From individual behaviour to population models: a case study using swimming algae.

Area of Science:

• Marine biology
• Mathematical modeling
• Computational fluid dynamics

Background:

• Understanding the spatial-temporal distribution of phytoplankton is crucial for marine ecology.
• Individual cell behavior significantly influences population-level dynamics.

Purpose of the Study:

• To develop and compare two random-walk models linking individual swimming algae behavior to population-level advection-diffusion models.
• To investigate how different random-walk assumptions affect population distribution predictions.
• To account for arbitrary bias and variable swimming speeds in algal movement.

Main Methods:

• Analysis of swimming algae trajectories.
• Development of two advection-diffusion models based on distinct random-walk behaviors (velocity jump and velocity diffusion).
• Incorporation of non-weak bias and variable swimming speed into the models.

Main Results:

• The mean upward swimming speed for Heterosigma akashiwo was calculated at 40 microm s(-1).
• Diffusion constants ranged from 2 x 10^3 to 4 x 10^4 microm^2 s(-1), varying with model specifics.
• Substantially different population-level predictions were obtained from the two modeling approaches when applied to the same empirical data.

Conclusions:

• The choice of random-walk assumptions significantly impacts population-level predictions in advection-diffusion models.
• Existing theoretical tools may be insufficient for accurately approximating algal behavioral characteristics.
• Further development of theoretical frameworks is needed for robust modeling of phytoplankton spatial-temporal distributions.