May 28th, 2009 ecoli
Dr. James Holland Jones has an (older) post on scientific uncertainty and fat tails on his monkey’s uncle blog. Its one of the better explanations I’ve read, so do your self a favor and get educated. He also asks:
As scientists with an interest in policy, how do we communicate this type of uncertainty?
Before you can even ask this question, you have to ask if scientists, biologists in particular, are even interested in communicating uncertainty. Statistics and math are just not stressed in undergrad bio courses, and not at all in high school, so students are coming up with very little conceptions about uncertainty in data. I admit to being guitly of this but, unlike myself, how many scientists are willing to learn? Do their egos permit discussing statistical uncertainty?
This reminds me of one of Jorge Chan’s PhD comics on the science news cycle:
The cycle is exacerbated even in the first step, when scientists are not even well trained to understand or compute uncertainty themselves.
Posted in education, link out, mathematics, musings | No Comments »
May 26th, 2009 ecoli
As someone who is about to lose their previous form of health care insurance coverage, I thought the front page “conversation” on scienceblogs is appropriate.
I don’t want to get into the specifics of the debate, but I thought it was especially interesting that the overwhelming perspective on scienceblogs.com is from the left ‘pro-universal’ side. What is it that makes scientists particularly liberal, especially on this issue? Consider that the economics of the issue is far from settled and that scientists are intimately familiar with the darkside of government funding.
Posted in link out, medicine, musings | No Comments »
April 13th, 2009 ecoli
From Dr. Jekyll & Mrs. Hyde
I have been spending off hours on PubMed, trying to discover the rational basis for the host of rules pregnant women are adjured to obey:
–Don’t eat unpasteurized cheese (Brie, Gorgonzola, feta, chevre…all the good stuff)
–Don’t eat deli meats unless they’ve been heated to steaming
–Don’t even think about licking the bowl clean of cookie batter
–Sushi? Do you want the baby to die, or what?
–Lying on your back past the fourth month is going to give the critter brain damage
–A sip of wine? Why not just smoke crack and be done with it?
I’m not talking “old wives’ tales your grandmother produces.” These things are specifically listed as fetal death-traps in publications ranging from the leaflets I was handed at the ob-gyn to “What to Expect When You’re Expecting,” probably the single most popular pregnancy book available.
But here’s the funny thing. When you look for actual studies about these things on PubMed, you keep thinking that you’ve entered the wrong search terms, because so little comes up.
Expectant mothers are, generally, hypersensitive to urban legends and even random tidbits that sound like they could be scientifically plausible. Maybe they should chill out.
Posted in link out, medicine, musings | 1 Comment »
March 16th, 2009 ecoli
In my last post I introduced Mathematical biology by explaining simple, 1st order, linear, differential systems.
Now, I’d like to get into non-linear systems, which better represent biological phenomenon, because the solutions output is rarely in direct proportion to the input.
Consider, for example, an enzymatic reaction. At low levels of substrate concentration, adding more substrate has a direct correlation with the amount of product form. However, the concentration of enzyme in this case limits the maximum velocity of the reaction, because the enzyme gets saturated with substrate. Therefore consider the changing population of Substrate and product like this:
-dS/dt = dP/dt = Vmax x [S] / (Km + S)
This is the Michaelis-Menten equation. Plotted it looks like this:
On the y axis is reaction velocity (dS/dt) and the y axis is substrate concentration. While this equation is specific for enzymatic reactions, a similar model for logistic growth can be applied to natural populations, growing in a limiting environment.
Consider first a continously growing population of a single species. As we went over last time, the size of population N at time n determines the population at Nn+1. Although the population can only be assesed at censuses, let us consider a continuosly reproducing species.
If a population doubles during every time period of τ then we get population growth that looks like this:
Time Number
0 N0
τ 2N0
2τ 4N0
3τ 8N0
This is a clear example of exponential growth – the coefficient of xN0 doubles for every linear increase of τ. The general equation which fits this exponential growth is N(t) = N0 2^(t/τ) - In the above chart, t is always given as a function of the doubling time.
Let us now consider natural death in a population (assume no competition). In this case, contrary to the growth rate, the death rate is directly proportional to the size of the population.
dN/dt = -γN where γ is the per capita death rate which, when solved, gives N(t) = N0 e^(-γt) an exponentially decaying function.
To combine terms and get a useful model for a growing species, lets first put the birth equation into a more usable form:
N(t) = N0 2^(t/τ) = N0 e^ln 2 * (t/τ) and let β = (ln2)/τ so that N(t) = N0 e^(βt) and dN/dt = βN(t)
Combining the growth and death terms, we get:
dN/dt = βN(t) – γN(t) = (β – γ) N(t) => N(t) = N0 e^(β – γ)t
for all β > γ you get an exponentially growing population.
