Variation in risk in single-species discrete-time models

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Traditional discrete-time population models often display complex dynamics like chaos at high reproductive rates.
• These models typically lack the incorporation of juvenile risk, a measure of vulnerability to density-dependent mortality.

Purpose of the Study:

• To investigate how variability in juvenile risk affects the stability of discrete-time population models.
• To determine the conditions under which risk variation stabilizes population dynamics, regardless of the net reproductive rate (R).

Main Methods:

• Analysis of a broad class of discrete-time population models.
• Inclusion of both density-independent and density-dependent juvenile risk.
• Identification of specific risk distribution shapes that confer stability.

Main Results:

• Variability in juvenile risk generally stabilizes population equilibrium.
• For both density-independent and density-dependent risk, specific distribution shapes were identified that ensure stability for all values of R.
• The shape of the risk distribution is the critical factor for stabilization, superseding the magnitude of variation.

Conclusions:

• Incorporating variability in juvenile risk offers a stabilizing mechanism for population models.
• The geometric properties of the risk distribution are more influential than the extent of risk variation in determining population stability.
• Findings highlight the importance of considering individual-level variation in ecological models.