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12

The answer is chance or, even better, contingency. About your calculations, it is true that the theoretical sequences are almost unlimited, but the basic scaffolds are not. Very different sequences can fold into the same basic scaffold and have a similar reactivity/function. So, even if not all the sequences have been explored on this planet, most of the ...


6

This question is really asking for examples, and the list of ways that knowledge of physics can be used in biology could be very long. However, here are a couple of examples: Systems ecology, especially with regard to energy and nutrient flow. This type of ecology can be strongly influenced by physics. For one example see the book Theoretical Ecosystem ...


5

These kind of equations (the Michaelis-Menten [MM] like term) denote saturation kinetics. The basic mechanistic assumption behind saturation kinetics is this: A rate (of lets say product formation) is dependent on the concentration of a molecule such that the rate increases linearly with increase in the concentration of the molecule. Example 1: Substrate ...


5

The frequency fluctuations will be determined by a standard model of selection as found in any basic population genetics text. In this scenario they take a very basic form: during each long period $i$ the frequency of $A_1$ increases from $f_i$ to $f_i\cdot (1+s_1)^{n_1}$ and during each short period $j$ the frequency of $A_1$ decreases from $f_j$ to ...


5

First of all, here is a program which simulates the evolution of the G-matrix over multiple generations, it's a few years old (they seem to have stopped developing it) and I've only played with it briefly. This could solve how to model the evolution of the G-matrix. Fisher's fundamental theorem is a great place to start off with the theory of this: The ...


4

I am presenting a speculative approach since nobody has mentioned about any existent models yet. Assuming that selection is based on performance in certain tasks; performance is a function of traits which in-turn is a function of genotype. Performance is a non-linear function of genotype and selection imposes a cutoff/bandpass filter on the performance ...


4

That's an interesting model, because mosquitoes are vectors for serious illnesses, so are pretty well studied. One team of scientists are working on genetically altering mosquitoes in Africa to make them unable to transmit the parasite that causes malaria. As the mosquitoes breed, it spreads through the population. In an interview, the lead researcher ...


4

Is the standard Lotka-Volterra (LV) model an exact fit for insulin-glucose (IG) dynamics? No. Can a similar model built on the same principles capture most of the essential features of the IG dynamics? Absolutely. How to capture most of the insulin-glucose dynamics using a slightly modified Lotka-Volterra model We can figure out how to change the LV ...


3

The writings by Samir Okasha (philosopher of biology/science) could be a good starting point. In his book Evolution and the Levels of Selection, he explicitly uses the Price equation to discuss selection at multiple levels (e.g. chapter 2.3: Price's equation in a hierarchical setting), and also derives a multi-level version of the Price equation: ...


3

Fishers Geometric Model (FGM) is a theoretical prediction about the adaptation process in traits. There are a number of things to establish before attempting comprehend FGM. Firstly, shifts in an adaptive landscape, in natural scenarios, are generally quite small. Because populations have been evolving for such a long time and the small shifts in adaptive ...


3

First of all, there is a very heated debate about this in the field of social evolution at present, and you aren't likely to get a conclusive answer. One theorist may give you one answer, but another will vehemently disagree. I'll start by logically answering your questions in reverse order! Question 2: Can you please provide an intuitive explanation of why ...


2

I'd like to add a few books to to the above suggestions. The book by Sean Rice "Evolutionary Theory: Mathematical and Conceptual Foundations" covers a lot of ground, including allele-based models, quantitative genetics, Price's formalism, and MLS. If you're interested in social evolutionary models, I found R. McElreath and R. Boyd "Mathematical Models for ...


2

No it isn't necessary to breathe in CO2 from the atmosphere. For the buffer system your brain detects the amount of CO2 (H+ which is an indicator of excess or too little CO2) and adjusts your breathing automatically to compensate so that your blood's pH stays normal. No outside CO2 is needed. Your kidneys also play a similar role but the lungs are what ...


2

Your logic looks correct to me. Essentially, what you are doing is uniformly distributing the regulator among the available mRNA. Note that even when using Hill functions to model transcription, the ratio of transcription factor (TF) concentration to the number of TF binding sites must be large - otherwise, you would have to consider binding ratios even at ...


2

What you are looking for sounds like the mechanism for a fold-change detector. I would recommend looking at these two papers: The incoherent feedforward loop can provide fold-change detection in gene regulation As an example of this working in a real system, I recommend looking at the NFkB pathway, as recently detailed by Suzanne Gaudet: Fold Change of ...


