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      "body": "Congratulations @callimico! You received a personal award!\n\n<table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@callimico/birthday2.png</td><td>Happy Steem Birthday! - You are on the Steem blockchain for 2 years!</td></tr></table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@callimico) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=callimico)_</sub>\n\n\n**Do not miss the last post from @steemitboard:**\n<table><tr><td><a href=\"https://steemit.com/steemitboard/@steemitboard/downvote-challenge-add-up-to-3-funny-badges-to-your-board\"><img src=\"https://steemitimages.com/64x128/https://steemitimages.com/0x0/![](https://cdn.steemitimages.com/DQmUuJkZdnSpHVWssxF82ntymqXg4Pvk6K6bYvckUYVRsnj/image.png)\"></a></td><td><a href=\"https://steemit.com/steemitboard/@steemitboard/downvote-challenge-add-up-to-3-funny-badges-to-your-board\">Downvote challenge - Add up to 3 funny badges to your board</a></td></tr></table>\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
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      "title": "New series: Pain in animals",
      "body": "Just last month, [Switzerland became the first country in the world to ban the practice of boiling lobsters alive](https://www.independent.co.uk/news/science/lobsters-boil-alive-cooking-ban-taste-animal-pain-uk-switzerland-welfare-a8217921.html#commentsDiv). But do lobsters even feel pain? In my upcoming posts, I will talk about pain in animals, what we know and what we don't know.\n\n### But first, an introduction\n\nI've cared deeply about animals for as long as I can remember. So great was my childhood fascination that I decided to become a biologist already in elementary school. As I'm currently in the process of writing my Master's thesis in biology, that dream has almost come true. For a self-proclaimed friend of animals, however, the topic of my thesis may come across as paradoxical: pain in crustaceans. I'm torturing crabs, basically. \n\n![](https://steemitimages.com/DQmer7yNB9TKjHczGrkVMUv9grMw9nfRLMEBj6w4kyx12At/image.png)\n\"You monster!\" [Image by D. Hazerli](https://commons.wikimedia.org/wiki/File:Common_shore_crab_2.JPG)\n\nAllow me a few lines to justify my actions:\n\n1. The purpose of my experiments is to find out _if_ crustaceans are capable of suffering.  If not, I've done no harm. If they do, I take solace in the fact that...\n1. ... the stuff I'm subjecting  my crabs to is quite mild (a spray of hot water on the claw) and causes no visible injuries.\n\nBut still, why study pain in crustaceans? For one thing, many are treated harshly by humans. Lobsters are boiled alive, crabs have their claws ripped off and [prawns have their eyestalks cut off to increase fertility](https://www.omicsonline.org/the-effects-of-eyestalk-ablation-on-the-reproductive-and-immune-function-of-female-macrobrachium-americanum-2155-9546.1000156.php?aid=10097); if crustaceans do suffer, they suffer a lot!\n\nCrustaceans are interesting experimental subjects, because their nervous system is simpler than the ones in animals we currently believe to feel pain, i.e. mostly vertebrates (here's [a review](https://www.researchgate.net/publication/266794956_Defining_and_assessing_animal_pain)). In other words, demonstrating behaviour in crustaceans consistent with pain would lower the threshold at which we start to assume pain in animals based on brain capacity. If an animal can feel pain, it also means that it has a form of consciousness. Which is what really fascinates me the most. You and I might care about animals, but to what extent do the animals themselves care about anything?\n\nCrustaceans belong to the arthropods, the most numerous animal group on the planet, both in terms of species and number of individuals. The group also includes insects, chelicerates (e.g. spiders and scorpions) and myriapods (millipedes and centipedes). If just a fraction of these creatures feel pain, then the amount of suffering in the world is much greater than we might have anticipated.\n\n![](https://steemitimages.com/DQmP7yB114rtVTVgHqYuDNq9NDZhBPfh7LHjUiGSDq2pazD/image.png)\n[Image by Nick Beeson](https://commons.wikimedia.org/wiki/File:AnimalsRelativeNumbers.png)\n\nOr maybe you've already anticipated it. A common reaction from people I tell about my research (oh, the awkward first encounters...) is this:\n\n\"But why shouldn't they feel pain?\"\n\nThis is not just anthropomorphism. Several of my conversation partners note that pain is an evolutionary advantage that allows us to detect when something hurts us, so we can avoid it. This would seem to be the case for crabs and humans alike.\n\n### Nociception and pain\n\nHowever, inability to feel pain does not entail failure to detect harm. In pain research, a distinction is made between nociception and pain. Nociception is the ability to record painful stimuli as sensory input. These input may be used to trigger reflex actions that require no conscious awareness. Alternatively, they may provoke pain. Pain is a subjective feeling of discomfort, something that makes it notoriously difficult to study in non-human animals (and sometimes in humans, too). To appreciate the fact that nociception is a distinct phenomenon, consider the classic case of putting your hand on a hot stove. It hurts, so you quickly withdraw your hand. Except, [that's not the order of events](http://physiologyplus.com/withdrawal-reflex/). As you touch the stove, nervous signals travel to the spinal cord and then back to the muscles in your arm. Other signals continue up the spinal cord and into your brain where a series of brain centers collectively produce the unpleasant sensation of burning. This processing takes time, and by the time you become aware of your mistake, you've already moved your hand. What's the point in pain, then? [Several options have been suggested](http://www.bib.uab.es/veter/expo/benestar/assessment%20of%20pain.pdf). One of them is that pain allows us to remember harmful experiences, so we can avoid them in the future. Keep our hands off the stove, so to speak. \n\nOne way of distinguishing nociception from pain in animals could therefore be to demonstrate learning in response to a noxious stimulus. Another way is to demonstrate a motivational trade-off, i.e. showing that the animal responds differently to the same noxious stimulus, if the motivation to endure it is altered.\n\nNone of these methods are perfect. Motivational trade-offs and learning behaviour can both be encoded in a robot, a presumably painless system. Nevertheless, given that robots can even be made to mimic human pain to a great extent, there has to be a point where we accord to other animals the benefit of the doubt. A clear demonstration of learning from harm could be this point.\n\nHow do crustaceans fare in this regard? Have a look in [the review I mentioned](https://www.researchgate.net/publication/266794956_Defining_and_assessing_animal_pain) or stay tuned for my next post.",
