Suppose that a collection of plants is to be classified in terms of four distinct characteristics. The classification is based on whether a plant has a particular characteristic or not. Thus, each plant can be represented by a four digit binary number. The number 1011, for example, would label plants having the first, third and fourth characteristics, but lacking the second. A total of seven four-digit binary numbers end up as labels for the categories of plants: 1111, 1110, 1011, 1010, 0110, 0011, 0010.

Assuming that all of the plants have evolved from the original species labeled 0010; that any given mutation will result in the presence of only one new characteristic; and that once a given characteristic is present, it remains, construct a phylogenetic tree for these plants.