Gather the data

If we are going to reproduce this analysis, we will first need togather the data. Thankfully, the data is available as supplementarymaterial from the publisher’s website. We provide a copy of this datawith the package:

library(rotl)

## This dataset is available from the publisher's study website:egg_data<-read.csv(system.file("extdata","egg.csv",package ="rotl"),stringsAsFactors =FALSE)## }head(egg_data)

##                   animal                   Spp       Lndim Measure Neggs## 1 Zonotrichia_leucophrys White-crowned sparrow 0.000000000  volume   294## 2      Passer_domesticus         House sparrow 0.009407469  volume   149## 3        Serinus_canaria                Canary 0.000000000  volume    52## 4          Turdus_merula    European blackbird 0.021189299  volume    82## 5    Agelaius_phoeniceus  Red-winged blackbird 0.218316086  volume   394## 6    Quiscalus_mexicanus  Great-tailed grackle 0.281894985    mass   822##   Nclutches        ESr Type         StudyID Year        D        EN         Zr## 1        73 0.14004594 stat        Mead1987 1987 3.421918  85.91673 0.14097244## 2        31 0.11175203 stat     Cordero2000 2000 4.045161  36.83413 0.11222075## 3        21 0.49679140 stat     Leitner2006 2006 2.180952  23.84279 0.54503712## 4        54 0.38598540 stat     Martyka2010 2010 1.414815  57.95812 0.40707397## 5       106 0.07410136  raw Weatherhead1985 1985 3.173585 124.14982 0.07423744## 6       205 0.05178834  raw     Teather1989 1989 3.407805 241.21099 0.05183471##           VZr## 1 0.012060292## 2 0.029555954## 3 0.047978211## 4 0.018195675## 5 0.008254242## 6 0.004197959

The most important variable in this dataset isZr, whichis anormalizedeffect size for difference ,in size between eggs that contain malesand females. Values close to zero come from studies that found the sexof an egg’s inhabitant had little effect in its size, while largepositive or negative values correspond to studies with substantial sexbiases (towards males and females respectively). Since this is ameta-analysis we should produce the classicfunnel plot witheffects-size on the y-axis and precision (the inverse of the samplestandard error) on the x-axis. Here we calculate precision from thesample variance (Vzr):

plot(1/sqrt(egg_data$VZr), egg_data$Zr,pch =16,ylab ="Effect size (Zr)",xlab ="Precision (1/SE)",main ="Effect sizes for sex bias in egg size among 51 brid species")

plot of chunk eggs_in_a_funnel

In order to use this data later on we need to first convert it to astandarddata.frame. We can also convert theanimal column (the species names) to lower case, and removethe underscores in their names, which will make it easier to match nameslater on:

egg_data<-as.data.frame(egg_data)## Convert taxon names to lower caseegg_data$animal<-tolower(egg_data$animal)## Let's remove the underscores (_) from the taxon namesegg_data$animal<-gsub("_"," ", egg_data$animal)

Find the species in OTT

We can use the OTL synthesis tree to relate these species. To do sowe first need to find Open Tree Taxonomy (OTT) IDs for each species. Wecan do that with the Taxonomic Name Resolution Service functiontnrs_match_names:

taxa<-tnrs_match_names(unique(egg_data$animal),context ="Animals")

## Warning in tnrs_match_names(unique(egg_data$animal), context = "Animals"):## partial argument match of 'context' to 'context_name'

head(taxa)

##            search_string            unique_name approximate_match ott_id## 1 zonotrichia leucophrys Zonotrichia leucophrys             FALSE 265553## 2      passer domesticus      Passer domesticus             FALSE 745175## 3        serinus canaria        Serinus canaria             FALSE 464865## 4          turdus merula          Turdus merula             FALSE 568572## 5    agelaius phoeniceus    Agelaius phoeniceus             FALSE 226605## 6    quiscalus mexicanus    Quiscalus mexicanus             FALSE 743411##   is_synonym          flags number_matches## 1      FALSE                             1## 2      FALSE                             1## 3      FALSE sibling_higher              1## 4      FALSE                             1## 5      FALSE                             1## 6      FALSE                             1