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      "body": "Consider the following calculation:\n\n![](https://steemitimages.com/DQmSYFFBBe6UjaYzWpvumy24ZdZaZpV59tQjCNepn4fnPpg/image.png)\n\nIn elementary school, I was taught to solve this kind of problem by borrowing tens to fill in the missing ones, hundreds to fill in missing tens and so on:\n\n![](https://steemitimages.com/DQmPRMsSVHE6cdje4k1KCzu8cuJt3aA53pyrg5BDEtR84uD/image.png)\n\nThis method is annoying in cases where you have to do a lot of borrowing, so I came up with an alternative approach. Whereas subtraction from a number like 2018 is likely to involve some borrowing (since 2, 0 and 1 are low digits), the number 999 never will. Therefore, let’s split up the previous problem like this:\n\n![](https://steemitimages.com/DQmT8pNiWMQ23tETLsfq2LqjrjGLsGSs3bd1WMNacZjmDhS/image.png) \n\nThis subtraction is much faster to make than the previous one, but now we need to add the difference between 2018 and 999. Fortunately, we don’t have to think hard to find this difference: simply subtract one from the first digit in 2018 and add one to the last:\n\n![](https://steemitimages.com/DQmQUnTt5RN6dDwrVENuKmotVzeyDbBtstoMJ2iFdAQCS6d/image.png)\n\nThen, do the addition:\n\n![](https://steemitimages.com/DQmWag4VVD1fMgLeQCNtiFTNakH59Lqf1sA6G6UusYC9Fbn/image.png)\n\nProblem solved! Here’s the general two-step procedure for subtracting a number y from a number x:\n\n1: Subtract y from a number consisting of as many 9’s as the number of digits in x, minus 1. Don’t waste time writing out every 9; just use a shorthand like this:\n\n![](https://steemitimages.com/DQmPD4bTq5D7oJQTV6RYf5SpEyXzMVsLhresChYL7XgPGKE/image.png)\n\n2: Add the result to the number x from which you’ve lowered the first digit by 1 and increased the last digit by 1.\n\nIf you’re accustomed to the classic method I mentioned at the beginning, you might not find my approach to be faster right away. However, it is advantageous in calculations where x and y are large, and y has higher digit values than x.\nHere’s a full solution to a subtraction problem, with x=210323 and y=89669:\n\n![](https://steemitimages.com/DQmb81GxxBtCa64TJJTLrEBaJ9YvKPvSddxWsFjRJmDNpg9/image.png)\n\nDo you know a better method for doing subtractions by hand? Please let me know!",
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      "body": "If forced to write out the steps, then the old method is definitely faster for an example like 2018 - 9. But I would argue that you shouldn't require any algorithm to solve that one ;). \n\nFor typical elementary school puzzles, the difference in effort required to carry out the calculations is negligible, in which case the old method may be preferable, because it's more obvious from the writing what is going on. As the number of digits increase, I believe the amount of extra time required increases less with my method.",
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      "body": "Beautiful. This certainly is more efficient for examples like the one you've shown (2018 - 779), but what about (2018 - 9)? I wonder what method is the most efficient on average.",
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      "body": "Key word borrow equals usery ! We were taught wrong to begin with !But I see a lot of us are waking up ! I  you have some time check up on my post on why the Computer Keyboard Is Dead !",
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      "body": "Consider the following calculation:\n\n![](https://steemitimages.com/DQmSYFFBBe6UjaYzWpvumy24ZdZaZpV59tQjCNepn4fnPpg/image.png)\n\nIn elementary school, I was taught to solve this kind of problem by borrowing tens to fill in the missing ones, hundreds to fill in missing tens and so on:\n\n![](https://steemitimages.com/DQmPRMsSVHE6cdje4k1KCzu8cuJt3aA53pyrg5BDEtR84uD/image.png)\n\nThis method is annoying in cases where you have to do a lot of borrowing, so I came up with an alternative approach. Whereas subtraction from a number like 2018 is likely to involve some borrowing (since 2, 0 and 1 are low digits), the number 999 never will. Therefore, let’s split up the previous problem like this:\n\n![](https://steemitimages.com/DQmT8pNiWMQ23tETLsfq2LqjrjGLsGSs3bd1WMNacZjmDhS/image.png) \n\nThis subtraction is much faster to make than the previous one, but now we need to add the difference between 2018 and 999. Fortunately, we don’t have to think hard to find this difference: simply subtract one from the first digit in 2018 and add one to the last:\n\n![](https://steemitimages.com/DQmQUnTt5RN6dDwrVENuKmotVzeyDbBtstoMJ2iFdAQCS6d/image.png)\n\nThen, do the addition:\n\n![](https://steemitimages.com/DQmWag4VVD1fMgLeQCNtiFTNakH59Lqf1sA6G6UusYC9Fbn/image.png)\n\nProblem solved! Here’s the general two-step procedure for subtracting a number y from a number x:\n\n1: Subtract y from a number consisting of as many 9’s as the number of digits in x, minus 1. Don’t waste time writing out every 9; just use a shorthand like this:\n\n![](https://steemitimages.com/DQmPD4bTq5D7oJQTV6RYf5SpEyXzMVsLhresChYL7XgPGKE/image.png)\n\n2: Add the result to the number x from which you’ve lowered the first digit by 1 and increased the last digit by 1.\n\nIf you’re accustomed to the classic method I mentioned at the beginning, you might not find my approach to be faster right away. However, it is advantageous in calculations where x and y are large, and y has higher digit values than x.\nHere’s a full solution to a subtraction problem, with x=210323 and y=89669:\n\n![](https://steemitimages.com/DQmb81GxxBtCa64TJJTLrEBaJ9YvKPvSddxWsFjRJmDNpg9/image.png)\n\nDo you know a better method for doing subtractions by hand? Please let me know!",
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      "title": "Alternative approach to subtractions",
