Fig S1. Systematic review flow diagram (PRISMA diagram, Liberati et al. 2009) of how we identified, screened, and checked eligibility of all the papers we found during our literature review.

Fig S2. Phylogenetic tree used to estimate phylogenetic relatedness in our meta- analytic models. Since we did not have of the same genus, we used genus tree tips. Colours indicate groups within the same order. Tree built using iTOL

(https://itol.embl.de/).

Fig. S3. Hedges’ g value (circle) and corresponding confidence intervals (lines) for species, pairing method (whether contests were paired for body size or not), component measured (e.g., length, width, mass), type of display (i.e., displaying weapon, body size, or not displaying) and function of the weapon during the contests

(see topic 3). Study demonstrates which samples were taken from the same study

(references below). Larger grey circles denote studies with larger sample sizes.

Silhouettes were taken from phylopic. Grey rows were selected randomly to facilitate visual separation of groups.

REFERENCES FROM FIGURE 1

1 = Briffa, 2008; 2 = Palaoro et al., 2014; 3 = Kim, Jang, & Choe, 2011; 4 = Hoem et al., 2007; 5 = Hongo, 2003; 6 = Karino, Niiyama, & Chiba, 2005a; 7 = Dale & Slagsvold, 1995; 8 = Jennions & Backwell, 1996; 9 = Kelly, 2006; 10 = Martínez-Cotrina, Bohórquez- Alonso, & Molina-Borja, 2014; 11 = Molina‐Borja, Padron‐Fumero, & Alfonso‐Martin, 1998; 12 = Okada & Miyatake, 2004; 13 = Olsson & Shine, 2000; 14 = Wilson et al., 2007; 15 = Yoshino, Koga, & Oki, 2011; 16 = Lobregat et al., 2019; 17 = Okada et al., 2011; 18 = Kojima & Lin, 2017; 19 = Barrette & Vandal, 1986; 20 = Songvorawit, Butcher, & Chaisuekul, 2018; 21 = Okada, Miyanoshita, & Miyatake, 2006; 22 = Okada & Miyatake, 2007; 23 = Walker & Holwell, 2018; 24 = Fea & Holwell, 2018; 25 = Ida & Wada, 2017; 26 = O’Brien & Boisseau, 2018; 27 = Nolen, Allen, & Miller, 2017; 28 = Nguyen & Stahlschmidt, 2019; 29 = Rink et al., 2019; 30 = Umbers et al., 2013; 31 = Souza et al., 2019; 32 = Potter, Wrensch, & Johnston, 1976; 33 = Sun et al., 2019; 34 = Graham & Angilletta, 2020; 35 = Sneddon, Huntingford, & Taylor, 1997; 36 = Sneddon et al., 2000; 37 = Dalosto et al., 2013; 38 = Guiasu & Dunham, 1997; 39 = Judge & Bonanno, 2008; 40 = Judge et al., 2010; 41 = Lailvaux & Irschick, 2007; 42 = McLean & Stuart-Fox, 2015; 43 = Moczek & Emlen, 2000; 44 = Green & Patek, 2015; 45 = Hall et al., 2010; 46 = Emlen, 1997; 47 = Bohórquez-Alonso et al., 2018; 48 = Munoz & Zink, 2012; 49 = Huyghe et al., 2005

Fig S4. When comparing only measures taken from crustaceans and , linear measures were still relatively more important to resolve contests than performance measures (QM1 = 18.198, p < 0.0001). The effect size, Hedges’ g, represents the mean standardized difference between winners and losers. Positive values denote that winners were larger than losers, while negative values represent the opposite. Dots represent the estimated values from a multilevel meta-analytic model considering

Hedges’ g as the response variable, weapon component as a moderator variable, and study ID, species ID, phylogeny, environment and pairing method as random variables. The error bars represent the 95% confidence interval of the estimate. The numbers above the error bars represent the number of effect size in each component. Table S1. Species that did not have the Pearson’s correlation coefficient between body size and weapon size in the same paper where the effect size was taken from . Thus, we searched for the coefficient in other papers for similar species that bore similar weapons.