All of these species are in OTT, but a few of them go by differentnames in the Open Tree than we have in our data set. Because the treerotl fetches will have Open Tree names, we need to create anamed vector that maps the names we have for each species to the namesOpen Tree uses for them:

taxon_map<-structure(taxa$search_string,names = taxa$unique_name)

Now we can use this map to retrieve “data set names” from “OTTnames”:

taxon_map["Anser caerulescens"]

##  Anser caerulescens ## "chen caerulescens"

Get a tree

Now we can get the tree. There are really too many tips here to shownicely, so we will leave them out of this plot

tr<-tol_induced_subtree(ott_id(taxa)[is_in_tree(ott_id(taxa))])

## Warning in collapse_singles(tr, show_progress): Dropping singleton nodes## with labels: mrcaott246ott5481, mrcaott246ott7145, mrcaott246ott928360,## mrcaott246ott1858, mrcaott246ott2907, mrcaott246ott3600042, mrcaott246ott7113,## Passeriformes ott1041547, mrcaott246ott3212, mrcaott246ott428578,## mrcaott246ott44866, mrcaott246ott5929, mrcaott246ott32658,## mrcaott246ott310390, mrcaott246ott176461, mrcaott246ott22325,## mrcaott246ott10351, mrcaott246ott193904, mrcaott246ott5934, mrcaott246ott1566,## mrcaott1566ott3598440, mrcaott1566ott496009, mrcaott1566ott59716,## mrcaott1566ott32651, mrcaott1566ott24297, mrcaott1566ott45312,## mrcaott1566ott22300, mrcaott22300ott35350, mrcaott22300ott547548,## mrcaott22300ott909199, mrcaott22300ott67150, mrcaott22300ott130294,## mrcaott22300ott3598245, mrcaott22300ott416087, mrcaott22300ott629342,## mrcaott22300ott416089, mrcaott22300ott107840, mrcaott364210ott451069,## mrcaott364210ott3598839, mrcaott3598839ott5341363, mrcaott19467ott431648,## mrcaott19467ott252687, mrcaott19467ott401023, mrcaott19467ott233446,## mrcaott19467ott168078, mrcaott19467ott1046624, mrcaott19467ott161293,## mrcaott19467ott46396, mrcaott46396ott46398, mrcaott46398ott168083,## mrcaott168083ott431676, mrcaott2175ott35326, mrcaott2175ott968664,## mrcaott2175ott259082, mrcaott2175ott59905, mrcaott2175ott2224,## mrcaott2224ott366470, mrcaott3364ott310375, mrcaott3364ott3370,## mrcaott4083ott35042, mrcaott4083ott370807, mrcaott4083ott469177,## mrcaott4083ott18592, mrcaott4083ott139823, mrcaott4083ott11712,## mrcaott4083ott95949, Erythrura ott465905, mrcaott24017ott389884,## mrcaott24017ott24025, mrcaott24025ott596763, mrcaott24025ott453058,## mrcaott24025ott141501, mrcaott141501ott966119, mrcaott141501ott865472,## mrcaott141501ott389883, mrcaott105913ott311555, mrcaott311555ott1082386,## mrcaott311555ott708327, mrcaott708327ott966122, mrcaott4088ott8371,## mrcaott4088ott5616, mrcaott5616ott28339, mrcaott5616ott6023,## mrcaott6023ott243614, mrcaott6023ott101225, mrcaott6023ott125079,## mrcaott125079ott463026, mrcaott125079ott765405, Zonotrichia (genus in## domain Eukaryota) ott789032, mrcaott125079ott265547, mrcaott125079ott265554,## mrcaott5620ott254662, mrcaott5620ott29804, mrcaott29804ott449580,## mrcaott29804ott449562, mrcaott29804ott86894, mrcaott29804ott93045,## mrcaott93045ott264496, mrcaott264496ott264500, mrcaott264500ott3597163,## mrcaott264500ott283668, Quiscalus