Add element to null (empty) List<T> Property

Add element to null (empty) List Property

null and an empty list are two different things: Adding an element to an empty list works fine, but if your property is null (as all reference-type properties are initially null), you need to initialize it with an empty list first.

You could use an auto-property initializer for that (see Kędrzu's answer), or you could manually initialize the list in the constructor:

class Maps
{
    public Maps()
    {
        AllAntsAtMap = new List<Ant>();
    }

    ...
}

(Since the property is declared in the superclass Maps, I'd do the initialization there rather than in the subclass Quadrangle.)

It is much simpler in C# 6:

protected List<Ant> AllAntsAtMap { get; set; } = new List<Ant>();

You should initialize AllAntsAtMap before usage. You can use the constructor for that:

public Quadrangle()
{
    AllAntsAtMap = new List<Ant>();
}