Species Reference

Loxoblemmus doenitzi Kuriwada T. (2016) Horn length is not correlated with calling efforts in the horn-headed cricket Loxoblemmus doenitzi (Orthoptera: Gryllidae). Entomol Sci. 19(3):228–32. Acheta domesticus Judge KA, Bonanno VL. Male Weaponry in a Fighting Cricket. PLoS ONE, 3(12). Gallotia galloti Herrel A, Spithoven L, Damme RV, Vree FD. Sexual dimorphism of head size in Gallotia galloti: testing the niche divergence hypothesis by functional analyses. Funct Ecol. 1999;13(3):289–97. Rangifer tarandus Melnycky, N. A., Weladji, R. B., Holand, Ø., & Nieminen, M. (2013). Scaling of antler size in reindeer (Rangifer tarandus): sexual dimorphism and variability in resource allocation. Journal of Mammalogy, 94(6), 1371-1379.

REFERENCES

BARRETTE, C. & VANDAL, D. (1986) Social Rank, Dominance, Antler Size, and Access to Food in Snow-Bound Wild Woodland Caribou. Behaviour 97, 118–146. Brill.

BOHÓRQUEZ-ALONSO, M.L., MESA-AVILA, G., SUÁREZ-RANCEL, M., FONT, E. & MOLINA- BORJA, M. (2018) Predictors of contest outcome in males of two subspecies of Gallotia galloti (: Lacertidae). Behavioral Ecology and Sociobiology 72, 63.

BRIFFA, M. (2008) Decisions during fights in the house cricket, Acheta domesticus: mutual or self assessment of energy, weapons and size? Behaviour 75, 1053–1062.

DALE, S. & SLAGSVOLD, T. (1995) Female Contests for Nest Sites and Mates in the Pied Flycatcher Ficedula hypoleuca. Ethology 99, 209–222.

DALOSTO, M.M., PALAORO, A.V., COSTA, J.R. & SANTOS, S. (2013) Aggressiveness and life underground: the case of burrowing crayfish. Behaviour 150, 3–22. Brill. EMLEN, D.J. (1997) Alternative reproductive tactics and male-dimorphism in the horned beetle Onthophagus acuminatus (Coleoptera: Scarabaeidae). Behavioral Ecology and Sociobiology 41, 335–341.

FEA, M. & HOLWELL, G. (2018) Combat in a cave-dwelling wētā (Orthoptera: Rhaphidophoridae) with exaggerated weaponry. Animal Behaviour 138, 85–92.

GRAHAM, Z.A. & ANGILLETTA, M.J. (2020) Separating noise and function in systems of animal communication: a comparative study of aggressive signaling in crayfish. bioRxiv, 2020.08.03.234419.

GREEN, P.A. & PATEK, S.N. (2015) Contests with deadly weapons: telson sparring in mantis shrimp (Stomatopoda). Biology Letters 11, 20150558.

GUIASU, R.C. & DUNHAM, D.W. (1997) Initiation and Outcome of Agonistic Contests in Male Form 1 Cambarus robustus Girard, 1852 Crayfish (Decapoda, Cambaridae). Crustaceana 70, 480–496.

HALL, M.D., MCLAREN, L., BROOKS, R.C. & LAILVAUX, S.P. (2010) Interactions among performance capacities predict male combat outcomes in the field cricket. Functional Ecology 24, 159–164.

HOEM, S.A., MELIS, C., LINNELL, J.D.C. & ANDERSEN, R. (2007) Fighting behaviour in territorial male roe deer Capreolus capreolus: the effects of antler size and residence. European Journal of Wildlife Research 53, 1–8.

HONGO, Y. (2003) Appraising Behaviour During Male-male Interaction in the Japanese Horned Beetle Trypoxylus dichotomus septentrionalis (Kono). Behaviour 140, 501– 517.

HUYGHE, K., VANHOOYDONCK, B., SCHEERS, H., MOLINA‐BORJA, M. & DAMME, R.V. (2005) Morphology, performance and fighting capacity in male lizards, Gallotia galloti. Functional Ecology 19, 800–807.

IDA, H. & WADA, K. (2017) Aggressive behavior and morphology in Scopimera globosa (De Haan, 1835) (Brachyura: Dotillidae). Journal of Crustacean Biology 37, 125– 130.

