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Keywords:

  • habitat management;
  • hunting behaviour;
  • prey conservation;
  • prey visibility;
  • search theory;
  • vegetation height

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Predators hunting by sight often search for prey from elevated perches or hovering positions above the prey habitat. Theory suggests that prey visibility depends strongly on predator perch height and distance, but their quantitative effects have not been experimentally tested in natural habitats.
  • 2
    We estimate for the first time how prey visibility depends on predator perch height, distance and vegetation height in an open natural habitat, based on visibility measurements of two targets: a mounted bird and a graduated plate, from five perch heights (0·2–8 m) and six distances (5–120 m).
  • 3
    For both targets, their proportion visible increases strongly with observer perch height and proximity. From the lowest perch, visibility of the target bird declines to < 5% beyond 20 m distance, but 40% of it remains visible from the highest perch even at 120 m.
  • 4
    Models of predator search suggest that hunting success and predation rate depend strongly on the prey detection rate, which is expected to decline with distance r approximately as rd. However, d, the distance decay parameter, has not previously been empirically estimated in natural predator habitats. For distance – prey visibility relationships similar to those observed here, we find a realistic estimate of d to be 2·1–2·4.
  • 5
    The results demonstrate the crucial role of relative perch and vegetation height for prey visibility, which is of relevance for habitat management. The strong increase of prey visibility with predator search height suggests that removal of predator perches can improve the survival of endangered prey populations in open habitats. Conversely, perch preservation or addition can improve habitat suitability for some predator species where perches are rare or lacking.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Search tactics can strongly influence predator hunting success and prey risk with population consequences for both parties, and are therefore of considerable ecological interest. Predator search models relate hunting success to aspects such as search mode, movement pattern, search height, habitat characteristics, prey density and detectability (e.g. Andersson 1978, 1981a; Huey & Pianka 1981; Rice 1983; Ehlinger 1989; O’Brien et al. 1989; Tye 1989; Getty & Pulliam 1991; Kramer & McLaughlin 2001). Empirical studies have explored predator search and tested theoretical predictions (e.g. Andersson 1981b; Moreno 1984; Carlson 1985; Gendron 1986; Ehlinger 1989; Sonerud 1992; Getty & Pulliam 1993; Kramer & McLaughlin 2001), but several important aspects of predator search remain to be investigated.

Predators of many kinds search visually for prey from elevated perches or hovering positions above the prey habitat, including fish (e.g. Ehlinger 1989; McLaughlin & Grant 2001), reptiles (e.g. Moermond 1979; Losos 1990) and birds (e.g. Preston 1957; Robinson & Holmes 1982; Moreno 1984; Sonerud 1992; Cresswell 1996; Jenkins 2000; Leyhe & Ritchison 2004). Many predators use pause-travel tactics, moving some distance between successive perches or other stable pause positions (e.g. Andersson 1981a; Robinson & Holmes 1982; Newton 1986; Ehlinger 1989; O’Brien et al. 1989; Tye 1989; Losos 1990; Getty & Pulliam 1991, 1993; Sonerud 1992; Cresswell 1996; Poole et al. 2007; reviewed by Kramer & McLaughlin 2001). Searching from a fixed position increases the predator's ability to discover prey and can have several other advantages (see Kramer & McLaughlin 2001). For example, searching from a perch can greatly reduce energy costs compared to hovering in birds (e.g. Pennycuick 1989). Perching at an elevated site is also part of anti-predator vigilance of many animals (e.g. Wright et al. 2001).

Theory and tests show that perch height and distance can strongly influence prey detectability and predator hunting success (e.g. Andersson 1981a; Carlson 1985; Getty & Pulliam 1991, 1993; Sonerud 1992; Widén 1994; Malan & Crowe 1997). In an aviary experiment with two perch heights, Carlson (1985) found that the probability of prey detection increased with predator–prey proximity and perch height. However, although prey visibility, the proportion of the prey visible, is an important determinant of prey detectability (see Theory below), there is no quantitative analysis of prey visibility in relation to predator search height and distance in open natural habitats (for forest, see Post & Götmark 2006). Such quantitative data are needed to better understand predator search behaviour and ecology, including habitat choice, space use and activity patterns, as well as anti-predator tactics in prey (Caro 2005). This knowledge can also be important for the management of threatened populations.

