# Tutor profile: Jesse M.

## Questions

### Subject: Environmental Science

Based on the understanding of how energy moves up the tropic trophic pyramid, what change can humans make to conserve large amounts of energy on a global scale?

It is a basic rule that only 10% of the energy is conserved by consumers from what they eat. The rest of the energy is lost in the form of heat. What this means that the way energy transfers from one organism to another is not very efficient and that most of the energy that hits the earth is lost. Of all the solar energy from sun that hits the earth, plants only are able to use around 10% in the process of photosynthesis. Of the energy available in all producers (plants), only 10% of the energy consumed will be transferred to the next trophic level. This next level would be made up of herbivores like cows. The 10% pattern would continue to the next level to any organism eating the cow and so on. When thinking about conserving this energy we need to consider how this energy moves up this trophic cascade and where humans fall in the trophic pyramid. When a human eats a cow, they are really getting 1/100th the amount of energy in terms of the sun compared to what they get from eating just eating plants. So a switch to a plant only diet would conserve large amounts of energy based on a understanding the trophic cascade.

### Subject: Biology

What is the Red Queen Hypothesis and how does it inform our understanding of the evolution of sexual reproduction?

The Red Queen Hypothesis gets its name from the famous scene in the Lewis Carroll novel Through the Looking-Glass where Alice and the Red Queen have to constantly run to stay in the same place. This is the same situation that hosts and parasites find them selves in and the "running", in this case, refers the evolutionary arms race between the host's defenses and the parasites anti-defenses. To expand on this, if a host does not have a good defense system against a parasite, they will not contribute as much to the gene pool as individuals with better defenses against the parasites because they will be out competed by those that are uninfected. This means that hosts are under extreme selective pressure to constantly change in response to the parasites that are present in the environment. If they are not able adapt quickly enough, it could lead to the extinction of the host species. On the other side of the coin, parasites need to adapt just as quickly. When a useful mutation arises in the in the host that allows it to evade the parasite, it could quickly lead to the extinction of the parasite. Both species are constantly changing to keep up with the changes in the other and, like Alice and the Red Queen, need to constantly run to not go extinct. This same arms race is happening with many competing species like predator and prey interactions and Red Queen Hypothesis dynamics can be applied but it is most helpful to think of parasite and host interactions when considering the evolution of sexual reproduction. Sexual Reproduction is a conundrum and seems to be extremely costly when compared to asexual reproduction. Asexual reproduction allows an organism to have more offspring over time, genetically identical offspring, and does not have to spend time and energy to find a mate. All of these sound great and do work well for a many species but ,when we think in terms the Red Queen Hypothesis and parasites, a strong case can be made for sexual reproduction. Lets consider the following situation: you are a little multi-cellular organism that reproduces asexually that has been living in a pond with plentiful food and no predators for the past thousand years. You have huge population build up of all identical individuals over that time and you are the most dominant organism in this pond. All of a sudden, a parasite is introduced that you have absolutely no resistance to and your entire population is decimated in the span of ten years. It does not matter how quickly you reproduce because all your offspring are immediately infected by this parasite. This scenario probably played out countless times over evolutionary time and the populations that had the best chance were those that had the ability to introduce genetic diversity to offspring. Sexual Reproduction allows species to do exactly that and the payoff must be great because it outweighs all of the costs combined. The ability to produce genetically diverse offspring have host species a leg up against parasites and allowed room for some offspring to develop resistance. The Red Queen Hypothesis shows us that the pressures acting on the species stuck in the constant running is strong enough to explain whole shifts in reproductive strategy.

### Subject: Calculus

Find the derivative of the following: $$2(5x^{2}+3x+10)^{4}e^{x^{3}+2x^{2}}$$

Just looking at this you can tell it will be a monster of a problem but do not give up now because this is far from impossible. We see there is a polynomial raised to an exponent so that should yell chain rule but also there are two functions being multiplied so that tells us to be thinking product rule and lastly there is the dreaded e. Instead of trying to attack this all in one go lets take a step back and see if we chip away at the problem one piece at a time. In this case, nothing can be started until we address the product rule because we cannot take any derivatives while there is a multiplication between the functions. A brief reminder: the product rule states when [f(x)g(x)]'= f(x)g'(x) + f'(x)g(x). Applying the product rule to our really big and complex problem, we get $$2(5x^{2}+3x+10)^{4}(e^{x^{3}+2x^{2}})'$$+$$(2(5x^{2}+3x+10)^{4})'e^{x^{3}+2x^{2}}$$. Now that we have applied the product rule, we can just focus on where we need to apply the chain rule. We can see that $$(2(5x^{2}+3x+10)^{4})'$$ will have to be solved by the chain rule because it is a polynomial raised to an exponent. So let us solve this portion. First, the chain rule states that the exponent is multiplied to the coefficient and subtracted by 1. Then, the polynomial is left alone but the whole function is multiplied by the derivative of the polynomial. What this looks like in our problem is we go from $$(2(5x^{2}+3x+10)^{4})'$$ to $$8(5x^{2}+3x+10)^{3}(10x+3)$$. Derivatives of $$e^x$$ are a slightly different story but we can still apply the chain rule. When dealing with an "e" raised to anything, the derivative will be the "e" and its exponent left alone then multiplied the derivative of the exponent. So in the case of $$e^{x^{3}+2x^{2}}$$, the derivative would be $$e^{x^{3}+2x^{2}}(3x^{2}+4x)$$. With all of the derivatives in hand, we can pull all the pieces together and get one more step closer to solving this problem. After applying the product rule then chain rule to the problem we now have: $$2(5x^{2}+3x+10)^{4}e^{x^{3}+2x^{2}}(3x^{2}+4x)+8(5x^{2}+3x+10)^{3}(10x+3)e^{x^{3}+2x^{2}}$$. Now, you could do some condensing to make this look a little nicer but this is the derivative and we were able to take an impossible looking problem and solve it by taking it one step at a time.

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