Anita. Behav., 1987, 35, 1215-1224
Search paths of foraging common shrews S o r e x a r a n e u s
G R A H A M J. P I E R C E
Culterty FieM Station, Newburgh, Ellon, Aberdeenshire AB4 0AA, U.K.
Abstract. The searching behaviour of common shrews, Sorex araneus, was observed as they foraged for
prey hidden in a grid of wells in a small arena. The search paths are described and their efficiency compared
to that of a simulation model. The shrews searched more efficiently than a random (neutral) model, and
were approkimately as efficient as the 'optimal' model. The efficiency of the model, however, declined
more rapidly than that of the shrews with increasing length of search path. It is probable that the shrews
were able to increase their searching efficiency by remembering where they had searched: the shrews are
shown to have used a simple memory rule, namely alternating right and left turns.
The decisions made by foragers include how to
allocate time to food patches, which prey to eat and
how to locate prey (Pyke et al. 1977). Of these, the
question of how foragers locate prey has received
relatively little attention (see reviews by Krebs et al.
1983; Pyke 1984).
Searching behaviour has several components.
First, some foragers have access to a range of
'foraging modes', e.g. they may switch between sitand-wait and actively searching strategies depending on conditions (Andersson 1981; Janetos 1982).
Second, there is the question of how fast to travel
while searching. Beyond the unilluminatingsuggestion that the optimal strategy ~isto travel as fast as
possible all other things being equal (Norbert 1981;
Pyke 1981), Gendron & Staddon (1983) identified a
possible trade-off between the rate at which prey
are encountered and the forager's ability to detect
them. Third, there is the choice of search path.
Numerous authors have described 'area-restricted
searching', in which the forager turns more frequently or moves more slowly after finding an item
of prey (e.g. Banks 1954; Bond 1980; Carter &
Dixon 1982; Nakamuta 1982).
Some attempts have been made to describe
optimal search paths, usually working on the
assumption that foragers should maximize their
rate of energy intake while searching. The best
strategy depends upon the amount of information
available to the forager. Pyke (1978a) makes the
distinction between 'sensory foragers', which can
detect and orientate to prey from a distance, and
'harvesters' which detect prey only at very close
range. Common shrews, Sorex araneus, have poor
senses of vision, smell and hearing (Pernetta 1973),
and appeared not to be able to detect prey at a
distance under experimental conditions in this
study. They have therefore been regarded as harvesters.
Following from the earlier work of Beukema
(1968) and Cody (1971), Pyke (1978a) constructed
a model in which a forager moved between points
on a grid, each step being a unit move in one of the
four compass directions (north, south, east or west)
relative to current heading. The direction of movement at each step was selected at random, the
probabilities associated with each direction being
derived from a truncated or circular normal distribution. The optimal movement pattern was defined
as that maximizing the number of different grid
points visited. Since all moves were of unit length,
for a forager searching at a constant speed this is
equivalent to maximizing the rate at which prey are
encountered.
Pyke showed that optimal directionality (the
difference between the frequency of forwards and
backwards moves when left and right turns are
equally fi-equent) is higher on bigger grids and for
shorter foraging bouts. Foraging efficiency is
greater if the boundary is non-reflecting (i.e. the
forager does not bounce back at 180~ and if the
forager can remember its past movements and (for
example) alternate left and right turns.
For a harvester foraging in an arena, searching
efficiency will be maximized if it searches systematically, i.e. it visits each resource point only once and
travels by the shortest possible route. For harvesters that do not search systematically, there will be
an optimal set of directional probabilities, which
maximizes the number of different grid points
visited.
In this study, the searching behaviour of corn-
1215
Animal Behaviour, 35, 4
1216
m o n shrews was observed as they h u n t e d for
r a n d o m l y distributed items of prey hidden in a grid
of 225 wells. The searching strategy employed by
shrews u n d e r these conditions m i g h t be applicable
to, say, foraging in a p a t c h of leaf litter. The search
p a t h s arc described, the effects o f prey type, prey
density a n d the capture of prey are investigated,
a n d searching efficiency is c o m p a r e d to that o f a
simple model derived from that in Pyke (1978a).
