Our study aims to identify and understand how several ecological factors relate to parasite abundance in a colonial animal. However, we are uncertain on how to interpret a factor (density) that is significant both as an interaction (density*spatial location) and as a quadratic term (density2). Please note that the interaction with density in its quadratic form (density2*spatial location) is not significant.
As we understand, when a factor is significant in both its linear form (e.g., synchrony) and in interaction (synchrony*temperature), the interpretation of its relationship with the response variable should always take into account the other interacting variable, in this example, temperature. In our case, however, the factor in issue is significant in its quadratic form and in its linear form when in interaction. Our main interest is to correctly interpret the relationship between density and parasite abundance. Can we ignore density´s quadratic form and focus only on density's interaction with spatial location? Or do we need to consider both of these relationships for interpretation?
EDIT I analyzed data with generalized linear mixed models (GLMM).