Here we measure prey visibility as a function of predator perch height, distance from prey, vegetation height and microtopography in coastal pastures. Predators in this habitat often use perches when searching for prey, and predation risk is often high for eggs and young of many species (e.g. Grant et al. 1999; Whittingham & Evans 2004; Wallander et al. 2006). In addition, non-lethal effects of predators may often intensify their impact on prey populations (reviewed by Preisser et al. 2007; Cresswell 2008), for instance if prey species avoid otherwise suitable habitat near predator perches. Based on the visibility measurements we also estimate how prey detection will depend on predator search height and distance. Theory suggests that prey detection rate decreases with distance r approximately as rd, where d is the distance decay parameter (see below). Providing a first empirical estimate of d in natural habitats is therefore another purpose.

theory

The probability of visually detecting a distant target is proportional to the solid angle Ω it subtends in the observer's visual field (e.g. Koopman 1980). For a given prey at distance r, the probability that the predator will detect it in a short time interval of length dt is given approximately by dt K/rd. The quantity K/rd, called prey detection intensity (or instantaneous rate of detection; see Koopman 1980; Andersson 1981a; Getty & Pulliam 1991), is composed of two main parts: (i) prey detectability K, which depends on aspects such as light, atmospheric conditions, sensory ability of the predator, and size, shape, visible area, coloration, background matching, movements and sounds of the prey; (ii) the exponential distance dependence r−d of the solid angle Ω subtended by the prey in the visual field of the predator (Fig. 1), where d is the distance decay parameter. Sensitivity analysis suggests that d is a major determinant of predator-prey encounter rate (Getty & Pulliam 1991).

image

Figure 1. Relationships between perch height h, prey – perch (base) distance x, and predator–prey distance r, for a prey upon a perfect plane (left of perch), and in a natural habitat (right). On a perfect plane, the visual (solid) angle Ω subtended by the prey in the view of the predator decreases approximately quadratically with distance, as r−2. In the natural habitat, vegetation and uneven ground partly conceal the prey. This reduces the solid angle of the visible part of the prey faster than as r−2, depending on perch height (see main text).

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For a fully visible prey, the distance decay rate of Ω is inverse quadratic, r−2, for purely geometric reasons (Fig. 1). For terrestrial or benthic prey in open habitats, the exponent or distance decay parameter d in the relationship rd is likely to be > 2, probably between 2 and 3, or even > 3 (Andersson 1981a). The reason is that in most natural habitats, Ω also decreases because concealing vegetation and uneven ground reduce the proportion of the target that is visible (Fig. 1). How much d is larger than 2 in natural habitats is unknown. Because its magnitude is expected to be important for predator hunting success, predation rate and prey risk, d is of primary interest for empirical tests (Andersson 1981a; Getty & Pulliam 1991).

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

habitat characteristics

We studied seven coastal pastures in SW Sweden (between 56°55′ N; 12°21′ E and 57°24′ N; 12°07′ E) 17–24 May 2005. This is about halfway through the season when waders breed in this habitat, two months after the spring start of vegetation growth, and about the time when cattle are released on the pastures. Vegetation height thereafter usually varies little during most of the summer and fall, owing to a balance between growth and grazing. The study areas were flat, with short vegetation typical of coastal pasture. Altitude differences were usually < 2 m over distances of 0·5 km or more. The vegetation consisted mainly of grasses (Poaceae) and a few tufts of sedge (Juncus sp.). We estimated grass sward height to the nearest centimetre using a measuring stick for every 5 m along a 120-m transect starting from each perch. Sward height was where 80% of the vegetation within 1 dm of the stick was below that height (direct measurement method, Stewart et al. 2001). An approximate measure of transect topography was taken at the same points, as the lowest visible reading of the measuring stick (below which it was concealed by uneven ground) for a 1·8-m (eye height) observer with binoculars standing at the base of the perch.

