Re: What type of math problems do Marine biologists encounter?/use example

Dear Emily,

I apologize for the delay. You need to understand that science is a 
mathematical endeavor. Math is the language and the currency of science. 
There are some areas of scientific investigation that are descriptive. For 
example the role of the naturalist comes to mind, people who describe the 
organisms they find, classify and categorize them. But as you will see, 
even this role has matured into a mathematical one. 

Marine biology and most other developed sciences have progressed from 
descriptive to predictive. That is, rather than describing what we see 
around us, most scientists seek to explain the processes at work and make 
some kind of prediction. These predictions are often made in the language 
of mathematics. Predictions help us test whether or not our explanations 
are correct. 

I will begin with some of the math I personally utilize.

Much of what is done is the lab on a daily basis involves chemistry, 
preparation of standard solutions, media etc. at different concentrations. 
This involves relatively simple arithmetic calculations. Students most 
often get lost or confused in the long series of calculations sometimes 
required. Probably the single most useful technique for this kind of 
calculation is UNIT CANCELLATION, incredibly handy!

Algebra and trigonometry as well as calculus are used to analyze data. 
These allow me to model the reactions I am studying. For example, one area 
that I have investigated is the relationship between light level and 
algal photosynthesis. There are several mathematical models or formulae 
used describe the curve that is generated from the data. One includes a 
hyperbolic tangent function, another uses exponents to the base e and there 
are others that are more complex. So how do we decide which is best? That 
is where statistics comes in. The models are tested statistically using 
model fitting statistics. These calculate how well the line described by 
the mathematical function we are using fits the data. These often require 
that derivatives of the variables be examined (= calculus).

There are many other ways math is used in marine biology. For example, 
investigators examining field data (as opposed to experimental data) may 
use the principles of chaos theory to explain what looks like random 
fluctuations. Satellite oceanographers use a variety of algorithms to 
relate satellite color data to biomass. Even systematists and taxonomists, 
scientists who categorize organisms in order understand evolutionary 
relationships, utilize mathematics in the form of cladistics (a statistical 
grouping method).

The list of math uses goes on and on, but it gets easier and easier to 
do the math with every new computer advancement. The one thing a computer 
can't do is understand why we choose the math functions it is told to 
perform, though. So, even though calculation gets easier, scientists still 
need to understand math.

Hope this helps.