METHODS
C o m m o n shrews were t r a p p e d near N e w b u r g h ,
Aberdeenshire (2~
57~
and m a i n t a i n e d
in captivity for at least 2 weeks prior to use in
experiments. The shrews were trained to forage in a
plywood a r e n a (0.66 x 0.66 m) with wooden sides
and a Perspex roof. The roof was set a b o u t 3 cm
above the base, providing the shrews with dorsal
contact, i n the base of the a r e n a was drilled a grid
of 225 wells (11 m m diameter, 10 m m deep, 44 m m
between centres), in which prey could be hidden.
Shrews gained access to the a r e n a from a nest box
(containing hay a n d a water bottle) attached to the
middle of one side of the arena. This a p p a r a t u s is
based on t h a t used by B a r n a r d & B r o w n (1981).
T h e shrews were m a i n t a i n e d o n a diet consisting
primarily of blowfly larvae and pupae (Calliphora
spp). D u r i n g experiments, one or two types of prey
were available. Type 1 prey were blowfly pupae.
Type 2 prey were p u p a e inserted into lengths of
plastic drinking straw: they thus h a d a similar
energy content b u t were more difficult to handle.
Preliminary observations indicated t h a t shrews
would a t t e m p t to eat type 2 prey a n d were able to
extract the flesh o f the pupa. All pupae were t a k e n
from a stock culture a n d it is assumed t h a t they h a d
a c o n s t a n t average energy content.
In the first series of experiments, six c o m m o n
shrews were offered the two types of prey at various
total a n d relative densities. The c o m b i n a t i o n s of
n u m b e r s of prey used (type 1 to type 2) were: 10: 10,
10:20, 10:40, 20:10, 20:20, 20:40, 30:30, 40:10,
40:20, 40:40. The order in which the different
c o m b i n a t i o n s were presented was r a n d o m i z e d for
each shrew. In order to test whether searching
b e h a v i o u r would differ if only one type of prey was
available, further experiments were conducted in
which three c o m m o n shrews were offered 30 prey of
one type, the types being alternated in successive
experiments. Table i gives details of the shrews
used in these experiments.
Table I. Shrews used for search path analysis
Captive
number
Sex
7
8
12
16
19
22
30
38
46
Female
Male
Male
Male
Male
Female
Male
Female
Female
Age
Body
weight
(g)
Number of
experiments
Adult
Adult
Adult
Adult
Adult
Subadult
Adult
Subadult
Subadult
10.5
10-5
11.5
12.5
12.0
7'5
12"0
8.0
7.0
11
I1
11
6
10
20
18
9
9
Prior to each experiment, the predetermined
n u m b e r o f prey was distributed in r a n d o m l y
selected wells, a m a x i m u m of one item per well. The
shrew was removed from its cage a n d held in the
nest box for 1 h, without food, before being allowed
access to the arena. Its foraging b e h a v i o u r was then
recorded over 20 min, as timed f r o m first entry into
the arena.
Behaviour in the a r e n a was recorded on videotape. At the end of an experiment, the entrance to
the a r e n a was closed a n d the shrew replaced in its
cage.
A shrew was considered to have searched a well if
its snout passed immediately over the well. Direct
o b s e r v a t i o n of searching shrews revealed dipping
m o v e m e n t s of the snout as a shrew passed over a
well, but this could n o t be discerned from the
videotapes.
The n u m b e r o f prey handled was recorded for
each experiment, as were the coordinates of the
wells from which they were removed. Searching for
prey a n d h a n d l i n g prey were assumed to be
m u t u a l l y exclusive: a l t h o u g h the shrews sometimes
m o v e d to the nest box or to the edge of the a r e n a to
eat, these m o v e m e n t s were n o t included in the
search paths.
E n c o u n t e r rates were estimated as the n u m b e r of
wells containing prey over which a searching shrew
passed, divided by the total searching time. The
p a t h s followed by searching shrews were transcribed o n t o m a p s of the a r e n a a n d subsequently
digitized. The search paths of each shrew were
analysed to determine average travel speed, path
length, the n u m b e r of different wells visited, the
frequencies of turns in different directions, the
b o u n d a r y rule (reflecting or non-reflecting) and
Pierce." Search paths of shrews
efficiency (the number of different wells visited
divided by path length).
