Functional connectivity in ruminants: A generalized state-dependent modelling approach

<div><p>Animal behaviour is increasingly seen as an important component in maintaining functional connectivity between patches in fragmented landscapes. However, models that explicitly incorporate behavioural trade-offs are rarely applied to landscape planning problems like connectivity. The aim of this study was to explore how state-dependent behaviour influenced functional connectivity between patches from a theoretical perspective. We investigated how inter-patch distances influenced functional connectivity using a dynamic state variable model framework. The decision making process of an individual ruminant facing fitness trade-offs in staying in its patch of origin or moving to another patch at various distances were explicitly modelled. We incorporated energetic costs and predation costs of feeding, ruminating, and resting while in the patch and for transit between patches based on inter-patch distance. Functional connectivity was maintained with isolated patches when they offered high intake and the inactivity of rumination associated with rapid gut fill resulted in reduced predation risk. Nevertheless, individuals in high energetic state often would forgo moving to another patch, whereas individuals in poor energetic states were forced to accept the cost of movement to best meet their requirements in the distant patch. The inclusion of state-dependent behavioural models provides important insights into functional connectivity in fragmented landscapes and helps integrate animal behaviour into landscape planning. We discuss the consequences of our findings for landscape planning to show how the approach provides a heuristic tool to assess alternative scenarios for restoring landscape functional connectivity.</p></div

Titrating the energetic equivalence of patch isolation.

<p>Example of the energetic equivalence of isolation as assessed by a titration experiment. This represents the marginal rate of substitution of energy for isolation and indicates the incentives needed in the second patch to restore functional connectivity. At an inter-patch distance of 4 DU, increasing motivation was presented to individuals (simulated with a sigmoid fitness function) in the form of increased intake, given as multiples of baseline values (and absolute intake values). The proportion of time spent in the isolated patch (patch 2) was recorded. There is non-zero use of the patch at an intake of 10 and substantial use at an intake of 15.</p

Landscape schematic.

<p>Patch-specific rates of intake, rumination, and predation risk for the patch of origin (patch 1) and the distant patch (patch 2) and the transit costs between patches as a function of the distance units (DU) between patches.</p

Simulation scenarios for functional connectivity.

<p>Patch based motivation investigates the influence of patch enhancement of the distant patch (patch 2) relative to the starting patch (patch 1), this was done by increasing the intake rate and rumination rate, and decreasing the patch specific predation rate, respectively. The remaining simulation scenarios reflected situations where movement behaviour enhanced functional connectivity over and above patch enhancement. We consider movement and anti-predator behaviour are mutually exclusive to one another. In this situation a reduction either the travel cost or the in-transit predation risk results in an increased cost or risk in the other rate, respectively. <i>d</i> is the distance from patch 1 to patch 2. In all cases patch 1 remains at baseline conditions.</p

Transit based scenarios of functional connectivity.

<p>Effects of transit costs on functional connectivity for individuals using a linear (a) or sigmoid (b) fitness function given a 2x higher intake rate in patch 2 than in patch 1 when individuals can alter their in-transit behaviour. The red boxes and line indicate the connectivity under baseline energetic cost and risk of predation for transit (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0199671#pone.0199671.t001" target="_blank">Table 1</a>), the blue boxes and line refer to the connectivity under 2x baseline energetic cost and 1/2 risk of predation for transit, and the green boxes and line refer to 1/2 energetic cost and 2x predation risk for transit. These in-transit scenarios are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0199671#pone.0199671.t002" target="_blank">Table 2</a>, while within each scenario all other parameters held constant at baseline values (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0199671#pone.0199671.t001" target="_blank">Table 1</a>).</p

Patch based scenarios of functional connectivity.

<p>Functional connectivity measured as the proportion of time spent in the distant patch (patch 2) with respect to increasing inter-patch distances (DU) for individuals modelled using a linear (a) or sigmoid (b) fitness function. The red boxes and line indicate where motivation to move from patch 1 (origin) to patch 2 is maintained by higher intake in patch 2, the blue boxes and line refer to the motivation to move to patch 2 maintained by a reduction in predation risk, and the green boxes and line refer to the motivation to move to patch 2 maintained by a higher rumination rate. These patch based scenarios are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0199671#pone.0199671.t002" target="_blank">Table 2</a>, while within each scenario all other parameters held constant at baseline values (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0199671#pone.0199671.t001" target="_blank">Table 1</a>).</p

Functional connectivity and the effectiveness of the behavioural refuge.

<p>The influence of the behavioural refuge (effectiveness of anti-predator behaviour) during inactivity on functional connectivity, measured as the proportion of use of patch 2, when inactivity forms a complete refuge (i.e., predation rate during inactivity = 0) or inactivity conveys no anti-predator benefit (i.e., predation during inactivity = predation risk during foraging). Individuals modelled with a linear fitness function are given in the blue boxes, while individuals modelled with a sigmoid fitness function are given in the red boxes. Inter-patch distance is 2 DU and patch 2 has an increased intake rate relative to patch 1 while all other values remain constant at baseline values.</p

CWD Surveillance Data in Alberta from 2011 to 2013 for validation

This data was used for validating/evaluating the CWD risk model predictions. Mule deer and white-tailed deer were harvested by hunters in East-Central Alberta from 2000 to 2010. Deer heads were submitted to a laboratory for testing for the presence of CWD