Landscape fragmentation and pollinator movement within agricultural environments: a modelling framework for exploring foraging and movement ecology

Pollinator decline has been linked to landscape change, through both habitat fragmentation and the loss of habitat suitable for the pollinators to live within. One method for exploring why landscape change should affect pollinator populations is to combine individual-level behavioural ecological techniques with larger-scale landscape ecology. A modelling framework is described that uses spatially-explicit individual-based models to explore the effects of individual behavioural rules within a landscape. The technique described gives a simple method for exploring the effects of the removal of wild corridors, and the creation of wild set-aside fields: interventions that are common to many national agricultural policies. The effects of these manipulations on central-place nesting pollinators are varied, and depend upon the behavioural rules that the pollinators are using to move through the environment. The value of this modelling framework is discussed, and future directions for exploration are identified.

scientific effort is currently being devoted to understanding this decline (Potts et al., 30 2010), in an effort to identify strategies for both arresting and reversing it (Brown & 31 However, the value of corridors is debatable: corridors can both aid pollinators to 45 move through the environment (such as through giving visual signposting or an 46 obstruction-free route) and hinder their movement (such as by providing physical 47 barriers) through the environment ( be harmful if they allow the spread of invasive species (Procheş et al., 2005). Even if 50 a corridor is demonstrated to be a useful feature to add to the environment, the 51 corridor on its own may not provide extra value to the landscape, as the composition 52 of the landscape adjacent to the corridors may also contribute to how well they 53 function (Baum et al., 2004). 54 55 Because the evidence is relatively mixed for the value of these mitigation strategies, 56 we therefore need to better understand the effects that these different environmental 57 manipulations have on the pollinators that live within them. As well as observational 58 studies comparing existing manipulations, we can conduct experimental 59 manipulations (Jenerette & Shen, 2012). We can also investigate the biology and 60 effects of the manipulations using theoretical models, which allow us to explore many 61 different scenarios without conducting expensive and time-consuming field trials. 62 Careful model formulation allows us to identify aspects of the biology of the 63 pollinating species that may impact on how they interact with the environment. In 64 particular, as urged by Lima & Zollner (1996), we can tie concepts from behavioural 65 ecology with landscape ecology, to better inform how organisms are interacting with 66 the habitat in which they live. behavioural ecology (e.g. Rands et al., 2004;Rands, 2012). We would expect 80 that the foraging decisions and movements of pollinators will be affected by local 81 resource availability, resource quality, and the ease of locating resources and moving 82 through the environment. In turn, these can be tied to the physical composition of the 83 landscape. All of these factors will be changing dynamically, and will be subject to 84 weather, interference from other foragers, and anthropogenic change within the 85 environment. Spatially-explicit individual-based techniques are therefore ideal for 86 exploring the effects of habitat fragmentation and change on the behaviour of 87 pollinators nesting within the environment, as they allow us to consider the effects of 88 behavioural rules within a spatially complex environment. 89

90
Here, I develop a framework for considering pollinator movement within the 91 environment, using a spatially-explicit individual-based model of the behaviour of a 92 central-place forager that is nesting within its environment. I build on the spatially-93 rotated 90º clockwise from its current direction of travel is the 'right' square (and the 144 pollinator travels 'right'). Similarly, the squares that would be entered if the pollinator 145 rotated 180º and 270º clockwise are the 'backwards' and 'left' squares respectively 146 (with the pollinator travelling 'backwards' and 'left'). 147 148 I assume movement follows a correlated random walk. If we initially ignore the 149 contents of the grid, the unadjusted probabilities that the pollinator moves either 150 forwards or backwards are p F and p B . I assume that the pollinator's unadjusted 151 tendency to deviate from going forwards is symmetrical, so the chances of moving to 152 the squares on the left or right sides have equal probabilities, both p S , where p F + p B + 153 2p S = 1. However, the probabilities that the pollinator moves into neighbouring 154 squares is also influenced by the pollinator's tendency to switch between habitat 155 types. I assume that the content of its current location is c current , and the contents of the 156 neighbouring squares forward, backward, left and right of the current square are c F , 157 c B , c L and c R respectively. I then assume an adjusted preference m i for entering square 158 i where switching habitat type incurs a reduction r, such that 159 The actual probability a i that an individual moves in direction i is calculated as 163 ) . Using these four probabilities of movement, the 164 pollinator then randomly picks its direction of movement for the period. were of a single thickness: this meant that every cell in a hedgerow was connected via 179 at least one of its edges to another hedgerow cell (see Figure 1 for an example). 180

181
For each environment, a switching reduction r was randomly selected from (0, 1), and 182 a random constant v was randomly selected from (0,1). Single model runs were then 183 calculated using the environment field description, each with systematic alteration of 184 The modelling of the environment was similar to Model 2, but within each 201 environment, r was randomly chosen value within (0,1). For each environment, a 202 basal landscape of fields with hedgerows was created as described in Model 1, and 203 pollinator movement statistics were calculated. Five of the fields were then randomly 204 selected as set-asides, and all the squares within these set-aside fields were filled with 205 wild hedgerow vegetation (see Figure 1 for a sketch of how this was implemented), 206 and pollinator movement statistics were calculated. Five more fields were then filled 207 as set-asides (giving the environment ten set-asides in total), with movement statistics 208 calculated. This addition of five set-aside fields with movement calculations was 209 repeated until fifty of the original fields had been filled as set-asides. The modelling of the environment and calculation of movement was calculated in a 230 similar way to Model 3. However, rather than filling fields as set-asides, the basal 231 environments were altered by cumulatively removing the hedgerows between fields. 232 An individual hedge was considered to be the grid squares designated as hedgerow 233 that fall between two identifiable field seeds, similar to a vertex in a Voronoi 234 tesselation. Movement statistics were calculated for the basal environment and then 235 after every four consecutive hedgerow removals, meaning that movement statistics 236 were calculated after 0, 4, …, 40 hedges were removed (see Figure 2 for a sketch of 237 how this was implemented). Factorial sensitivity analysis (Hamby, 1994) for the 238 effects of p F , p S and r on Model 4 were conducted in a similar way to those described 239 above for Model 3, but by systematically increasing the number of hedgerows 240 removed over the range (0, 4, …, 40) rather than the number of set-asides present.  Although there was an effect of increasing the number of hedgerows removed from 308 the environment upon the maximum distance a forager travelled away from its nest 309 (Table 1), this effect did not yield a easily describable trend (Figure 6a     Overall changes in mean summary statistics of pollinator movement for the different models.

Figure 1
Illustration of how set-asides were added into the landscape.
The left hand panel shows a 101 × 101 cell landscape generated using 30 randomly placed field seeds, where white cells represent agricultural crops and black cells represent wild land or hedgerows. Set-aside fields are added by randomly selecting fields containing agricultural crops, and resetting the cells within the field as wild land. Moving from left to right, each successive panel has two additional agricultural fields redesignated as set-aside. Note that this is a simplified sketch: the results described consider a larger landscape and add more than two fields at each assay point.
The left hand panel shows a 101 × 101 cell landscape generated using 30 randomly placed field seeds, where white cells represent agricultural crops and black cells represent wild land or hedgerows. Hedgerows are removed by randomly selecting adjacent fields, and removing the cells between them that were initially designated as hedgerows. Moving from left to right, each successive panel has four additional hedgerows removed.