To evaluate search-path efficiency, the searching
behaviour of the shrews was simulated using a
Pascal program in which an animal moved around
a square grid of 225 wells. Paths were generated as
series of independent steps, each step being a
movement to an adjacent well. At each step the
animal chose its direction of movement, independently of previous moves, selecting at random from
the set of directions in which shrews actually
moved. The probabilities of moves in the various
directions summed to one but were not necessarily
equal. (Directional probabilities were fixed relative
to the axis of motion of the animal rather than to
the grid.) The rule of movement at the boundary of
the grid was chosen to represent that used by the
shrews (see below).
As a baseline, a neutral or random version of the
simulation was used: in this case, moves in all the
allowed directions were equally likely. The simulation was also used to find the set of directional
probabilities that maximized searching efficiency,
and the efficiency of the shrews was compared with
this 'optimum'.
RESULTS
Description of Searching Behaviour
Over 20 min, shrews typically made a series of
visits to the arena, totalling approximately 5 min,
during which they searched for and consumed
items of prey. Sometimes items of prey were taken
back to the nest box before being eaten; on other
occasions the shrews ate items whcre they were
found. The average speed of movement (over 20
min) while searching varied between 71 and 204
mm/s. Examples of search paths are illustrated in
Fig. 1.
N o n e of the search-path parameters measured
varied in relation to prey density or the types of
prey available for any of the shrews, so all data
were combined for each shrew.
Efficiency
The total distance moved by the shrews while
searching was measured for each visit to the arena,
as a multiple of the distance between the centres of
two adjacent wells in the arena (44 ram). The
distances covered in diagonal movements were
1217
16
12
4
o
d
C
o 16
8
_L
4
0~
0
4
8
12
16 0
4
8
12
16
X coordinate
Figure l. An example of search paths: shrew 46, experiment 4. (a) visits 1 10, (b) visits 11--20, (c) visits 21-30, (d)
visits 31 39. The nest box was at [8,0] and the wells have
coordinates [x,y] where x and y are in the range 1-15.
obtained using Pythagorus' theorem. Converting
to metres, the average distance covered per visit
varied between 0-48 and 3-21 m, and the average
distance covered over 20 min varied between 4.46
and 22.48 m.
On average, the shrews visited between 9 and 50
different wells during each visit to the arena, and
between 78 and 190 over 20 min. Thus they
searched up to 25% of wells per visit, and up to
80% over 20 min.
A measure of the efficiency of searching is given
by the ratio of the number of different wells
searched to the distance travelled while searching.
When distance is measured in multiples of the
distance between adjacent wells, efficiency can take
values between 0 and 1. The average efficiency for
single visits was higher than the average efficiency
over 20 min (Table II), indicating that the shrews
revisited parts of the arena searched during previous visits.
The efficiency of observed paths was negatively
correlated with distance travelled, both for single
visits and over 20 min (Table III). The relationship
between efficiency and path length for single visits
was approximately linear, and was expressed as a
linear regression, for each shrew (Table IV). An
example is shown in Fig. 2.
Animal Behaviour, 35, 4
1218
Table II. Efficiency (the number of different wells visited while
searching divided by distance travelled), over single visits and
over complete experiments
Per visit
Shrew Median
7
8
12
16
19
22
30
38
46
0-84
0.82
0.88
0.94
0-68
0.80
0.81
0.73
0.88
Per experiment
95%, C L
N
Median
95% CL
N
(0.78q3.88)
(0.764).89)
(0-86 0.95)
(0-90-0.96)
(0.64 0.73)
(0.74-0.84)
(0.79-0-85)
(0.63 0.79)
(0.67-0.96)
70
44
46
87
52
94
77
85
185
0-48
0.55
0.63
0.39
0.34
0.52
0.54
0.42
0.40
(0.414).59)
(0-454).73)
(0.46 0.77)
(0.34-0.51)
(0.27-0.52)
(0.44 0.64)
(0.47-0.58)
(0.25 0.54)
(0.21 0.53)
11
11
11
6
9
14
18
9
9
The values given are medians, with approximate 95% confidence limits in brackets (see Campbell 1974 for calculation of
interval estimates for the median). N is the sample size, i.e. the
number of visits or the number of experiments.
Table III. Correlations between efficiency and
distance travelled
Shrew
7
8
12
16
19
22
30
38
46
Single visits
Over 20 min
-0.30
(70)*
-0.93
0.33 (44)*
-0.53
-0.69
(46) . . . .
