According to conventional theory, yawning takes place when people are bored or sleepy and serves the function of increasing alertness by reversing, through deeper breathing, the drop in blood oxygen levels that are caused by the shallow breathing that accompanies lack of sleep or boredom.(TPO18, 45)

conventional /kən'vɛnʃənl/ adj. 传统的;老套的，千篇一律的;约定的

alertness /ə'lə:tnis/ n. 警戒，机敏

reverse /rɪ'vɜːs/ v. 使(某物)反转; 将(某物)翻转;转变

我是分界线，大家先一遍速读看是否理解

(According to conventional theory), yawning takes place (when people are bored or sleepy)and serves the function (of increasing alertness) (by reversing, through deeper breathing, the drop in blood oxygen levels) (that are caused by the shallow breathing) (that accompanies lack of sleep or boredom).(TPO18, 45)

分析：

这个句子的主干就是：

yawning takes place and serves the function

修饰一：(According to conventional theory)，介词短语

中文：根据传统理论

修饰二：(when people are bored or sleepy)，从句

中文：当人们感到厌烦或困倦时

修饰三：(of increasing alertness)，介词短语

中文：增强警觉

修饰四：(through deeper breathing)，插入语

中文：通过深呼吸

修饰五：(by reversing, through deeper breathing, the drop inblood oxygen levels)，介词短语，注意这里修饰四的插入语隔开了，断句别出错

中文：通过浅呼吸逆转血液中氧含量的下降

修饰六：(that are caused by the shallow breathing)，从句，修饰the drop in blood oxygen levels托福考试官方网站

中文：是通过浅呼吸导致的

修饰七：(that accompanies lack of sleep or boredom)，从句修饰，theshallow breathing

中文：伴随着缺乏睡眠或厌烦

参考翻译：

根据传统理论，打哈欠会在当人们感到厌烦或困倦时发生，并且打哈欠通过深呼吸逆转血液中氧含量的下降(这种下降是由伴随着缺乏睡眠或厌烦的浅呼吸造成的)起到提升警觉的作用。