一個普遍被使用的數理統計方法－齊普夫定律，1994年被Mantegna與他的研究團隊使用在基因序列k字串的發生頻率與其排名的解析上（k字串齊普夫解析)，強調非編碼區有類語言的冪次規則。不過，這樣的結論被大量的質疑與討論。 我們整理不同的齊普夫分佈研究領域，發現觀察的重點雖不盡相同，但事件總數為N時，各別事件在隨機狀態時機率均為1/N。然而，基因序列在序列的p(序列A+T含量所佔比)越遠離一半時，各別字串的機率在隨機狀態差異越大，因此在非隨機狀態中，機率不等是受到p與生物特徵兩個因素造成，影響齊普夫分佈的解析判斷。 這個研究中，我們運用不同p的基因體序列與其對應的隨機序列的數據，證實k字串齊普夫子集解析法可以去除p的影響，改善k字串齊普夫解析難以定義隨機序列冪次的障礙，確立子集解析的優勢。 另外，我們擬合四個函式（直線、指數、對數、冪次）選定足以代表物種特徵的「高頻字」（高頻率出現的字串），並嘗試找出865個物種高頻字冪次的普適性。研究結果顯示物種的冪次與其物種複雜度有關，傳達基因複製的演化結果。 Zipf’s law is a characterization of the relation between the frequency of any word in a text and the ranking of that word in the frequency table. It states that if the text is that of a natural language, then the frequency versus ranking relation is an approximate power law. For a few years in the mid to late 1990’s Zipf’s law was intensely discussed in the context of genomic sequences, but no clear consensus was reached as to whether, as a general rule, the word frequencies -- a genomic a word is an oligonucleotide of a given length; we call a k-nucleotide word a k-mer -- in genomic sequences, or some specific portion thereof, obey a Zipf’s law. Here we revisit the issue by studying the frequency versus ranking relations of a large number of complete genomes, and of parts of genomes having different biological functions. We show that the nucleotide composition has an influence on the frequency versus rank relation of a genomic sequence that is strong enough to mask whatever Zipf’s-law behavior the sequence may possess. Once this influence is removed, then all genomes obey the same broadly defined classes of Zipf’s laws, with the most important class-defining factor being the length of k-mers, or the integer k. For eukaryotes, the Zipf’s laws for the exonic and intronic segments of the genome differ significantly. Based on the observation that the Zipf’s law of a sequence is determined by the subset of k-mers having the highest frequencies (of occurrence), we derive a relation between the Zipf’s-law exponent and the high-frequency tail of the frequency distribution, and infer that for genomes in general the high-frequency tail is best represented by an exponential function, as opposed to linear, logarithmic, or power-law functions.