0-44
-0.77
(87)***
-0.77
-0.63
(52) . . . .
0-91
-0.30
(94)**
-0.89
-0.12
(77)
0.97
0.14 (85)
-0.93
- 0 . 0 0 (185)
-1.00
(11)**
(11)*
(11)
(6)
(9)**
(14)**
(18)**
(9)**
(9)***
Spearman's rank correlation coefficients, with
sample sizes and levels of significance. Significance values are for two-tailed tests.
*P<0.05; **P<0.01; ***P<0.001.
Directionality
D i v i d i n g t h e s e a r c h p a t h s i n t o steps, a step b e i n g
a m o v e m e n t f r o m o n e well to t h e next, t h e c h a n g e
in d i r e c t i o n o f t h e p a t h at e a c h s t e p w a s m e a s u r e d .
F o r w a r d s , b a c k w a r d s a n d s i d e w a y s m o v e s to a d j a c e n t wells m a d e u p 70 7 5 % o f all m o v e s . D i a g o n a l
m o v e s to a d j a c e n t wells a c c o u n t e d for a f u r t h e r
2 0 % o f m o v e s . A s s u m i n g t h a t all s t e p s were
i n d e p e n d e n t , t h e ' relative f r e q u e n c i e s o f different
m o v e s were u s e d to derive p r o b a b i l i t i e s f o r e a c h
k i n d o f m o v e (see T a b l e V).
The paths had the following characteristics.
(1) F o r w a r d s m o v e s ( t u r n i n g a n g l e = 0 ~ were t h e
most common type of movement.
(2) B a c k w a r d s m o v e s were v e r y rare.
(3) L e f t a n d r i g h t t u r n s o c c u r r e d w i t h s i m i l a r
frequencies.
Table IV. Regressions of efficiency on distance travelled for single visits
Shrew
Intercept
a
Variance
a
Slope
b
Variance
b
Sample size
N
7
8
12
16
19
22
30
38
46
0.85
0.84
0.94
0.96
0"80
0.83
0.79
0.73
0.83
6-01x10 4
1"50 x l0 -3
4.15 x 10 -4
9.81x10 5
8.01 x 10 -4
3.53 x 10 4
9.90x10 4
5.97x10 4
1.91xl0 4
_7.45x10-4
- 9 . 3 8 x l0 -4
- 2 . 1 6 x 10 3
-1.75x10 3
- 1"40 x 10 3
9.43 x 10 4
-1.73x10 4
2 . 1 3 x 1 0 -4
6.20x10 5
1.9xl0 6
5.5 x l0 7
1.6x 10-7
5.0x10 8
7.0 x 10 8
1.3 x 10 -7
2.0x10 v
1-8x10 7
1.0xl0 7
70
44
46
87
52
94
77
85
185
Student's t-test for testing the null hypothesis: b - 0 .
P
<0.05
<0.05
<0.05
<0-05
<0.05
Pierce. Search paths o)Cshrews
1 .o
may of course behave quite differently when the
b o u n d a r y is defined only by a change in the density
of food particles rather than by a physical barrier.
d~
~ _ o . 9 o ~8"O o
o
~
o
o
~
co
@
o~
o
o
0"8
o
o
o
0.7
o
o
o
~
o
o
o ~176
o
Oo
o
~
o
Effect of prey capture
~
o
o
o
g
o
LIJ
o
0.6)
%0
001o ~
.
1219
2'o
Distance
I
4'0 ' d0 ' do '10'o '12'0
( 1 unit : 44mm = distance
adjacent wells )
between
i
I
,40
centres
of
Figure 2. An example of searching efficiency: the efficiency of paths for single visits as a function of path length
for shrew 7. The line is the fitted linear regression.
