Ecology

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R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2022). Available online at: https://www.R-project.org More

This Hubble image captures a set of galaxies that are unusual because they seem not to have dark matter.Credit: NASA/ESA/P. van Dokkum, Yale Univ.

Galaxies without dark matter baffle astronomersScientists have long thought that galaxies cannot form without the gravitational pull of the mysterious material known as dark matter. But one group of astronomers thinks it might have observed a line of 11 galaxies that don’t contain any of the substance, and could all have been created in an ancient collision (P. van Dokkum et al. Nature 605, 435–439; 2022).This kind of system could be used to learn about how galaxies form, and about the nature of dark matter itself. However, some researchers are not convinced that the claim is much more than a hypothesis.The finding centres on two galaxies, called DF2 and DF4, that were described in 2018 and 2019. Their stars moved so slowly that the pull of dark matter was not needed to explain their orbits, so the team concluded that the galaxies contained no dark matter.In the latest research, scientists identified between three and seven new candidates for dark-matter-free galaxies in a line between DF2 and DF4, as well as strange, faint galaxies at either end.“If proven right, this could certainly be exciting for galaxy formation. However, the jury is still out,” says Chervin Laporte, an astronomer at the University of Barcelona in Spain.Northern Australian tree deaths double in 35 yearsThe rate at which trees are dying in the old-growth tropical forests of northern Australia each year has doubled since the 1980s, and researchers say climate change is probably to blame.The findings, published in Nature on 18 May, come from an extraordinary record of tree deaths catalogued at 24 sites in the tropical forests of northern Queensland over the past 49 years (D. Bauman et al. Nature https://doi.org/hv67; 2022).The research team recorded that 2,305 trees across 81 key species had died since 1971. But from the mid-1980s, tree mortality risk increased from an average of 1% a year to 2% a year (see ‘Increasing death rate’). Of the 81 tree species that the team studied, 70% showed an increase in mortality risk over the study period.The study found that the rise in death rate occurred at the same time as a long-term trend of increases in the atmospheric vapour pressure deficit, which is the difference between the amount of water vapour that the atmosphere can hold and the amount of water it does hold at a given time. The higher the deficit, the more water trees lose through their leaves, which can lead to sustained stress and eventually tree death.

Europe’s first farming populations descend mostly from farmers in the Anatolian peninsula, in what is now Turkey.Credit: Fatih Kurt/Anadolu Agency/Getty

Ancient DNA maps ‘dawn of farming’Sometime before 12,000 years ago, nomadic hunter-gatherers in the Middle East made one of the most important transitions in human history: they began staying put and took to farming.Two ancient-DNA studies have now homed in on the identity of the hunter-gatherers who settled down.Researchers sequenced the genomes of 15 hunter-gatherers and early farmers who lived in southwest Asia and Europe, along a key migration routes into Europe — the Danube River (N. Marchi et al. Cell https://doi.org/gp49rr; 2022).The team found that ancient farmers in Anatolia — now Turkey — descended from repeated mixing between distinct hunter-gatherer groups from Europe and the Middle East. These groups first split at the height of the last Ice Age, some 25,000 years ago. Modelling suggests that the western groups nearly died out, before rebounding as the climate warmed.Once established in Anatolia, the researchers found, early farmers moved west into Europe in a stepping-stone-like way, beginning around 8,000 years ago. They mixed occasionally — but not extensively — with local hunter-gatherers.The findings chime with those of a similar ancient-genomics study posted on the bioRxiv preprint server this month (M. E. Allentoft. et al. Preprint at bioRxiv https://doi.org/hv7g; 2022). More

The custom code used to clean occurrence records and construct SDMs is available at (github.com/RhettRautsaw/ VenomMaps). We used the following R16 packages for data cleaning, manipulation, species distribution modeling, and Shiny app creation: tidyverse17 readxl18, data.table19, sf20, sp21,22, rgdal23, raster24, smoothr25, ape26, phytools27, argparse28, parallel16, memuse29, dismo30, rJava31, concaveman32, spThin33, usdm34, ENMeval35, kuenm36, shiny37, leaflet38, leaflet.extras39, leaflet.extras240, RColorBrewer41, ggpubr42, ggtext43, and patchwork44.Updating occurrence record taxonomyOur goal was to update and reconstruct the distributions of New World pitvipers. We used the Reptile Database45 (May 2021) as our primary source for current taxonomy which included the following genera: Agkistrodon, Atropoides, Bothriechis, Bothrocophias, Bothrops, Cerrophidion, Crotalus, Lachesis, Metlapilcoatlus, Mixcoatlus, Ophryacus, Porthidium, and Sistrurus. However, to ensure we captured all New World pitvipers records, we incorporated all members of the family Viperidae (all vipers and pitvipers) into our pipeline for updating occurrence record taxonomy (i.e., to account for errors in the recorded latitude, longitude, or if subfamily was not recorded).First, we collected global occurrence records for “Viperidae” from GBIF (downloaded 2021-08-19)46, Bison (downloaded 2021-08-19)47, HerpMapper (only New World taxa; downloaded 2021-08-19)48, Brazilian Snake Atlas49, BioWeb (downloaded 2021-07-07)50, unpublished data/databases from RMR, GJV, EPH, LRVA, MM, and CLP, and georeferenced literature records totaling 373,673 species-level records, 292,425 of which are New World pitvipers. Given the fluidity of taxonomy, records were often associated with outdated names. For example, Crotalus mitchelli pyrrhus was elevated to Crotalus pyrrhus51, but may still be recorded as the former in a given repository (e.g., GBIF). To correct taxonomy in our database, we checked records against a list of synonyms found on the Reptile Database and compared them to current taxonomy. If species and subspecies columns matched the same taxon (or no subspecies was recorded), then species IDs were not altered. If species and subspecies IDs did not match the same taxon, we updated taxonomy by minimizing the number of changes required to a given character string. We then manually checked all changes.Constructing distribution mapsNext, we collected preliminary distribution maps from the International Union for Conservation of Nature (IUCN; downloaded 2018-11-27)52, Global Assessment of Reptile Distributions (GARD) v1.153, Heimes54, Campbell and Lamar55, and unpublished maps. We manually curated distribution maps for all New World pitvipers in QGIS using the occurrence records, previous distribution maps, and recent publications for each taxon (note that distributions for Old World Viperidae have not yet been updated). We used a digital relief map (maps-for-free.com) and The Nature Conservancy Terrestrial Ecoregions (TNG.org)56 to identify clear distribution boundaries (e.g., mountains). We then clipped the final distributions to a land boundary (GADM v3.6)57 and smoothed the distribution using the the “chaikin” method in the R package smoothr25.Occurrence-distribution overlapOur initial taxonomy check was only concerned with records for which a subspecies was recorded and had since been elevated to species status. Therefore, many records with no assigned subspecies likely remained associated with an incorrect or outdated generic and/or specific identification. Fortunately, taxonomic changes are typically associated with changes in the species’ expected distribution. For example, when Crotalus simus was resurrected from C. durissus, the distribution of C. durissus was split: the northern portion of its range in Central America now represented the resurrected species (C. simus) and the southern portion of its range remained C. durissus55. Yet, occurrence records in Central America often remain labelled as C. durissus in data repositories. Therefore, we spatially joined records with the newly reconstructed species distribution maps to determine if they overlapped with their expected distribution (Old World taxa were joined with the GARD 1.1 distributions53).Briefly, we developed a custom function (occ_cleaner.R) to perform the spatial join and update taxonomy. First, we calculated the distance for each record to the 20 nearest distributions within 50 km (full overlap resulted in a distance of 0 m). Next, we calculated the phylogenetic distance between the recorded species ID and each species with which that record overlapped using the tree from Zaher et al.58 and adding taxa based on recent clade-specific publications (bind.tip2.R; see github.com/RhettRautsaw/VenomMaps for full list of references and details). If records overlapped with their expected species, no changes were made. If records fell outside of their expected distribution, we filtered the potential overlapping and nearby species (within 50 km) to minimize phylogenetic distance. If multiple species were equally distant (i.e., share the same common ancestor), we attempted to minimize geographic distance. If multiple species remained equally distant in both phylogenetic and geographic distance, we flagged the record to be manually checked. We also flagged records if a species’ taxonomy had changed and records were additionally flagged as potentially dubious if the taxonomic change had a phylogenetic divergence greater than 5 million years. We manually checked all flagged records and returned records to their original species ID if species identity remained uncertain. We flagged these records as potentially dubious, along with records that fell outside of their expected distribution (within 50 km), and removed all flagged records for species distribution modeling. Our final cleaned database contained 344,998 global records, of which 275,087 were New World pitvipers.Species distribution modelingWe attempted to infer SDMs for the 158 species of New World pitvipers currently recognized by the Reptile Database (May 2021) and additionally modeled the three subspecies of Crotalus ravus separately based on recommendations for species status elevation by Blair et al.59 for a total of 160 species. We developed a unix-executable R script (autokuenm.R) designed to take occurrence records, distribution maps, and environmental data and prepare these data for species distribution modeling with kuenm36. We chose to use kuenm – and MaxEnt v3.4.460 – because it has been shown to have good predictive power61 and fine-tuning of this algorithm has performance comparable to more computationally intensive ensembles62,63. Additionally, MaxEnt allows for flexibility in parameter selection64 and can function entirely with presence data14.Prior to autokuenm, to account for sampling/spatial bias during SDM, we created a