ott743410, mrcaott283673ott673386,## mrcaott283673ott741944, mrcaott283673ott735243, mrcaott213448ott213452,## mrcaott213448ott1009279, mrcaott213448ott213451, mrcaott213454ott430627,## mrcaott430627ott498751, mrcaott430627ott617797, mrcaott430627ott3597159,## mrcaott99175ott364331, Xanthocephalus ott364336, mrcaott6366ott28332,## mrcaott6366ott88283, mrcaott6366ott341465, mrcaott6366ott157599,## mrcaott6366ott178457, mrcaott6366ott405215, mrcaott6366ott238142,## mrcaott6366ott6375, mrcaott6375ott119724, mrcaott6375ott238137,## mrcaott238137ott328909, mrcaott238137ott464865, Haemorhous ott3601758,## mrcaott9416ott840030, mrcaott9416ott96148, mrcaott9416ott7068473, Passer## ott515158, mrcaott9416ott407769, mrcaott9416ott25628, mrcaott9416ott407764,## mrcaott9416ott68955, mrcaott9416ott73636, mrcaott1488ott72472,## mrcaott1488ott63797, mrcaott1488ott284404, mrcaott1488ott107463,## mrcaott1488ott17016, mrcaott1488ott44217, mrcaott1488ott16185,## mrcaott16185ott274931, Hirundinidae ott897681, mrcaott16185ott67916,## mrcaott67916ott67921, mrcaott67916ott368059, mrcaott67916ott67920,## Delichon ott922719, mrcaott107476ott177058, mrcaott107476ott271376,## mrcaott107476ott337752, mrcaott337752ott7661935, mrcaott337752ott337762,## mrcaott337752ott7068616, mrcaott2375ott73144, mrcaott2375ott124085,## mrcaott2375ott71358, mrcaott2375ott814750, mrcaott2375ott61147,## mrcaott84656ott123763, mrcaott123763ott728471, mrcaott123763ott258794,## mrcaott4820ott409116, mrcaott4820ott17162, mrcaott4820ott20998,## mrcaott4820ott20989, mrcaott4820ott58860, mrcaott4820ott23690,## mrcaott4820ott20996, mrcaott4820ott11462, mrcaott4820ott140440,## mrcaott4820ott197505, mrcaott4820ott75978, mrcaott4820ott11315,## mrcaott4820ott5933, mrcaott5933ott60465, mrcaott5933ott25637,## mrcaott25637ott199843, mrcaott25637ott473431, mrcaott25637ott686166,## mrcaott25637ott111993, mrcaott25637ott183621, mrcaott183621ott501241,## mrcaott501241ott3598010, mrcaott501241ott597018, mrcaott686165ott686168,## mrcaott60456ott662804, mrcaott60456ott75990, Pica ott776480, Falconiformes## ott212187, Falconidae ott212186, mrcaott47588ott225286, mrcaott47588ott748842,## mrcaott47588ott201377, mrcaott201377ott773020, Cerchneis ott3596159,## mrcaott179290ott352521, mrcaott179290ott624976, mrcaott179290ott624973,## mrcaott179290ott624974, mrcaott179290ott432111, mrcaott5272ott92263,## mrcaott5272ott24121, Scolopacidae ott887699, mrcaott24121ott217797,## mrcaott24121ott45306, mrcaott24121ott654830, mrcaott24121ott214779,## mrcaott24121ott651066, mrcaott651066ott1090732, mrcaott7639ott306220,## mrcaott7639ott57833, mrcaott7639ott383929, mrcaott7639ott279504,## mrcaott7639ott47401, mrcaott7639ott341047, mrcaott7639ott234666,## mrcaott7639ott341034, mrcaott7639ott285543, Sterna