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.已有理论模型被建立，用于解析动物如何抉择退出争斗。此类模型针对资源持有潜力（resource holding potential, RHP）与争斗时长之间的关联提出了可检验的预测，其预设RHP各性状间呈线性关系。然而，RHP性状可能依据幂律随体型缩放；此外，不同RHP性状间的资源投入或存在差异。本文中，我们提出了一个涵盖体型与其他RHP性状间异速生长关系的模型。首先，我们将RHP性状划分为进攻性性状（即造成伤害的能力）与防御性性状（即争斗中的持续能力）。防御性性状可进一步细分为损伤耐受能力（即承受伤害的能力）与耐力。随后我们对三类情境进行建模：(i) RHP各性状间存在幂次关系；(ii) 个体在防御与进攻性状上的投入存在差异；(iii) 进攻性状与损伤耐受能力与体型呈正相关或负相关关系。我们针对体型匹配的伤害性争斗构建了三类模型：(1) 进攻能力随体型呈超线性增长；(2) 损伤耐受能力随体型呈超线性增长；(3) 进攻能力随体型呈超线性增长，但损伤耐受能力随体型呈次线性增长。我们的分析表明，若RHP性状呈线性缩放，则当前的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。然而，当存在幂次关系时，我们可预期出现非线性关联。在此类情境下，争斗时长随体型增大而增长至峰值，随后开始下降。因此，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认知，并有助于解决当前理论与实证数据间的不一致性。