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? 0 6! 6! 6! ] ] ] ] ] ] ] y y ] ] ] ] ] ] ] 6! ] ] ] ] ] ] ] ] ] : Supplementary material for "Individual dispersal decisions affect fitness via maternal rank effects in male rhesus macaques" by Wei, Kulik, Ruiz-Lambides & Widdig
Supplementary Table S1: Results of the GLMMs investigating the relationship between natal dispersal age and five fitness traits. Survival (N = 840) and post-dispersal longevity (N = 402) were fitted as binomial responses, probability to reproduce (N = 297), age at first reproduction (N = 252) and LRS (N = 84) as were fitted with a Poisson error structure. Predictors with p < 0.05 are marked in bold.
traitPredictorEstimateSEzpsurvival (1st year after dispersal)Intercept7.95022.142natal dispersal age0.00010.0010.1280.898maternal rank-0.24391.805-0.1350.893co-residence with mother-0.00070.001-0.4630.643post-dispersal longevity (years)Intercept1.69140.489natal dispersal age-0.00010.0003-0.4690.639probability to reproduceIntercept-0.66151.363natal dispersal age0.0010.00042.4240.015maternal rank0.59040.6050.9760.329co-residence with mother0.00040.0010.3090.757age at 1st reproduction (years)Intercept2.02800.198natal dispersal age-0.000030.000-0.7500.454maternal rank-0.11040.089-1.2470.212co-residence with mother0.000010.0000.0740.941LRSIntercept0.63080.276natal dispersal age0.00050.00013.651< 0.001maternal rank0.70640.2922.4200.016
Random intercepts were fitted for maternal ID, birth group and cohort. For survival, probability to reproduce and age at first reproduction and LRS, random slopes were fitted for natal dispersal age and maternal rank within birth group and cohort, for post-dispersal longevity random slopes were fitted for natal dispersal age within birth group and cohort.
Supplementary methods
We fitted Linear Mixed Models (LMM) and Generalized Linear Mixed Models (GLMM) using the R-package "lme4" (version 1.0-6 ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"WJVdJHz6","properties":{"formattedCitation":"{\\rtf \\super 1\\nosupersub{}}","plainCitation":"1"},"citationItems":[{"id":20741,"uris":["http://zotero.org/groups/21925/items/QN9MZ32N"],"uri":["http://zotero.org/groups/21925/items/QN9MZ32N"],"itemData":{"id":20741,"type":"book","title":"lme4: Linear mixed-effects models using Eigen and S4","version":"R package version 1.0-6","URL":"http://CRAN.R-project.org/package=lme4","author":[{"family":"Bates","given":"Douglas"},{"family":"Maechler","given":"Martin"},{"family":"Bolker","given":"Ben"},{"family":"Walker","given":"Steven"}],"issued":{"date-parts":[["2014"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 1).
Variation in dispersal age
To identify variables related to variation in dispersal age we log-transformed natal dispersal to fit model assumptions of a Gaussian response. As measures of the population environment we fitted population size and the number of groups on CS when the focal reached dispersal age (i.e. three years of age). As measures of the group environment we fitted adult group size and adult sex ratio when the focal was three years old. As measures of the maternal environment we used maternal rank, maternal family size (i.e. number of adult female relatives up to 1st cousins at focal age 3) and, as a proxy for maternal experience, the number of offspring (surviving the first year) produced by the mother until a focal male's birth. We further scored if the focal had familiar older brothers that had already dispersed when the focal reached dispersal age and accounted for orphaned focals by counting the number of days the mother was present in the first 1000 days of life. As we expected the effects of some predictors to be dependent on other predictors we fitted interactions between adult group size and adult sex ratio, adult group size and maternal family size and between population size and the number of groups on CS.
