Competing methods to Probabilistic Boolean Networks (PBNs) for modeling gene regulatory networks include:

1. Dynamic Bayesian Networks (DBNs): These provide a framework for modeling time-dependent interactions among genes using probabilistic rules with a temporal component.
2. Ordinary Differential Equations (ODEs): Used for continuous modeling of gene expression levels, providing detailed dynamics that include the rate of change of gene expression over time.
3. Stochastic Differential Equations (SDEs): Similar to ODEs but incorporate random fluctuations to model the inherent noise in biological systems more accurately.
4. Agent-based Models (ABMs): These simulate the actions and interactions of autonomous agents (cells, molecules) to assess their effects on the system as a whole.
5. Artificial Neural Networks (ANNs): Employed for pattern recognition and predictive modeling in complex gene regulatory networks, especially when large datasets are available.
6. Graphical Gaussian Models (GGMs): Used for inferring the structure of gene networks based on the assumption of multivariate normal distributions.

These methods vary in their assumptions, computational requirements, and the type of data they are best suited for, making them more or less appropriate depending on the specific objectives and available biological data.