bias file by using the pooled New World pitviper occurrence records as representative background data65,66,67,68. Specifically, we converted occurrence records to a raster and performed two-dimensional kernel density estimation (kde2d) with the MASS package with default settings69 and rescaled the kernel density by a factor of 1000 and rounded to three decimal places. This was then used as input to factor out sampling bias by MaxEnt. We then ran autokuenm, which is designed to subset/partition the cleaned occurrence records for a given species and prepare additional files for SDM. We first defined M-areas – or areas accessible to a given species – using the World Wildlife Fund Terrestrial Ecoregions70. Biogeographic regions represent distributional limits for many species and are reasonable hypotheses for the areas accessible to a given species71,72. To do this, we created alpha hulls from the subset of occurrence records for a given species using concaveman32 with default settings. We then identified regions with at least 20% of the region covered by the alpha hull and merged these regions together to form our final M-area. All environmental layers and the bias file were cropped to this M-area which was used as the geographic extent for modeling. We then randomly selected 5% of records to function as an independent test set for final model evaluation. Next, we generated 2000 random background points across the cropped environmental layers and used ENMeval to partition occurrence records into four sets using the checkerboard2 pattern35. Note that the background points here were not used in MaxEnt. One of the four partitions was selected at random to be used as the testing set; the remaining three partitions were used for training the MaxEnt models. If the number of occurrence records in the independent test set was less than five, then we used the training partition for final model creation and used the testing partition for final model evaluation.We tested the top-contributing variables from three sets of environmental layers: (1) bioclimatic variables, (2) EarthEnv topographic variables73, and (3) a combination of these variables. To select the top-contributing variables in each set, we wrote a custom function (SelectVariables) which used a combination of MaxEnt permutation importance and Variable Inflation Factors (VIF) to remove collinearity while keeping the variables that contributed the most to the model. Compared with variable selection via principal component analysis loadings, the permutation importance and VIF methodology demonstrated significant improvement in MaxEnt model fit. First, we designed SelectVariables to run MaxEnt using dismo::maxent with default settings and then extracted the permutation importance. We removed variables if they had 0% permutation importance. Next, we calculated VIF with usdm::vif and then iteratively removed variables by selecting the variables with two highest VIF values and removing whichever variable had the lowest permutation importance. We then recalculated VIF and repeated the process until the maximum VIF value was less than 10. Finally, we recalculated permutation importance with the remaining variables using dismo::maxent with default settings and removed variables with less than 1% permutation importance to create the final variable sets. This process was done for each species independently.With the final environmental variable, testing, and training sets, we generated SDMs using kuenm. First, we created candidate calibration models with multiple combinations of regularization multipliers (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 8, 10), feature classes (l, q, h, lq, lp, lt, lh, qp, qt, qh, pt, ph, th, lqp, lqt, lqh, lpt, lph, lth, qpt, qph, qth, pth, lqpt, lqph, lqth, lpth, qpth, lqpth), and sets of environmental predictors (bioclimatic, topographic, combination) totaling 2,958 candidate models per species. We then ran each model in parallel using GNU Parallel74. Next, we evaluated the candidate models and selected the best models using statistical significance (partial ROC), prediction ability (omission rates; OR), and model complexity (AICc) with the “kuenm_ceval” function with default settings. Specifically, models were only considered if they were statistically significant and had an OR less than 5%. If no models passed the OR criteria, the models with the minimal OR were considered. Finally, any remaining models were filtered to those within 2 AICc of the top model (Supplementary Table 1). In addition to evaluating and comparing all models together, we evaluated bioclimatic-only and combination-only models separately since these two sets of environmental variables were expected to be the best performing models given the ubiquity of bioclimatic variables in species distribution modeling (Supplementary Table 1).We generated 10 bootstrap replicates for each of the “best” calibration models using the “kuenm_mod” function. We also performed jackknifing to assess variable importance and models were output in raw format. We evaluated the final models using “kuenm_feval” with default settings. To select the best model for each comparative set (i.e., all, bioclimatic-only, and combination-only sets), we filtered the final evaluation results to minimize the OR and maximize the AUC ratio (Supplementary Table 2). If multiple models remained and were considered equally competitive, we averaged these models together (Supplementary Table 3). Because we performed three different set of comparisons, there were three “best” models per species, so we again aimed to minimize the OR and maximize the AUC ratio to select a final model for each species (Supplementary Table 4). We then converted our final models into cloglog format for visualization and threshold the models using a 10th percentile training presence cutoff (Fig. S2). Both conversion and thresholding functions are provided as R functions (raw2log, raw2clog, raster_threshold in functions.R; github.com/RhettRautsaw/VenomMaps). More