To control for the possibility that males born early in the season would also disperse earlier than those born late in the season we fitted the age at the onset of the mating season in the focal's third year of life as a fixed effects control predictor. We chose this measure rather than the male's birth date relative to the onset of the birth season to account for the steady progressing of the mating and birth season on CS over the years ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"JAwUAhoq","properties":{"formattedCitation":"{\\rtf \\super 2\\nosupersub{}}","plainCitation":"2"},"citationItems":[{"id":20827,"uris":["http://zotero.org/groups/21925/items/EMMUDHRD"],"uri":["http://zotero.org/groups/21925/items/EMMUDHRD"],"itemData":{"id":20827,"type":"article-journal","title":"Discovery of a secular trend in Cayo Santiago macaque reproduction","container-title":"American Journal of Primatology","page":"227-237","volume":"78","issue":"2","source":"Wiley Online Library","abstract":"Reproductive synchrony and the consequent clustering of births are hypothesized to be regulated by seasonal changes in rainfall and food availability. Such climate-related seasonality is, however, questionable in tropical populations occupying temporally invariant habitats year round. Using the long-term data of the Cayo Santiago rhesus macaques from 1973 to 2013, this study distinguishes synchrony (a greater than chance clustering of births) from seasonality (a cluster of births during a period of the year when abiotic conditions are favorable) and shows that females are highly synchronized (>72% of births in a 3-month period) but the effects of environmental zeitgebers on reproduction are overridden by biological factors. Specifically, biotic and abiotic factors including (i) loss of immature offspring; (ii) population density; (iii) age at delivery; (iv) rainfall; and (v) changes in colony management were modeled in relation to the annual onset of births and the median birth date. Females experiencing loss of immature offspring had an interbirth interval of <365 days in average and the proportion of these females increased up to 48% due to changes in colony management overtime, although reproductive synchrony increased with increasing population density. A secular trend in both the onset of births and the median date of birth is documented and the model predicts that the median birth date will advance across all calendar-based seasons by 2050. The secular trend in reproduction appears to be triggered by changes in the age at delivery of females, the absence of physiological constraints from maternal investment due to offspring loss, shorter interbirth interval, and a higher degree of coordination due to increasing population density. This study challenges the reproductive phenology previously described for rhesus macaques highlighting the importance of long-term studies in addressing the ultimate causes of reproductive synchrony. Am. J. Primatol. 2015 Wiley Periodicals, Inc.","DOI":"10.1002/ajp.22502","ISSN":"1098-2345","journalAbbreviation":"Am. J. Primatol.","language":"en","author":[{"family":"Hernndez-Pacheco","given":"Raisa"},{"family":"Rawlins","given":"Richard G."},{"family":"Kessler","given":"Matthew J."},{"family":"Delgado","given":"Diana L."},{"family":"Ruiz-Lambides","given":"Angelina V."},{"family":"Sabat","given":"Alberto M."}],"issued":{"date-parts":[["2016",2,1]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 2. We further fitted the identity of the mother, the male's birth group and cohort as random effects. To avoid underestimating p-values of within subjects test predictors we fitted random slopes for all predictors that varied within each level of a random effect (see Tab. 1; ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"Bh9y6uru","properties":{"formattedCitation":"{\\rtf \\super 3\\nosupersub{}}","plainCitation":"3"},"citationItems":[{"id":5486,"uris":["http://zotero.org/groups/21925/items/QEEU95XH"],"uri":["http://zotero.org/groups/21925/items/QEEU95XH"],"itemData":{"id":5486,"type":"article-journal","title":"Random effects structure for confirmatory hypothesis testing: Keep it maximal","container-title":"Journal of Memory and Language","page":"255-278","volume":"68","issue":"3","source":"ScienceDirect","abstract":"Linear mixed-effects models (LMEMs) have become increasingly prominent in psycholinguistics and related areas. However, many researchers do not seem to appreciate how random effects structures affect the generalizability of an analysis. Here, we argue that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades. Through theoretical arguments and Monte Carlo simulation, we show that LMEMs generalize best when they include the maximal random effects structure justified by the design. The generalization performance of LMEMs including data-driven random effects structures strongly depends upon modeling criteria and sample size, yielding reasonable results on moderately-sized samples when conservative criteria are used, but with little or no power advantage over maximal models. Finally, random-intercepts-only LMEMs used on within-subjects and/or within-items data from populations where subjects and/or items vary in their sensitivity to experimental manipulations always generalize worse than separate F1 and F2 tests, and in many cases, even worse than F1 alone. Maximal LMEMs should be the gold standard for confirmatory hypothesis testing in psycholinguistics and beyond.","DOI":"10.1016/j.jml.2012.11.001","ISSN":"0749-596X","shortTitle":"Random effects structure for confirmatory hypothesis testing","journalAbbreviation":"J Mem Lang","author":[{"family":"Barr","given":"Dale J."