Functional Phylogenies

我们现在经常使用不同生物的基因序列来猜测它们的共同祖先。生物的基因序列是一长串符号。但是，如果我们只知道它们的形状信息，而不知道每一种生物的一系列符号，我们怎么能讨论共同的祖先呢？虽然这是一个特别困难的情况，但这是很常见的。我们周围的许多物体都在进化和改变它们的形状，但它们没有基因序列。例如，从牙刷到汽车等消费品的形状都在不断进化，但没有人认为它们有基因组。对形状的过去进化进行推断，以及猜测哪些形状有共同的祖先，这些挑战都是公认的。应对这一挑战的标准方法是提取描述感兴趣形状的数字集，并使用这些汇总集来猜测过去的情况。这个提议采取了一种不同的方法。我们的目标是开发数学技术，利用形状本身，而不是它们的总结，来推断过去。这种方法有一些优点：它使用了我们拥有的更多信息；它使我们能够描述产生形状进化的过程；它使我们能够猜测看不见的祖先的形状（而不是猜测他们的一组有限的特征）。这一提议旨在通过考虑数学函数的演化来推进形状演化的研究。功能系统发育类似于基因进化树，它是一个随时间变化的数学函数，而不是基因序列。我们将通过以下方式验证我们的理论：使用计算机生成的数据；进行“空间汉语耳语”实验；以及研究罗马语言中单词的发音是如何演变的。我们的“空间汉语耳语”实验将包括绘制曲线的任务，一个接一个，这样复制的小错误就会导致曲线形状的缓慢漂移。我们对语音进化的研究首先将现代说话者的声音转换成形状，然后利用我们对罗曼语进化树的信心这一事实。正如关于当前基因序列的信息使我们能够猜测过去生物体的序列一样，这种方法可能使我们能够测试关于我们再也听不到的语言声音的假设。这项工作与那些对设计未来形状感兴趣的人以及对过去形状感兴趣的人有关。通过了解过去的形状演变，人们可以利用它来产生合理的形状转换，这可能有助于产品设计。这项工作的目的是获取一组形状，并猜测哪些形状与哪些形状最相关：这在与形状进化无关的领域非常有用。检测不寻常或熟悉形状的能力与许多公共和商业挑战相关，从发现不寻常的车辆到猜测字母的形状。

We now regularly use the genetic sequences of different creatures to make guesses about their common ancestors. A creature's genetic sequence is a long string of symbols. But how can we discuss common ancestors if, instead of knowing strings of symbols about each creature, we only have information about their shapes? Though this is a particularly difficult situation, it is very common. Many objects in the world around us evolve and change their shape but do not have a genetic sequence. For example, the shapes of consumer items, from toothbrushes to cars, are under continual shape evolution but no-one supposes they have genomes. The challenge of making inferences about the past evolution of shapes, and of making guesses about which shapes have recent ancestors in common, is well established. The standard approach to this challenge is to extract sets of numbers that describe the shapes of interest and to use these summary sets to make guesses about the past. This proposal takes a different approach. We aim to develop mathematical techniques that use the shapes themselves, rather than summaries of them, to make inferences about the past. This approach has some advantages: it uses more of the information that we have; it allows us to characterize the process that yields shape evolution; and it allows us to make guesses about the shapes of unseen ancestors (rather than guesses about a restricted set of their features).This proposal aims to advance the study of shape evolution by considering the evolution of mathematical functions. A functional phylogeny is akin to a genetic evolutionary tree where it is a mathematical function, rather than a genetic sequence, that changes through time. We will test our theory by: using computer generated data; performing `Spatial Chinese Whispers' experiments; and investigating how the pronunciation of words has evolved in Romance languages. Our `Spatial Chinese Whispers' experiments will involve the task of drawing curves, one after the other, so that small errors in copying yield a slow drift in curve shape. Our investigation of speech sound evolution first converts the sounds of modern speakers into shapes and then exploits the fact that we are confident about the evolutionary tree of Romance languages. Just as information about current genetic sequences allow us to make guesses about the sequences of past organisms, this approach might allow us to test hypotheses about the sounds of languages we can no longer hear.This work has relevance to those interested in designing shapes for the future, as well as those interested in past shapes. By understanding past shape evolution one can use this to generate reasonable shape transformations which might help in product design. This work aims to take sets of shapes and to make guesses about which is most related to which: this can be very useful in areas which have nothing to do with shape evolution. The ability to detect unusual or familiar shapes has relevance to numerous public and commercial challenges from spotting unusual vehicles to guessing the shapes of letters.