Some chemical reactions proceed from reactant (Species A) to
product (species B) in a steadfast manner, viz.,
A
→ B
That is, as reactant A is consumed, B is produced. In general, however, most reactions proceed
through a series of steps which lead to the observed products. These reaction steps are referred to as the mechanism
of the reaction. For example, the
Lotka-Volterra reaction converts species A to species B by means of the following mechanistic steps:
(1) A + X → 2X
(2) X + Y → 2Y
(3) Y → B
A → B. This mechanism
predicts that the intermediate species X (blue) and Y (amber) will oscillate in
concentration as depicted in the accompanying graph. The x-axis in the plot is time and the y axis
is the concentrations of species X and Y.
This type of reaction is called an oscillating reaction, an
example of which is the Briggs-Rauscher Reaction shown in a YouTube video
posted by kviht:
If you're still awake after that soothing video you may have
noticed that the blue species and the amber species alternately dominated in
concentration. You may also have noticed
that I labeled the two species as Rabbits (blue) and Foxes (amber) in the above
plot. This is because Alfred Lotka, who
proposed the above reaction mechanism as a theoretical chemical exercise in
1920, realized a few years later that this mechanism would also describe the population
dynamics of a closed predator-prey animal system. Vito Volterra independently came to the same
conclusion at about the same time. Thus,
in the mechanism above, species A becomes rabbit food (grass, clover, whatever)
present in great abundance, species X corresponds to the rabbits who reproduce after
eating A, Y denotes the foxes who reproduce after eating rabbits, and B stands
for foxes that have passed on by natural causes. As the population of foxes increases it
becomes a bad day for bunnies and the rabbit population plunges. When the greedy foxes deplete the rabbit
population, the foxes fade away. Not so
many foxes allows the rabbit population to recover, then spike, and so on.
So, the next time you're walking through the woods and you spot a sly fox slinking about, warn him about Lotka-Volterra and the dangers of rabbit over-indulgence.
