# Eco System

In biology, eco system is important as matter for environmental problems. In the study of eco system, there are studies of heredity, evolution and the distribution of sex, but I do not explain here.

Ordinary differential equations are important as a mathematical tool for eco system. Lotka-Volterra equation and system dynamics are such tools using ordinary differential equations.

## Mathematical Biology

There are two kinds. One is with statistics . The other is with simulation . I introduce below about the simulation field.

### Logistic Equation

Logistic equation is the equation,
dX/dt = a * X ( 1- b * X ).

If there is not "(b * X)" part, X increases as an exponential function. But "(b * X)" gives the limit of resources.

This equation is also important in environmental economics .

### Lotka-Volterra Equation

Lotka-Volterra equation is used to study the numbers of creatures.

### Game Theory

Game theory is used to study the difference of strategy of players.

### Lattice Model

2D lattice model simulation is used in the study of fire expansion of a forest.

### Dynamic Programming

One of mathematical programming tool. This is a model of timing for action.

### Algebraic Biology

Algebraic Biology makes formulation of the laws of creatures by the symbolic logic. It is exciting.

## Niche

Kinds of food and places to live are diifferent by kinds of creatures. It is calles "niche". Competition increases by niche.

"Niche" is a word used in Management and Marketing as a target to avoid competition.

## Microorganism

Microorganism is used like a medicine to purify the environment. But I want to know it as creatures.

Extinction of creatures are warned as environmental problems. I think the warning is for the creatures we can see, for example, the animals. It is interesting that what is happening in the field of microorganism.

## Cycle of Substances

Eat-eaten relationship and flow occurs the cycle of substances. In eco system, oxygen, carbon, nitrogen, phosphorus and sulfur are important.

Trades of Crops causes the flow that does not happen in the nature.

NEXT   Flow (Fluid Mechanics) 