},{"family":"Levy","given":"Roger"},{"family":"Scheepers","given":"Christoph"},{"family":"Tily","given":"Harry J."}],"issued":{"date-parts":[["2013",4]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 3). For this purpose we excluded the nine males born into group O from the analysis because some predictors did not vary within this random effects level. This reduced the total number of males used in the model to 912. All covariates were z-transformed to a mean of zero and a standard deviation of one to get comparable estimates and facilitate model convergence ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"UGYpIRpS","properties":{"formattedCitation":"{\\rtf \\super 4\\nosupersub{}}","plainCitation":"4"},"citationItems":[{"id":4567,"uris":["http://zotero.org/groups/21925/items/KJCTZD6N"],"uri":["http://zotero.org/groups/21925/items/KJCTZD6N"],"itemData":{"id":4567,"type":"article-journal","title":"Simple means to improve the interpretability of regression coefficients","container-title":"Methods in Ecology and Evolution","page":"103-113","volume":"1","issue":"2","source":"CrossRef","abstract":"1. Linear regression models are an important statistical tool in evolutionary and ecological studies. Unfortunately, these models often yield some uninterpretable estimates and hypothesis tests, especially when models contain interactions or polynomial terms. Furthermore, the standard errors for treatment groups, although often of interest for including in a publication, are not directly available in a standard linear model. 2. Centring and standardization of input variables are simple means to improve the interpretability of regression coefficients. Further, refitting the model with a slightly modified model structure allows extracting the appropriate standard errors for treatment groups directly from the model. 3. Centring will make main effects biologically interpretable even when involved in interactions and thus avoids the potential misinterpretation of main effects. This also applies to the estimation of linear effects in the presence of polynomials. Categorical input variables can also be centred and this sometimes assists interpretation. 4. Standardization (z-transformation) of input variables results in the estimation of standardized slopes or standardized partial regression coefficients. Standardized slopes are comparable in magnitude within models as well as between studies. They have some advantages over partial correlation coefficients and are often the more interesting standardized effect size. 5. The thoughtful removal of intercepts or main effects allows extracting treatment means or treatment slopes and their appropriate standard errors directly from a linear model. This provides a simple alternative to the more complicated calculation of standard errors from contrasts and main effects. 6. The simple methods presented here put the focus on parameter estimation (point estimates as well as confidence intervals) rather than on significance thresholds. They allow fitting complex, but meaningful models that can be concisely presented and interpreted. The presented methods can also be applied to generalised linear models (GLM) and linear mixed models.","DOI":"10.1111/j.2041-210X.2010.00012.x","ISSN":"2041210X, 2041210X","language":"en","author":[{"family":"Schielzeth","given":"Holger"}],"issued":{"date-parts":[["2010",2,10]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 4.
We fitted the models using Maximum Likelihood (rather than Restricted Maximum Likelihood; ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"YtbQzlb3","properties":{"formattedCitation":"{\\rtf \\super 5\\nosupersub{}}","plainCitation":"5"},"citationItems":[{"id":972,"uris":["http://zotero.org/groups/21925/items/5XHRJP34"],"uri":["http://zotero.org/groups/21925/items/5XHRJP34"],"itemData":{"id":972,"type":"article-journal","title":"Generalized linear mixed models: a practical guide for ecology and evolution","container-title":"Trends in Ecology & Evolution","page":"127-135","volume":"24","abstract":"How should ecologists and evolutionary biologists analyze nonnormal data that involve random effects? Nonnormal data such as counts or proportions often defy classical statistical procedures. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. Despite the availability of accurate techniques for estimating GLMM parameters in simple cases, complex GLMMs are challenging to fit and statistical inference such as hypothesis testing remains difficult. We review the use (and misuse) of GLMMs in ecology and evolution, discuss estimation and inference and summarize [`]best-practice' data analysis procedures for scientists facing this challenge.","DOI":"10.1016/j.tree.2008.10.008","shortTitle":"Generalized linear mixed models: a practical guide for ecology and evolution","author":[{"family":"Bolker","given":"Benjamin M."},{"family":"Brooks","given":"Mollie E."},{"family":"Clark","given":"Connie J."},{"family":"Geange","given":"Shane W."},{"family":"Poulsen","given":"John R."