1
Appendix S2. Detailed description of the movement model
2
3
We simulated movements of individuals using the model developed by Cattarino et al.
4
(2013). This model simulates movement of individuals as a first-order, correlated random
5
walk (Kareiva & Shigesada 1983). First-order correlated random walk models assume that
6
the direction of each move depends on the location and direction of the last move (Kareiva &
7
Shigesada 1983). These models also can be extended to incorporate mechanisms for the
8
response of movements to landscape patterns (Gardner & Gustafson 2004). We modified
9
slightly the model developed by Cattarino et al. (2013) to allow each individual to adopt two
10
movement modes: foraging movements conducted within foraging areas and searching
11
movements conducted between foraging areas (see Fig. S3 for an example of a simulated
12
movement).
13
Every time step, individuals moved each movement step by covering a certain
14
distance, which depended on the movement mode. In a foraging movement step, individuals
15
moved an Euclidean distance of one cell (df). In a searching movement step, individuals
16
moved an Euclidean distance, ds, chosen at random from a truncated exponential distribution,
17
e   d s
f (d s ) 
(Vogel et al. 2009), with rate parameter β, expected searching distance
1  e d max
18
equal to E(ds), and maximum searching distance dmax equal to 50 cells. We calculated the
19
parameter β for different values of E(ds), by setting the 50th percentile equal to E(ds).
20
Individuals covered the distance ds by taking cell-to-cell moves between adjacent
21
cells. An individual could move into one of the eight cells surrounding its current location.
22
The probability, Pi, of moving to cell, i, was
1
Pi 
i w j
8
(S2.1)
 w
k 1
k
k
23
where Φi is the probability of taking a particular turning angle (i.e. by moving to cell i), in the
24
absence of land-cover preference, and wj is the habitat preference parameter for land cover
25
type j (i.e. habitat or non-habitat). The denominator of equation (S2.1) acts as a normalizing
26
constant and ensures the probabilities, Pi, add to one.
27
In order to introduce a directional bias caused by the persistence of moving in the
28
same direction of the last move, we assumed that turning angles, θi, between successive cell-
29
to-cell moves followed a truncated normal distribution, ranging between -180 and +180, with
30
mean zero and variance  turn . The probability, Φi, to take a particular turning angle by
31
moving to cell i, in the absence of any habitat selection and given the direction of the
32
2
previous move, was expressed as a function of  turn such that
2
i 
 i  22.5
 f ( ,
 
2
turn
)d
(S2.2)
 i 22.5
33
where θi is the turning angle to cell i relative to the previous movement direction and
34
2
2
f ( ,  turn
) the normal probability density function, with mean zero and variance,  turn
, equal
35
to one, i.e. θ ~ N(0,  turn ). The turning angles to move to the centers of the eight
36
neighborhood cells could only take the discrete values of 0°, 45°, 90°, 135°, 180° (-180°), -
37
135°, -90° and -45°. Therefore, equation (S2.2) calculates Φi as the integral of the turning
38
angle probability density function 22.5° either side of the discrete angle for a move to the
39
2
center of each cell, with the distribution truncated at 180°. When  turn = 1 the direction of
40
successive movement steps, in absence of habitat preference, is correlated (i.e. straight
2
2
41
2
movements). The higher the value of  turn , the lower is the degree of correlation between
42
successive movement steps, i.e., the movement path approaches a random walk.
43
Individuals continued to take cell-to-cell moves until they had covered the Euclidean
44
distance in a particular mode, and they had found a habitat cell. Therefore, the actual distance
45
da, moved through cell-to-cell moves, depended on the spatial distribution of the habitat. By
46
forcing individuals to move a whole Euclidean distance, during a movement step in each
47
mode, we assumed that the distance was an evolutionary trait that species had evolved in
48
response to forces affecting individual fitness, such as density-dependent dynamics (Rousset
49
& Gandon 2002).
50
The number of foraging and searching steps was calculated, respectively, by dividing
51
the actual distance moved through cell to cell moves, da, in each mode, by the Euclidean
52
distance moved (df or ds). In doing so, we assumed that individuals that move large distances
53
during searching, as part of their life histories, did not incur any additional fitness cost,
54
because they have evolved behaviors to reduce the risk of mortality during the search (e.g.,
55
they move faster) (Zollner & Lima 2005). We modelled landscape, and foraging area,
56
boundaries as a torus, with the bottom row adjoining the top row and the rightmost column
57
adjoining the left-most column.
3
58
References
59
Cattarino, L., McAlpine, C.A. & Rhodes, J.R. (2013) The consequences of interactions
60
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Kareiva, P.M. & Shigesada, N. (1983) Analyzing insect movement as a correlated random
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Vogel, R.M., Hosking, J.R.M., Elphick, C.S., Roberts, D.L. & Reed, J.M. (2009) Goodness
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Zollner, P.A. & Lima, S.L. (2005) Behavioral tradeoffs when dispersing across a patchy
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