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In this study, we aimed to determine if tropical cyclones in the northwestern GOM differentially affected mesozooplankton community structure. We found that multivariate community structure varied between storm and non-storm years. However, among the three hurricanes, only the post-Harvey mesozooplankton communities were distinct from years where no storms occurred. Multivariate dispersion, a measure of variance within community structure, did not differ between storm and non-storm years. This result refutes our hypothesis that variability in zooplankton community structure would be higher during storm years opposed to non-storm years. Our prediction that post-storm mesozooplankton communities would differ from non-storm communities was supported, as was our expectation that mesozooplankton community structure varied among storms. We hypothesized that due to the major flooding and rainfall of Harvey, reduced salinity would likely be the main driver of mesozooplankton community differences relative to non-storm years. This expectation was partially met; differences in mesozooplankton community structure between Harvey and years with no storms were driven by salinity, stratification, and ‘distance-from-shore’ rather than solely salinity. This indicates that NWGOM zooplankton community structure varies holistically with biophysical conditions rather than being primarily driven by one or two dominating factors24. Moreover, we found that the presence of Hurricane Harvey, rather than temperature, explained the second greatest amount of variance in zooplankton community structure reflecting the importance of considering how complex disturbance mechanisms might compound and result in a unique ecological responses following a tropical cyclone. The overall PSEM showed that high salinity was directly associated with reduced fluorescence and depressed zooplankton abundance. Higher abundances were found to result in higher community dominance (i.e., lower evenness). Conversely, high salinities indirectly reduced zooplankton evenness via greater water column stratification. Lower fluorescence at higher salinities supports the spatial patterns in NWGOM phytoplankton identified by Kurtay et al.20 following Hurricane Harvey. Those authors observed declines in overall phytoplankton abundance and communities increasingly dominated by cells  More

Data preparationHistorical dataThe primary source of data is historical parish registers, which have been transcribed under the supervision of many of the study authors over a number of decades, primarily for evolutionary demographic research. Our dataset (Supplementary Data 1) includes nine European populations, including some for which the positive relationship between maternal lifetime twinning status and maternal total births has been described previously5,6,8,10. Details for the populations used in this study are given in Table 1 and in Supplementary Table 14. The sourcing of each dataset and the socio-ecological background of each population have already been described in previous studies (see Table 1 for references). Overall, there is no reason to suspect a high level of consanguinity in these populations62, so our analyses do not account for the variable level of relatedness between individuals. The datasets cover pre-industrial periods in which the lifetime reproductive success was high and the majority of people were living and working in agrarian communities, except for the Samis (from northern Finland and Sweden) who made their living fully or in part from a combination of herding, fishing and hunting. The smooth decline of the probability of parity progression with parity (Fig. 4a) suggests that mothers did not effectively limit their reproductive success with the aim of achieving a small family size, as found in populations that have undergone a demographic transition.Data selectionWe use the term family to describe a mother and all individuals to whom she gave birth over her life. For our analyses, all families considered met the following criteria: the mother’s age was known at a monthly resolution and her life course traced until at least age 45 (approximating full reproductive life), the birth year and month of all offspring must have been recorded and consecutive births were all at least nine months apart from one another. In the case of one population (Norway) and of a few observations in the other populations, the month of birth was not available. These data were thus not considered in the results presented in main text because some of our analyses require an accurate estimation of the interbirth interval. Most analyses are thus based on data from eight populations. Nevertheless, the slope of the negative relationship between twinning and total birth remained very similar irrespectively of whether or not such data were included (Supplementary Fig. 5), which suggests that the exclusion of Norwegian data does not alter our main conclusions. Information on the populations considering also the data for which the birth months were missing is provided in