Modelling and parameter inference of predator–prey dynamics in heterogeneous environments using the direct integral approach

Abstract

Most bacterial habitats are topographically complex in the micro scale. Important examples include the gastrointestinal and tracheal tracts, and the soil. Although there are myriad theoretical studies that explore the role of spatial structures on antagonistic interactions (predation, competition) among animals, there are many fewer experimental studies that have explored, validated and quantified their predictions. In this study, we experimentally monitored the temporal dynamic of the predatory bacterium Bdellovibrio bacteriovorus, and its prey, the bacterium Burkholderia stabilis in a structured habitat consisting of sand under various regimes of wetness. We constructed a dynamic model, and estimated its parameters by further developing the direct integral method, a novel estimation procedure that exploits the separability of the states and parameters in the model. We also verified that one of our parameter estimates was consistent with its known, directly measured value from the literature. The ability of the model to fit the data combined with realistic parameter estimates indicate that bacterial predation in the sand can be described by a relatively simple model, and stress the importance of prey refuge on predation dynamics in heterogeneous environments.

Insight into the Possible Use of the Predator Bdellovibrio bacteriovorus as a Probiotic

“…Although Hobley's model is based on an idealized environment, it is the one that is most practical for using B. bacteriovorus as an antimicrobial agent. Another study examined the behavior of B. bacteriovorus against Burkholderia stabilis in a structured environment consisting of sand under various regimes of wetness and showed that predation dynamics are influenced by environmental conditions [92]. This is relevant considering that in vivo environments are more structurally complex than buffer systems.…”

Bacterial predation under changing viscosities

“…It has been shown that constructed habitats largely change BALO predatory dynamics (Hol et al ., ; Dattner et al ., ), but our results suggest that the macro‐molecular environment also alters predator–prey interactions. This is relevant to the applications of BALOs against pathogenic bacteria as BALOs have been tested as possible treatments for lung infections, whereby they should be active in mucus, and in plasma (Shatzkes et al ., ; Baker et al ., ), two habitats totally different in terms of spatial structure as well as in macro‐molecular composition.…”

A two-stage approach for estimating the parameters of an age-group epidemic model from incidence data

“…The direct estimation of model parameters is referred to in the literature as the “direct integral method” in the context of ordinary differential equations. 37,40,41 To be more specific, Dattner et al. 40 show that the direct integral method is n-consistent ( n stands for the sample size) for estimating parameters of fully observed systems of ordinary differential equations linear in functions of the parameters, while Vujačić et al.…”

“…We call such a model “semi-linear in the parameters.” Modification of the direct integral method to models of ordinary differential equations semi-linear in the parameters was studied in Dattner et al. 41 Next we suggest a modification for the discrete case of equation (1). Let ψ stand for the set of additional parameter values not including β that one would wish to estimate (i.e.…”