      "body": "Consider the following calculation:\n\n![](https://steemitimages.com/DQmSYFFBBe6UjaYzWpvumy24ZdZaZpV59tQjCNepn4fnPpg/image.png)\n\nIn elementary school, I was taught to solve this kind of problem by borrowing tens to fill in the missing ones, hundreds to fill in missing tens and so on:\n\n![](https://steemitimages.com/DQmPRMsSVHE6cdje4k1KCzu8cuJt3aA53pyrg5BDEtR84uD/image.png)\n\nThis method is annoying in cases where you have to do a lot of borrowing, so I came up with an alternative approach. Whereas subtraction from a number like 2018 is likely to involve some borrowing (since 2, 0 and 1 are low digits), the number 999 never will. Therefore, let’s split up the previous problem like this:\n\n![](https://steemitimages.com/DQmT8pNiWMQ23tETLsfq2LqjrjGLsGSs3bd1WMNacZjmDhS/image.png) \n\nThis subtraction is much faster to make than the previous one, but now we need to add the difference between 2018 and 999. Fortunately, we don’t have to think hard to find this difference: simply subtract one from the first digit in 2018 and add one to the last:\n\n![](https://steemitimages.com/DQmQUnTt5RN6dDwrVENuKmotVzeyDbBtstoMJ2iFdAQCS6d/image.png)\n\nThen, do the addition:\n\n![](https://steemitimages.com/DQmWag4VVD1fMgLeQCNtiFTNakH59Lqf1sA6G6UusYC9Fbn/image.png)\n\nProblem solved! Here’s the general two-step procedure for subtracting a number y from a number x:\n\n1: Subtract y from a number consisting of as many 9’s as the number of digits in x, minus 1. Don’t waste time writing out every 9; just use a shorthand like this:\n\n![](https://steemitimages.com/DQmPD4bTq5D7oJQTV6RYf5SpEyXzMVsLhresChYL7XgPGKE/image.png)\n\n2: Add the result to the number x from which you’ve lowered the first digit by 1 and increased the last digit by 1.\n\nIf you’re accustomed to the classic method I mentioned at the beginning, you might not find my approach to be faster right away. However, it is advantageous in calculations where x and y are large, and y has higher digit values than x.\nHere’s a full solution to a subtraction problem, with x=210323 and y=89669:\n\n![](https://steemitimages.com/DQmb81GxxBtCa64TJJTLrEBaJ9YvKPvSddxWsFjRJmDNpg9/image.png)\n\nDo you know a better method for doing subtractions by hand? Please let me know!",
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      "permlink": "re-h725-do-invertebrates-feel-pain-20180318t142911168z",
      "title": "",
      "body": "Nice read! I liked this part in particular: \"In conclusion, the difficulty of drawing a line between the species that can be used without any concern and the pain-sensitive species in the same group, does not by itself justify drawing an arbitrary line.\"\n\nI've been working on/off on the topic of pain in crustaceans for about a year now, and I still don't know what to believe. In my opinion, the article by Magee and Elwood currently provides some of the best support in favor of pain, (along with this http://science.sciencemag.org/content/344/6189/1293). And yet, it's not terribly convincing. If you have a look at Fig. 1 in Magee and Elwood's article, you'll see that on the tenth trial, about a third of all crabs still entered a shock chamber. Better than would be expected by change, but not much. If the learning ability of crabs is really this bad, one can't help but wonder how much they benefit from it in nature. If the answer is: \"they don't\", then what benefit does pain provide that nociceptive reflexes don't?\n\nThe fact that anxiety-like behavior can be induced with electric shock and then removed pharmacologically in the same way in humans and crayfish (see the linked article) makes me think that decapods do feel pain. But I won't feel safe in drawing that conclusion until I've seen evidence of more complex harm-induced learning.",
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      "title": "",
      "body": "Congratulations @callimico! You have completed some achievement on Steemit and have been rewarded with new badge(s) :\n\n[![](https://steemitimages.com/70x80/http://steemitboard.com/notifications/votes.png)](http://steemitboard.com/@callimico) Award for the number of upvotes\n\nClick on any badge to view your own Board of Honor on SteemitBoard.\nFor more information about SteemitBoard, click [here](https://steemit.com/@steemitboard)\n\nIf you no longer want to receive notifications, reply to this comment with the word `STOP`\n\n> Upvote this notification to help all Steemit users. Learn why [here](https://steemit.com/steemitboard/@steemitboard/http-i-cubeupload-com-7ciqeo-png)!",
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      "body": "@@ -4379,16 +4379,23 @@\n  O. Baum\n+ (2008)\n : %22Under\n",
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      "title": "How to draw an evolutionary tree: UPGMA",
      "body": "@@ -4053,16 +4053,23 @@\n  O. Baum\n+ (2008)\n : %22Under\n",
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      "body": "@@ -3889,88 +3889,8 @@\n tree\n-, drawn with tools from http://iubio.bio.indiana.edu/treeapp/treeprint-form.html\n :%0A%0A!\n@@ -3993,12 +3993,180 @@\n %2520tree.png)\n+%0A%0A### Book reference%0AMarketa Zvelebil and Jeremy O. Baum: %22Understanding Bioinformatics%22%0A%0A### Tree-drawing tool%0Ahttp://iubio.bio.indiana.edu/treeapp/treeprint-form.html\n",
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      "body": "@@ -4323,8 +4323,176 @@\n arisons.\n+%0A%0A### Book reference%0AMarketa Zvelebil and Jeremy O. Baum: %22Understanding Bioinformatics%22%0A%0A### Tree-drawing tool%0Ahttp://iubio.bio.indiana.edu/treeapp/treeprint-form.html\n",
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      "body": "Your advice about character is sound. As for the purpose, roles and obligations, your mindset is too rigid. You don't need God for your marriage to be meaningful. And if a man is good at cooking, or a woman is good with financial matters, why not let them do what they're good at? \n\nYou put it very nicely yourself:\n\n\"That it worked for others doesn't mean it'll work for you\"\n\nWhy is that, you think? Because people are different. I can assure you that a lot of people would be more happy in marriage if they ignored the gender roles you postulate.",
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      "title": "How to draw an evolutionary tree II: maximum parsimony",
      "body": "@@ -1255,18 +1255,18 @@\n esis abo\n-ve\n+ut\n  the rel\n",