JENNIONS, M.D. & BACKWELL, P.R.Y. (1996) Residency and size affect fight duration and outcome in the fiddler crab Uca annulipes. Biological Journal of the Linnean Society 57, 293–306.

JUDGE, K.A. & BONANNO, V.L. (2008) Male Weaponry in a Fighting Cricket. PLoS ONE 3.

JUDGE, K.A., TING, J.J., SCHNEIDER, J. & FITZPATRICK, M.J. (2010) A lover, not a fighter: mating causes male crickets to lose fights. Behavioral Ecology and Sociobiology 64, 1971–1979.

KARINO, K., NIIYAMA, H. & CHIBA, M. (2005) Horn Length Is the Determining Factor in the Outcomes of Escalated Fights Among Male Japanese Horned Beetles, Allomyrina dichotoma L. (Coleoptera: Scarabaeidae). Journal of Insect Behavior 18, 805–815.

KELLY, C.D. (2006) Fighting for harems: assessment strategies during male–male contests in the sexually dimorphic Wellington tree weta. Animal Behaviour 72, 727–736.

KIM, H., JANG, Y. & CHOE, J.C. (2011) Sexually dimorphic male horns and their use in agonistic behaviors in the horn-headed cricket Loxoblemmus doenitzi (Orthoptera: Gryllidae). Journal of Ethology 29, 435–441.

KOJIMA, W. & LIN, C.-P. (2017) It takes two to tango: functional roles, sexual selection and allometry of multiple male weapons in the flower beetle Dicronocephalus wallichii bourgoini. Biological Journal of the Linnean Society 121, 514–529.

LAILVAUX, S.P. & IRSCHICK, D.J. (2007) The Evolution of Performance‐Based Male Fighting Ability in Caribbean Anolis Lizards. The American Naturalist 170, 573– 586.

LOBREGAT, G., GECHEL KLOSS, T., PEIXOTO, P.E.C. & SPERBER, C.F. (2019) Fighting in rounds: males of a neotropical cricket switch assessment strategies during contests. Behavioral Ecology 30, 688–696.

MARTÍNEZ-COTRINA, J., BOHÓRQUEZ-ALONSO, M.L. & MOLINA-BORJA, M. (2014) Morphological and behavioural correlates of contest success in male yellow- headed geckos, Gonatodes albogularis: sequential assessment or self-assessment? Behaviour 151, 1535–1554.

MCLEAN, C.A. & STUART-FOX, D. (2015) Rival assessment and comparison of morphological and performance-based predictors of fighting ability in Lake Eyre dragon lizards, maculosus. Behavioral Ecology and Sociobiology 69, 523–531.

MOCZEK, A.P. & EMLEN, D.J. (2000) Male horn dimorphism in the scarab beetle, Onthophagus taurus: do alternative reproductive tactics favour alternative phenotypes? Animal Behaviour 59, 459–466.

MOLINA‐BORJA, M., PADRON‐FUMERO, M. & ALFONSO‐MARTIN, T. (1998) Morphological and Behavioural Traits Affecting the Intensity and Outcome of Male Contests in Gallotia galloti galloti (Family Lacertidae). Ethology 104, 314–322.

MUNOZ, N.E. & ZINK, A.G. (2012) Asymmetric Forceps Increase Fighting Success among Males of Similar size in the Maritime Earwig. Ethology 118, 943–954.

NGUYEN, K. & STAHLSCHMIDT, Z.R. (2019) When to fight? Disentangling temperature and circadian effects on aggression and agonistic contests. Animal Behaviour 148, 1–8.

NOLEN, Z.J., ALLEN, P.E. & MILLER, C.W. (2017) Seasonal resource value and male size influence male aggressive interactions in the leaf footed cactus bug, Narnia femorata. Behavioural Processes 138, 1–6. O’BRIEN, D.M. & BOISSEAU, R.P. (2018) Overcoming mechanical adversity in extreme hindleg weapons. PLoS ONE 13.

OKADA, K., MIYANOSHITA, A. & MIYATAKE, T. (2006) Intra-sexual Dimorphism in Male Mandibles and Male Aggressive Behavior in the Broad-Horned Flour Beetle Gnatocerus cornutus (Coleoptera: Tenebrionidae). Journal of Insect Behavior 19, 457–467.