T o test for the occurrence o f area-restricted
searching following the capture of an item of prey,
correlations between the angle turned at each step
a n d the n u m b e r of steps taken since capturing an
item o f prey were evaluated. If an item of prey was
t a k e n back to the nest box to be eaten, all steps
taken until the next item was captured were
discounted from the analysis. The shrews sometimes moved to the edge of the arena to eat,
inevitably resulting in a new direction when they
Table V. The total number of steps, summed over all search paths, for each
shrew, and the proportion of steps that were turns in various directions relative
to the axis of motion of the shrew (directional probabilities)
Shrew Total
7
8
12
16
19
22
30
38
46
2642
1581
1390
2455
3899
3391
4160
3086
4934
P(N)
P(S)
P(W)
P(E)
0.409
0.538
0.371
0.451
0.434
0.369
0-400
0-480
0.494
0-008
0.013
0.016
0.006
0.010
0.019
0.011
0.011
0.007
0.153
0.101
0.166
0.151
0-156
0-168
0.178
0.132
0.132
0-147
0.091
0.172
0.158
0.165
0.159
0.182
0-132
0.122
P(NW) P(NE) P(SW) P(SE)
0,092
0.093
0.079
0-077
0.067
0-092
0.071
0.081
0.102
0-094
0.076
0.094
0.087
0.059
0.073
0-070
0'066
0"087
0.031
0.017
0.027
0-023
0.011
0.027
0.027
0.021
0.012
0.018
0-0t6
0-023
0.018
0-016
0-033
0-022
0-024
0.014
N = n o r t h (i.e. straight ahead), S=south (i.e. backwards), etc.
(4) The average change in direction was close to
0 ~ for all shrews (Table VI).
(5) Overall, directionality took values between
0.35 a n d 0"53 (Table VI).
Behaviour at the boundary
U p o n reaching the edge of the arena, forwards
moves to a n o t h e r well were always impossible, and
diagonal-forwards, left, or right moves were sometimes excluded depending on the angle of
approach. Pyke (1978a) defined two types of
b o u n d a r y behaviour: reflecting a n d non-reflecting.
In the former, the angle of return equals the angle
of incidence. In the latter, the forager simply selects
fi'om those directions still available.
The shrews were 'reflected' in only 3% of
encounters with the b o u n d a r y of the grid (59 o u t of
2146 encounters excluding visits to the nest box).
O f these, only 13 were b a c k w a r d s moves. Shrews
resumed searching. To remove this effect, the first
step after every prey capture was deleted from the
analysis. F o r each shrew, data from all experiments
were combined.
A significant negative correlation was f o u n d for
shrew 30 only ( r = - - 0 - 2 3 , N = 1 9 7 1 , P < 0 0 5 ) .
T h u s there is evidence of area-restricted searching
only for this individual.
The Efficiency of Searching Behaviour
The shrews did not search the arena systematically, which means either that they must be
regarded as not h a v i n g maximized their searching
efficiency, or their failure to search systematically
must be regarded as a constraint on the strategy
used, a n d the optimization problem reconstructed
within these limits. T h e latter course has been
Animal Behaviour, 35, 4
1220
Table VI. Average angle turned between consecutive steps
along a search path, and the average directionality of the
paths
Shrew
Average
Sample
size
Directionality
7
8
12
16
19
22
30
38
46
--0.033
--0.028
0-035
0.023
0.019
-0.037
0'001
--0.003
--0.031
2642
158l
1390
2455
3849
3391
4160
3086
4934
0-400
0-526
0.355
0.445
0.424
0.350
0.389
0.470
0.486
The values given use all data from each shrew. Average
angles are measured in radians. (The average angle is the
angle whose sine and cosine are equal to the mean sine
and mean cosine of the sample angles.) Directionality is
the difference between the probabilities of moving forwards and backwards.
shrews were all more efficient than the neutral
model. (The differences are significant, since the
95% confidence limits do not overlap.)
The best strategy
The efficiency of the simulation was investigated
for a range of sets of directional probabilities, using
the simplifying a s s u m p t i o n t h a t the probability
distribution was symmetrical a b o u t the axis of
m o t i o n of the forager. Visits of 25, 50, 100 a n d 150
steps were simulated, varying each m e m b e r o f the
set of directional probabilities t h r o u g h the range 0 1, a n d repeating each simulation 20 times. The best
strategy for each path length, a n d the associated
efficiencies and directionalities, a p p e a r in Table
VII. Referring back to Table VI, it can be seen that
the shrews followed search paths of lower overall
1"C
0 .e . . . . . . . . . . . . .
7~
followed, using a simulation model to find optimal
search p a t h characteristics.