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      "title": "How to draw an evolutionary tree II: maximum parsimony",
      "body": "In [my previous post](https://steemit.com/science/@callimico/how-to-draw-an-evolutionary-tree-upgma), I described how to use the algorithm UPGMA to construct an evolutionary tree from a distance matrix. It was fast and straightforward, but we had to make the assumption that evolution took place at the same rate throughout the tree. The next method, maximum parsimony, does not assume this and conceptually it is as simple as UPGMA. The drawback is that maximum parsimony is a lot slower. UPGMA singles out the optimal tree, under the assumptions of the algorithm, and does not attempt to score any other tree. Using maximum parsimony, you need to check all possible trees one at a time (there are probably algorithms that can speed up this process, but I don't know them).\n\nMaximum parsimony assumes that the correct tree is the one that requires the fewest evolutionary changes. The rationale is this: Every evolutionary change is an event with a probability below 1. If you consider two such events, the probability that both of them happen is lower than the probability that just one of them does. Just like rolling two sixes with a pair of dice is less probable than rolling six with one of them.\n\nTo apply maximum parsimony, we first need a hypothesis above the relationship between the taxa we want to investigate. We will look at five taxa, labeled A-E, and postulate the following phylogeny:\n\n![UPGMA tree.png](https://steemitimages.com/DQmRVoQ1NBxhEWxdRigpQB2dmixrnQ1gYWGJgHs7N171BUE/UPGMA%20tree.png)\n\nNow, our task is to check how probable this tree is. Or rather, how parsimonious. Unlike UPGMA, there is no need for a distance matrix. We just need to know a set of traits and how they appear in our taxa. Using molecular data, these traits would be bases in a DNA or RNA sequence, or amino acids in a protein. First, write up the set of traits in each taxon. Disregard any trait that does not differ between taxa, or differs in a single taxon only. Next, we could try to assume an ancestral state, i.e. the set of traits at the root of the tree. But this would be guessing, and guesses are usually time-consuming. Instead, we can apply a method known as Fitch's algorithm.\n\nInstead of assuming anything about the root of the tree, we start from the leaves (the taxa) and work our way down, one trait at a time. Because this is just an example, we will only look at one trait here. Let's replace the names of the taxa with the trait, a DNA base from a particular locus:\n\n![maximum_parsimony.png](https://steemitimages.com/DQmeUoWk2T2nFyvoKQkYbyceoCKqrirNcYNuhdWF1etawSN/maximum_parsimony.png) \n\nIt's fairly obvious that our current hypothesis isn't optimal; the C's are not each other's closest relative. But for the sake of the example, let's try and figure this out the hard way.\n\nLook at the two upper leaves. Both have A's so we can assume that their most recent common ancestor also had this base:\n\n![maximum_parsimony2.png](https://steemitimages.com/DQmNaB8S37aY8z1do34KD7K8zkbAcvQDyKwUdw84MLbuajL/maximum_parsimony2.png)\n\nThe two bottom leaves have different bases. Therefore, the ancestral character could be either a C or a T. Similarly, the ancestral node connecting the three upper leaves could have either an A or a C:\n\n![maximum_parsimony3.png](https://steemitimages.com/DQmPSCM5TcqJNcftgfMPhsWVMNcm4LswpacZfCXkJUfX6G9/maximum_parsimony3.png)\n\nAt the root of the tree, the character could be either an A, a C or a T. However, C was an option in both of the nodes following the root node, so we go with a C:\n\n![maximum_parsimony4.png](https://steemitimages.com/DQmcxcFw6a1BjJvBTzRF9uUjh8WP7ew6DpihdxkQiCELkdt/maximum_parsimony4.png)\n\nThe number of ambiguous nodes, two, is the number of changes we have to assume to arrive at our current hypothetical tree. Curiously, this is actually the same number we would arrive at, had our hypothesis grouped the A's as sister taxa and the C's as sister taxa:\n\n![maximum_parsimony5.png](https://steemitimages.com/DQmZeK7HtZzrqb2585XE8JKaR86CfufVXtyrWceUHFi9ooW/maximum_parsimony5.png)\n\nThus, in this very simplistic example, we don't have enough information to single out the best solution by maximum parsimony. In practice, this would not be a problem, because you would never apply maximum parsimony unless you had more than a single trait to use for comparisons.",
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      "title": "How to draw an evolutionary tree II: Maximum parsimony",
      "body": "In [my previous post](https://steemit.com/science/@callimico/how-to-draw-an-evolutionary-tree-upgma), I described how to use the algorithm UPGMA to construct an evolutionary tree from a distance matrix. It was fast and straightforward, but we had to make the assumption that evolution took place at the same rate throughout the tree. The next method, maximum parsimony, does not assume this and conceptually it is as simple as UPGMA. The drawback is that maximum parsimony is a lot slower. UPGMA singles out the optimal tree, under the assumptions of the algorithm, and does not attempt to score any other tree. Using maximum parsimony, you need to check all possible trees one at a time (there are probably algorithms that can speed up this process, but I don't know them).\n\nMaximum parsimony assumes that the correct tree is the one that requires the fewest evolutionary changes. The rationale is this: Every evolutionary change is an event with a probability below 1. If you consider two such events, the probability that both of them happen is lower than the probability that just one of them does. Just like rolling two sixes with a pair of dice is less probable than rolling six with one of them.\n\nTo apply maximum parsimony, we first need a hypothesis above the relationship between the taxa we want to investigate. We will look at five taxa, labeled A-E, and postulate the following phylogeny:\n\n![UPGMA tree.png](https://steemitimages.com/DQmRVoQ1NBxhEWxdRigpQB2dmixrnQ1gYWGJgHs7N171BUE/UPGMA%20tree.png)\n\nNow, our task is to check how probable this tree is. Or rather, how parsimonious. Unlike UPGMA, there is no need for a distance matrix. We just need to know a set of traits and how they appear in our taxa. Using molecular data, these traits would be bases in a DNA or RNA sequence, or amino acids in a protein. First, write up the set of traits in each taxon. Disregard any trait that does not differ between taxa, or differs in a single taxon only. Next, we could try to assume an ancestral state, i.e. the set of traits at the root of the tree. But this would be guessing, and guesses are usually time-consuming. Instead, we can apply a method known as Fitch's algorithm.