A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.