Demographic Methods Cluster

Coordinator: Fernando Colchero


The aim of the cluster is to develop novel demographic models and statistical methods to explore the causes and consequences of the age-specific trajectories of survival across the tree of life. We are a group of interdisciplinary researchers spanning mathematics, statistics, formal demography and biology most of whom have strong mathematical and statistical interests and skills, especially Aburto, Basellini, Baudisch, Canudas-Romo, Caswell, Colchero, Danko, Ebeling, Gampe, Kjærgaard, Lenart, Medford, Missov, Nemeth, Pascariu, Rau, Riffe, Rizzi, Schöley, Steiner, Stott, Thinggaard, Vaupel and Villavicencio. Our work can be divided into five main research areas:


1) Bayesian Survival Trajectory Analysis (BaSTA):

Demographers often study datasets that are riddled with missing records and partial information. To overcome such limitations, Colchero, when he was at MPIDR, developed the general approach of “Bayesian Survival Trajectory Analysis” and made it publicly available through the now popular R package BaSTA (Colchero and Clark 2012, Colchero et al 2012). This framework has been applied, for example, to estimate age-specific mortality from 16th Century marriage records (Villavicencio et al. 2015) and to test hypotheses on the existence of negative senescence in indeterminate growers by treating age and size as latent states (Colchero & Schaible 2014). In a recent research article published in the journal PNAS, we extended the BaSTA framework a Bayesian hierarchical model that builds on the multi-event framework was applied to estimate age and to estimate age-specific mortality and dispersal for populations in which one or both sexes disperse from the study area.


Relevant publications:

Colchero F & JS Clark (2012) Bayesian inference on age-specific survival for censored and truncated data. J Anim Ecol 81:139-149

Colchero F, OR Jones & M Rebke (2012) BaSTA: an R package for Bayesian estimation of age-specific survival from incomplete mark-recapture/recovery data with covariates. Met Ecol Evol 3:466-470

Zajitschek F, T Jin, F Colchero & A Maklakov (2014) Aging differently: diet- and sex-dependent late-life mortality patterns in Drosophila melanogaster. J Geron A 69:666-674.

Colchero, F & R Schaible (2014) Mortality as a bivariate function of age and size in indeterminate growers. Ecosphere 5:161.

Larson, SM, F Colchero, OR Jones, L Williams, E Fernández-Duque (2016) Age and sex-specific mortality of wild and captive populations of a monogamous pair-bonded primate (Aotus azarae). Am J Primat 78:315-325.

Dahlgren JP, F Colchero, OR Jones, D-I Øien, A Moen & N Sletvold (Accepted) Actuarial senescence in a long-lived orchid challenges our current understanding of ageing. Proc Roy Soc B.

Barthold, JA, C Packer, A Loveridge, DW Macdonald, F Colchero (2016) Dead or gone? Bayesian inference on mortality for the dispersing sex. Ecol Evol 6: 4910–4923.

Barthold, JA, A Loveridge, DW Macdonald, C Packer, F Colchero (2016) Bayesian estimates of male and female African lion mortality for future use in population management. J Appl Ecol 53:295-304.

Colchero F, R Rau, OR Jones, J Barthold, DA Conde, A Lenart, L Nemeth, A Scheuerlein, J Schoeley, C Torres, V Zarulli, J Altmann, DK Brockman, AM Bronikowski, LM Fedigan, A Pusey, TS Stoinski, KB Strier, A Baudisch, SC Alberts & JW Vaupel (Accepted) The emergence of longevous populations. PNAS.

Colchero F, A.E. Aliaga, OR Jones and DA Conde (Under review) Individual heterogeneity determines sex differences in mortality in a monogamous bird with reversed sexual dimorphism. J Anim Ecol.

Colchero F, OR Jones, DA Conde, et al., A Baudisch, J-M Gaillard (In progress) Strong mortality and fertility assumptions influence perceived population dynamics and extinction risk.

Schaible R, Gruber H, Philipp EER, Scheuerlein A, Colchero F  (In progress) Colonization of New Marginal Habitats, Effects for Life History for the Long-lived Ocean Quahog Arctica islandica.

