A basic equation for population dynamics with destruction of breeding habitats and its application to outbreak of cyprinid herpesvirus 3

In reproduction, many animal species migrate to local habitats that are appropriate for reproduction and for growth of newly born offspring. The examples are ubiquitous among crabs, freshwater fishes, amphibians, migratory birds, and sea animals. We propose a basic equation for population dynamics of such animals, assuming that the number of offspring is proportional to the area of the local breeding habitats as a first approximation. This equation is very simple to be solved analytically, and useful for representing environmental issues of habitat destruction and degradation. According to the equation, the adult density in breeding habitats increases temporarily during habitat destruction and returns to the original density afterwards. The temporal peak value is higher for a larger proportion of area with destruction, a higher temporal rate of destruction, and a higher survival probability of the adults. In contrast, habitat degradation results simply in a decrease of the adult density in breeding habitats. Using this equation, we will discuss the vulnerability of populations to epidemic diseases due to temporal local high densities with decreasing breeding habitats by human activities, exemplifying an outbreak of cyprinid herpesvirus 3 for wild carps in Lake Biwa.