Branching process
A branching process is like a family tree where each person has children, who in turn have more children, and so on. In this process, we start with one person who starts the chain. This person is referred to as the "ancestor" or "root" of the tree.
Think of a family tree like your own. Your grandparents are your ancestors, and you are a part of one of the branches of their tree. You likely have siblings, cousins, and other family members who are also part of the same branch, and they all have their own children. Together, these children form new branches of the tree.
In a branching process, we can think of each person as having a certain number of children, and we can represent this with a probability distribution. For example, we might say that each person has a 50% chance of having one child, a 30% chance of having two children, and a 20% chance of having three children.
As the process continues, each child can also have a probability distribution that describes their own children. We call this the "offspring distribution". Through this way of thinking, we can model how the tree grows and how the number of branches and individuals change over time.
Overall, a branching process helps us understand how populations grow and how they can become extinct or grow infinitely. It's like a giant family tree, but for groups of things, and by understanding how these things "grow" and "reproduce," we can make predictions about their evolution over time.
Think of a family tree like your own. Your grandparents are your ancestors, and you are a part of one of the branches of their tree. You likely have siblings, cousins, and other family members who are also part of the same branch, and they all have their own children. Together, these children form new branches of the tree.
In a branching process, we can think of each person as having a certain number of children, and we can represent this with a probability distribution. For example, we might say that each person has a 50% chance of having one child, a 30% chance of having two children, and a 20% chance of having three children.
As the process continues, each child can also have a probability distribution that describes their own children. We call this the "offspring distribution". Through this way of thinking, we can model how the tree grows and how the number of branches and individuals change over time.
Overall, a branching process helps us understand how populations grow and how they can become extinct or grow infinitely. It's like a giant family tree, but for groups of things, and by understanding how these things "grow" and "reproduce," we can make predictions about their evolution over time.
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