prey visibility

We measured target (prey) visibility T (proportion of target visible, ranging from 0 to 1) in full daylight from artificial perches in the pastures. To achieve a realistic range of perch heights at each transect, we used seven relatively flat and open pastures that were accessible by a lorry with skylift (3 pastures) or had a bird-watching tower at least 7 m high (4 pastures). Target visibility was measured along 120 m transects from each perch (skylift or tower) at 5, 10, 20, 40, 80 and 120 m distances, and from each of five perch heights: 0·2, 1, 2, 4 and 8 m. Within a pasture, the different transects did not cross and were separated by an angle ≥ 45° measured from the starting point. Transects were subjectively chosen as representative for the site. Because accessibility differed between sites, so did the number of transects, which totalled to 20 (Morups Tånge 1, Galtabäck 2, Getterön 3, Fyrstrandsfjorden 6, Båtafjorden 3, Ölmevalla 3 and Tjolöholm 2).

To estimate prey visibility we used two targets: a rectangular plate for high accuracy of visibility readings, and a more natural target, a taxidermic mount of ringed plover Charadrius hiaticula, 17 cm in length and 7 cm from belly to crown (no legs). The proportion visible of the bird was estimated subjectively in 10% steps. The plate, 10 cm high and 12·5 cm wide, was divided into 10 alternating black and white horizontal lines that were each 1 cm high and easy to see also from the longest distances. We placed the targets vertically on the ground, long side facing the perch, and estimated for every distance and perch height the proportion of target visible. For accuracy, we used binoculars (10×) up to 40 m, and a spotting scope (20–60×) at longer distances. To eliminate inter-individual variance only one of us (JW) did all target visibility readings. To avoid unnecessarily complex statistical analyses (Johnson 1999; Murtaugh 2007), we mainly present estimates with standard errors, plus pair-wise comparisons that show the consistency of the effects of height and distance.

We estimated the distance decay of prey detection by calculating, for each perch height and predator-target distance r, the product T r−2 between target visibility T and the geometrical distance-dependent decay (r−2) of the solid angle Ω subtended by the target (Fig. 1). Multiplication by T takes account of the added distance decay in Ω that is caused by reduced prey visibility because of obstructing vegetation and topography. We can then estimate the exponential distance decay parameter d of predator search models (see Theory). This is done by nonlinear least squares regression (de Levie 2004) of the parameters k and d in the exponential model k rd that produces the best fit to the observed values of T r−2. The regression parameter k is then a component of prey detectability K (see Theory).

The probability of visually detecting a target is proportional to the solid angle it subtends in the observer's visual field (e.g. Krendel & Wodinsky 1960; Rubin & Walls 1969; Treisman 1975; Koopman 1980). This is the case as long as the angle does not exceed a few deg2 (see e.g. Treisman 1975), a requirement that is fulfilled here. For the larger of the two targets (1·25 × 1·00 dm) at the shortest perch-target distance (5 m), the proportion of the observer's visual sphere subtended by the target is < 1·25/4 Π 502 ≈ 0·00004, corresponding to a solid angle of about 1·7 deg2.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

habitat characteristics

Mean sward height of the 20 transects was 5·4 ± 1·6 cm (SD of the 20 means), the range of transect means was 2·9–9·3 cm, and the range of the 480 individual vegetation measures was 0–20 cm. The mean of the topographic measures from the 20 transects was 11·2 ± 3·0 cm (SD of the 20 means), the range of transect means was 5·3–15·1 cm, and the range of all 480 measures was 0–88 cm.

prey visibility

As theoretically expected in open habitats (Andersson 1981a), target visibility T increased greatly with predator perch height and proximity (Fig. 2). For short distances (up to 10 m) most of the increase with perch height took place already from 0·2 to 2 m. At longer distances there was considerable increase in target visibility also from 2 to 4 and 4 to 8 m. The quantitative effect of perch height can be seen, for each of the six distances in Fig. 2, as the increase in visibility that occurs with vertical progression from the lowest (0·2 m) to the highest (8 m) perch height (ordinate). The increase in visibility with perch height is very consistent. None of the curves in Fig. 2 cross, and in each of the 24 pair-wise comparisons that can be done for each target type by moving, for a given distance, from one perch height to the next higher, target visibility increased.

image

Figure 2. The visibility of both target types (bird and plate) increases strongly with perch height, and decreases with increasing predator–target distance. The curve for each of the five perch heights is based on means ± SE for the 20 transects (see Methods). Standard errors can be multiplied by 2·1 to obtain approximate 95% confidence limits, but for visual clarity this has not been done in the figures.

