Modeling Growth and Spread of Dandelion through Integrodifferential Equations

Dandelion is remarked for its unique seed wind-dispersal strategy and resilience to environment. To better understand biological and ecological traits of dandelions, this study models the population spread of dandelion spread under different conditions. An Integrodifferential Equation (IDE) models the spread of dandelions over time on an open one-hectare plot of land. The IDE breaks down population spread into growth and dispersal. Population growth is governed by a set of Delayed Differential Equations which models the seeds, germinated seedlings, blooming, and mature stages of dandelions. Each stage is delayed from the previous one according to the biological pattern, and the proportion of successful conversion between states is determined based on daily temperature and sunshine level. The Wald Kernel is used to simulate wind dispersal of dandelion seeds through a one-hectare field. The kernel is adjusted based on wind speed distribution, wind direction, and precipitation. It is found that 15◦C, sufficient sunshine, and warm winters are ideal for dandelion spread. The model is then applied to simulate the spread of dandelions with environmental data in Edinburgh and Sydney, representatives of inclement and tropical climate.