Supplementary Table 14.Twin identificationIn our data, the maximum number of offspring to constitute a multiple birth was three. We use the term twin(s) to refer to offspring who were the result of the same multiple birth (including 1745 sets of twins sensu stricto and 19 sets of triplets in the filtered dataset and, respectively, 1915 and 20 in the dataset including observations that lack birth months). Although twins are sometimes explicitly indicated in the data sources, this is not always the case. Thus, for the sake of consistency across our populations, twin births were identified when at least two individuals born to the same mother appeared with similar birth dates, according to strict criteria: if the exact birth dates were available, then offspring were identified as twins if their birth dates were no more than one day apart. If the exact birth dates were not available, then an identical birth year and month were considered sufficient for positive twin identification.Analyses and simulationsCharacterisation of the relationship between twinning and fertilityWe began by characterising the relationship between lifetime twinning status and maternal total births by fitting two models. For the first, we used a Generalised Linear Mixed-effects Model (GLMM) to investigate whether the mothers of twins (twinners) had experienced a larger or smaller number of births than mothers who only had singletons (non-twinners). We fitted this GLMM on the mother-level data with the R package spaMM63 using the call:$$begin{array}{c}{{{rm{fitme}}}}left({{{{rm{births}}}}}_{{{{rm{total}}}}}sim 1+{{{rm{twinner}}}}+(1|{{{rm{pop}}}}),right.\ {{{rm{data}}}}={{{rm{mother}}}}_{{{rm{level}}}}_{{{rm{data}}}},\ left.{{{rm{family}}}}={{{rm{Tnegbin}}}}({{{rm{link}}}}={hbox{“}}{{{mathrm{log}}}}{hbox{”}})right)end{array}$$
(1)
The response variable births_total refers to all births recorded over a mother’s observed lifetime (count data). The term 1 informs the function to fit an intercept (which happens by default, but is indicated here for clarity). The predictor twinner refers to maternal lifetime twinning status (binary: twinner vs non-twinner) and is modelled as a fixed effect. The term pop refers to the population identity (qualitative variable with eight levels) and is modelled by a Gaussian random effect acting on the intercept, which allows for the modelling of the heterogeneity between populations that is not captured by the fixed effects. The argument family is used to define the error structure and the link function of the GLMM (more on this below).In a second model, we reversed which variable is used as a response and which is used as the fixed-effect predictor. This allowed us to analyse how maternal total births predicted the probability of a mother producing twins during her lifetime using the call:$$begin{array}{c}{{{{{rm{fitme}}}}}}left({{{{{rm{twinner}}}}}} sim 1+{{{{{rm{births}}}}}}_{{{{{rm{total}}}}}}+(1|{{{{{rm{pop}}}}}}),right.\ {{{{{rm{data}}}}}}={{{{{rm{mother}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ left.{{{{{rm{family}}}}}}={{{{{rm{binomial}}}}}}({{{{{rm{link}}}}}}={hbox{“}}{{{{{rm{logit}}}}}}{hbox{”}})right)end{array}$$
(2)
The fitted models 1 and 2 are depicted in Fig. 1a, b and Supplementary Tables 1,2. While models 1 and 2 represent two sides of the same coin, the fit of both models is justified because each model formulation provides complementary information: expressing the effect of twinning on fertility relates to previous work5,6,7,8,9,10,57 and expressing the effect of fertility on twinning is a first step toward identifying what shapes twinning propensity, the focus of this paper.For the model predicting total births (model 1), we chose to use a negative binomial error structure. Using this error structure produced a fit of the data that was better than a (truncated) Poisson—the usual alternative for count data—as evidenced by much smaller marginal and conditional AIC values64. Here we specifically used a truncated negative binomial distribution because the data do not possess zeros by construction (only mothers are present in the dataset, i.e. there are no nulliparous women). For the model predicting lifetime twinning status (model 2), we chose a binomial error structure which is appropriate for binary data.Modelling the proportion of twin births among all births per mother is an effective way to avoid biases caused by differences in exposure to the risk of having twins affecting the relationship between twinning and fertility. For this, we fitted the following third model:$$begin{array}{l}{{{{{rm{fitme}}}}}}left({{{{{rm{cbind}}}}}};({{{{{rm{twin}}}}}}_{{{{{rm{total}}}}}},{{{{{rm{singleton}}}}}}_{{{{{rm{total}}}}}})right.\ sim ,1+{{{{{rm{births}}}}}}_{{{{{rm{total}}}}}}+(1|{{{{{rm{pop}}}}}}),\ ,{{{{{rm{data}}}}}}={{{{{rm{mother}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ ,left.{{{{{rm{family}}}}}}={{{{{rm{binomial}}}}}};({{{{{rm{link}}}}}}={hbox{“}}{{{{{rm{logit}}}}}}{hbox{”}})right)end{array}$$
(3)