\n\nInstead of assuming anything about the root of the tree, we start from the leaves (the taxa) and work our way down, one trait at a time. Because this is just an example, we will only look at one trait here. Let's replace the names of the taxa with the trait, a DNA base from a particular locus:\n\n![maximum_parsimony.png](https://steemitimages.com/DQmeUoWk2T2nFyvoKQkYbyceoCKqrirNcYNuhdWF1etawSN/maximum_parsimony.png) \n\nIt's fairly obvious that our current hypothesis isn't optimal; the C's are not each other's closest relative. But for the sake of the example, let's try and figure this out the hard way.\n\nLook at the two upper leaves. Both have A's so we can assume that their most recent common ancestor also had this base:\n\n![maximum_parsimony2.png](https://steemitimages.com/DQmNaB8S37aY8z1do34KD7K8zkbAcvQDyKwUdw84MLbuajL/maximum_parsimony2.png)\n\nThe two bottom leaves have different bases. Therefore, the ancestral character could be either a C or a T. Similarly, the ancestral node connecting the three upper leaves could have either an A or a C:\n\n![maximum_parsimony3.png](https://steemitimages.com/DQmPSCM5TcqJNcftgfMPhsWVMNcm4LswpacZfCXkJUfX6G9/maximum_parsimony3.png)\n\nAt the root of the tree, the character could be either an A, a C or a T. However, C was an option in both of the nodes following the root node, so we go with a C:\n\n![maximum_parsimony4.png](https://steemitimages.com/DQmcxcFw6a1BjJvBTzRF9uUjh8WP7ew6DpihdxkQiCELkdt/maximum_parsimony4.png)\n\nThe number of ambiguous nodes, two, is the number of changes we have to assume to arrive at our current hypothetical tree. Curiously, this is actually the same number we would arrive at, had our hypothesis grouped the A's as sister taxa and the C's as sister taxa:\n\n![maximum_parsimony5.png](https://steemitimages.com/DQmZeK7HtZzrqb2585XE8JKaR86CfufVXtyrWceUHFi9ooW/maximum_parsimony5.png)\n\nThus, in this very simplistic example, we don't have enough information to single out the best solution by maximum parsimony. In practice, this would not be a problem, because you would never apply maximum parsimony unless you had more than a single trait to use for comparisons.",
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      "body": "[In my first post](https://steemit.com/science/@callimico/why-you-re-more-closely-related-to-a-salmon-than-a-salmon-is-to-a-shark-understanding-evolutionary-phylogenies), I explained how to read a phylogenetic tree, a tree depicting the relationship between different taxa, i.e. groups of organisms. [In my second post](https://steemit.com/science/@callimico/why-we-trust-in-dna-to-tell-us-how-organisms-are-related), I explained what data forms the basis of such trees, and why molecular data are preferred over morphological (appearance-related) data. Now, the time has come to look into the process of constructing the trees, once we have our data.\n\nEven with a relatively small number of taxa, the number of possible trees connecting them is huge. To find the most plausible tree, we need to make some assumptions and apply an appropriate algorithm. It may seem weird that several algorithms exist for calculating the \"best\" tree when, in reality, only one tree can be correct for any given dataset. Fortunately, the algorithms tend to agree quite well with each other. Some algorithms are fast, others are slower but make less drastic assumptions. With modern-day computers, even algorithms in the slow end of the spectrum can often be applied in a matter of seconds. Therefore, it's generally inadvisable to apply a fast, sloppy technique unless you have a good reason to assume that the underlying assumptions hold true. And yet, that's exactly the kind of technique I'm going to teach you in this post. Why? Because it's fast and one of the few that you can apply with pen and paper in a reasonable amount of time. Slightly more complicated techniques will follow in later posts.\n\nI used to pronounce UPGMA letter by letter, but my wonderful statistics teacher always pronounced it like a real word (\"up g'mah\"), and I've adopted the habit. UPGMA stands for Unweighted Pair Group Method with Arithmetic Mean and is a lot easier than it sounds.\n\nFirst off, we need a matrix listing the number of differences (e.g. base differences in homologous DNA sequences) between different taxa. Here's a mocked-up dataset with five taxa, labeled A-E:\n\n![](https://steemitimages.com/DQmcSGFw1ahbi86m4gYChSz3odrx2CX9pFRGaai1keX3xyM/image.png)\n\nThe first step is very simple. Just locate the shortest distance in the matrix:\n\n![](https://steemitimages.com/DQmUbZSjPrNP1xCvwoSRPxoprXhNDHthZYyba3gFSHUprzx/image.png)\n\nThis is the distance between taxon A and taxon E. Since this is the shortest distance between any two taxa, we assume that A and E are each other's closest relative. We therefore group them together as AE and proceed to construct a new matrix with one row and one column less than the first one:\n\n![](https://steemitimages.com/DQmbJaje95rdNWtqB2z9nEUrFW1ZNZ9QzrbxDvyeL2RsedD/image.png)\n\nHow did we obtain the new distances? By taking averages.  For instance, the distance between A and B in the first matrix was 10, and the distance between B and E was 11. The distance from B to the new cluster AE is 10.5, the average of 10 and 11. This is where UPGMA makes a critical assumption, namely that _the rate of evolution is constant throughout the tree_. More complicated algorithms do not assume a constant rate of evolution, but for the sake of simplicity we accept it here. Distances that do not involve our newly formed cluster are not changed in the new matrix; the distance from C to D continues to be 12.\n\nThe shortest distance in the new matrix is the one connecting AE and C, so let's form the cluster AE-C and draw another matrix:\n\n![](https://steemitimages.com/DQmanAucqaNK7ZUXDBkwWQvr8qPiCiRqVs5pfFmaRStVPGS/image.png)\n\nSame procedure as last time: take averages and find the smallest distance. This time, it's the one connecting B and D. This concludes our analysis:\n\n![](https://steemitimages.com/DQmUwiZ5JpnSmT4vFqecdBdMu7GFmY3s2iyaUvTpp3MVy66/image.png)\n\nHere's the tree, drawn with tools from http://iubio.bio.indiana.edu/treeapp/treeprint-form.html:\n\n![UPGMA tree.png](https://steemitimages.com/DQmRVoQ1NBxhEWxdRigpQB2dmixrnQ1gYWGJgHs7N171BUE/UPGMA%20tree.png)",