O n approximately 95% of occasions, shrews
selected directions, relative to current heading,
from the set n o r t h , north-east, east, south-east,
south, south-west, west, north-west. The simulated
animal therefore selected only f r o m these directions at each step. The shrews treated the b o u n d a r y
of the a r e n a as non-reflecting, so w h e n the simulated animal reached the edge of the grid it selected
moves at r a n d o m until the move selected allowed it
to stay in the arena. Average visits to the a r e n a by
the shrews consisted of 30 90 steps, with 4-20 visits
being m a d e over 20 min. Visits of 10, 20 . . . . 100
steps were simulated.
The neutral model
One h u n d r e d visits to the arena were simulated,
10 each o f 10, 2 0 , . . . 100 steps. All directional
probabilities were set equal (i.e. each m e m b e r of the
set took the value 0.125). The efficiency of this
neutral model, as a function of p a t h length, is
described by the linear regression e q u a t i o n with
parameters: intercept, a = 6 . 4 1 x 1 0
I (variance
4 " 7 0 x 1 0 - 4 ) ; slope, b = - 2 . 0 8 x 1 0
3 (variance
9 x 1 0 - 8 ) ; regression t-test, b < 0 at P < 0 " 0 5 ,
dJ'= 98.
C o m p a r i n g this regression with those obtained
for the shrews (Figs 3 a n d 4), it can be seen t h a t the
9
] .........................
................
0"6
0.4
c~
t.u
-...
0"2
~ohl
I
I
40
Distance
I
810
I
(1 u n i t = 4 4 r a m = d i s t a n c e
adjacent
wells )
I
120
between
I
160
centres
of
Figure 3. Comparison of the efficiency of (l) shrew 38 with
that of (2) the neutral model. The solid lines are
regressions of efficiency on path length and the dotted
lines are 95% confidence limits. Shrew 38 was one of the
two least efficient shrews, but is clearly more efficient than
the model.
~ t.o
2~
~ o.a
g ~ o. e
R
o~ o.4
-~ o . ~
~
0
2'0
Distance
4'0
6TO ' 8~0
( 1 unit = 44mm=distance
adjacent
wells
between
centres
loo
of
)
Figure 4. Regressions of efficiency on path length for all
nine shrews. Also shown are regressions for the neutral
model and systematic searching.
Pierce. Search paths of shrews
1221
Table Vll. Directional probabilities, directionality and efficiency for the best
strategies for paths of various lengths (P(NE)=P(NW), P(E)=P(W),
P(SE) = P(SW))
Probabilities
Number
of steps
P(N) P(NE) P(E) P(SE) P(S) Directionality Efficiency
150
100
50
25
0'67
0'67
0"67
0"71
0
0
0
0
0"17
0-17
0"17
0-14
0
0
0
0
0
0
0
0
0"67
0"67
0"67
0"71
0'660
0"754
0'818
0"935
See Tables V and VI for definitions.
directionality t h a n predicted by this simulation,
a n d would therefore be expected to be less efficient.
F o r short visits (25 steps), optimal directionality
is higher t h a n for longer visits. The efficiency o f any
one strategy inevitably declines with increasing
path length. The simulation was r u n 1000 times,
using the optimal strategy for longer visits, to
derive the regression of efficiency on p a t h length:
intercept, a = 9 ' 5 4 x 10 ~ (variance 5 . 5 0 x 10-s);
slope, b = - 2 " 5 2 x 10 -3 (variance 1.43x 10 8);
regression t-test, b < 0 at P < 0-05, df= 998.
C o m p a r i n g this regression with t h a t for a shrew
(shrew 7, Fig. 5), it can be seen t h a t the efficiencies
of the model a n d the shrew are similar over a range
of p a t h lengths. However, the simulation is more
efficient over short distances, a n d less efficient over
long distances, t h a n the shrew: the slopes of the two
regression lines are significantly different (d test,
d = 3 ' 9 1 , P < 0 . 0 0 1 ) . Performing the same test on
data from the other shrews, a significant difference
was f o u n d for seven out of the other eight shrews.
