The "four-color issue" in ecology for considering ecosystem boundaries

Abstract. Ecosystem boundaries are important structures in defining ecosystems. To date, ecologists have not extensively considered which boundaries are important in explaining ecological phenomena in order to simplify ecological theories. The four-color theorem in mathematics maintains that only four colors are required to color a set of regions so that no two adjacent regions have the same color. Before being proven in 1976, the theorem was considered the "four-color issue", which proposed that a small number of colors were required to separate regional boundaries. Applying the principle of "four-color issue" to the ecological field, we can also examine reducing the number of ecosystem boundaries considered. That is, we can ask ourselves the following question: "how many boundaries of an ecosystem should be considered for ecology"? Here, I suggest a principle of ecosystem boundaries as the "four-color issue of ecology", and propose that this will be an important step toward advancing knowledge in ecology and conservation biology. In addition, I introduce graph theory, developed from the four-color theorem, which can be useful for estimating ecosystem boundaries.