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      "body": "[In my first post](https://steemit.com/science/@callimico/why-you-re-more-closely-related-to-a-salmon-than-a-salmon-is-to-a-shark-understanding-evolutionary-phylogenies), I explained how to read a phylogenetic tree, a tree depicting the relationship between different taxa, i.e. groups of organisms. [In my second post](https://steemit.com/science/@callimico/why-we-trust-in-dna-to-tell-us-how-organisms-are-related), I explained what data forms the basis of such trees, and why molecular data are preferred over morphological (appearance-related) data. Now, the time has come to look into the process of constructing the trees, once we have our data.\n\nEven with a relatively small number of taxa, the number of possible trees connecting them is huge. To find the most plausible tree, we need to make some assumptions and apply an appropriate algorithm. It may seem weird that several algorithms exist for calculating the \"best\" tree when, in reality, only one tree can be correct for any given dataset. Fortunately, the algorithms tend to agree quite well with each other. Some algorithms are fast, others are slower but make less drastic assumptions. With modern-day computers, even algorithms in the slow end of the spectrum can often be applied in a matter of seconds. Therefore, it's generally inadvisable to apply a fast, sloppy technique unless you have a good reason to assume that the underlying assumptions hold true. And yet, that's exactly the kind of technique I'm going to teach you in this post. Why? Because it's fast and one of the few that you can apply with pen and paper in a reasonable amount of time. Slightly more complicated techniques will follow in later posts.\n\nI used to pronounce UPGMA letter by letter, but my wonderful statistics teacher always pronounced it like a real word (\"up g'mah\"), and I've adopted the habit. UPGMA stands for Unweighted Pair Group Method with Arithmetic Mean and is a lot easier than it sounds.\n\nFirst off, we need a matrix listing the number of differences (e.g. base differences in homologous DNA sequences) between different taxa. Here's a mocked-up dataset with five taxa, labeled A-E:\n\n![](https://steemitimages.com/DQmcSGFw1ahbi86m4gYChSz3odrx2CX9pFRGaai1keX3xyM/image.png)\n\nThe first step is very simple. Just locate the shortest distance in the matrix:\n\n![](https://steemitimages.com/DQmUbZSjPrNP1xCvwoSRPxoprXhNDHthZYyba3gFSHUprzx/image.png)\n\nThis is the distance between taxon A and taxon E. Since this is the shortest distance between any two taxa, we assume that A and E are each other's closest relative. We therefore group them together as AE and proceed to construct a new matrix with one row and one column less than the first one:\n\n![](https://steemitimages.com/DQmbJaje95rdNWtqB2z9nEUrFW1ZNZ9QzrbxDvyeL2RsedD/image.png)\n\nHow did we obtain the new distances? By taking averages.  For instance, the distance between A and B in the first matrix was 10, and the distance between B and E was 11. The distance from B to the new cluster AE is 10.5, the average of 10 and 11. This is where UPGMA makes a critical assumption, namely that _the rate of evolution is constant throughout the tree_. More complicated algorithms do not assume a constant rate of evolution, but for the sake of simplicity we accept it here. Distances that do not involve our newly formed cluster are not changed in the new matrix; the distance from C to D continues to be 12.\n\nThe shortest distance in the new matrix is the one connecting AE and C, so let's form the cluster AE-C and draw another matrix:\n\n![](https://steemitimages.com/DQmanAucqaNK7ZUXDBkwWQvr8qPiCiRqVs5pfFmaRStVPGS/image.png)\n\nSame procedure as last time: take averages and find the smallest distance. This time, it's the one connecting B and D. This concludes our analysis:\n\n![](https://steemitimages.com/DQmUwiZ5JpnSmT4vFqecdBdMu7GFmY3s2iyaUvTpp3MVy66/image.png)\n\nHere's the tree, drawn with tools from http://iubio.bio.indiana.edu/treeapp/treeprint-form.html:\n\n![UPGMA tree.png](https://steemitimages.com/DQmRVoQ1NBxhEWxdRigpQB2dmixrnQ1gYWGJgHs7N171BUE/UPGMA%20tree.png)",
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      "title": "How to compare two DNA sequences by hand - the Needleman-Wunsch algorithm",
      "body": "First of all, no sane person working in bioinformatics would spend time comparing DNA sequences by hand with all the fast digital tools available (here's one: https://blast.ncbi.nlm.nih.gov/Blast.cgi?PAGE_TYPE=BlastSearch&PROG_DEF=blastn&BLAST_PROG_DEF=blastn&BLAST_SPEC=GlobalAln&LINK_LOC=BlastHomeLink). Still, any bioinformatician would do well to understand the technique, in part because it contains an element of subjectivity.\n\nTwo DNA sequences that share a common origin are said to be homologous. It could be the gene for insulin in humans and the one in cattle. The genes are called orthologs when they are both homologous and come from different species. Homologous gene sequences differ, because the ancestral sequence has mutated in different places in the lineages descending from it. The mutation can be a substitution:\n\nAACGT to ACCGT\n\nAn insertion:\n\nAACGT to AACCGT\n\nOr a deletion:\n\nAACGT to ACGT\n\nWhen DNA is transcribed into RNA, it is read in triplets, pieces of three adjacent bases. The three corresponding RNA bases are later translated into an amino acid. Substitutions tend to be the least harmful mutations, because they each affect zero or at most one amino acid. Three-base insertions or deletions are also relatively harmless, because the addition or removal of a triplet means one amino acid more or less in the finished protein (I stress _relatively_ harmless; even substitutions can be lethal if they occur in a bad spot). Insertions or deletions of base numbers not divisible by three are bad news, because they disturb the reading frame of the sequence, potentially affecting all amino acids downstream from the mutation. They are called frameshift mutations and usually lead to the translation of a non-functional protein.