Moving-habitat models: A numerical approach

• Published in: Mathematical biosciences 2021-11, Vol.341, p.108711-108711, Article 108711
• Main Authors: MacDonald, Jane S., Bourgault, Yves, Lutscher, Frithjof
• Format: Article
• Language: English
• Subjects: Climate Change; Climate models; Coordinates; Density; Diffusion rate; Ecosystem; Finite difference method; Geographical distribution; Global climate; Habitat preferences; Habitats; Humans; Individual movement behaviour; Mathematical analysis; Mathematical models; Models, Biological; Moving-habitat models; Population; Population Dynamics; Population studies; Populations; Reaction-diffusion equations; Reaction–diffusion equation; Species extinction; Temperature preferences; Transient dynamics
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2021.108711

As the global climate changes, biological populations have to adapt in place or move in space to stay within their preferred temperature regime. Empirical evidence suggests that shifting speeds of temperature isoclines are location and elevation dependent and may accelerate over time. We present a mathematical tool to study transient behaviour of population dynamics within such moving habitats to discern between populations at high and low risk of extinction. We introduce a system of reaction–diffusion equations to study the impact of varying shifting speeds on the persistence and distribution of a single species. Our model includes habitat dependent movement behaviour and habitat preference of individuals. These assumptions result in a jump in density across habitat types and generalize previous studies. We build and validate a numerical finite difference scheme to solve the resulting equations. Our numerical scheme uses a coordinate system where the location of the moving suitable habitat is fixed in space and a modification of a finite difference scheme to capture the jump in density. We explore a variety of shifting-speed scenarios and contribute insights into the mechanisms that support population persistence through time in shifting habitats. One common finding is that a strong bias for the suitable habitat helps the population persist at faster shifting speeds, yet sustains a smaller total population at slower shifting speeds. •Conformal moving meshes capture jumps in density from individual movement behaviour.•We consider growing domains and accelerating speeds of climate change.•A numerical approach provides insight on transient dynamics.•High preference for the unsuitable habitat can positively impact total population.•High preference for the suitable habitat can lead to faster extinction.