},{"family":"Stevens","given":"M. Henry H."},{"family":"White","given":"Jada-Simone S."}],"issued":{"date-parts":[["2009"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 5) to achieve more reliable p-values. Model assumptions of normally distributed and homogeneous residuals were checked visually, which did not indicate any obvious deviation from these assumptions. To check for collinearity we determined Variance Inflation Factors (VIF, ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"3MwkyI7w","properties":{"formattedCitation":"{\\rtf \\super 6\\nosupersub{}}","plainCitation":"6"},"citationItems":[{"id":271,"uris":["http://zotero.org/groups/21925/items/377D6876"],"uri":["http://zotero.org/groups/21925/items/377D6876"],"itemData":{"id":271,"type":"book","title":"Discovering statistics using SPSS","publisher":"Sage Publications, London","number-of-pages":"62","author":[{"family":"Field","given":"A"}],"issued":{"date-parts":[["2005"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 6) for a standard linear model excluding the random effects using the function "vif" in the package "car" ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"w1rYR54v","properties":{"formattedCitation":"{\\rtf \\super 7\\nosupersub{}}","plainCitation":"7"},"citationItems":[{"id":6995,"uris":["http://zotero.org/groups/21925/items/VTE26CSQ"],"uri":["http://zotero.org/groups/21925/items/VTE26CSQ"],"itemData":{"id":6995,"type":"book","title":"An {R} Companion to Applied Regression, Second Edition","publisher":"Sage","publisher-place":"Thousand Oaks CA","event-place":"Thousand Oaks CA","URL":"http://socserv.socsci.mcmaster.ca/jfox/Books/Companion","author":[{"family":"Fox","given":"John"},{"family":"Weisberg","given":"Sanford"}],"issued":{"date-parts":[["2011"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 7. VIFs were below 1.48 in all cases and thus indicated collinearity to be no issue. We assessed model stability by excluding subjects from the data one at a time. The estimates of these sets of models were similar to the coefficients of the original model, indicating that no influential cases exist. We assessed the significance of the full model by comparing it to a null model comprising only the control predictor, random intercepts and random slopes using a Likelihood Ratio Test (R function "anova", test = "Chisq"). P-values for the individual effects were obtained with Likelihood Ratio Tests using the function "drop1". We removed interactions with a p-value < 0.1 from the model to facilitate the interpretation of main terms but kept all other terms in the model.
Natal dispersal age and fitness
For investigating survival to one year after dispersal we used all focal males that remained on CS for a full year after dispersal or died a natural death within the year (n = 840). For post-dispersal longevity we used all focal males that had died naturally on CS before 2014 (n = 402). As paternity was only systematically assessed for offspring from 1992 onwards, we restricted analyses of reproductive success to males maturing after 1992 (i.e. from cohorts 1989 or later). The probability to reproduce was assessed for males who had sired offspring or had died naturally on CS without siring offspring (n = 297). Data on age at first reproduction were available for 254 focal males. LRS was assessed for 87 males that reproduced and died naturally on CS before 2014.
For each fitness trait we calculated a GLMM using the function "glmer". Survival of the first year after dispersal and the probability to reproduce were fitted as binomial response variables (yes/no), post-dispersal longevity (in years), age at first reproduction (in years) and LRS were fitted with a Poisson error structure. Age at natal dispersal (in days) was fitted as the only test predictor. As control predictors we included individual traits that tended to affect age at natal dispersal, i.e. maternal rank and co-residence with the mother in order to assess whether fitness traits were affected by age at natal dispersal or a phenotypically correlated trait. In all models we further included identity of the mother, the male's birth group and cohort as random effects and fitted all possible random slopes. For this purpose we excluded the only males from cohort 2008 and group Q from the analysis of age at first reproduction (resulting in an n of 252) to allow fitting random slopes within the respective random effects. For the same reason we removed the only males from cohorts 1999 and 2006 as well as from group Q from the analysis of LRS, reducing the n for this analysis to 84. None of the models were overdispersed (dispersion parameters 0.18 1.07) and variance inflation factors indicated collinearity to be no issue (all VIFs < 1.12). We assessed model stability by excluding random effects levels from the data one at a time. The model on post-dispersal longevity was highly instable when the control predictors were included in the model; we therefore ran this model without control predictors but including all random terms. Models on the other fitness traits and the model on post-dispersal longevity without control predictors produced stable results when single levels were excluded. We assessed the significance of natal dispersal age using the z and corresponding P value provided by the function "glmer".
