Paternal age effects on offspring fitness in four populations

Main result

Paternal age effect in a sibling comparison design, adjusting for average paternal age, maternal age, number of siblings, number of older siblings, being last born, birth cohort, and parental loss.

We find that the children of older fathers consistently have fewer childrens in all four populations, when compared to their siblings.

Main model results

Reproductive timing

Much reporting on increasing parental ages tends to focus on ages at first birth (dashed lines) and hence seems at times unduly alarmist. Parental ages at all births (solid lines) show an increase since 1970 too, but are still lower than in the four Swedish regions of our historical Swedish data (1737-1880). The biggest difference is in fact not the slight delay of age at first birth in modern Sweden, but the much earlier reproductive stoppage (ages at last birth, dotted lines).

Hence, contrary to many people’s intutitions, in modern Sweden (1947-1959, gray) the average child was born to a younger parent than in our pre-industrial populations (1737-1880, green). This is mostly because people stopped having children earlier and to a lesser degree because people started having children ca. 1 year earlier. In contemporary Sweden (2010), the average parental age for both mothers and fathers is still lower than in our historical Swedish data.

In the below plot, we have compared all four populations ages at first and last births. The data for modern Sweden focuses on children born 1947 to 1959. Especially, mothers’ ages at last births stand out: In all historical datasets, it was still common for mothers to reproduce beyond the age of 40, reproductive stoppage for both men and women occurs much earlier in modern Sweden. Further descriptive comparisons on reproductive timing and other parameters.



Comparison of descriptives across populations.

Main models

Comparison of the main models across populations.

Selective episodes

Comparison of the selective episode models across populations. Selective episode comparison


Comparison of the results of robustness checks in different populations. Robustness check comparison

Plausibility checks

How do the obtained effect sizes on number of children compare to estimates of genome-wide deleterious mutation rate times the mean selection coefficient against a deleterious heterozygous mutation (Hayward et al., 2015) and how to the effect sizes on infant survival compare to calculations of the mutation-attributable effect size computed in Gratten et al. (2016).


In this document, all Helper functions functions that are used throughout, are documented.

This make file was used to generate this website (some code was run manually on the cluster).

The statistical models using brms were documented in a standardised fashion, this is documented here, model summary.

The main model reports, selective episode reports, main model reports were also generated in a standardised fashion.

Authors & Acknowledgements

Corresponding author: Ruben C. Arslan, Georg August University Göttingen
Kai P. Willführ, Emma M. Frans, Karin J. H. Verweij, Paul-Christian Bürkner, Mikko Myrskylä, Eckart Voland, Catarina Almqvist, Brendan Zietsch, & Lars Penke

This supplementary website has been archived on DOI.

RCA thanks Holger Sennhenn-Reulen, Jarrod Hadfield, author of MCMCglmm, and Ben Bolker, co-author of lme4, for their statistical advice.


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Image credits
Kreuzkirche Pilsum, Krummhörn

Pilsumer Kirche 2010.jpg
Pilsumer Kirche 2010“ von kaʁstn Disk/Cat - Eigenes Werk. Lizenziert unter CC BY-SA 3.0 de über Wikimedia Commons.

Basilica of Sainte-Anne-de-Beaupré, Québec

Church of Sainte Anne de Beaupre.jpg
Church of Sainte Anne de Beaupre” by Detroit Publishing - Licensed under Public Domain via Wikimedia Commons.

Skellefteå landsförsamlings kyrka, Sweden

Skellefteå landsförsamlings kyrka (2010).
Skelleftea landskyrka main view” av Xauxa Håkan Svensson - Eget arbete. Licensierad under CC BY-SA 3.0 via Wikimedia Commons.

Statistics Sweden, Statistiska centralbyrån, Örebro Office, Sweden

SCB Örebro
SCB Örebro” by Edaen. Licensed under CC BY 3.0 via Wikimedia Commons.

Package bibliography
Session info (with package versions)
library(brms, warn.conflicts = F, quietly = T)
library(bayesplot, warn.conflicts = F, quietly = T)
## This is bayesplot version 1.2.0
## R version 3.3.2 (2016-10-31)
## Platform: x86_64-apple-darwin13.4.0 (64-bit)
## Running under: OS X El Capitan 10.11.6
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## other attached packages:
##  [1] bayesplot_1.2.0  brms_1.7.0       Rcpp_0.12.9      pander_0.6.0    
##  [5] broom_0.4.1.9000 dtplyr_0.0.1     dplyr_0.5.0      data.table_1.9.6
##  [9] knitr_1.16       plyr_1.8.4       reshape2_1.4.2   stringi_1.1.2   
## [13] stringr_1.1.0    lubridate_1.6.0  formr_0.4.2      QuantPsyc_1.5   
## [17] MASS_7.3-45      boot_1.3-18      psych_1.6.9      car_2.1-3       
## [21] Hmisc_4.0-0      ggplot2_2.2.1    Formula_1.2-1    survival_2.40-1 
## [25] lattice_0.20-34  foreign_0.8-67   formatR_1.4      rmarkdown_1.2   
## loaded via a namespace (and not attached):
##  [1] tidyr_0.6.0          assertthat_0.1       rprojroot_1.1       
##  [4] digest_0.6.11        packrat_0.4.8-1      R6_2.2.0            
##  [7] chron_2.3-47         backports_1.0.4      acepack_1.4.1       
## [10] MatrixModels_0.4-1   stats4_3.3.2         coda_0.19-1         
## [13] evaluate_0.10        lazyeval_0.2.0       minqa_1.2.4         
## [16] SparseM_1.74         nloptr_1.0.4         rpart_4.1-10        
## [19] Matrix_1.2-7.1       labeling_0.3         splines_3.3.2       
## [22] lme4_1.1-12          loo_1.1.0            munsell_0.4.3       
## [25] rstan_2.15.1         mnormt_1.5-5         mgcv_1.8-16         
## [28] rstantools_1.2.0     htmltools_0.3.5      nnet_7.3-12         
## [31] tibble_1.2           gridExtra_2.2.1      htmlTable_1.7       
## [34] matrixStats_0.51.0   grid_3.3.2           nlme_3.1-128        
## [37] gtable_0.2.0         DBI_0.5-1            magrittr_1.5        
## [40] StanHeaders_2.15.0-1 scales_0.4.1         latticeExtra_0.6-28 
## [43] RColorBrewer_1.1-2   tools_3.3.2          abind_1.4-5         
## [46] parallel_3.3.2       pbkrtest_0.4-6       yaml_2.1.14         
## [49] inline_0.3.14        colorspace_1.3-2     cluster_2.0.5       
## [52] quantreg_5.29

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