But of course, exponential growth is never seen in nature (with people being the exception). This is because finite resources limit growth. Therefore competition ensures that the death rate will exceed the birth rate under certain conditions. Rather than defining these rates as complex functions, we can substitute the logistics equation of growth (which pretty accurately describes population growth).
dN/dt = (β – γ) N(t) [1-(N/k)]; where the new term (k) is the carrying capacity of the population (which can usually be determined experimentally and depends on the most limiting resource).
solving the logistics equation gives:
N(t) = kNoe^(Rot) / [K - No+ No^(Rot)] where Ro = (β – γ).
The logistics curve, N(t), looks something like the above (ignore the negative portion). Here growth is initially exponential but flattens out to K. (K equals Nmax).
In our next episode, we will consider growth on non-continuously reproducing species and intraspecific competition.
Posted in ecology, mathematics, musings | 19 Comments »
March 12th, 2009 ecoli
I’m taking my first mathbio class this semester and I would like to share with you all the insights I’ve learned so far.
Most biological processes are 1st order dynamic systems. Meaning that, unlike many physical phenomena, the ‘momentum’ of a system has no affect on the trajectory. The only state that plays a role on the current state is the one directly preceding it.
Consider 2 changing populations with the same birth rate and no natural deaths. Lets say one starts at a 10 individuals and the other starts at 15. In the next generation, both populations double; 20 and 30. In population two, I now remove 10 individuals and allow the populations to double again. Both populations will end up with 40 individuals. Even though the second population started out with more, the only state that matters is the one directly preceding it.
Lets consider a linear, 1st order, system with two variables;
dx/dt = ax + by and dy/dt = cx/dy
What are some properties of this system (that we can extend to linear dynamic systems in general)?
1) at x = y = 0, the velocities are zero
2) If velocity at (x,y) is (Vx,Vy)
AND velocity at (x2,y2) is (Vx2,Vy2)
Then V(x1+x2,y1+y2) = (Vx1+Vx2,Vy1+Vy2)
3) If V @ (x,y) is (Vx,Vy)
then V @ (cx,cy) is (cVx,cVy)
Here is an example of the above. Consider:
dx/dt = -x & dy/dt = -y
In the graph we see a description of the differential equation system. Every arrow represents the velocity; direction and magnitude. All paths point towards the origin, and spot at the stationary point at (0,0).
Lets know consider a more complicated system with two variables.
dx/dt = x + y & dy/dt = -x + y
Again, at (x,y), V = 0. When y = 0, dx/dt = x and dy/dt = -x
In this scenario, we have a unique case at x = y; dx/dt = 2x and dy/dt = 0
Graphing this system of equations, we get something like:
In this system, we get what looks like an destabilizing stationary point at the origin, with a spiral shape pushing outwards.
If you were to imagine x and y as 2 populations over time, it would look as if x and y alternating maximums, but both maximums getting higher as time progresses:
While its doubtful that a population of two species look like this in nature, it helps demonstrate how changing populations over time can be modeled with differential equations. For example, if species y is a predator of species x and species x has ample resources to grow, a growth pattern like this could occur, as blooms in one species causes a bloom in the other, and species x is able to take advantage of crashing y populations, and ample other resources to rebuild its own numbers even greater than before.
I continue this series next time with more modeling of populations.
Posted in ecology, mathematics, medicine, musings | No Comments »
October 6th, 2008 ecoli
In the post peak-oil era (and even before it) the ability to walk (or comfortably bike, at least) to destinations will be come increasingly important.
What’s the easiest way to judge how walkable a neighborhood is? By determining if there’s anything close by worth walking to.
That’s what this website is designed to calculate. It takes into consideration the distances to destinations that Google maps has scores and assigns your neighborhood an arbitrary value based on the types of attractions around it and how far they are.
All you do is type in your address: The walking score of my neighborhood is a 32 (car dependent) :-(
The most walkable cities? In order: San Fran, NYC, Boston and Chicago.
It’s an interesting idea for a website that will no doubt play a significant role in the real estate market. I myself have used the website is helping decide my top picks for medical schools.
I feel that the increased urbanization of america is inevitable, and that the era of the suburban catastrophe will drawing to a close. With that in mind, (if you’re a real estate investor) buying property with high walking scores might not be a bad idea.
Post your scores here.
Posted in link out, musings | 7 Comments »
August 7th, 2008 ecoli
This story has been big in the news lately. As you probably have already heard, the person who sent anthrax spores (Bacillus anthracis) through the mail has commited suicide. The culprit is army scientist Bruce Ivins.
