Resource-Limited Growth, Competition, and Predation: A Model and Experimental Studies with Bacteria and Bacteriophage

Abstract

We present a model of resource-limited population growth, competition, and predation based on what we believe to be biologically realistic assumptions about the relationship between resources and the growth of primary consumers and about the interaction of the primary consumers with the predators that prey upon them. Consideration is given to an equable habitat in which resources are continually supplied and wastes are continually removed. The general properties of this model are examined and two specific cases are studied in some detail: (i) one resource, one prey, and one predator, and (ii) one resource, two prey, and one predator. Particular consideration is given to the conditions which will permit the continued coexistence of the interacting populations. In conceiving this model we were guided by the specific case of bacteria and their virulent viruses. To study its validity we compare the theoretical predictions with the experimental results from continuous-culture populations of the bacterium E. coli and the phage T2. Structurally stable equilibria with all populations coexisting are possible when the number of distinct predator populations is not more than the number of distinct prey populations and the number of the latter is not more than the sum of the number of resources and the number of predator populations. For one resource, one prey, and one predator there are stable states of coexistence. Given specific resource utilization functions, the levels of these equilibria or oscillations and the range of parameter values required for stability can be determined. In situations where a stable equilibrium exists for the one predator-one prey system, a second population of primary consumers which is totally resistant to predation can also be maintained. Sufficient conditions for this to occur are that the resistant population have a lower intrinsic growth rate than the sensitive but that the former can, nevertheless, survive and multiply living on the resources present in the one predator-one prey system. If, however, this second species of primary consumer becomes slightly sensitive to predation, it may then entirely displace the original sensitive population. Stable equilibria were observed in glucose minimal continuous cultures containing T2 sensitive E. coli B and T2 phage. The equilibrium concentration of glucose and the densities of the populations were similar to those predicted by the model. However, with the estimated values of the parameters, the experimental system fell in the range where the model predicted that the oscillations would increase to the point where the populations would eventually become extinct. Stable equilibria were also observed for a glucose-limited chemostat culture containing T2 phage together with a T2-sensitive clone of E. coli B and a T2-resistant strain of E. coli K12. This system fulfilled the conditions under which the theory predicts that stable coexistence will occur. We discuss the validity of this model as a general analogue of resource limited growth, competition, and predation in planktonic species. We also consider the implications of these theoretical and experimental results for the general theory of competition and predation and for the specific problem of coexistence for bacteria and their virulent viruses.