Natal dispersal age, place of reproduction and group choice
To investigate the relationship between natal dispersal age and where males first reproduced we used focal males born in cohort 1989 or later with known age of first reproduction. We excluded the only male born in group Q and the only male from cohort 2008 from the analysis to allow the inclusion of natal dispersal age within birth group and cohort as a random slope (resulting in an N of 252 males). The GLMM was slightly underdispersed (dispersion parameter 0.53) and removal of subjects one at a time indicated no influential cases to exist. We assessed the significance of natal dispersal age using the z and corresponding P value provided by the function "glmer".
Detailed information on reproduction before natal dispersal was available for 94 males, for whom we determined if they had sired offspring with females from their natal group (i.e. within-group offspring) or from other groups (i.e. extra-group offspring). We considered infants to be extra-group offspring if the male resided in another group than the infant's mother on the day the infant was conceived. The conception date was determined by subtracting the mean gestation length of 166.5 ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"ehHulbah","properties":{"formattedCitation":"{\\rtf \\super 8\\nosupersub{}}","plainCitation":"8"},"citationItems":[{"id":5728,"uris":["http://zotero.org/groups/21925/items/RC9GC4ZX"],"uri":["http://zotero.org/groups/21925/items/RC9GC4ZX"],"itemData":{"id":5728,"type":"article-journal","title":"Gestation length in rhesus macaques (Macaca mulatta)","container-title":"International Journal of Primatology","page":"95-104","volume":"14","DOI":"10.1007/BF02196505","shortTitle":"Silk, Short et al. 1991 Gestation length in rhesus macaques","journalAbbreviation":"Int J Primatol","author":[{"family":"Silk","given":"J.B."},{"family":"Short","given":"J."},{"family":"Roberts","given":"J."},{"family":"Kusnitz","given":"J."}],"issued":{"date-parts":[["1993"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 8 from the infant's birth date. Because gestation length may vary by some days (SD of 7.4 days ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"XSWPYoxT","properties":{"formattedCitation":"{\\rtf \\super 8\\nosupersub{}}","plainCitation":"8"},"citationItems":[{"id":5728,"uris":["http://zotero.org/groups/21925/items/RC9GC4ZX"],"uri":["http://zotero.org/groups/21925/items/RC9GC4ZX"],"itemData":{"id":5728,"type":"article-journal","title":"Gestation length in rhesus macaques (Macaca mulatta)","container-title":"International Journal of Primatology","page":"95-104","volume":"14","DOI":"10.1007/BF02196505","shortTitle":"Silk, Short et al. 1991 Gestation length in rhesus macaques","journalAbbreviation":"Int J Primatol","author":[{"family":"Silk","given":"J.B."},{"family":"Short","given":"J."},{"family":"Roberts","given":"J."},{"family":"Kusnitz","given":"J."}],"issued":{"date-parts":[["1993"]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} 8) we did not consider infants with an assumed conception date of 10 days of the natal dispersal date.
The model testing if having fathered offspring in another group affected group choice during natal dispersal was slightly underdispersed (dispersion parameter 0.713) and the model was stable with regards to the removal of single cases. As in the other GLMMs, the significance of the test predictor was assessed using the z and corresponding P value provided by the function "glmer".
ADDIN ZOTERO_BIBL {"custom":[]} CSL_BIBLIOGRAPHY 1. Bates, D., Maechler, M., Bolker, B. & Walker, S. lme4: Linear mixed-effects models using Eigen and S4. (2014).
2. Hernndez-Pacheco, R. et al. Discovery of a secular trend in Cayo Santiago macaque reproduction. Am. J. Primatol. 78, 227237 (2016).
3. Barr, D. J., Levy, R., Scheepers, C. & Tily, H. J. Random effects structure for confirmatory hypothesis testing: Keep it maximal. J. Mem. Lang. 68, 255278 (2013).
4. Schielzeth, H. Simple means to improve the interpretability of regression coefficients. Methods Ecol. Evol. 1, 103113 (2010).
5. Bolker, B. M. et al. Generalized linear mixed models: a practical guide for ecology and evolution. Trends Ecol. Evol. 24, 127135 (2009).
6. Field, A. Discovering statistics using SPSS. (Sage Publications, London, 2005).
7. Fox, J. & Weisberg, S. An {R} Companion to Applied Regression, Second Edition. (Sage, 2011).
8. Silk, J. B., Short, J., Roberts, J. & Kusnitz, J. Gestation length in rhesus macaques (Macaca mulatta). Int. J. Primatol. 14, 95104 (1993).
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