In this model, the variable twin_total refers to the mother’s total number of twin births (i.e. one for each twinning event), singleton_total refers to the lifetime number of singleton births, and the cbind() function serves to indicate the fitting function to model the frequency of twinning events based on these two variables, which is interpreted as number of successes and failures of a binomial experience. The fitted model 3 is depicted in Fig. 2 and Supplementary Table 3.We modified model 3 so as to test whether the effect of total births differed significantly between populations. To do so, we considered that the effect of populations on total births could either be modelled as an interaction between fixed effects or as a random slope. For the former representation, we thus compared the fit of a model with linear predictor structure defined in spaMM as 1+births_total*pop to that of a model with the structure 1+births_total+pop. For the latter representation, we compared the fit with linear predictor structure 1+births_total + (1|pop) (i.e. model 3 as introduced above) to that of 1+births_total + (1+births_total|pop). We performed this testing procedure by comparing the likelihood ratio between each pair of alternative fits to the expectation of such a ratio under the null hypothesis. The distribution of the statistics used for the test was computed using 1000 parametric bootstrap replicates, which we generated using the function anova() provided by spaMM63. The test revealed a small non-significant variation in slopes between populations (see Results). For the sake of simplicity, we thus considered the effect of births_total the same across populations in all other analyses.Modelling life-history events using GLMMsTo reveal the biological mechanisms responsible for the relationship between twinning and fertility, we first fitted statistical models describing how age, parity and twin/singleton status, as well as individual and population differences influenced three key life-history events: parity progression (PP), the duration of interbirth intervals (IBI) and the twinning outcome of births (T). These models were fitted on birth-level data by the following calls:$$begin{array}{l}{{{{{rm{fitme}}}}}}left({{{{{rm{PP}}}}}} sim 1+{{{{{rm{twin}}}}}}+{{{{{rm{poly}}}}}}({{{{{rm{cbind}}}}}}({{{{{rm{age}}}}}},,{{{{{rm{parity}}}}}}),,{{{{{rm{best}}}}}}_{{{{{rm{order}}}}}})right.\ ,+,(1|{{{{{rm{maternal}}}}}}_{{{{{rm{id}}}}}})+(1|{{{{{rm{pop}}}}}}),\ ,{{{{{rm{data}}}}}}={{{{{rm{birth}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ ,{{{{{rm{family}}}}}}={{{{{rm{binomial}}}}}};({{{{{rm{link}}}}}}={hbox{“}}{{{{{rm{logit}}}}}}{hbox{”}})end{array}$$
(4)
$$begin{array}{l}{{{{{rm{fitme}}}}}}left({{{{{rm{IBI}}}}}} sim 1+{{{{{rm{twin}}}}}}+{{{{{rm{poly}}}}}};({{{{{rm{cbind}}}}}}({{{{{rm{age}}}}}},,{{{{{rm{parity}}}}}}),{{{{{rm{best}}}}}}_{{{{{rm{order}}}}}})right.\ ,+,(1|{{{{{rm{maternal}}}}}}_{{{{{rm{id}}}}}})+(1|{{{{{rm{pop}}}}}}),\ ,{{{{{rm{data}}}}}}={{{{{rm{birth}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ ,left.{{{{{rm{family}}}}}}={{{{{rm{negbin}}}}}}({{{{{rm{link}}}}}}={hbox{“}}{rm log} {hbox{”}})right)end{array}$$
(5)
$$begin{array}{l}{{{{{rm{fitme}}}}}}left({{{{{rm{T}}}}}} sim 1+{{{{{rm{poly}}}}}}({{{{{rm{cbind}}}}}}({{{{{rm{age}}}}}},,{{{{{rm{parity}}}}}}),,{{{{{rm{best}}}}}}_{{{{{rm{order}}}}}})right.\ ,+,(1|{{{{{rm{maternal}}}}}}_{{{{{rm{id}}}}}})+(1|{{{{{rm{pop}}}}}}),\ ,{{{{{rm{data}}}}}}={{{{{rm{birth}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ ,left.{{{{{rm{family}}}}}}={{{{{rm{binomial}}}}}};({{{{{rm{link}}}}}}={hbox{“}}{{{{{rm{logit}}}}}}{hbox{”}})right).end{array}$$
(6)
The response variables of models 4, 5 and 6 are thus PP, IBI and T, which refer to whether the mother went on to reproduce again or not (a boolean), the duration of the interbirth interval between the focal birth and the next (a discrete number of months) and whether the birth resulted in twins or not (a boolean), respectively. In addition to the terms that have already been defined, we now have the term poly(cbind(age, parity), best_order) to code for a polynomial describing the effect of maternal age, parity and their possible interaction. The two-variable polynomial function was applied on maternal age (with a monthly resolution) and parity (i.e. the current birth rank). Such a polynomial term allowed us to explore the influences of maternal age and parity on each response variable while encompassing the non-linearity of these predictors. We also have the predictor variable twin, which is a boolean that indicates if the previous birth event of a given mother resulted in twins or not (the variable twin and T are the same, but we used two different names to clarify when it is used as a response or as a predictor). Finally, we have the random effect “maternal identity” (maternal_id), which is used to represent intrinsic variation among mothers, that is, heterogeneity of expected response among individuals, beyond that due to the fixed effects and the population random effect. This random effect therefore measures maternal intrinsic fertility (in models 4 & 5) and twinning propensity (in model 6).To determine the best polynomial order (best_order) for the polynomial term we attempted orders from 0 to 6 and selected, for each model, the order leading to the model fit associated with the smallest marginal AIC. A polynomial of order 6 is sufficient to fit very complex shapes. Polynomial orders obtained by this procedure are given in the summary tables of the model fits given in Supplementary Tables. Importantly, maternal age and parity are highly correlated together (Spearman’s rho = 0.69), unequally correlated to response variables and exert non-linear effects. These are precisely the conditions in which collinearity issues are the most severe65. This justifies why we considered them jointly in all statistical models, as well as why we did not attempt to partition their respective biological effects in our analyses (except for the visual representation in Fig. 4).In order to study how the lifetime twinning status influenced maternal age at first birth, we also fitted the following model:$$begin{array}{l}{{{{{rm{fitme}}}}}}left({{{{{rm{AFB}}}}}} sim 1+{{{{{rm{twinner}}}}}}* {{{{{rm{births}}}}}}_{{{{{rm{total}}}}}}_{{{{{rm{fac}}}}}}+(1|{{{{{rm{pop}}}}}}),right.\ ,{{{{{rm{data}}}}}}={{{{{rm{mother}}}}}}_{{{{{rm{level}}}}}}_{{{{{rm{data}}}}}},\ ,left.{{{{{rm{family}}}}}}={{{{{rm{negbin}}}}}}({{{{{rm{link}}}}}}={hbox{“}}{rm log} {hbox{”}})right)end{array}$$
