1. The following matrix gives a set of cognate words meaning 'ox' in several dif- ferent...

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1. The following matrix gives a set of cognate words meaning 'ox' in several dif- ferent languages. Language Word Pronunciation Avestan uxshan uksan Chuvash vgr English OX oks Finnish hrk hrk Hungarian kr kr Mongolian iker Sanskrit uksa uksa Sumerian gu4.r gur Tatar Turkish kz igez kz These words show several changes that have different weights. Assume the following weights: 0 for the exchange of one vowel with another vowel. 1 for the insertion of a word initial vowel or /v/. .1 for the deletion of a word final vowel. .1 for the insertion of a word final consonant or syllable. Examples: -n, -k. 1 for the interchange of a vowel and a consonant. Example: sa as. 1 for the exchange of a fricative with another fricative. Example: s z. 1 for the exchange of a velar with another velar. Example: g k. 1 for the exchange of a velar with a glottal. Example: g h. 2 for the exchange of a fricative and /r/. Examples: sr, and r 8. When there are several different possible ways of deriving one word from an- other, we always assume the path with the smallest total weight. (a) (25 points) Find the distance matrix and a hypothetical evolutionary tree generated by the UPGMA algorithm. (b) (25 points) Find the common mutation matrix and a hypothetical evolu- tionary tree generated by the CMM algorithm. 1. The following matrix gives a set of cognate words meaning 'ox' in several dif- ferent languages. Language Word Pronunciation Avestan uxshan uksan Chuvash vgr English OX oks Finnish hrk hrk Hungarian kr kr Mongolian iker Sanskrit uksa uksa Sumerian gu4.r gur Tatar Turkish kz igez kz These words show several changes that have different weights. Assume the following weights: 0 for the exchange of one vowel with another vowel. 1 for the insertion of a word initial vowel or /v/. .1 for the deletion of a word final vowel. .1 for the insertion of a word final consonant or syllable. Examples: -n, -k. 1 for the interchange of a vowel and a consonant. Example: sa as. 1 for the exchange of a fricative with another fricative. Example: s z. 1 for the exchange of a velar with another velar. Example: g k. 1 for the exchange of a velar with a glottal. Example: g h. 2 for the exchange of a fricative and /r/. Examples: sr, and r 8. When there are several different possible ways of deriving one word from an- other, we always assume the path with the smallest total weight. (a) (25 points) Find the distance matrix and a hypothetical evolutionary tree generated by the UPGMA algorithm. (b) (25 points) Find the common mutation matrix and a hypothetical evolu- tionary tree generated by the CMM algorithm.