Cellulose biodegradation models; an example of cooperative interactions in structured populations

¹ Department of Mathematics, University of Maryland, College Park, USA.
pjabin@umd.edu
² Department of Mathematics, University of California, Los Angeles, USA.
amiroshn@gmail.com
³ Department of Mathematics and Statistics, University of Massachusetts Amherst, USA.
young@math.umass.edu

Received: 4 September 2016
Revised: 14 March 2017
Accepted: 20 April 2017

Abstract

We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the population of micro-organisms. We then use the corresponding models in the context of multiple-trait populations. This leads to classical, logistic type, reproduction rates limiting the growth of large populations but also, and more surprisingly, limiting the growth of populations which are too small in a manner similar to the effects seen in populations requiring cooperative interactions (or sexual reproduction). This study thus offers a striking example of how some mechanisms resembling cooperation can occur in structured biological populations, even in the absence of any actual cooperation.