Ivins worked with Anthrax in order to develop a vaccine, so one might think this is hypocritical to his work. However, current investigations lead us to beleive that Ivins was psychologically disturbed. Prosecuters speculate that Ivins was hoping to incense the public awareness of anthrax and hopefully get more funding. I guess scientists will go a long way to get research grants these days, but this is a new low.
My concern is how this event will ultimately change things for microbiologists and infectious disease researchers (a community I consider myself a part of). My lab doesn’t have anthrax, but we do have plenty of other deadly infectious diseases like Francisella tulerensis (tularemia), Yersinia pestis (bubonic plauge) and Borellia (Lyme’s disease).
Will researchers now have to get psych evals before we’re allowed to work with pathogens? Are intitutions going to tighten security, make us take even more safety classes, hire guards to check bags and not let us work alone? I hate to be the one to point this out, but it wouldn’t be exactly difficult to take pathogens out of the lab and even undergrads are given keys to the labs.
I have to sacrifice ease of access for security, but maybe the risks aren’t worth it? It just takes one incident to ruin it for the rest of us.
Perhaps (and hopefully) I’m wrong, and this will blow over as a unique incident, but it wouldn’t surprise me if universities, national and armed forces labs will at least start to discuss greater security measures.
Posted in medicine, microbiology, musings, news | 2 Comments »
August 5th, 2008 ecoli
Now that I got that bit of unpleasentness out of the way, I will hopefully have more time for my poorly underused blog.
The actual test wasn’t too bad, and I actually was able to have some fun with it. Especially on the verbal and writing sections. There was a passage on Libertarianism philosophy, centered around natural rights and property, so that was right up my alley.
I also got to write an entire essay extolling the virtues of free market captilism (so it was just like the stuff I write about on my own).
All in all it was a hell-ish experience. I had to take a 5 hour exam on 3 hours of sleep, but hopefully my score is good enough so I don’t have to repeat it.
Posted in musings | 2 Comments »
July 29th, 2008 ecoli
I’ve been reading a biography Adam Smith, who I had previously thought of as an economist, but have since learned that he is a moral philosopher, who studied under Hutcheson and was a good friend of David Hume.
From this work, I’ve realized how important the insights of the enlightenment thinkers were to later theories by biologists such as Charles Darwin.
In his Theory of Moral Sentiments, Smith tried to explore human behavior in a way fairly unique to the time. Recognizing morality as unique to humans, previous thinkers chalked it up to a gift from a diety. Smith wasn’t so sure, or at least looked to people’s behavior in public and private to understand how a sense of morality develops.
One thing that Smith observed is societal pressures creating a standard or norm for public behavior, which could deviate in private. Smith recognized societal standards as a powerful force to shape emotions and therefore behavior. People strive to have a similar emotional level as the people around you, which creates an acceptable medium for public emotional displays, and therefore the behaviors in response to outward emotion.
What I found interesting is that Smith recognized the importance of human interactions, where most others tended to focus on the personal, in dealing with theories of morality (be it the ridiculous supernatural or the slightly more reasonable, all actions are essentially selfish). This idea that society and personal interactions are powerful in shaping human psychology lines up nicely with my ideas about human evolution.
While Smith did not have an inclination of evolution and was not terrible concerned with how morality could have come about, I think his ideas were essential for the eventual development of Darwinism.
The enlightenment thinkers developed new ideas about psychology, behavior, and human interactions and all scales that did not rely on some supernatural force. They did for biology and social sciences what Galileo and Newton did for cosmology and physics: they started the notion that human behavior can be studied in a systematic way by studying aspects of humans and human society. This change in thinking was essential, I think for the study of biological organisms as adaptable.
Posted in evolution, musings | 2 Comments »
July 1st, 2008 ecoli
As science blogging is becoming an ever more popular way for scientists to communicate and express themselves, the pressure is mounting to bring the best bloggers to a particular site, as Coturnix has noticed.
I’m glad ScienceForums.net has a slice of science blog pie, and have watched with pleasure as Swans on Tea, and even my own little blog, have begun to grow some popularity.
I think the market is quickly becoming saturated with new bloggers, however, fairly soon only people who already have ‘celebrity’ status, and bloggers with original ideas will be able to capture the share of readership.
Currently, sources like Discover magasine are trying to capture on the success of Scienceblogs.com, and even recruiting their writers. Blog hosting sites may have start offering greater incentive for bloggers to stay (*cough*).
Judging from the success of Scienceblogs.com, it appears that having a collaborative source for blogs seems like the way to go, especially for start-up bloggers. There seems to be little point in investing in a domain name if nobody reads the blog.
This also brings up the interesting thought, that I expect we will have to deal with soon, of who owns the content posted in a blog, if the blog’s hoster isn’t the writer of the blog.
These types of issues and competition between blogging sites seems to be another thing that limits what blogs can do.
Posted in link out, musings | 3 Comments »
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