(7)
In this model, the response variable AFB corresponds to the age at first birth expressed as a number of months (discrete data) and the predictor births_total_fac corresponds to a qualitative variable referring to maternal total births (10 levels: 1, 2, …, 9, 10 + ). We here considered a possible interaction between twinner and births_total_fac. We used the negative binomial family as in model 1 but as for model 5 there is no need to consider here the truncated form of the distribution. All other terms have already been defined. The fitted model is depicted in Supplementary Fig. 1 and Supplementary Table 7.Marginal predictions for GLMMsAll predictions shown in plots or given in text represent marginal predictions. This means that the predictions for the quantities of interest (maternal lifetime births, twinning probabilities and age at first birth) are a function of coefficients of the fixed effects, and of the variance of the random effects. To be more precise, we averaged, over the fitted distribution of random effects, the predictions expressed on the scale of the response (i.e. back-transformed from the scale of the linear predictor) and conditional on the fixed and random effects. Unlike the traditional conditional predictions computed for a specific value of the random effects (often 0), such computation provides unbiased predictions and should be favoured in the context of GLMMs where random effects act non-additively on the expected response (which is the case when the link function of the model is not identity66). We estimated 95% intervals for these marginal predictions (CI95%) using parametric bootstraps with the help of the function spaMM_boot() from the R package spaMM and boot.ci() from the R package boot. More details can be found by looking at the code of the functions compute_predictions() and compare_prediction() in our supporting R package twinR (see Code availability).Simulating the life history of mothersWe produced an individual-based simulation model of human female life history to investigate the contribution of four mechanisms to the relationship, shown in Fig. 2, between per-birth twinning probability and maternal total births—an approach generally known as pattern-oriented modelling67. Each simulation proceeds in the following way: first, we initialised the simulation with representations of the exact same mothers present in the observed dataset, setting their population and maternal identities as the real ones, their starting ages at the observed values for age at first birth and their parity to one. Following this initialisation, the virtual lives of mothers proceeded as multiple iterations of a sequence of three life-history events, informed by statistical models (see below) and subject to the hypothesis being tested (Supplementary Figs. 3, 4). Specifically, for each mother, the twin/singleton status (T) of the current birth was first determined using a GLMM predicting T. Then, whether or not she will go on to reproduce at least once more was determined by simulating her parity progression status (PP) using a GLMM predicting the parity progression probability. For mothers who do continue reproducing, we finally used a third GLMM to determine the length of the interval between the current birth and the next one (IBI). At each iteration, a mother’s parity is increased by one, and age is increased by the simulated length of the interbirth interval. All predictions were performed conditionally on the value for the predictor characterised by both fixed and random effects. The process of simulating PP, IBI and T was then reiterated until all women had ceased reproduction, which happens necessarily since the probability of parity progression is lower than one. We also set this probability to zero once women reached 60 years old to save computation time in particular simulation scenarios leading to unrealistic life histories (and bad goodness of fit). Note that the maximum recorded age at which a mother gave birth was 55.1 years in our data. For the same reason, we also capped the maximum simulated duration for the interbirth interval to 30 years.Drawing life-history events from the fit of the model formulas shown above for models 4, 5 and 6 corresponds to simulating the scenario PISH (i.e. all four hypothetical mechanisms are activated). For simulating other simulation scenarios, we had to fit additional GLMMs derived from models presented above. Specifically, the term twin was dropped from model 4 to deactivate mechanism P (model 8; Supplementary Table 8); the term twin was dropped from model 5 to deactivate mechanism I (model 9; Supplementary Table 9); the term poly(cbind(age, parity), best_order) was dropped from model 6 to deactivate the mechanism S (model 10 and 11; Supplementary Tables 10, 11); and the term (1|maternal_id) was dropped from model 6 to deactivate mechanism H (model 11 and 12; Supplementary Tables 11, 12).Testing candidate mechanisms using simulationsTo test how each mechanism or association of mechanisms influenced the relationship between twinning and fertility, we ran simulations under each possible set of activated or inactivated mechanisms. We tested all possible sets