OKADA, K. & MIYATAKE, T. (2004) Sexual Dimorphism in Mandibles and Male Aggressive Behavior in the Presence and Absence of Females in the Beetle Librodor japonicus (Coleoptera: Nitidulidae). Annals of the Entomological Society of America 97, 1342–1346.

OKADA, K. & MIYATAKE, T. (2007) Ownership-dependent mating tactics of minor males of the beetle Librodor japonicus (Nitidulidae) with intra-sexual dimorphism of mandibles. Journal of Ethology 25, 255–261.

OKADA, K., SUZAKI, Y., OKADA, Y. & MIYATAKE, T. (2011) Male Aggressive Behavior and Exaggerated Hindlegs of the Bean Bug Riptortus pedestris. Zoological Science 28, 659–663.

OLSSON, M. & SHINE, R. (2000) Ownership influences the outcome of male-male contests in the scincid , Niveoscincus microlepidotus. Behavioral Ecology 11, 587–590.

PALAORO, A.V., DALOSTO, M.M., COSTA, J.R. & SANTOS, S. (2014) Freshwater decapod (Aegla longirostri) uses a mixed assessment strategy to resolve contests. Animal Behaviour 95, 71–79.

POTTER, D.A., WRENSCH, D.L. & JOHNSTON, D.E. (1976) Aggression and Mating Success in Male Spider Mites. Science 193, 160–161.

RINK, A.N., ALTWEGG, R., EDWARDS, S., BOWIE, R.C.K. & COLVILLE, J.F. (2019) Contest dynamics and assessment strategies in combatant monkey beetles (Scarabaeidae: Hopliini). Behavioral Ecology 30, 713–723.

SNEDDON, L.U., HUNTINGFORD, F.A. & TAYLOR, A.C. (1997) Weapon size versus body size as a predictor of winning in fights between shore crabs, Carcinus maenas (L.). Behavioral Ecology and Sociobiology 41, 237–242.

SNEDDON, L.U., HUNTINGFORD, F.A., TAYLOR, A.C. & ORR, J.F. (2000) Weapon strength and competitive success in the fights of shore crabs (Carcinus maenas). Journal of Zoology 250, 397–403.

SONGVORAWIT, N., BUTCHER, B.A. & CHAISUEKUL, C. (2018) Resource Holding Potential and the Outcome of Aggressive Interactions between Paired Male Aegus chelifer chelifer (Coleoptera: Lucanidae) Stag Beetles. Journal of Insect Behavior 31, 347– 360.

SOUZA, A.T., RIBAS, F.O., MOURA, J.F., MOREIRA, C., CAMPOS, J. & ILARRI, M.I. (2019) Influence of temperature on intraspecific, unbalanced dyadic contests between crabs. PeerJ 7, e7845. SUN, C., ZHANG, C., GU, H., JIANG, T. & FENG, J. (2019) Self-assessment strategy during contest decisions between male Great Himalayan leaf-nosed bats. Behavioral Ecology and Sociobiology 73, 45.

UMBERS, K.D.L., TATARNIC, N.J., HOLWELL, G.I. & HERBERSTEIN, M.E. (2013) Bright turquoise as an intraspecific signal in the chameleon grasshopper (Kosciuscola tristis). Behavioral Ecology and Sociobiology 67, 439–447.

WALKER, L.A. & HOLWELL, G.I. (2018) The role of exaggerated male chelicerae in male– male contests in New Zealand sheet-web spiders. Animal Behaviour 139, 29–36.

WILSON, R.S., ANGILLETTA JR., M.J., JAMES, R.S., NAVAS, C. & SEEBACHER, F. (2007) Dishonest Signals of Strength in Male Slender Crayfish (Cherax dispar) during Agonistic Encounters. The American Naturalist 170, 284–291.

YOSHINO, K., KOGA, T. & OKI, S. (2011) Chelipeds are the real weapon: cheliped size is a more effective determinant than body size in male–male competition for mates in a hermit crab. Behavioral Ecology and Sociobiology 65, 1825.