The temperature-size rule (TSR) states that ectotherms mature at smaller adult body size in warmer conditions. Such a rule may have the potential to explain size response of fossil organisms to past temperature variations, but its validity in deep time has been seldom tested. The generality of this rule was investigated here by compiling data documenting the size record of three conodont genera (Palmatolepis, Ancyrodella and Polygnathus) at different spatial and temporal scales during the Late Frasnian and the Famennian, characterized by short- and long-term temperature variations. Statistical models were used to investigate the relationship between conodont size and oxygen isotope values, considered as paleotemperature proxies. Comparison of evolutionary models further allowed to test alternative modes of size variation such as stasis or punctuation.

The TSR was not validated as a general rule explaining size variation in these fossil records, being only observed as a large-scale geographic trend during a time-slice. The only strong support for temperature being the driver of temporal variations was found regarding the size of Palmatolepis during the Kellwasser period, but the relationship was reverse to the expectation of the TSR. The absence of general TSR pattern is probably due to the interference of many other factors (demography and mortality patterns, temperature tolerance, size reduction due to stress) whose relative importance may depend on the time interval and the genus considered. Rather than a correlation with environmental proxies, evolutionary models suggested the occurrence of a synchronous shift in Palmatolepis size around 369 Ma (Palmatolepis termini conodont Zone) in several outcrops, raising questions about the environmental forcing beyond this shift. Departures from the expected TSR may thus provide relevant insights into the complex interplay of physical, tectonic and eco-evolutionary processes impacting size evolution in deep time.

温度-体型规则（TSR）指出，变温动物在温暖的条件下成熟时体型较小。这样的规则可能有可能解释化石生物体的大小对过去温度变化的反应，但其在深层时间的有效性很少经过测试。本文通过汇编记录晚弗拉斯期和法门期三个牙形刺属（掌石属、角形藻属和长颌属）在不同空间和时间尺度上的大小记录的数据，研究了这一规则的普遍性，其特征是短期和长期温度变化。 。使用统计模型研究牙形刺大小与氧同位素之间的关系值，被视为古温度代理。进化模型的比较进一步允许测试大小变化的替代模式，例如停滞或标点符号。

TSR 并未被验证为解释这些化石记录中大小变化的一般规则，仅作为时间片期间的大规模地理趋势进行观察。对于温度是时间变化的驱动因素的唯一强有力的支持是关于Kellwasser 时期掌鳞鱼的大小，但这种关系与 TSR 的预期相反。一般 TSR 模式的缺失可能是由于许多其他因素（人口统计和死亡率模式、温度耐受性、压力导致的体型减小）的干扰，这些因素的相对重要性可能取决于时间间隔和所考虑的属。进化模型表明掌鳞目动物发生了同步转变，而不是与环境指标相关在几个露头中，其大小约为 369 Ma（掌石末端牙形刺区），引发了有关这种转变之外的环境强迫的问题。因此，与预期 TSR 的偏离可能会为影响深层次尺寸演化的物理、构造和生态演化过程的复杂相互作用提供相关见解。