In many situations, when we have a group of people, they all formopinions on a subject. Everyone in a population influences each others opinion. Naturally, people how the opinion of children are influenced by other children differs from how adults influence their opinions. Between different age groups there are all kind of different interactions.
This thesis aims to model how such opinions evolve and influence each other over time. First We assume an individual can either have a negative or positive opinion on a subject. To model this, we use the Ising model, originally developed for the description of magnetism in metals. We model opinion changes as random processes influenced by the opinion of other individuals in the population. We divide the population into subgroups of people who interact similarly. In this thesis, we prove that if we make the total group of people larger and larger, this random process becomes a deterministic process. Just like when you flip a coin infinitely many times, you end up with heads 50% of the time. We then determine how the different populations influence each other’s opinions. Understanding group opinion dynamics can help explain the spread of misinformation on social media, the emergence and disappearance of political parties, or how companies can predict or start trends.

We investigate the migratory behaviour of juvenile loggerhead sea turtle (Caretta caretta) hatchlings within a region of the North Atlantic Gyre. To do so, we develop and compare an individual based (IB) model and a partial differential equation (PDE) model, specifically an advection-diffusion equation derived from a position-jump process. We compare their behaviour and show that they yield similar results, but that there are still some differences between the two. Using the IB model we assess survival probabilities of hatchlings in recent years (2016-2023), revealing that survival rates are statistically significantly (𝑝-value = 2.62 ⋅ 10^−6) not constant over time in this region. However, there could be global events that influence the survival probability, as years 2019 and 2023 have a large deviation in survival probability.