A spatial age-structured model of perennial plants with a seed bank.

Integrodifference model;Perennial;Seed bank;Spreading seed;Structured;Traveling waves

Kimberly Ilene Meyer

University:University of Louisville

Department:Mathematics

关键词: Integrodifference model;    Perennial;    Seed bank;    Spreading seed;    Structured;    Traveling waves;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=1969&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

We formulate an integro-difference model to predict the growth and spatialspread of a perennial plant population with an age-structured seed bank. We allowthe seeds in the bank to be of any age, producing an infinite system of equations.The production of new seed can be density-dependent and so the function describingthis growth is allowed to be non-monotone. The functions describing the seedbank are linear. We develop properties about the non-spatial model, including theexistence of a positive steady-state and conditions under which solutions convergeto this steady-state. We also show that when the origin is unstable, the systemhas a spreading speed and that this spreading speed is characterized as the slowestspeed of a class of traveling wave solutions. We conduct numerical simulations ofa truncated version of this model which show that both the perennial term andthe seed bank can have a stabilising effect on the population. On the other hand,traveling wave solutions may exhibit different patterns of fluctuations includingperiodic oscillations and chaotic tails.