2

I'm not sure I understand the question. You've elegantly demonstrated that only a tiny fraction of all protein sequences could possibly exist, but then asked why only a tiny fraction of all protein sequences do exist. Your conclusions about independent origins of life having no proteins in common are accurate, but also consider that you as a human being have ...


2

The fraction of polymorphic sites that exist in a population is dependent on the biology of the organism. For instance, you would expect to find different rates of polymorphism in related plants that have different breeding systems, e.g. in Silene [1]. Past bottlenecks are also expected to decrease polymorphisms [2]. So, the answer to your question would ...


2

Your intuitions all seem correct. Coalescent simulation should be faster, because you don't track the entire population history over all t generations as you do in the forward simulation. Rather, as you work backwards in time you are tracking a smaller and small population. And with coalescent simulations it is probably very hard to incorporate the full ...


2

I've worked on a couple of these for biofuel production. The answer varies widely according to plant P and how well studied plant P is. In terms of what data is used, it includes but is not limited to: temperature, insolation, length of the day, cloud cover, rain, soil composition, soil type, soil density, other local effects like wind or pests, altitude, ...


2

Here there are a couple that I own: The "classic" from Uri Alon touches many of the topics you mention. It is easy to read and goes relatively deep into the methods. There seems to be a new edition (if you search it in Amazon it will pop up), but it was planned for last year's April and then delayed so no so clear when will be actually published. For the ...


2

One example of what you may consider to be a macroevolutionary change is a whole-genome-duplication, or polyploidy event. These are not uncommon in plants, and can promote speciation due to a reproductive barrier arising between the polyploid progeny and the diploid parents. You can find many papers about this topic, here is one from 2009: ...


2

His notion of systemic mutations involved the postulation of massive chromosomal rearrangements (not mere recombination/crossing-over) as mediators of speciation in one-step. While whole genome duplications have been shown to induce speciation (see, for example, cryptic speciation in Hyla versicolor) they are not large scale rearrangements as he suggested. ...


2

Reiterating the above comments. Have a look at Tajima's D. It provides an estimate for the number of segregation sites for a population under a neutral mutation model. The general form of the estimation for a diploid population is $E[S]=4N\mu\sum_{i=0}^{n-1} \frac{1}{i}$. Here the mutation rate of is per-genome not per-site, so $\mu=L * 10^{-9}$ where $L$ ...


2

Interpreting your question as "would the Lotka-Volterra predator-prey model be a good model for the glucose-insulin system?" my answer is "no". The predator-prey equations capture assumptions about how prey and predator interact with each other, and how they would fare on their own. These assumptions are not equivalent to any reasonable assumptions about the ...


2

A Poisson process follows these postulates: $\lim\limits_{h\to0+}\frac{P(N_h=1)}h=\lambda$ i.e. the probability of occurrence one event in a very small interval of time is equal to the macroscopic rate or intensity ($\lambda\,$). $P(N_h\geqslant2)=o(h)$ i.e. the probability of occurrence of more than one events in an infinitesimal interval is essentially ...


1

Trait z is represented by k genes: z1....zk (I am using k instead of l because the former is visually differentiable from 1 ). For simplicity let's assume that there is only one mutable site in a gene. So a mutation can impart a change of $\pm \Delta z$. Starting from initial state of z at zero, the system will proceed to equilibrium where the rate of ...


1

I am not sure what your question is but here is an example that may interest you. The three sunflower species Helianthus anomalus, H. deserticola, and H. paradoxus are all of hybrid origin of the same two "parent species" (H. annuus and H. petiolaris). Major ecological transitions in wild sunflowers facilitated by hybridization is a paper that will ...


1

Let's take the opposite extreme, $K=0$, so that each site has an independent effect on fitness. Without loss of generality, we can say that at each locus $n$, the $1$ allele confers an advantage $s_n$ over the $0$ allele. Then there is just one local optimum, the global optimum, at $\vec{1}$, so $M_1=1$ (and $P_m=2^{-N}$). The key difference is that in the ...


1

No, mammals need not take in CO2 from atmosphere. The body's homeostatic function will maintain its composition by checking the amount of CO2 released out by lungs. So certainly animals would survive if put in a CO2 free atmosphere.


1

Fry (2010) borrowed his variables from Kidwell et al. (1977). Kidwell defines the fitness of each genotype as, $w_{m1}$, $w_{f1}$ = male and female fitness of the A$_1$A$_1$ genotype. $w_{m2}$, $w_{f2}$ = male and female fitness of the A$_1$A$_2$ genotype. $w_{m3}$, $w_{f3}$ = male and female fitness of the A$_2$A$_2$ genotype. Kidwell then establishes ...



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