\n\nBecause of their potential for causing frameshifts, indels (insertions or deletions) are less frequently preserved in the course of evolution than substitutions. When aligning two homologous DNA sequences of unequal length, the occurence of an indel has to be assumed. This is represented by a gap:\n\nA_CGT\nAACGT\n\nWe may even choose to assume an indel between sequences of the same length, if it makes for a better alignment. But since indels are often severe, their inclusion should be punished. That is, we apply a gap penalty.\n\nThere is a multitude of different ways to compare even short DNA sequences. Without an algorithm to locate the best options, the computers of today would not be able to handle even a small fraction of the genetic information currently published. Fortunately, the Needleman-Wunsch algorithm (developed by Saul B. Needleman and Christian D. Wunsch) makes for optimal alignment of large sequences. Short sequences can be aligned by hand. The rest of this post will describe the procedure.\n\n## How to run a Needleman-Wunsch algorithm\n\nFirst, draw a matrix. Each side should be the length of one of the sequences you want to compare, plus one cell. We are going to compare two sequences of 6 and 7 bases, respectively, so we need a 7x8 matrix:\n\n![matrix1.png](https://steemitimages.com/DQmRZ7miqppgzdMkxBjbmL9rPcMG5WBDpkiTMTbfEKNBaam/matrix1.png)\t\t\t\t\n\nYou will notice that I have already filled out part of the matrix. Indeed, this is a bit premature. We first need to decide on a match score, a mismatch score and a gap penalty. This is the subjective part of the algorithm. I have used 1, 0 and -1. If in doubt, one can try to run the same alignment several times with different scores to see how much this affects the final results.\n\nThe idea is to start in the upper left corner of the matrix and work your way down the alignment. A diagonal move means that you are simply comparing the next base in sequence 1 to the next base in sequence 2. A horizontal or vertical move signifies the introduction of a gap in, respectively, the vertical and horizontal sequence. Since our gap penalty is -1, every expansion of the gap in the same direction adds -1 to the total score unless we obtain a match.\n\nNow, lets attempt to align our first base. We have three options, but the first two are rather silly. We could introduce a gap in sequence 1 and then a gap in sequence 2. Or we could introduce a gap in sequence 2 and then a gap in sequence 1. Or we could just avoid gaps altogether and align the first base in sequence 1 with the first in sequence 2. You might have guessed what I prefer, but take a look at the scores to be sure:\n\nOption 1: -1 + (-1) = -2\nOption 2: -1 + (-1) = -2\nOption 3: 0\n\n0 > -2. We put 0, because we got a mismatch (A and C). At this point, it's preferable to a gap, so we put a 0 in the matrix.\n\n![matrix2.png](https://steemitimages.com/DQmdpZY7cTXQipuLXYdz8ss1a6sNK2LfNixd4GQHcbufWSn/matrix2.png)\n\nNow, we just need to fill out the rest of the matrix. It's important to put the best option in each cell based on the three cells that precede it to the west, north west and north.\n\n![](https://steemitimages.com/DQmXtLrivb5gAs3cgZ9LsbpnrTHNyn3hS5x943QLUdWqT19/image.png)\n\nThe new 0 was chosen as the best of these three options:\n\nOption 1: Add a gap in sequence CCATTAG by moving right after aligning A and C: \n0 [A and C mismatch] + 1 [C and C match] + (-1) [new gap] = 0\n\nOption 2: Add a gap in sequence ACCTAG by moving downwards after aligning A and C: \n0 [A and C mismatch] + 0 [A and C mismatch] + (-1) [new gap] = -1\n\nOption 3: Align the second base in ACCTAG with the first base in CCATTAG by moving diagonally after introducing a gap in CCATTAG:\n-1 [gap in CCATTAG] + 1 (C and C match) = 0\n\nOption 1 and 3 are equally good and beat option 2, so we put a 0 in the cell.\n\nWe continue to add new numbers to the matrix, one slash at a time: \n\n![](https://steemitimages.com/DQmUp7jqJyyqSPo8jPS7Ja9J3JnYgTC2SKsHpvJigFz6oGx/image.png)\n\n![](https://steemitimages.com/DQmQv3y1WR7TZBZSaN8aG77U2LS9hE1XpTFydT89AKyrdTQ/image.png)\n\nFast-forward...\n\n![](https://steemitimages.com/DQmNVvbmjGDBrqLtH7BrqvrCPiZ6HiqGxbHbskWf7DUUR9u/image.png)\n\nOur final score is the number in the lower right corner, in this case 2. The next step is to trace back through the matrix to see which alignment patterns led to this score. We ask ourselves: Which of the preceding cells could have produced the number 2. There are two options:\n\n![](https://steemitimages.com/DQmbpRMZJ2oMu3yztjALT3byaCE9K7Yn1N7cKca7XCqBpxD/image.png)\n\nWe now follow each path back to the upper left corner. I've used blue color here, because it was faster in Word, but it's more helpful to draw arrows so you can see each individual path right away:\n\n![](https://steemitimages.com/DQmcDM7AxrMk3KJ27KhgNGqYfBNiqNv48o4o6Qj1mtpzgwt/image.png)\n\nThere are three possible paths here, each of them producing an optimal alignment. The first one is:\n\n![](https://steemitimages.com/DQmcoEp6cYcrAyKwwTqGJVxkgKB7mCHfGFxyZJ7maKXHvMC/image.png)\n\nIt corresponds to the following alignment:\n\n![](https://steemitimages.com/DQmXguzUqNz2GECkneJX5uNkG8qXpVPqkJBE5bbMANZETVS/image.png)\n\nThese are the other options:\n\n![](https://steemitimages.com/DQmZZyifHSQdtueRWy9LqMGQVSjY4P8gj2BjbkHU3fZ7G9c/image.png)\n\n![](https://steemitimages.com/DQmUqMa1VNJyr9k1wWDGMvrZitvzU4BvyG3dJGXfrvYnjXp/image.png)",
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      "title": "How to compare two DNA sequences by hand - the Needleman-Wunsch algorithm",