The simulation was repeated using the set of
probabilities derived from the observed frequencies
of moves for the shrews. The simulation was run
100 times using directional probabilities from
shrew 7. The relationship between efficiency and
p a t h length for the simulated paths is given by a
linear regression with p a r a m e t e r values: intercept,
a = 8 . 1 1 x 10 i (variance 3.11 x 10 4); slope,
b = - 2 . 1 2 x 10 3 (variance 6-0 x 10-8); regression
t-test, b < 0 at P < 0"05, dr= 98.
This simulation was less efficient t h a n the 'best'
strategy, but also less efficient t h a n shrew 7,
especially for longer paths (Fig. 6). Similar results
were o b t a i n e d using data from the other shrews.
Thus, failure to use the ' o p t i m a l ' set o f directional
probabilities is not the only source o f discrepancy
between the shrews and the model.
1"0
1"0
'~- 0-8
0-8
~
0.6
0.4
0.4
0.~
o
0.~
klJ
w
f
Distance
2'0
i
410
I
6JO
( 1 unit = 44mm = distance
adjacent wells )
i
810
between
i
100
c e n t r e s of
Figure 5. Comparison of the efficiency of (1) a moderately
efficient shrew, number 7, with that of (2) the 'optimal'
model. The solid lines are regressions of efficiency on path
length and the dotted lines are 95% confidence limits.
Shrew 7 was arbitrarily chosen for this comparison, as
being a typical shrew.
I
I
20
Distance
I
I
40
q
i 0
I
J
80
( 1 unit = 44mm ; distance
adjacent wells )
I
I
100
J
~)/
1 0
I
i
140
b e t w e e n c e n t r e s of
Figure 6. Comparison of the efficiency of (1) a moderately
efficient shrew, number 7, with that of (2) a simulation
using directional probabilities derived from data for
shrew 7. The solid lines are regressions of length and the
dotted lines are 95% confidence limits. Shrew 7 was
arbitrarily chosen for this comparison, as being a typical
shrew.
Animal Behaviour, 35, 4
1222
Reasons Jor the Jailure of the simulation
There are several ways in which the search paths
of shrews m a y differ from the assumptions of the
model.
(1) P a t h characteristics m a y change with increasing time spent in the arena. Frequencies of turns in
the eight m a i n directions were calculated separately
for the first, second, third, etc., visits to the arena,
s u m m i n g over all experiments for each shrew. Chisquared tests indicated significant heterogeneity
between visits for seven out o f nine shrews,
a l t h o u g h evidence o f a systematic trend was found
only for shrew 30. F o r this animal, average directionality was positively correlated with visit
n u m b e r ( S p c a r m a n ' s rank correlation coefficient,
r = 0 . 9 0 5 , N = 9 , P < 0-05).
(2) P a t h characteristics m a y differ in different
parts o f the arena, e.g. at the edge, or in response to
local variations in prey density. Frequencies o f
turns in the eight main directions were calculated
separately for m o v e m e n t s u n d e r different circumstances (see Table VIII): m o v e m e n t s from a nonedge point, m o v e m e n t s immediately after hitting
the edge at right angles, m o v e m e n t s immediately
after hitting the edge diagonally, a n d m o v e m e n t s
following a move along the edge.
Sets of directional frequencies for each class of
m o v e m e n t were c o m p a r e d using chi-squared tests.
(The comparisons excluded frequencies for directions that were unavailable or t o o k zero values in
one or b o t h classes.) Significant differences
between at least some pairs of classes were found
for all shrews. One obvious p a t t e r n (see Table VIII
for data on shrew 30; very similar results were
o b t a i n e d for all shrews) was for shrews to move
straight ahead relatively more frequently following
a straight-ahead m o v e along the edge t h a n following a move from a non-edge point, even allowing
for there being fewer available directions in which
to move. In other words, the shrews showed edgeseeking behaviour. A l t h o u g h this result is contrary
to the assumptions of the simulation, edge-seeking
would tend to reduce searching efficiency (directionality away from the edge was even lower t h a n
suggested by the overall values in Table VI).
