Estimating tusk masses in proboscideans: a comprehensive analysis and predictive model

The size of tusks in proboscideans has numerous implications for their function, biology, ecology, and other aspects of both extant and extinct species. Yet, no prior studies have explored the relationship between the linear dimensions of tusks and their corresponding masses. Here, methods for estimating the masses of proboscidean tusks based on their length and circumference are introduced for the first time. Through extensive regression analysis on a large dataset of tusk dimensions and recorded masses, a robust regression equation was developed. Additionally, it was found that converting tusk volume to kilograms using the cylinder formula yielded highly accurate tusk mass estimates in proboscideans. Also, the potential average tusk sizes of living elephant species under optimal conditions, before the devastating impact of humans, were estimated. The upper incisors of proboscideans remained relatively small until the Late Miocene when tusk sizes comparable to those of living elephants first appeared. Mammoths, along with certain mammutids, stegodonts, and anancines, developed notably larger tusks relative to their body size compared to extant elephants. The largest tusks were identified in derived Plio-Pleistocene proboscideans within Mammuthus, Palaeoloxodon, and Mammutidae clades, with some species bearing tusks weighing above 200 kg per side. World record-sized tusks far surpassed this figure.长鼻目（Proboscidea）动物的象牙尺寸，对其功能、生物学特性、生态学特征以及现存与灭绝物种的诸多其他方面均具有重要意义。迄今为止，尚无任何研究探讨象牙线性尺寸与其对应质量之间的关联。本研究首次提出基于象牙长度与周长估算长鼻目象牙质量的方法：研究团队通过对涵盖象牙尺寸与实测质量的大型数据集开展大量回归分析，构建了稳健的回归方程。此外，研究证实，利用圆柱体积公式将象牙体积换算为千克，可对长鼻目象牙质量实现高精度估算。研究还估算了在人类活动带来破坏性影响之前的最优生存条件下，现存象类物种的潜在平均象牙尺寸。长鼻目的上门齿始终维持相对小巧的形态，直至晚中新世，与现存象类尺寸相当的象牙才首次出现。相较现存象类，猛犸象、部分乳齿象科（Mammutidae）类群、剑齿象属（Stegodon）物种以及互棱齿象亚科（Anancinae）类群的象牙相对于其体型显著更大。研究在演化衍生的上新世-更新世长鼻目类群中发现了尺寸最大的象牙，这些类群涵盖猛犸象属（Mammuthus）、古菱齿象属（Palaeoloxodon）以及乳齿象科（Mammutidae）演化支，部分物种的单支象牙质量可达200千克以上。创世界纪录的巨型象牙则远超这一数值。