In the game Cambrian Feast we look at the population dynamics of a species of fish. We assume that in a given time period - based on a certain constant value for the rate of growth - the population of a school of fish doubles. The user needs to choose a value for the rate of growth and then see what the doubling time is. For example, if the rate of growth is 10% then the doubling time is 6.931 years. If the rate of growth is 30% then the doubling time is 2.31 years and so on.
IMPORTANT NOTE: In this game we are equating one year to one minute. Therefore, if the player chooses 10% rate of growth then a given number of fishes at the beginning of the game will double in number in 6.931 minutes. Similarly, if the player chooses the rate of growth to be 30% then a given number of fishes at the beginning of the game will double in 2.31 minutes. And, so on.
POPULATION BIOLOGY: A BIT OF PALEONTOLOGY
Fishes, or their very distant ancesors, first appeared on earth around 530 million years during the Cambrian period and in an epoch that is now commonly characterized by "Cambrian Explosion". Sharks, a kind of fish, also originated during the Cambrian-Ordovician period around 488 million years ago that is more technically called the Great Ordovocian Bio- diversification Event. In this game we assume that a shark primarily feeds on smaller fishes that multiply copiously underwater.
POPULATION MATHEMATICS: EXPONENTIAL GROWTH
A large number of real life phenomena are mathematically modelled accoding to exponenial growth dynamics. Exponential growth of variable is given by the differential equation
Where, N, represents the variable and Î» the rate of growth. The left hand side of the above differential equation shows the rate of change of the variable, Nn, over a certain time period. If N(t) is the value of the variable at time equal to t and N(0) is the value of the variable at the start of the time, i.e. when time was equal to zero, then the solution of the above equation is given by
Where, ln stands for natural logarithm. Or, using the familiar exponential notation, e, we can write
Given the equation above, we can estimate the doubling time for the value of the variable, N(t), for the variable to double in value N(t) should be equal to 2N(0). This means that the doubling time, t(2) will be given (up to four decimal places) by
Population dynamics is an interaction between the fields of population biology and population mathematics. Population biology, a part of evolutionary biology, is not concerned with any mathematical modelling and population mathematics is not concerned with any biological arguments. However, population dynamics combines both these fields to create an understanding of the biological process of evolution and opulation growth using mathematical modelling.
In this game one second represents one year in real life.