For starters, let us admit the obvious that we use a number of physical and chemical variables to explain the behaviour of living things. We can model these variables as sets and make a number of possible histories with various values for each variable. If we find a set that best explains the data, we say that the model is most likely to be correct. Similarly, we can say that models are parsimonious in the sense that they give the most accurate predictions.
There are a number of problems with this approach however. For starters it is very easy to make a mistake if you are just working with a small number of variables. More importantly, even if you manage to fit a model onto a limited number of variables, the resulting prediction will only be as precise as the size of the model. This is because the numbers involved – particularly the space and time dimensions – can significantly affect the accuracy of the predictions. For this reason, a large numerical solution is often a waste of time because it may not be well suited for a particular experiment.
It is sometimes asked why models used in biology are not more precise, when the answer is that the numbers involved are too small to ensure a high degree of accuracy. The answer to why this is so is that although the numbers may be small, there are a number of important physical factors that are important in biological processes. To illustrate, consider how a bee builds a honeycomb. To achieve this, it uses a number of complex physical and chemical processes.
One of the most important physical processes is called ‘conversion’ where sugars are transformed into nectar which is then stored by the bees for later use. The honey is then collected by the worker, who then uses a proboscis to extract the honey. To do this, the worker must stretch and turn from side to pry the comb from between the combs. Although the actual movements can be difficult, the overall process is very precise and requires a lot of attention. Therefore, it is likely that a model of this process in natural settings would be easier to predict than a model where it had been done by a robot.
Another example is where an individual sees a particular tree. Some people can simply walk over it, identify it’s features and make a judgment about the likelihood of spotting a particular species. For other people, it may be a matter of years before they are successful at making a guess as to what the tree is. One way around this problem is to take a numerical simulation of the process. In this case, the exact numerical simulation is used, but it is based on a random process rather than a physical process.
Why are models of real life useful in biology? Because real life is full of complicated processes that can only be studied using sophisticated and exact instruments. These instruments include molecular models, supercomputers and software that can run for millions of hours without any human intervention. The same is true for many of the processes in the biosphere; because it is impossible to actually duplicate the exact conditions of real life, models of these processes are used instead as a guide.
Another reason why models of real life are important is because they offer a unique way of visualizing the world around us. Biology is a field where observation and experience are critical. A mathematical model of a particular process, for instance, can help a student better understand how to interpret data or how to simulate a system of operation. There are many situations in which it is not feasible to do these things with the human eye, but the models can help bridge the gap.
When a student asks the question “Why are mathematical models useful in biology?” they should be able to answer with confidence. The models will allow them to explore previously unnoticed biological processes that could have been missed by experiment or experimentation. Simulations might help us learn more about how real biological processes work, and it is also possible that such knowledge could one day lead to the creation of a completely accurate model of the real biological processes.