Colchero F & BY Kiyakoglu (In progress) Bayesian estimation of individual heterogeneity in mortality parameters.



2) Estimation of smooth distributions from coarsely grouped demographic data:

Another accomplishment of the Cluster is the development of non-parametric methods, based on penalized composite link models (Rizzi et al. 2015, 2016), for ungrouping coarsely aggregated data to estimate continuous age trajectories. Ungrouping such data might be desirable for several reasons: Intervals can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. We propose a versatile method for ungrouping histograms that makes use of modest assumptions and is therefore suitable for most applications in demography and epidemiology.


Relevant publications:

Rizzi S, Gampe J, Eilers PHC (2015) Efficient Estimation of Smooth Distributions from Coarsely Grouped Data. Am J Epidemiol 182(2):138-147

Rizzi S, Thinggaard M, Engholm G, Christensen N, Johannesen TB, Vaupel JW, Jacobsen R (2016). Comparison of non-parametric methods for ungrouping coarsely aggregated data. BMC Medical Research Methodology 16:1-12

Dahlgren J, Rizzi S, Schweingruber F, Hellmann L, Büntgen U (2016) Age distributions of Greenlandic dwarf shrubs support concept of negligible actuarial senescence. Ecosphere (in press).


3) Age-stage structured populations:

Members of the Cluster including Caswell and Steiner are also interested in expanding classical age-only-structured population methods to age-stage-structured populations to advance our understanding of the interplay between age- and stage-dynamics (e.g., Steiner et al. 2014). Much research in demography focuses on age-only-structured populations. However the diversity in senescence patterns suggest that stages, be they determined  developmental, morphological, physiological or (epi)genetically, play a significant role in shaping life courses. In order to advance our understanding of the interplay between age- and stage-dynamics, we expand classical age-only-structured population methods to age-stage-structured populations. In deriving new measures of reproductive timing we relate the reproductive rate to fitness and thereby highlight the complex interplay of trait dynamics, timing, and level of reproduction. Moreover the underlying drivers of stage dynamics that generate individual level dynamics remain little explored, and we do not know to what degree such individual level dynamics are adaptive, mal-adaptive or neutral. To approach such evolutionary questions about selective forces shaping life course dynamics we derived new sensitivities on stage dynamics and related them to selective forces on vital rates and fitness.


Relevant publications:

Steiner UK, Tuljapurkar S, Coulson T (2014) Generation Time, Net Reproductive Rate, and Growth in Stage-Age-Structured Populations Am Nat 183(6):771-783.

Steiner UK, Gaston AJ, Tuljapurkar S (in progress) Drivers of diversity in individual life courses: Sensitivity of the population entropy of a Markov chain.



4) Discrete approximations to continuous demographic functions:

Demographic data are generally discrete, pertaining to finite populations observed at points in time. Key formulas, however, often assume infinite populations and continuous time. Consider, for example, Keyfitz's entropy given by

Different numerical approximations can yield very different results. Using simulated data from specified survival functions l(x), a team of researchers (Schöley, Pascariu, Villavicencio, Danko, Jouvet, Sherman, Stott, Torres and Baudisch), from the Methods Cluster and the Pace and Shape Cluster, are developing an R package ( that uses discrete approximations that come closest to the exact value implied by the continuous formula.


5) Novel demographic functions:

High points in the life of the Cluster are when members get together to discuss new results in formal demography. For example, when a death is averted at a young age, lifespan inequality decreases but when a death is averted at an old enough age, lifespan inequality increases: Aburto and others are developing equations to determine the age separating these two outcomes for various measures of lifespan inequality. Villavicencio and Riffe (2016) and Canudas-Romo and Zarulli (2016) made further contributions to the study of life lived vs. life left. Missov, Lenart, Nemeth, Canudas-Romo and Vaupel (2015) discuss Gompertz curves with the mode as a parameter. Wensink and Baudisch working with Caswell showed “The rarity of survival to old age does not drive the evolution of senescence” (2016) and with Wrycza there can be “No senescence despite declining selection pressure” (2014).


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