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For a given perch height, targets became less visible at increasing distance (Fig. 2) because of concealing vegetation and uneven ground. The reduction in visibility with increasing distance was clear: among the 50 pair-wise comparisons that can be done for the two targets in Fig. 2 by moving, for a given perch height, from one distance to the next longer, target visibility decreased in 45 cases, and increased (marginally) in only 5 cases.

At long distances, vegetation and topography that exceed the stature of the target are expected to make it invisible from the perch. This expectation is corroborated by scatter-plots of visibility in relation to distance and vegetation height. As an example, Fig. 3 shows how the visibility of the bird target depends on vegetation and distance for 8 m perch heights. Similar relationships apply also at lower perch heights, but distance is then relatively more important, as the target is more concealed by vegetation and uneven ground.

image

Figure 3. Scatter-plot of target visibility from 8 m perch height, in relation to perch-target distance and vegetation height, for the bird target (data points represent transects; see Methods). At long distances (80 and 120 m), target visibility is usually low or zero if the vegetation is higher than the target (7 cm). At the shortest distances (20 m and less), the target is visible also in higher vegetation. (For clarity, the result for distance 5 m is not shown; it is similar to that for 10 m, with 100% visibility for most transects.)

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At the lowest perches, the visibility of both targets declined steeply to low values with increasing distance, for instance to < 20% at 40 m for the bird target and perch height ≤ 2 m (Fig. 2). For the plate target, visibility was generally higher and declined less strongly with increasing distance (Fig. 2). From the highest perch (8 m), target visibility at 120 m was still > 60% for the plate and 40% for the bird, demonstrating the importance of search height for prey visibility at long distances.

Visibilities of the two targets were highly correlated and changed with perch height and distance in similar fashion (Fig. 2). For each of the 20 transects we calculated the bird – plate correlation, based on the 30 pairs of visibility values (0·2–8 m perch height and 5–120 m distance). Each of these 20 correlation coefficients was positive (P < 0·001, two-sided sign test), with range 0·81–0·92 and mean 0·885 ± 0·007 (SE). The main difference between the two targets was a consistently lower visibility of the bird. In each of the 30 pair-wise comparisons that can be done with different combinations of perch height and distance (Fig. 2), the plate target was more visible than the bird. At the longest distances the bird target was largely invisible from the lowest perches, but visibility increased greatly with perch height (Fig. 2).

distance decay parameter

For each of the five perch heights and the two target types, we estimated (as described in the Methods) the distance decay parameter d and the regression parameter k that together produced the best fit of k/rd to the function T/r2 at the six distances where T was measured for each search height (Fig. 2). The 10 estimates of d range between 2·13 and 2·39 (Table 1). The regressions produced good fits of k/rd to the function T/r2, as shown by the high R2 values.

Table 1.  Estimated parameters d and k in nonlinear least squares regression of the function k/rd that gives the best fit to T/r2 (observed target visibilities T in Fig. 2, multiplied by the corresponding geometric distance decay factor r−2*). R2 is the coefficient of determination. See main text for further explanation
Perch height and target typedkR2
  • *

    Distance in Fig. 2 (abscissa) is between target and perch base. Predator – target distance is r = (x2 + h2)1/2, where x is perch – target distance and h is perch height (Fig. 1).

0.2 m, bird2·390·380·9992
″ plate2·130·570·9995
1 m, bird2·280·800·9992
″ plate2·170·950·9998
2 m, bird2·371·380·9998
″ plate2·181·181·0
4 m, bird2·371·641·0
″ plate2·261·510·9998
8 m, bird2·372·180·9999
″ plate2·171·411·0

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

predator perch height and prey visibility

The results show that prey visibility increases greatly with predator search height, helping explain why high perches offer a great search advantage for predators of partly concealed terrestrial prey in open habitats, such as avian predators of insects and small rodents in grassland (e.g. Sonerud 1992; Widén 1994; Malan & Crowe 1997; Leyhe & Ritchison 2004), and piscine predators of benthic prey (e.g. McLaughlin & Grant 2001). Attacking from a higher position can also give the predator several other advantages, such as greater prey capture success (e.g. Götmark & Post 1996; Jenkins 2000).