ott16767,## mrcaott285543ott341030, mrcaott285543ott738509, mrcaott285543ott966606,## mrcaott285543ott966604, mrcaott22965ott738512, mrcaott22965ott80679,## mrcaott22965ott558955, mrcaott22965ott154126, mrcaott22965ott241571,## mrcaott22965ott282132, mrcaott22965ott414141, mrcaott22965ott704174,## mrcaott22965ott704175, mrcaott22965ott324050, mrcaott22965ott353849,## mrcaott22965ott75913, mrcaott75913ott335736, mrcaott306645ott450107,## mrcaott425206ott887691, mrcaott425206ott515355, mrcaott119599ott993041,## mrcaott119599ott509055, mrcaott698969ott4947414, mrcaott147723ott219032,## Stercorariidae ott168297, Stercorarius ott742632, mrcaott742640ott742641,## mrcaott57823ott57827, mrcaott57823ott242771, mrcaott57823ott112937,## mrcaott112937ott129402, mrcaott112937ott454019, mrcaott112937ott242776,## mrcaott242776ott313115, mrcaott242776ott704464, mrcaott242776ott331994,## mrcaott331994ott413796, mrcaott9830ott86672, mrcaott9830ott90560,## mrcaott9830ott324158, mrcaott9830ott55044, mrcaott9830ott285638,## mrcaott9830ott117726, Sulidae ott452462, mrcaott170197ott403772, Sula ott160486,## mrcaott170197ott5859716, mrcaott170197ott429615, mrcaott429615ott1030312,## Procellariiformes ott452461, mrcaott18206ott31011, mrcaott31011ott71459,## Diomedeidae ott85277, mrcaott71459ott320282, Phoebastria ott941509,## mrcaott320282ott320284, Sphenisciformes ott494366, Spheniscidae ott494367,## mrcaott60413ott3600120, mrcaott60413ott4130813, mrcaott60413ott4130835,## mrcaott60413ott4130830, mrcaott60413ott3600127, mrcaott60413ott4130831,## mrcaott60413ott3600124, mrcaott60413ott3600128, mrcaott60413ott3600129,## mrcaott60413ott4130819, mrcaott60413ott4130817, mrcaott60413ott60417,## mrcaott60413ott3600131, mrcaott60413ott917663, Eudyptes ott494364,## mrcaott82219ott116946, mrcaott116946ott219197, mrcaott134466ott494361,## Pygoscelis ott494365, mrcaott134466ott783352, mrcaott5021ott198671,## mrcaott5021ott75792, Cuculiformes ott212171, mrcaott75792ott212172,## mrcaott75792ott3601282, mrcaott75792ott119216, mrcaott119216ott212175,## mrcaott119216ott169265, mrcaott169265ott550039, mrcaott169265ott462546,## mrcaott462546ott3596355, mrcaott462546ott1050027, Cuculus ott1041429,## mrcaott549514ott7068132, mrcaott549514ott3596308, mrcaott549514ott3596307,## mrcaott549514ott3596306, mrcaott549514ott792626, mrcaott17146ott57819,## Columbiformes ott363030, mrcaott17146ott45505, mrcaott45505ott50388,## mrcaott45505ott506098, mrcaott45505ott51607, mrcaott51607ott277822,## mrcaott51607ott67614, mrcaott51607ott244134, Columba ott938415,## mrcaott51607ott277817, mrcaott277817ott320359, mrcaott320359ott493986,## mrcaott320359ott767317, mrcaott320359ott921832, mrcaott320359ott938416,## Galliformes ott837585, mrcaott4765ott6520194, mrcaott4765ott109888,## mrcaott4765ott75785, mrcaott4765ott104461, mrcaott4765ott151684,## mrcaott4765ott54193, mrcaott4765ott49319, mrcaott4765ott3596087,## mrcaott4765ott415487, mrcaott4765ott51354, mrcaott4765ott446490, Tetraoninae## ott999677, mrcaott4765ott55929, mrcaott4765ott539045, mrcaott4765ott234824,## Centrocercus ott728081, mrcaott53700ott572162, mrcaott53700ott466627,## mrcaott53700ott309383, mrcaott53700ott102722, mrcaott102722ott137547, Phasianus## ott102718, mrcaott49310ott102705, mrcaott49310ott153554, mrcaott153554o

