Markov models and network analysis reveal sex‐specific differences in the space‐use of a coastal apex predator

Abstract

Understanding the links between external variables such as habitat and interactions with conspecifi cs and animal space-use is fundamental to developing eff ective management measures. In the marine realm, automated acoustic tracking has become a widely used method for monitoring the movement of free-ranging animals, yet researchers generally lack robust methods for analysing the resulting spatial-usage data.In this study, acoustic tracking data from male and female broadnose sevengill sharks Notorynchus cepedianus , collected in a system of coastal embayments in southeast Tasmania were analyzed to examine sex-specifi c diff erences in the sharks ' coastal space-use and test novel methods for the analysis of acoustic telemetry data.Sex-specifi c space-use of the broadnose sevengill shark from acoustic telemetry data was analysed in two ways: Th e recently proposed spatial network analysis of between-receiver movements was employed to identify sex-specifi c space-use patterns. To include the full breadth of temporal information held in the data, movements between receivers were furthermore considered as transitions between states of a Markov chain, with the resulting transition probability matrix allowing the ranking of the relative importance of diff erent parts of the study area.Both spatial network and Markov chain analysis revealed sex-specifi c preferences of diff erent sites within the study area. Th e identifi cation of priority areas diff ered for the methods, due to the fact that in contrast to network analysis, our Markov chain approach preserves the chronological sequence of detections and accounts for both residency periods and movements.In addition to adding to our knowledge of the ecology of a globally distributed apex predator, this study presents a promising new step towards condensing the vast amounts of information collected with acoustic tracking technology into straightforward results which are directly applicable to the management and conservation of any species that meet the assumptions of our model.

Combining network theory and reaction–advection–diffusion modelling for predicting animal distribution in dynamic environments

“…For example, Fox and Bellwood (2014) showed that coral reef fishes had spatial networks with small world properties, such that the concentration of fishing effort at known aggregation sites could increase the risk of extinction of coral reef fish species. The potential effect that a disturbance could exert on the coral reef fish community remains an assumption that cannot be fully evaluated using only network analysis, because the temporal dynamic of movement is then ignored (Stehfest et al, 2015). Ferrari et al (2014) showed the utility of using dynamic network models for studying dynamical processes.…”

“…Although graph theory can provide crucial information on animal movements within a patch network, inference on population space use dynamics still requires an understanding of the temporal dimension of movement patterns (Jacoby & Freeman, 2016;Nathan et al, 2008). For example, network analysis alone failed to identify preferred sites for a population of broadnose sevengill shark Notorynchus cepedianus, because it did not account for residency period in the different sites (Stehfest, Patterson, Barnett, & Semmens, 2015). Integration of the temporal dimension of movement into a network requires the use of dynamic models, such as a reaction-advection-diffusion model (Barrat, Barthelemy, & Vespignani, 2008).…”

Spatial behavior of two coral reef fishes within a Caribbean marine protected area

“…Instead of using a spatial network based on counts of directed movements between receivers as proposed by Jacoby et al (2012), which ignores temporal characteristics of movements such as residency periods, we followed the Empirical derived Markov chain (EDMC) analysis proposed by Stehfest et al (2015) which takes into account this temporal dimension. A Markov chain is a random process that undergoes transitions from one state to another (in our case from receiver to receiver) on a state space.…”

“…To identify preferred use of locations (i.e. receivers) from the movement network, we calculated the eigenvector centrality of each node which is a measure not only of the centrality of a state, but also of the centrality of the states it is connected to (see Stehfest et al, 2015). It is calculated as the dominant eigenvector of the movement network or adjacency matrix and is equivalent to the weighted proportion of the total number of paths in a network going to or coming from a given node (Newman, 2004).…”

Spatial separation without territoriality in shark communities

“…We used telemetry to answer two questions: 1) what is the order of habitat preference and movement rates between habitats for blacktip and grey reef sharks, and 2) what is the degree of intra-specific movement rates of individuals between 'sub-habitats' within habitat types? To determine species level habitat preferences and movement among habitats, we performed spatial empirically derived Markov chain (EDMC) analyses (Stehfest et al 2015). EDMC analysis is a form of spatial network analysis that uses a discrete time, stationary Markov chain approach to model the temporal dimension of movements including residency and transition duration (Stehfest et al 2015).…”