Moth Mating: Modeling Female Pheromone Calling and Male Navigational Strategies to Optimize Reproductive Success

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period

From signalling to cell behaviour : modelling multi-scale organization in single and collective cellular systems

Individually and collectively, cells are organized systems with many interacting parts. Mathematical models allow us to infer behaviour at one level of organization from information at another level. In this thesis, I explore two biological questions that are answered through the development of new mathematical approaches and novel models. (1) Molecular motors are responsible for transporting material along molecular tracks (microtubules) in cells. Typically, transport is described by a system of reaction-advection-diffusion partial differential equations (PDEs). Recently, quasi-steady-state (QSS) methods have been applied to models with linear reactions to approximate the behaviour of the PDE system. To understand how nonlinear reactions affect the overall transport process at the cellular level, I extend the QSS approach to certain nonlinear reaction models, reducing the full PDE system to a single nonlinear PDE. I find that the approximating PDE is a conservation law for the total density of motors within the cell, with effective diffusion and velocity that depend nonlinearly on the motor densities and model parameters. Cell-scale predictions about the organization and distribution of motors can be drawn from these effective parameters. (2) Rho GTPases are a family of protein regulators that modulate cell shape and forces exerted by cells. Meanwhile, cells sense forces such as tension. The implications of this two-way feedback on cell behaviour is of interest to biologists. I explore this question by developing a simple mathematical model for GTPase signalling and cell mechanics. The model explains a spectrum of behaviours, including relaxed or contracted cells and cells that oscillate between these extremes. Through bifurcation analysis, I find that changes in single cell behaviour can be explained by the strength of feedback from tension to signalling. When such model cells are connected to one another in a row or in a 2D sheet, waves of contraction/relaxation propagate through the tissue. Model predictions are qualitatively consistent with developmental-biology observations such as the volume fluctuations in a cellular monolayer. The model suggests a mechanism for the organization of tissue-scale behaviours from signalling and mechanics, which could be extended to specific experimental systems.Science, Faculty ofMathematics, Department ofGraduat

Patterns produced by the IBM.

<p>Patterns produced by the IBM.</p

Examples of patterns obtained by various direction-dependent interaction rules.

<p>Parameters and rules (submodel) are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198550#pone.0198550.t003" target="_blank">Table 3</a>, and boundary conditions are periodic.</p

Social interaction kernel parameter values.

<p>Social interaction kernel parameter values.</p

Submodels and social interaction forces.

<p>Submodels and social interaction forces.</p

Parameter values produce spatial patterns.

<p>Parameter values produce spatial patterns.</p

Density plots of patterns obtained by various direction-dependent interaction rules.

<p>Bright colours indicate high numbers of individuals, where the number density of individual is normalized by the total number of individuals. Density estimates are obtained via a kernel smoothing estimate from the corresponding trajectories in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198550#pone.0198550.g004" target="_blank">Fig 4</a>. Subfigures correspond to the patterns shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198550#pone.0198550.g004" target="_blank">Fig 4</a>. Parameters and rules (submodel) are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198550#pone.0198550.t003" target="_blank">Table 3</a>.</p

Social interaction zones.

<p>Cartoon depiction of the three social interaction zones surrounding an individual at location <i>x</i>. Repulsion (<i>r</i>) acts over short distances from the reference individual at <i>x</i>, alignment (<i>al</i>) over intermediate distances, and attraction (<i>a</i>) over longer distances. These zones may be disjoint, as illustrated, or may overlap.</p

Density plots of patterns produced by the IBM with density-dependent speed.

<p>Bright colours indicate high numbers of individuals. The number density has been normalized to 1. Corresponding trajectories are shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198550#pone.0198550.g007" target="_blank">Fig 7</a>.</p