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Abstract：
Mathematical models have been widespread in biology since its emergence as a modern experimental science in the 19th century. Focusing on models in developmental biology and heredity, this article (1) presents the properties and epistemological basis of pertinent mathematical models in biology from Mendel\'s model of heredity in the 19th century to Eric Davidson\'s model of developmental gene regulatory networks in the 21st; (2) shows that the models differ not only in their epistemologies but also in regard to explicitly or implicitly taking into account basic biological principles, in particular those of biological specificity (that became, in part, replaced by genetic information) and genetic causality. The article claims that models disregarding these principles did not impact the direction of biological research in a lasting way, although some of them, such as D\'Arcy Thompson\'s models of biological form, were widely read and admired and others, such as Turing\'s models of development, stimulated research in other fields. Moreover, it suggests that successful models were not purely mathematical descriptions or simulations of biological phenomena but were based on inductive, as well as hypothetico-deductive, methodology. The recent availability of large amounts of sequencing data and new computational methodology tremendously facilitates system approaches and pattern recognition in many fields of research. Although these new technologies have given rise to claims that correlation is replacing experimentation and causal analysis, the article argues that the inductive and hypothetico-deductive experimental methodologies have remained fundamentally important as long as causal-mechanistic explanations of complex systems are pursued.
摘要：
自19世纪作为现代实验科学出现以来，数学模型已在生物学中广泛使用。专注于发育生物学和遗传模型，本文（1）从19世纪孟德尔的遗传模型到21世纪埃里克·戴维森的发育基因调控网络模型，介绍了生物学中相关数学模型的性质和认识论基础；（2）表明，这些模型不仅在认识论上不同，而且在明确或隐含地考虑基本生物学原理方面也不同。特别是那些具有生物学特异性的(那就变成了，在某种程度上,被遗传信息代替)和遗传因果关系。文章声称，无视这些原则的模型并没有持久地影响生物学研究的方向，尽管其中一些,比如阿西·汤普森的生物形态模型，被广泛阅读和钦佩，例如图灵的发展模式，刺激了其他领域的研究。此外，这表明成功的模型不是纯粹的数学描述或生物现象的模拟，而是基于归纳，以及假设演绎，方法论。大量测序数据和新的计算方法的最新可用性极大地促进了许多研究领域中的系统方法和模式识别。尽管这些新技术引起了人们的说法，即相关性正在取代实验和因果分析，本文认为，只要追求对复杂系统的因果机制解释，归纳和假设演绎的实验方法就仍然至关重要。
