Calculus was created to describe in mathematical language how a quantity changes over time. It is an extremely useful and powerful tool for building dynamics models. That's why calculus has been used for over a century to understand the behavior of ecological systems.
The following are turorials to help you understand basic calculus concepts that we use in many mathematical models in ecology.
A stochastic dynamic happens when we have more than one possible state for a system, and we can jump to each one with a certain probability. Therefore, even systems that start out the same can differ over time. For example, populations under stochastic dynamics can have different sizes at any given time, each with a probability of happening. In this case, the population size is a random variable.
Considering stochasticity is very important to understand ecological dynamics. With the stochastic models there were important theoretical advances, such as the neutral theory of biodiversity. Stochastic models also made the risk of extinction more evident in small populations or under large environmental variation.
The Markov Chains are used to describe ecological dynamics. They are models of stochastic processes in which time is discrete, and at each interval the system can change state, with a certain probability. The probabilities of changing from one state to another depend only on the present state ((Therefore, they can be expressed in transition matrices from time t to time t+1, as in Population matrix models - Tutorial in spreadsheets
The following are simple case scripts for Markov Chains.