robust) Survival Age

25. Real case study on Black-headed Gulls Not so simple in real life Case study on (famous) Black-headed gulls (J.-D. Lebreton) Suspicion of IH

26. Zones of unequal accessibility Detection strongly depends on birds position Detection heterogeneity

27. Detection heterogeneity (1) zone 1: nests inside the vegetation La Ronze pond

28. Detection heterogeneity (1) zone 1: nests inside the vegetation zone 2: nests on the edge of vegetation clusters La Ronze pond

29. Results - Pron et al. (2010) Okos Absence of survival IH

30. 00.20.40.60.81 0 10 20 Age Survivalprobabilities Absence of survival IH Estimation of survival senescence Results - Pron et al. (2010) Okos

31. 00.20.40.60.81 0 10 20 Age Survivalprobabilities Absence of survival IH Presence of detection and emigration IH Estimation of survival senescence Results - Pron et al. (2010) Okos

32. Absence of survival IH Presence of detection and emigration IH If IH ignored on temporary emigration, then senescence undetected Results - Pron et al. (2010) Okos

33. Results - Pron et al. (2010) Okos Absence of survival IH Presence of detection and emigration IH If IH ignored on temporary emigration, then senescence undetected See M. Lindbergs talk: Individual heterogeneity in black brant survival and recruitment with implications for harvest dynamics

34. Continuous mixture of individuals What if I have a continuous mixture of individuals? Use individual random-effect models CR mixed models (Royle 2008 Biometrics; Gimenez & Choquet 2010 Ecology)

35. Explain individual variation in survival No variation homogeneity Random effect in-between Saturated full heterogeneity i Individual random-effect models 2 ,~ Ni

36. Explain individual variation in survival No variation homogeneity Random effect in-between Saturated full heterogeneity i 2 ,~ Ni Individual random-effect models

37. Explain individual variation in survival No variation homogeneity Individual random effect in-between Saturated full heterogeneity i 2 ,~ Ni Individual random-effect models

38. Continuous mixture of individuals What if I have a continuous mixture of individuals? Use individual random-effect models (Royle 2008 Biometrics, Gimenez & Choquet 2010 Ecology) Mimic examples in Vaupel and Yashin (1985) with p < 1 using simulated data

39. 0 2 4 6 8 10 12 14 0.4 0.5 0.6 0.7 0.8 0.9 1 300 individuals logit(i(a)) = 1.5 - 0.05 a + ui ui ~ N(0,=0.5) Survival Age

40. 0 2 4 6 8 10 12 14 0.4 0.5 0.6 0.7 0.8 0.9 1 Expected pattern E(logit(i(a))) = 1.5 - 0.05 aSurvival Age

41. 0 2 4 6 8 10 12 14 0.4 0.5 0.6 0.7 0.8 0.9 1 Fit at the population level Survival Age

42. 0 2 4 6 8 10 12 14 0.4 0.5 0.6 0.7 0.8 0.9 1 Fit at the individual level with an individual random effectSurvival Age

43. Senescence in European dippers

44. with IH: onset = 1.94 Marzolin et al. (2011) Ecology Senescence in European dippers

45. without IH: onset = 2.28 with IH: onset = 1.94 Marzolin et al. (2011) Ecology Senescence in European dippers

48. Heritability in the wild Quantitative genetics: joint analysis of a trait and genealogical relationships Increasing used in animal and plant pops

49. Heritability in the wild Quantitative genetics: joint analysis of a trait and genealogical relationships Increasing used in animal and plant pops Animal models: mixed models incorporating genetic, environmental and other factors. Heritability: proportion of the phenotypic var. attributed to additive genetic var.

50. Heritability in the wild Quantitative genetics: joint analysis of a trait and genealogical relationships Increasing used in animal and plant pops Animal models: mixed models incorporating genetic, environmental and other factors. Heritability: proportion of the phenotypic var. attributed to additive genetic var. Combination of animal and capture- recapture models ?

51. The idea is the air (Cam 2009 EES) " [The animal model has] been applied to estimation of heritability in life history traits, either in the rare study populations where detection probability is close to 1, or without considering the probability of detecting animals (...) "

52. The idea is the air (Cam 2009 EES) " [The animal model has] been applied to estimation of heritability in life history traits, either in the rare study populations where detection probability is close to 1, or without considering the probability of detecting animals (...) " I think its Emmanuelle

53. Introducing the threshold model Main issue: survival is a discrete process, but theory well developed for continuous distributions

54. Main issue: survival is a discrete process, but theory well developed for continuous distributions Trick/idea: Survival is related to an underlying latent variable that is continuous Introducing the threshold model

55. Liability ind. i dies on (t,t+1) li,t N(i,t ,2) ind. i survives on (t,t+1)

56. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model iittii,t aebG ,

57. It can be shown that survival and mean liability are linked For some function G, we have: mean survival iittii,t aebG , Plug in the animal model

58. It can be shown that survival and mean liability are linked For some function G, we have: yearly effect mean survival 2 ,0~ tt Nb iittii,t aebG , Plug in the animal model

59. It can be shown that survival and mean liability are linked For some function G, we have: yearly effect mean survival non-genetic effect 2 ,0~ tt Nb 2 ,0~ ei Ne iittii,t aebG , Plug in the animal model

60. It can be shown that survival and mean liability are linked For some function G, we have: additive genetic effect yearly effect mean survival non-genetic effect 2 ,0~ tt Nb 2 ,0~ ei Ne AMNaa aN 2 1 ,0~,, iittii,t aebG , Plug in the animal model

61. Case study on blue tits in Corsica Blue tits Corsica 1979 2007 654 individuals, 218 fathers (sires), 215 mothers (dams), 12 generations. Mark-recapture data Social pedigree

62. median = 0.110 95% cred. int. = [0.006; 0.308] Additive genetic variance Papax et al. 2010 J of Evolutionary Biol.