The great increase in prey visibility with search height at long distances is important, because it increases the number of potential prey that can be discovered from the perch. Predators are therefore expected to discover increasing proportions of prey at longer distances with increasing search height (see also Andersson 1981a; Sonerud 1992). In accordance, 10 of 12 field studies found a positive correlation between predator perch height and distance to prey attacked (reviewed by Sonerud 1992; also see Malan & Crowe 1997).

The advantage of greater prey visibility at longer distances from high perches may be reduced, however, by lower capture success for long strikes (Sonerud 1992; Malan & Crowe 1997). And increased search height also increases predator–prey distance, which counteracts the effect of increased prey visibility and tends to reduce prey detectability. Therefore, many different and partly counteracting factors may influence optimal search height (Andersson 1981b). Controlled experimental tests with different perch heights and standardized prey, for example, combining and extending the approaches of Carlson (1985) and Sonerud (1992), can help clarify these aspects.

Visibility followed similar trends in relation to perch height and distance in both targets, but the bird target was less visible. Compared to the plate, the bird is lower (10 vs. 7 cm), and in lateral view has more of its area at low levels. This makes it more likely to be concealed by vegetation and uneven ground as distance increases, the distance decay of its visibility therefore being more rapid (greater values of d, Table 1).

target detection in relation to distance

The distance dependence of target detection is an important aspect of the predator search process (e.g. Andersson 1981a; Getty & Pulliam 1991, 1993). Developing search theory for naval operations, Koopman (1980) found an inverse cubic law, r−3, to be a useful approximation for the distance decay of the solid angle subtended by flat targets on a plane, such as the wake of ships at sea. The relationship, however, may be rather different for prey animals in vegetated natural habitats (Fig. 1, and Andersson 1981a). We therefore estimated the distance decay parameter d that provides the best fit of the function k/rd to the distance relationship of the solid angle Ω subtended by the visible part of the target, T/r2. The estimates range from 2·13 to 2·39. With predator search heights, habitats and prey types for which visibility – distance relationships are similar to those found here, a distance decay parameter d of magnitude 2·1–2·4 therefore appears realistic. For similar prey types in less even habitats with higher vegetation, such as clear-cuts studied by Sonerud (1992, 1997), larger values of d are likely to apply.

The parameter d at all five perch heights was greatest for the bird target (Table 1), as expected because it is smaller than the plate target, and therefore declines more rapidly in visibility with increasing distance (Fig. 2). As also expected when prey visibility decreases with reduced predator perch height (Fig. 2), so does the regression parameter k (Table 1), which reflects the general level of target visibility (regardless of distance r, the effect of which is taken account of by rd).

the importance of habitat and vegetation

The relationships found here seem likely to apply reasonably well in a range of open habitats with similar proportions between predator search height, prey size, vegetation height and topography. The relationships may then apply approximately not only for predators searching from trees or other physical perches, but also for swimming or flying predators hovering above the substrate of the prey (see Andersson 1981a; Ehlinger 1989; O’Brien et al. 1989; McLaughlin & Grant 2001). To some extent they may apply also for predators travelling at some speed above the substrate. However, prey detection ability is probably lower for a travelling predator (e.g. Friedman 1975; Andersson 1981a; Kramer & McLaughlin 2001).

Our results show that when prey (target) stature is in the same range as vegetation height, the latter may be of critical importance for prey visibility. Increased predator perch height can then render prey much more visible, also at long distances (Fig. 2). On the other hand, if prey are much taller than the vegetation they will usually be visible above it in an even habitat, rendering perch height less important. In contrast, prey that are much smaller than grass sward height are only visible from almost directly above. Such situations may instead favour hunting by ear (Rice 1982, 1983; Bye et al. 1992), which in turn can favour lower search height and continuous travel rather than pause-travel search (Andersson 1981a; Rice 1983).

