<p>Multi robot teams are well suited to perform tasks like covering and monitoring large spaces and/or distributing and searching for resources in the environment. To perform these tasks, teams require methods to address the long standing Multi Robot Task Allocation (MRTA) problem. Existing MRTA solutions focus on either assigning individual robots to tasks (microscopic) or modeling team-wide population dynamics deriving time-based robot allocation policies (macroscopic). In dynamic environments, microscopic methods require computationally expensive reallocation strategies and macroscopic methods lack model descriptiveness to achieve time-varying populations without replanning. In this work, we take inspiration from population modeling in other disciplines and present a nonlinear macroscopic ensemble allocation model that describes individual robot collaboration and has the potential for time-varying task assignment without the need for replanning populations. Our results demonstrate a range of possible time-varying task assignment behaviors that are potential solutions to handling known periodic environments or task changes. In addition, we explore the breakdown of classic macroscopic modeling assumptions and present model reinterpretations to mitigate their impact. Our simulation and experimental results demonstrate time-varying task assignment, which could be applied to tasks like environmental monitoring, collective construction, and resource distribution.</p>