and we thus built a total of 42 = 16 simulation scenarios (Supplementary Figs. 3, 4).For each simulation scenario, we ran simulation replicates (see Supplementary Notes for details and information on the numbers of replicates), then fitted model 3 on the dataset produced by each replicate and extracted the estimate for the slope associated with the term births_total in that model (β*). We then consider, in turn, that each simulation scenario may have generated the data. Each simulation scenario is thus considered as a null hypothesis which we aim at testing. Such a test is traditionally referred to as a goodness-of-fit test68. The result of such a test, a p-value, answers the question: what is the probability of obtaining a value equal to, or more extreme than, the statistic of interest, if the null hypothesis were true? The rejection of the null hypothesis by the test (i.e. a p-value ≤ 0.05) signifies a rejection of the null hypothesis, and thus, here, the rejection of a simulation scenario which represents a particular mechanism, or combination of mechanisms. In contrast, a large (i.e. non-significant) p-value would here denote support for the simulation scenario under consideration.A first candidate, as a statistic of interest to build our goodness-of-fit test, is the slope β*. However, when viewed as a goodness-of-fit test, the direct comparison of the observed and simulated slopes may be conservative when other life-history parameters are fitted to the data. This is because the data tend to be more likely given parameter values fitted to the data than given the actual (unknown) parameter values that generated the data. The goodness-of-fit test is however only guaranteed to provide uniformly distributed p-values (a feature necessary for the correctness of any null hypothesis testing) when samples are drawn under the latter parameter values. This is a general issue in statistics which has also been discussed long ago, for example, when the data-generating process is the normal distribution and a Kolmogorov–Smirnov test of goodness-of-fit is applied69. We thus designed and validated a specific procedure to correct for such bias while testing each simulation scenario (Supplementary Notes). In the text, we only report outcomes from this unbiased goodness-of-fit test (for details, see Supplementary Notes and Supplementary Table 13).Studying the effect of twinning propensity on the number of offspring using simulationsTo study how twinning propensity influences the total number of offspring that mothers produced during their lifetime, we ran two sets of simulations, each with 100 replicates. In the first set, we ran the simulation as described in the section “Simulating the life history of mothers” using the fits of the models associated with the simulation scenario PIS (i.e. fits of models 4, 5 and 12). In the second set, we did the same, except that we modified the intercept of the model predicting twinning events (fit of the model 12) by adding 2.5 to its intercept. We also tried other values, some smaller (e.g. 0.25), some larger (e.g. 5), to make sure that the magnitudes of the change of the intercept did not impact our qualitative statements. For each set of replicates, we extracted the twinning rate, the twinner rate, the mean number of offspring produced and the mean total number of births. We report the means of these metrics, as well as the 95% Central Range from simulation replicates (CR95%), which we directly computed by extracting the corresponding quantiles from the distribution generated by the replicates.Realism of the simulationsWe checked that the simulated life history closely matched that of the real mothers represented in our dataset beyond what is captured by the relationship between twinning and fertility. To do so, we compared different metrics related to fertility and twinning between the real and simulated data. We chose to perform this comparison under the simulation scenario PIS since it produces the best goodness-of-fit. The results of this quality check confirm that our simulations represent the reproductive lives of the mothers appropriately (Supplementary Fig. 6).Studying the effect of mortality on the number of offspring using simulationsTo account for the fact that not all offspring have the same expected survival, we also applied a survival weight to each simulated offspring before averaging the numbers for a given simulation set (baseline twinning propensity or enhanced, see Results). We used as weights the estimates for the probability of offspring survival between birth and adulthood provided by two publications associated with some of the data we used there. Specifically, following Helle et al.8, we used a weight of 0.603 for twins, 0.838 for singletons from twinners and 0.815 for singletons from non-twinners. Alternatively, following Haukioja et al.3, we used a weight of 0.337 for twins and 0.706 for singletons from all mothers.Implementation detailsAll statistical analyses were performed in R version 4.170. The main R packages we used were spaMM63 version 3.9.40 for the fit of all the statistical models, boot71,72 version 1.3-28 for the computation of confidence intervals based on parametric bootstraps, and R673 version 2.5.1 for defining the object used to run the simulations. The DESCRIPTION file from our package twinR (see Code availability) lists the additional R packages required for this project (e.g. those used for plotting and data manipulation).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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