63. Is IH significant? General question (Bolker et al. 2009 TREE) median = 0.110 95% cred. int. = [0.006; 0.308] Additive genetic variance Papax et al. 2010 J of Evolutionary Biol.

64. Is IH significant? General question (Bolker et al. 2009 TREE) median = 0.110 95% cred. int. = [0.006; 0.308] Additive genetic variance Papax et al. 2010 J of Evolutionary Biol. See T. Chamberts talk: Use of posterior predictive checks for choosing whether or not to include individual random effects in mark-recapture models.

66. Short musical interlude (ACDC) Wake up!

68. Fit models with 1, 2, 3, classes of mixture, and use AIC (Pledger et al. 2003 Biometrics) This strategy does the job in simulations (Cubaynes et al. 2012 MEE) Number of classes for finite mixtures?

69. Fit models with 1, 2, 3, classes of mixture, and use AIC (Pledger et al. 2003 Biometrics) This strategy does the job in simulations (Cubaynes et al. 2012 MEE) CR encounter histories are short in time, which ensures low number of classes Problem solved! Number of classes for finite mixtures?

70. Number of classes for finite mixtures? Fit models with 1, 2, 3, classes of mixture, and use AIC (Pledger et al. 2003 Biometrics) This strategy does the job in simulations (Cubaynes et al. 2012 MEE) CR encounter histories are short in time, which ensures low number of classes Problem solved! See Arnold et al. (2010 Biometrics) for an automatic method (RJMCMC)

71. Parametric approach assumes a distribution function F on the e Validity of normal random effect assumption? What if random-effect models? Non parametric Bayesian approach

72. Parametric approach assumes a distribution function F on the e Validity of normal random effect assumption? Main idea: Any distribution well approximated by a mixture of normal distributions where is a discrete mixing distribution What if random-effect models? Non parametric Bayesian approach F x( )= N x q,s 2 ( )Q dq( ) Q dq( )

73. Parametric approach assumes a distribution function F on the e Validity of normal random effect assumption? Main idea: Any distribution well approximated by a mixture of normal distributions where is a discrete mixing distribution Dirichlet process: What if random-effect models? Non parametric Bayesian approach F x( )= N x q,s 2 ( )Q dq( ) Q dq( ) F x( ) ph h=1 N N x qh,s 2 ( )

74. Case study on wolves (95-03) Wolf is recolonizing France Problematic interactions with human activities Heterogeneity suspected in the detection process Wide area Social species

75. Results on wolves 1 2 3 4 5 nb of clusters050150250

76. -0.2 0.2 0.6 1.0 0.01.5 detectability cluster 1 -0.2 0.0 0.2 0.4 024 detectability cluster 2 0.00 0.10 0.20 02040 detectability cluster 3 0.00 0.10 0.20 0150 detectability cluster 4 Results on wolves

77. Wolf survival 0.6 0.7 0.8 0.9 02468 SURVIVAL homogeneity

78. 0.80 0.85 0.90 0.95 1.00 0246810 SURVIVAL Wolf survival mixture of normals 0.6 0.7 0.8 0.9 02468 SURVIVAL homogeneity

81. Conclusions CR methodology is catching up with p=1 world IH needs to be accounted for Whenever possible, adopt a biological view and measure quality in the field If not, well, mixture or random-effect models

82. Tribute to MARK Rmi ChoquetGary White E-SURGE

83. Conclusions CR methodology is catching up with p=1 world IH needs to be accounted for Whenever possible, adopt a biological view and measure quality in the field Mixture of random-effect models Interpretation difficult / hazardous though How to choose between the two approaches? See T. Arnolds talk: Modeling individual heterogeneity in survival rates: mixtures or distributions?

84. Perspectives 1. More biology in heterogeneity 2. Fixed or dynamic heterogeneity? Only suggestions for future research

85. Perspectives 1. More biology in heterogeneity Detection is often considered nuisance Understanding the biology of IH in detection? Link with literature on personality See C. Senars talk: Selection on the size of a sexual ornament may be reverse in urban habitats: a story on variation in the black tie of the great Tit

86. Heterogeneity in detection

87. Daily detection probability for cliff swallows at two sites when flushing was (black) and was not done (grey)

88. Perspectives 2. Fixed or dynamic heterogeneity?

89. Diversity in life histories: traits (size, age at maturity), physiology, appearance Understanding diversity of life histories

90. Fixed heterogeneity: fixed differences in fitness components among individuals determined before or at the onset of reproductive life (Cam et al. 2002). This diversity is explained by?

91. Fixed heterogeneity: fixed differences in fitness components among individuals determined before or at the onset of reproductive life (Cam et al. 2002). Dynamic heterogeneity: diversity of state sequences due to stochasticity (Tuljapurkar et al. 2009 Ecol. Letters) Current debate on dynamic vs fixed heterogeneity This diversity is explained by?

92. Fixed or dynamic heterogeneity?

93. Fixed or dynamic heterogeneity? Multistate models with individual random effects and first- order Markovian transitions between states

94. Fixed or dynamic heterogeneity? Multistate models with individual random effects and first- order Markovian transitions between states Diversity better explained by models incorporating unobserved heterogeneity than by models including first- order Markov processes alone, or a combination of both

95. Fixed or dynamic heterogeneity? Multistate models with individual random effects and first- order Markovian transitions between states Diversity better explained by models incorporating unobserved heterogeneity than by models including first- order Markov processes alone, or a combination of both To be reproduced on other populations / species

96. Thanks a lot for listening!

97. Enjoy the Euring meeting!

my talk at euring 2013 on individual variability in capture-recapture models

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