## 1 Introduction  
The ability to learn from the local environment plays a crucial role in the survival of species. Various processes, such as interactions within social groups, competition with members of the same species, foraging behavior, and predator avoidance, profoundly influence how a species navigates and behaves in its surroundings [1; 2; 3]. Understanding and predicting the territories of different species depend on comprehending these processes. A compelling example of this phenomenon can be observed in wolves, where their movements are guided by vital information, including the scent of their pack, the scents of fellow pack members, pack density, and the location of wolf pups [4]. Spatial ecology has a keen focus on unraveling the mechanisms that underlie species movement and how these movements contribute to territory decisions. In light of the effects of climate change on the environment [5; 6] and its impact on species' territories [7], these issues have gained increasing importance in scientific research. Mathematical models leverage the mechanisms underlying territory decisions to predict how territories adapt in response to environmental changes, such as alterations in conspecific territories or resource density [8]. Specifically, mechanistic models offer a framework to investigate territory formation, building upon theories developed by field scientists for species movement. These models provide some advantages over statistical models, as they facilitate hypothesis testing for the driving forces behind animal movement, exhibit strong predictive capabilities, and can be validated using field measurements [9]. Mechanistic models have proven useful in describing various behaviors, including foraging [10; 11], aggregation [12], and home ranges [13; 14]. They encompass movement processes, conspecific influences, environmental pressures, and space utilization [15; 16; 17]. Earlier models, such as those proposed by [18; 19], incorporated diffusion and attraction to a central location, like a den site, to describe territories across different species. Over time, these models have been enriched with additional processes to better replicate territory patterns based on empirical data, including aspects like scent marking [9] and habitat selection [20]. Local advection-diffusion (AD) models have proven successful in predicting territories for species like wolves [4], coyotes [9], and meerkats [17]. For instance, in the case of meerkats, location data and environmental information are integrated into a local mechanistic model, enabling parameter estimation to describe territory formation among social groups of meerkats. One crucial feature of these models, which in some cases ensures their well-posedness, is an attraction to fixed den sites. In a way, den-site attraction represents the use of very specific nonlocal information, making these models well-suited for species known to maintain fixed den sites. Numerous mechanistic models proposed to understand animal territory formation have traditionally assumed that animals base their decisions solely on local information. However, the process of gathering information about the environment inherently involves nonlocal aspects. Animals rely on observations, sounds, and smells to gain insights into distant surroundings [21; 22; 23]. Additionally, studies have highlighted the significance of nonlocal advection in maintaining swarm coherence [24] and ensuring well-posed solutions in certain models [25; 26]. Furthermore, field observations of meerkats have provided evidence that they actively avoid locations where they have encountered members of rival groups previously, further emphasizing the importance of nonlocal interactions in certain species [17; 27]. As a result, mechanistic models incorporating nonlocal advection have garnered recent interest [25; 28; 29], along with relevant references. This study focuses on a nonlocal advection-diffusion model that elucidates the territory formation of social species with subgroups.