Data from: Weaponry and defenses in fighting animals: how allometry can alter predictions from contest theory

Theoretical models have been developed to understand how animals decide to withdraw from a contest. They provide testable predictions regarding the relationship between resource holding potential (RHP) and contest duration that assume linear relationships among RHP traits. However, RHP traits might scale with body size according to power laws. Furthermore, investment across different RHP-traits may vary. Herein, we provide a model that encompasses the allometric relationship between body size and other RHP-traits. First, we partition RHP traits into ‘offensive’ traits (i.e. the ability to inflict damage), and ‘defensive’ traits (i.e. persistence in a contest). Defensive traits may in turn be subdivided into ‘damage endurance’ or the ability to absorb damage, and ‘stamina’. We then model scenarios where: (i) there are power relationships among RHP-traits; (ii) individuals invest differently in defensive and offensive traits; (iii) offensive traits and damage endurance have a positive/negative relationship with body size. We modelled sized-matched injurious contests where (1) offensive capacity increases superlinearly with body size, (2) damage endurance increases superlinearly, and (3) offensive capacity increases superlinearly but damage endurance increases sublinearly. Our analyses indicate that if RHP traits scale linearly current predictions are upheld for injurious contests - contest duration increases with body size. However, with power relationships we can expect non-linear relationships. Here, contest duration increased with body size until a maximum, decreasing afterwards. Thus, considering allometric relationships between body size and RHP-traits may lead to new insights in animal contest theory and may help to solve discrepancies between current theory and empirical data.为阐释动物如何决策退出争斗，已有相关理论模型被构建。这些模型针对资源持有潜力（resource holding potential, RHP）与争斗时长间的关联提出了可检验的预测，且默认RHP各性状间呈线性关系。然而，RHP各性状可能随体型以幂律（power laws）形式进行尺度缩放，且不同RHP性状间的资源投入或存在差异。 本文中，我们构建了一个涵盖体型与其他RHP性状间异速生长关系（allometric relationship）的模型。首先，我们将RHP性状划分为‘攻击性状（offensive traits）’——即造成伤害的能力，与‘防御性状（defensive traits）’——即维持争斗的持久性。防御性状可进一步细分为‘损伤耐力（damage endurance）’，即承受伤害的能力，以及‘耐力（stamina）’。随后，我们对三类场景展开建模：（i）RHP各性状间存在幂律关系；（ii）个体在防御与攻击性状上的投入存在差异；（iii）攻击性状与损伤耐力与体型呈正/负相关。 我们针对三类具体情境构建了体型匹配的伤害性争斗（sized-matched injurious contests）模型：（1）攻击能力随体型呈超线性（superlinearly）增长；（2）损伤耐力随体型呈超线性增长；（3）攻击能力随体型呈超线性增长，但损伤耐力随体型呈亚线性（sublinearly）增长。 分析结果显示，若RHP性状呈线性尺度缩放，则当前理论预测在伤害性争斗中依然成立——即争斗时长随体型增大而增加。但当存在幂律关系时，二者可呈现非线性关联：争斗时长随体型增大先升至峰值，随后逐渐下降。 由此可见，考虑体型与RHP性状间的异速生长关系，可为动物争斗理论带来新的研究视角，亦有助于解决当前理论与实证数据间的矛盾。