DOI: 10.5061/dryad.mcvdnckbc
title: Diagnosing confounded Bateman gradients

description: The Bateman gradient is a fundamental metric of sexual selection, often
 interpreted as the fitness advantage individuals gain by increasing their
 number of mates. However, it is widely recognized that any traits
 influencing both mating success and reproductive success can confound the
 Bateman gradient, misrepresenting the strength of pre-copulatory sexual
 selection. Yet, the magnitude of this misrepresentation across different
 biological systems (e.g., differing in anisogamy or the strength of sperm
 competition), which covariates are most problematic, or how confounded
 relationships can be diagnosed to better interpret the Bateman gradient,
 remains largely unexplored. To address these gaps, we investigate nine
 plausible biological scenarios where the effect of male mating success on
 reproductive success is confounded. We find that covariances between male
 mating success and female fecundity or egg allocation confound the male
 Bateman gradient more strongly than covariances between male mating
 success and ejaculate traits. These differences in the impact of
 male-female versus male-male covariances are especially pronounced in
 systems with high levels of anisogamy and no sperm competition. We provide
 guidelines for empiricists to visually identify such covariations by
 recording mating order. Additionally, when the covariate is a confounder,
 not a mediator, we demonstrate that partial Bateman gradients allow better
 interpretation of the strength of pre-copulatory sexual selection. These
 insights into the mechanisms driving variation in the Bateman gradient
 allow us to clarify its meaning, identify scenarios where its
 interpretation might be problematic, and offer practical solutions to
 address this.
description: # Diagnosing confounded Bateman gradients Dataset DOI:
 [10.5061/dryad.mcvdnckbc](10.5061/dryad.mcvdnckbc) ## Description of the
 data and file structure This README.txt file was updated on 25/04/2025
 Paper associated with this archive Citation: Sanghvi et al, 2025.
 “Diagnosing confounded Bateman gradients”. Evolution. Originators Authors:
 Krish Sanghvi, Jonathan M. Henshaw, Alex Kacelnik, Tim Janicke, Irem Sepil
 Access information 1\. Licenses/restrictions placed on the data or code:
 CC0 1.0 Universal 2\. Data derived from other sources: None Data analysis
 and data files Software: R v4.3.1 Packages: lme4, lmerTest, Rmisc, tidyr,
 dplyr, ggplot2, performance, glmmTMB, DHARMa, ggpubr, MASS, effsize,
 broom, purrr FILES Data and code file overview This data repository
 consists of two code files and four data files. Code file: **1. BG
 sim.HTML**: R script HTML output that runs the entire simulation to
 generate data for the four biological systems and all scenarios therein.
 **2. BG-stats.HTML**: R script HTML output that uses the simulated data
 generated in “BG sim.HTML” to analyse this data, model partial Bateman
 gradients, and produce final results/figures presented in our study. Note:
 Empty cells imply no values being generated for that cell. These should
 not be treated as zeros- these “missing” values are not applicable for the
 specific rows they are associated with, thus missing. Data files: **1.
 LowAnisoNoComp2.csv** Description: Simulated data generated for the low
 anisogamy system without sperm competition. Variables • Replicate:
 Replicate number (1-20) • Male: Male ID within each replicate (1-2000) •
 Female: Female rank for each male (Mean = 8) • Offspring: Numbers of
 offspring produced by mated female that belong to focal male •
 EjaculateSize: Starting ejaculate size of male, before he encounters
 females • SpermTransferred: Numbers of sperm transferred by the male to
 each female rank in his mating sequence • FertilisableSperm: Proportion of
 sperm that are potent/are able to fertilise an egg/are viable • PropTrans:
 Proportion of his remaining sperm that a male transfers to a female •
 Eject: Proportion of a male’s transferred sperm that a female ejects •
 FemaleEggs: Number of eggs female has (i.e. female fecundity) •
 ProportionAllocated: Proportion of her available eggs that a female
 allocates to be fertilised by the current male • Male2Sperm: In sperm
 competition models, the numbers of potent sperm of the second male
 retained by the re-mating female. Due to absence of sperm competition,
 these values are missing for this system. • TotalFemalesMatedWith: Focal
 male’s mating success • TotalFemalesMatedWith_bins: Focal male’s binned
 mating success • Hypothesis; Simulated scenario (Null-H4.1) **2.