      "body": "First of all, no sane person working with bioinformatics would spend time comparing DNA sequences by hand with all the fast digital tools available (here's one: https://blast.ncbi.nlm.nih.gov/Blast.cgi?PAGE_TYPE=BlastSearch&PROG_DEF=blastn&BLAST_PROG_DEF=blastn&BLAST_SPEC=GlobalAln&LINK_LOC=BlastHomeLink). Still, any bioinformatician would do well to understand the technique, in part because it contains an element of subjectivity.\n\nTwo DNA sequences that share a common origin are said to be homologous. It could be the gene for insulin in humans and the one in cattle. The genes are called orthologs when they are both homologous and come from different species. Homologous gene sequences differ, because the ancestral sequence has mutated in different places in the lineages descending from it. The mutation can be a substitution:\n\nAACGT to ACCGT\n\nAn insertion:\n\nAACGT to AACCGT\n\nOr a deletion:\n\nAACGT to ACGT\n\nWhen DNA is transcribed into RNA, it is read in triplets, pieces of three adjacent bases. The three corresponding RNA bases are later translated into an amino acid. Substitutions tend to be the least harmful mutations, because they each affect zero or at most one amino acid. Three-base insertions or deletions are also relatively harmless, because the addition or removal of a triplet means one amino acid more or less in the finished protein (I stress _relatively_ harmless; even substitutions can be lethal if they occur in a bad spot). Insertions or deletions of base numbers not divisible by three are bad news, because they disturb the reading frame of the sequence, potentially affecting all amino acids downstream from the mutation. They are called frameshift mutations and usually lead to the translation of a non-functional protein.\n\nBecause of their potential for causing frameshifts, indels (insertions or deletions) are less frequently preserved in the course of evolution than substitutions. When aligning two homologous DNA sequences of unequal length, the occurence of an indel has to be assumed. This is represented by a gap:\n\nA_CGT\nAACGT\n\nWe may even choose to assume an indel between sequences of the same length, if it makes for a better alignment. But since indels are often severe, their inclusion should be punished. That is, we apply a gap penalty.\n\nThere is a multitude of different ways to compare even short DNA sequences. Without an algorithm to locate the best options, the computers of today would not be able to handle even a small fraction of the genetic information currently published. Fortunately, the Needleman-Wunsch algorithm (developed by Saul B. Needleman and Christian D. Wunsch) makes for optimal alignment of large sequences. Short sequences can be aligned by hand. The rest of this post will describe the procedure.\n\n## How to run a Needleman-Wunsch algorithm\n\nFirst, draw a matrix. Each side should be the length of one of the sequences you want to compare, plus one cell. We are going to compare two sequences of 6 and 7 bases, respectively, so we need a 7x8 matrix:\n\n![matrix1.png](https://steemitimages.com/DQmRZ7miqppgzdMkxBjbmL9rPcMG5WBDpkiTMTbfEKNBaam/matrix1.png)\t\t\t\t\n\nYou will notice that I have already filled out part of the matrix. Indeed, this is a bit premature. We first need to decide on a match score, a mismatch score and a gap penalty. This is the subjective part of the algorithm. I have used 1, 0 and -1. If in doubt, one can try to run the same alignment several times with different scores to see how much this affects the final results.\n\nThe idea is to start in the upper left corner of the matrix and work your way down the alignment. A diagonal move means that you are simply comparing the next base in sequence 1 to the next base in sequence 2. A horizontal or vertical move signifies the introduction of a gap in, respectively, the vertical and horizontal sequence. Since our gap penalty is -1, every expansion of the gap in the same direction adds -1 to the total score unless we obtain a match.\n\nNow, lets attempt to align our first base. We have three options, but the first two are rather silly. We could introduce a gap in sequence 1 and then a gap in sequence 2. Or we could introduce a gap in sequence 2 and then a gap in sequence 1. Or we could just avoid gaps altogether and align the first base in sequence 1 with the first in sequence 2. You might have guessed what I prefer, but take a look at the scores to be sure:\n\nOption 1: -1 + (-1) = -2\nOption 2: -1 + (-1) = -2\nOption 3: 0\n\n0 > -2. We put 0, because we got a mismatch (A and C). At this point, it's preferable to a gap, so we put a 0 in the matrix.\n\n![matrix2.png](https://steemitimages.com/DQmdpZY7cTXQipuLXYdz8ss1a6sNK2LfNixd4GQHcbufWSn/matrix2.png)\n\nNow, we just need to fill out the rest of the matrix. It's important to put the best option in each cell based on the three cells that precede it to the west, north west and north.\n\n![](https://steemitimages.com/DQmXtLrivb5gAs3cgZ9LsbpnrTHNyn3hS5x943QLUdWqT19/image.png)\n\nThe new 0 was chosen as the best of these three options:\n\nOption 1: Add a gap in sequence CCATTAG by moving right after aligning A and C: \n0 [A and C mismatch] + 1 [C and C match] + (-1) [new gap] = 0\n\nOption 2: Add a gap in sequence ACCTAG by moving downwards after aligning A and C: \n0 [A and C mismatch] + 0 [A and C mismatch] + (-1) [new gap] = -1\n\nOption 3: Align the second base in ACCTAG with the first base in CCATTAG by moving diagonally after introducing a gap in CCATTAG:\n-1 [gap in CCATTAG] + 1 (C and C match) = 0\n\nOption 1 and 3 are equally good and beat option 2, so we put a 0 in the cell.\n\nWe continue to add new numbers to the matrix, one slash at a time: \n\n![](https://steemitimages.com/DQmUp7jqJyyqSPo8jPS7Ja9J3JnYgTC2SKsHpvJigFz6oGx/image.png)\n\n![](https://steemitimages.com/DQmQv3y1WR7TZBZSaN8aG77U2LS9hE1XpTFydT89AKyrdTQ/image.png)\n\nFast-forward...\n\n![](https://steemitimages.com/DQmNVvbmjGDBrqLtH7BrqvrCPiZ6HiqGxbHbskWf7DUUR9u/image.png)\n\nOur final score is the number in the lower right corner, in this case 2. The next step is to trace back through the matrix to see which alignment patterns led to this score. We ask ourselves: Which of the preceding cells could have produced the number 2. There are two options:\n\n![](https://steemitimages.com/DQmbpRMZJ2oMu3yztjALT3byaCE9K7Yn1N7cKca7XCqBpxD/image.png)\n\nWe now follow each path back to the upper left corner. I've used blue color here, because it was faster in Word, but it's more helpful to draw arrows so you can see each individual path right away:\n\n![](https://steemitimages.com/DQmcDM7AxrMk3KJ27KhgNGqYfBNiqNv48o4o6Qj1mtpzgwt/image.png)\n\nThere are three possible paths here, each of them producing an optimal alignment. The first one is:\n\n![](https://steemitimages.com/DQmcoEp6cYcrAyKwwTqGJVxkgKB7mCHfGFxyZJ7maKXHvMC/image.png)\n\nIt corresponds to the following alignment:\n\n![](https://steemitimages.com/DQmXguzUqNz2GECkneJX5uNkG8qXpVPqkJBE5bbMANZETVS/image.png)\n\nThese are the other options:\n\n![](https://steemitimages.com/DQmZZyifHSQdtueRWy9LqMGQVSjY4P8gj2BjbkHU3fZ7G9c/image.png)\n\n![](https://steemitimages.com/DQmUqMa1VNJyr9k1wWDGMvrZitvzU4BvyG3dJGXfrvYnjXp/image.png)",
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