Dense forest vegetation may often conceal prey completely, even at relatively short distances. There is much variation between forest types in the height profile of foliage density (e.g. MacArthur & MacArthur 1961), but there may often be a relatively short range beyond which a potential prey is out of sight from most or all search heights. This can have important consequences for predators. For instance, the visibility of a prey then need not increase with predator search height, but may even decrease. Predators may then be more successful if searching from low or intermediate rather than the highest perches, and sparrowhawks Accipiter nisus tend to do so (Newton 1986; also see Post & Götmark 2006). Lower prey visibility may also in part explain why owls that locate prey by sounds are often important avian predators of terrestrial small rodents in forests, whereas raptors usually dominate this niche in open habitats (see del Hoyo et al. 1994, 1999). Predators hunting by ear can locate sounds even if the prey is visually concealed. Hunting terrestrial prey by ear is therefore likely to favour searching from low or intermediate levels (Andersson 1981a; Rice 1983), as often done by forest owls (Norberg 1970; Bye et al. 1992; Abbruzzese & Richison 1997).

management implications

Our results suggest that availability of sufficiently high perches can greatly increase predator hunting success and prey risk, and many observations and experiments show that man-made as well as natural perches attract hunting predators (e.g. Janes 1984; Sonerud 1992, 1997; Kay et al. 1994; Widén 1994; Cresswell 1996; Malan & Crowe 1997; Wolff et al. 1999; Sheffield et al. 2001; Leyhe & Ritchison 2004; Dzialak et al. 2007). Scarcity of perches may sometimes render an area unsuitable for breeding in raptors (Malan & Crowe 1997). Addition of perches, even if only a few metres high (Fig. 2), can therefore substantially improve habitat suitability for some predator species in areas where perches are rare or lacking (e.g. Widén 1994; Chandler et al. 1995; Malan & Crowe 1997; Sonerud 1997; Sheffield et al. 2001).

Predator preferences for perches can in turn lead to higher predation risk in their vicinity (e.g. Erikstad et al. 1982; Berg et al. 1992; Kay et al. 1994; Söderström et al. 1998), which may therefore be avoided by prey. For instance, birds nesting in open habitats tend to avoid forest edges, probably partly for this reason (reviewed by Caro 2005). In the coastal pastures studied here, nesting waders avoid the vicinity of even low, c.1 m high fence posts and stonewalls, often used by perching hooded crows (Wallander et al. 2006). In addition to increasing predation risk, predator perches may therefore reduce areas of suitable habitat for prey species such as ground-nesting birds in open landscapes. These and other non-lethal effects of perching predators may have strong negative impact on prey populations (reviewed by Preisser et al. 2007; Cresswell 2008).

The results in Figs 2 and 3 show that vegetation of similar height as the prey has a strongly concealing effect at long distance from even the highest perches, and at all but the shortest distances from low perches. Grazing regimes that lead to suitable sward height may therefore be important for conservation of threatened grassland birds (e.g. Ausden 2007; Tichit et al. 2007), by reducing predation and increasing reproductive success. But sward height can only partly counteract the effect of perches: even in twice as high vegetation, prey may still be visible at short to medium distances from perches (Figs 2, 3), removal of which can therefore reduce predation risk (also see Quinn & Cresswell 2004).

testing

The effects of perch height need to be further tested experimentally, by manipulating the availability of perches of various heights and recording the consequences for predators and prey as regards hunting success, predation risk and population consequences. Such experiments can also permit additional tests of prey visibility in relation to perch height and distance in natural habitats. Other systems that may offer suitable experimental conditions are lizards, and fishes searching (hovering) for benthic prey. Hovering height in fishes may be possible to control in aquaria or ponds using plexiglass plates at various levels, constraining from above the maximum hovering height of the fish. Such tests may also be combined with use of artificial prey of known conspicuousness, to achieve better control of prey detectability. The quantitative effect of prey movements on detectability is another poorly known aspect where experimental data would be welcome.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Authors thank Craig Benkman, Donald Blomqvist, Frank Götmark, Jörgen Johnsson, Donald Kramer, Peter Lindberg, Geir Sonerud, Allen Spaulding and an anonymous referee for helpful suggestions that improved the manuscript, and funding agencies FORMAS (JW) and the Swedish Research Council (MA) for financial support.

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  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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