Southern-Summer School on Mathematical Biology

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2018:groups:g7:start [2018/01/13 15:52] – [Assignments] muniz2018:groups:g7:start [2024/01/09 18:45] (current) – external edit 127.0.0.1
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 Autotomy, or self-amputation, is an active form of defense from predators in which an animal sheds a body part when attacked. Despite sounding strange, it is performed by many species of reptiles, insects, arachnids and mollusks. In insects and arachnids, the amputated body part is usually a leg, so that even when the part cannot be regrown, it has some sort of backup (insects and arachnids have lots of legs, in case you didn’t recall).  Autotomy, or self-amputation, is an active form of defense from predators in which an animal sheds a body part when attacked. Despite sounding strange, it is performed by many species of reptiles, insects, arachnids and mollusks. In insects and arachnids, the amputated body part is usually a leg, so that even when the part cannot be regrown, it has some sort of backup (insects and arachnids have lots of legs, in case you didn’t recall). 
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-{{    http://phenomena.nationalgeographic.com/files/2015/01/Scorpion.jpg?250}} 
  
 Recently, however, a very unusual and unexpected kind of autotomy has been discovered in arachnids: some scorpions of the family Butidae may self-amputate their tails. This it surprising  because the tail does not have a backup and cannot grow back, which means that the scorpions discard their main weapon. But there is more: the "tail" of the scorpion is actually the end of its abdomen, and by losing it the scorpion loses its anus! And yes, this does generate the sort of problem you are thinking about right now. Nevertheless, tailess scorpions can endure for months and can even reproduce. Recently, however, a very unusual and unexpected kind of autotomy has been discovered in arachnids: some scorpions of the family Butidae may self-amputate their tails. This it surprising  because the tail does not have a backup and cannot grow back, which means that the scorpions discard their main weapon. But there is more: the "tail" of the scorpion is actually the end of its abdomen, and by losing it the scorpion loses its anus! And yes, this does generate the sort of problem you are thinking about right now. Nevertheless, tailess scorpions can endure for months and can even reproduce.
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   - Start by building a general mathematical model to describe the situation in which an individual that meets a predator increases its survival chances if it sheds some body part. Remember that once the body part is “autotomized”, the individual will stay more exposed to predators and may suffer other effects from the amputation.   - Start by building a general mathematical model to describe the situation in which an individual that meets a predator increases its survival chances if it sheds some body part. Remember that once the body part is “autotomized”, the individual will stay more exposed to predators and may suffer other effects from the amputation.
-  - Advance into making your model more inspired in the specific case of the scorpion in the example. Remove from the model the option of re-growing lost body parts, and add the dynamics of losing additional tail sections described in the texts (after all, it is only via this process that the “autotomized” scorpions can poop). Can you use this model to make evolutionary predictions? For instance, assuming that the scorpions’ tendency to autotomize its tail is heritable, what should influence its frequency in the population? +  - Advance into making your model more inspired in the specific case of the scorpion in the example. Remove from the model the option of re-growing lost body parts, and add the dynamics of losing additional tail sections described in the texts (after all, it is only via this process that the “autotomized” scorpions can poop). Can you use this model to make population-level predictions? For instance, what factors modulate the proportion of autotomized individuals in the population? Or, what is the expected distribution of the number of tail sections in a scorpion population?
 ===== Bonus quest ===== ===== Bonus quest =====
-**Female vs male autotomists**: apparently females are less likely to amputate their tails than males, which may be related to their longer life-span. However, male scorpions may use their tails to court females, so that a male scorpion without a tail will have more difficulty in mating. Keeping in mind that males may attain higher reproductive success than any female by mating with several females, can you predict in which scenarios males should be less willing to shed their tails than females? <wrap tip>Tip:</wrap> if some males attain a very high mating success, others may remain unmated - each new scorpion has a single father and a single mother, so that the mean reproductive success of males and females must be the same. This is known as the Fisher condition. 
  
 +**Evolutionary dynamics**: can you modify your model to produce evolutionary predictions? For instance, what are the factors that make autotomy a strategy that can persist in a population? Also, assuming the scorpions’ tendency to autotomize its tail is heritable, what should influence its mean value in the population? <wrap tip>Tip:</wrap>  one way of thinking about natural selection is in terms of competition among individuals carrying different genes. After all, natural selection has been described as a struggle for existence by someone important.
 ===== Basic References ===== ===== Basic References =====
  
2018/groups/g7/start.1515858735.txt.gz · Last modified: 2024/01/09 18:45 (external edit)