 LowAnisoComp2.csv** Description: Simulated data generated for the low
 anisogamy system with sperm competition. Variables • Replicate: Replicate
 number (1-20) • Male: Male ID within each replicate (1-2000) • Female:
 Female rank for each male (Mean = 8) • Offspring: Numbers of offspring
 produced by mated female that belong to focal male • EjaculateSize:
 Starting ejaculate size of male, before he encounters females •
 SpermTransferred: Numbers of sperm transferred by the male to each female
 rank in his mating sequence • FertilisableSperm: Proportion of sperm that
 are potent/can fertilise an egg/are viable • PropTrans: Proportion of his
 remaining sperm that a male transfers to a female • Eject: Proportion of a
 male’s transferred sperm that a female ejects • FemaleEggs: Number of eggs
 female has (i.e. female fecundity) • ProportionAllocated: Proportion of
 her available eggs that a female allocates to be fertilised by the current
 male • Male2Sperm: In sperm competition models, the numbers of potent
 sperm of the second male retained by the re-mating female •
 TotalFemalesMatedWith: Focal male’s mating success •
 TotalFemalesMatedWith_bins: Focal male’s binned mating success •
 Hypothesis; Simulated scenario (Null-H4.1) **3. HighAnisoNoComp2.csv**
 Description: Simulated data generated for the high anisogamy system
 without sperm competition. Variables • Replicate: Replicate number (1-20)
 • Male: Male ID within each replicate (1-2000) • Female: Female rank for
 each male (Mean = 8) • Offspring: Numbers of offspring produced by mated
 female that belong to focal male • EjaculateSize: Starting ejaculate size
 of male, before he encounters females • SpermTransferred: Numbers of sperm
 transferred by the male to each female rank in his mating sequence •
 FertilisableSperm: Proportion of sperm that are potent/are able to
 fertilise an egg/are viable • PropTrans: Proportion of his remaining sperm
 that a male transfers to a female • Eject: Proportion of a male’s
 transferred sperm that a female ejects • FemaleEggs: Number of eggs female
 has (i.e. female fecundity) • ProportionAllocated: Proportion of her
 available eggs that a female allocates to be fertilised by the current
 male • Male2Sperm: In sperm competition models, the numbers of potent
 sperm of the second male retained by the re-mating female. Due to absence
 of sperm competition, these values are missing for this system. •
 TotalFemalesMatedWith: Focal male’s mating success •
 TotalFemalesMatedWith_bins: Focal male’s binned mating success •
 Hypothesis; Simulated scenario (Null-H4.1) **4. HighAnisoComp2.csv**
 Description: Simulated data generated for the high anisogamy system with
 sperm competition. Variables • Replicate: Replicate number (1-20) • Male:
 Male ID within each replicate (1-2000) • Female: Female rank for each male
 (Mean = 8) • Offspring: Numbers of offspring produced by mated female that
 belong to focal male • EjaculateSize: Starting ejaculate size of male,
 before he encounters females • SpermTransferred: Numbers of sperm
 transferred by the male to each female rank in his mating sequence •
 FertilisableSperm: Proportion of sperm that are potent/are able to
 fertilise an egg/are viable • PropTrans: Proportion of his remaining sperm
 that a male transfers to a female • Eject: Proportion of a male’s
 transferred sperm that a female ejects • FemaleEggs: Number of eggs female
 has (i.e. female fecundity) • ProportionAllocated: Proportion of her
 available eggs that a female allocates to be fertilised by the current
 male • Male2Sperm: In sperm competition models, the numbers of potent
 sperm of the second male retained by the re-mating female •
 TotalFemalesMatedWith: Focal male’s mating success •
 TotalFemalesMatedWith_bins: Focal male’s binned mating success •
 Hypothesis; Simulated scenario (Null-H4.1) **5. BG_slopes.csv**
 Description: Mean Bateman gradients for the High anisogamy system with
 sperm competition, generated from full and partial Bateman gradient
 models. Associated code is BG-stats.HTML. These values have been manually
 copied from the partial Bateman gradient simulation chunks in the
 associated code. Variables: • Scenario2: The Scenario ID with covariate
 label • Slope: Bateman gradient estimate • Fixed_effect: Fixed effects
 included in the linear model, to calculate the Bateman gradient, when
 reproductive success is the dependent variable. • System: High anisogamy,
 with sperm competition system • Scenario: Scenario ID ## Access
 information Other publicly accessible locations of the data: * NA Data was
 derived from the following sources: * NA