(3) Successive moves m a y not be independent:
the shrews m a y have increased their searching
efficiency by avoiding areas they had previously
searched. One simple m e m o r y rule that would
increase searching efficiency is to alternate right
and left turns. Looking at the sets of directional
frequencies for moves following left, right and
Table VIII. Total number of moves and directional probabilities for shrew 30
Class
Total
P(N)
P(S)
P(W)
P(E)
P(NW)
P(NE)
P(SW)
P(SE)
1
2
3
4
5
6
7
8
9
I0
I1
2095
183
64
88
587
813
781
788
512
281
1789
0.26
---0"69
0.75
0-23
0.21
0.39
0"12
0.29
0.01
0-02
0
0
0.01
0-01
0-01
0.01
0
0.01
0-01
0.23
0.44
0.23
0.42
0-03
-0.22
0-08
--
0'09
0.02
0-03
0.03
0.15
0.03
0.04
0' 16
0.13
0.02
-0.02
0.06
0.01
0-08
0.03
0-02
-0"18
0.38
0.09
0.22
0'05
0.26
0"09
0-39
0.19
0.04
0.26
0.70
0.04
0-09
0.07
0"09
0.28
0.05
0-78
-0-04
-0.09
0.11
0'08
0-33
0.06
0.01
0-06
0.01
0
0.06
0.02
Directional probabilities (see Table V for definition) were derived separately for different
classes of move. ( indicates non-available move.) Classes: (1) moves from a non-edge
point, (2) moves following a right-angle encounter with the edge, (3) moves following a
clockwise diagonal encounter with the edge, (4) moves following an anti-clockwise diagonal
encounter with the edge, (5) moves following a clockwise move along the edge, (6) moves
following an anti-clockwise move along the edge, (7) moves from a non-edge point
following a right turn, (8) moves from a non-edge point following a left turn, (9) moves from
a non-edge point following a forwards move, (10) moves from a non-edge point following a
diagonal move, (11) moves from a non-edge point following a non-diagonal move.
1223
P&rce. Search paths o f shrews
straight-ahead moves (see Table VIII for a typical
example), it is apparent that the shrews did tend to
alternate left and right turns, and there was no
directional bias following straight-ahead moves.
Non-independence of successive moves is also
apparent when comparing moves following diagonal moves and those following non-diagonal
moves: diagonal moves were relatively more frequent following a diagonal move.
DISCUSSION
The search paths of shrews in the arena showed
several features that Pyke's (1978a) simulation
suggests should be found: the shrews turned left
and right with approximately equal frequency,
rarely turned through 180 ~, and showed sensible
('non-reflecting') behaviour at the boundaries of
the grid. In c o m m o n with Pyke's simulation, the
shrews were more efficient when searching over
short distances than over longer distances.
Evidence of a change in searching behaviour
following the capture of an item of prey was found
for one shrew only. However, an increased rate of
turning following prey capture will be adaptive
only if prey are patchily distributed. In the present
study the distribution of prey was homogeneous,
which may account for the absence of changes in
turning rates following prey capture by most of the
shrews.
The shrews did not search the arena systematically. Assuming that search paths are a series of
independent steps in randomly selected directions,
the shrews performed more efficiently than the
neutral simulation of random searching behaviour
and were approximately as efficient as the optimal
simulation.
However, the efficiency of the simulation declined more rapidly than the efficiency of the shrews
as path length increased. Further analysis of directional frequencies revealed spatial and temporal
variation in the pattern of movements, but
although contrary to the assumptions of the simulation this cannot account for the superior efficiency of the shrews.
Evidence that the shrews searched more efficiently by remembering where they had searched is
provided by their tendency to alternate left and
right turns. This feature of search paths has
previously been reported for thrushes (Smith
1974a, b) and bumblebees (Pyke 1978b).
Is there some other model against which the
shrews' efficiency could be compared? If shrews
remember where they have searched, the optimal
strategy depends upon the length of memory.
Given a sufficiently long memory, systematic
searching should result. If shrews respond to local
depletion of prey, the optimal strategy will depend
upon the area sampled by the shrews in order to
assess local prey density. While both these ideas
suggest further experiments which might lead to a
better understanding of the mechanisms involved
in searching behaviour, it is apparent that no useful
functional model will be possible until the range of
strategies available to shrews is known.
ACKNOWLEDGMENTS
This work was supported by postgraduate studentship awards from the Natural Environment
Research Council and the University of Aberdeen,
and was supervised by Dr John Ollason. Dr Nigel
Dunstone, Dr Ian Patterson, Ian Robinson and
two anonymous referees provided helpful comments on the manuscript.
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(Received 8 May 1986," revised 22 August 1986; MS.
number: 2853)