<p>Microscopic models of traffic depend on how the dynamics of one vehicle following another is considered. Such models play a key role in design, optimisation, performance and control of transportation networks. Based on how these models are constructed, instabilities in traffic are observed, which may be observed in real life scenarios or can be a consequence of the inherent assumptions in the model. It is important to identify and quantify types and regions of instabilities for appropriate choice of analyses, control or intervention in transport networks, but inadequate research is present in this area. This paper addresses this gap by investigating traffic instabilities of Car Following Models (CFMs) and Multi-anticipative CFMs (MCFMs) that model Human Driven and Autonomous Vehicles, respectively. While string stability in a platoon, investigating how a perturbation in a vehicle propagating downstream affects vehicles upstream is studied for most CFMs and MCFMs, the spatio-temporal patterns of the disturbance wave is inadequately described by string instability. To address this gap, the paper investigates convective instability of such systems, which is defined based on the formed patterns, extending the limited existing work to two well known CFMs and MCFMs. Different types of instabilities are explored by simultaneously varying the key factors influencing the stability conditions. The paper identifies convective and nonlinear instabilities in different parameter regions in all the studied models. The framework used in this paper to assess instabilities in microscopic traffic models indicate that convective and nonlinear instabilities are observed in the class of MCFMs. The work subsequently quantifies how different instabilities are affected by increasing the perturbation strength, while demonstrating how the traditionally popular linear stability analysis that only consider local and string stability are incomplete in describing instabilities in microscopic models of traffic flow dynamics.</p>