plot(tr,show.tip.label =FALSE)

There are a few things to note here. First, the tree has no branchlengths. At present this is true for the whole of the Open Treesynthetic tree. Some comparative methods require either branch lengthsor an ultrametric tree. Before you can use one of those methods you willneed to get a tree with branch lengths. You could try looking forpublished trees made available by the Open Tree withstudies_find_trees. Alternatively, you could estimatebranch lengths from the toplogy of a phylogeny returned bytol_induced_subtree, perhaps by downloading DNA sequencesfrom the NCBI withrentrez or “hanging” the tree on nodesof known-age using penalized likelihood method inape::chronos. In this case, we will use only the topologyof the tree as input to our comparative analysis, so we can skip thesesteps.

Second, the tip labels contain OTT IDs, which means they will notperfectly match the species names in our dataset or the taxon map thatwe created earlier:

tr$tip.label[1:4]

## [1] "Ficedula_albicollis_ott107840" "Luscinia_svecica_ott274225"   ## [3] "Turdus_merula_ott568572"       "Sturnus_unicolor_ott366470"

Finally, the tree contains node labels for those nodes that match ahigher taxonomic group, and empty character vectors ("")for all other nodes. Some comparative methods either do no expect nodelabels at all, or require all labeled nodes to have a unique name(meaning multiple “empty” labels will cause and error).

We can deal with all these details easily.rotl providesthe convenience functionstrip_ott_ids to remove the extrainformation from the tip labels. With the IDs removed, we can use ourtaxon map to replace the tip labels in the tree with the species namesfrom dataset.

otl_tips<-strip_ott_ids(tr$tip.label,remove_underscores =TRUE)tr$tip.label<- taxon_map[ otl_tips ]

Finally, we can remove the node labels by setting thenode.label attribute of the tree toNULL.

tr$node.label<-NULL

egg_data<- egg_data[egg_data$animal%in% tr$tip.label, ]

Perform the meta-analysis

Now we have data and a tree, and we know the names in the tree matchthe ones in the data. It’s time to do the comparative analysis.Rutkowskaet al. usedMCMCglmm, a Bayesian MCMCapproach to fitting multi-level models,to perform their meta-analysis,and we will do the same. Of course, to properly analyse these data youwould take some care in deciding on the appropriate priors to use andinspect the results carefully. In this case, we are really interested inusing this as a demonstration, so we will just run a simple model.

Specifically we sill fit a model where the only variable that mightexplain the values ofZr is the random factoranimal, which corresponds to the phylogenetic relationshipsamong species. We also provideZvr as the measurement errorvariance, effectively adding extra weight to the results of morepowerful studies. Here’s how we specify and fit that model withMCMCglmm:

set.seed(123)if (require(MCMCglmm,quietly =TRUE)) {  pr<-list(R =list(V =1,nu =0.002),G =list(G1 =list(V =1,nu =0.002))  )  model<-MCMCglmm(Zr~1,random =~animal,pedigree = tr,mev = egg_data$VZr,prior = pr,data = egg_data,verbose =FALSE  )}else {  model<-readRDS(file =system.file("extdata","mcmcglmm_model.rds",package ="rotl"))}

## Warning in inverseA(pedigree = pedigree, scale = scale, nodes = nodes): no## branch lengths: compute.brlen from ape has been used

## Warning in sing.rm$coef: partial match of 'coef' to 'coefficients'

## Warning in x$n: partial match of 'n' to 'nu'## Warning in x$n: partial match of 'n' to 'nu'## Warning in x$n: partial match of 'n' to 'nu'## Warning in x$n: partial match of 'n' to 'nu'## Warning in x$n: partial match of 'n' to 'nu'## Warning in x$n: partial match of 'n' to 'nu'

Now that we have a result we can find out how much phylogeneticsignal exists for sex-biased differences in egg-size. In a multi-levelmodel we can use variance components to look at this, specifically theproportion of the total variance that can be explained by phylogeny iscalled the phylogenetic reliability,H. Let’s calculate theH for this model:

var_comps<-colMeans(model$VCV)var_comps["animal"]/sum(var_comps)

##     animal ## 0.00283581

It appears there is almost no phylogenetic signal to the data. Therelationships among species explain much less that one percent of thetotal variance in the data. If you were wondering, Rutkowskaetal. report a similar result, even after adding more predictors totheir model most of the variance inZr was leftunexplained.