Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Matrix population models are widely used but criticized for sensitivity to matrix dimension.
• This sensitivity is concerning for population growth rate (λ), an intrinsic population characteristic.
• Fast pathways (individuals moving up classes) may explain this sensitivity.

Purpose of the Study:

• To investigate the impact of matrix dimension (class width) on population growth rate (λ).
• To determine if fast pathways cause λ's sensitivity to matrix dimension.
• To assess the practical implications for tree species population dynamics.

Main Methods:

• Analyzed matrix population models with growth transitions from class i to i+1.
• Investigated conditions where λ is independent of class width (constant mortality and recruitment).
• Examined the role of fast and slow pathways as a diffusion process.
• Tested models with data from 53 tropical tree species.

Main Results:

• When mortality and recruitment are constant, λ is independent of class width, irrespective of growth rate.
• Fast and slow pathways act jointly as a diffusion process.
• For 53 tropical tree species, diffusion from common matrix dimensions was unrealistically strong.
• Sensitivity of λ to matrix dimension (1-10 cm class width) was small, less than sampling uncertainty.
• λ's change with class width varied by species.

Conclusions:

• The sensitivity of λ to matrix dimension is not solely due to fast pathways.
• Diffusion effects are more significant than previously thought for matrix population models.
• Class width has minimal impact on λ estimates for tropical tree species, despite the need to limit diffusion.