Mathematical modeling of sensing and feeding by copepods

Abstract

The ability to feed effectively is a fundamental skill required for survival. Microscopic crustaceans called copepods are a great example of an animal that are very adept at eating. They are tiny creatures, roughly on the order of 1 mm, and so their fluid environment is not like the water that we are accustomed to, but rather, is more like that of honey. To make things even more difficult, they have poor eyesight and are only able to detect the presence of light. Instead of using vision to detect the presence of food, they rely on other sensory mechanics like chemical signals and hydro-mechanical disturbances to remotely detect their prey. Another challenge they are presented with is moving a particle to a desired location for inspection and consumption. Given the high viscosity of their environment, particle transport is difficult since small objects near the boundary of a body will tend to stick to and move with the motion of the body. In this dissertation, we first create a model for three modes of feeding: sinking, swimming and hovering. For each of the three modes, we first create the flow fields by including the antennae, a feature often neglected in previous studies. Then, we measure the magnitude of the disturbance vector induced by a spherical particle located in a plane with sensor locations along the antennae. From this, a detectable volume is generated showing what the model could theoretically detect over a given period of time. What we discover is that sinking may be a preferable mode of feeding if the copepod were surrounded by food. If the copepod is unable to detect anything, then swimming might be best as it would increase the copepod's chances of encountering food. If the copepod came across a dense cluster of food, then positioning underneath the cluster could be the best mode as it would allow the copepod to funnel the food from above to its body. In the second and third chapter, we explore the copepod's ability to transport small particles using the Weis-Fogh fling and clap mechanism. Copepods have been observed performing this motion as early as the 1980's but there have been no mathematical models for the fling and clap in the Stokes regime. We investigate the efficacy of the motion by representing a pair of appendages as either a pair of rods or a pair of plates. What we discover is that both representations lead to a positive net displacement of particles in the desired direction and that increasing the maximum slope $a$ of the appendages lead to an increase in the displacement, specifically on the order of $a^2$ for small values of $a$.