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The role of numerical competence in a specialized predatory strategy of an araneophagic
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spider
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Short Title: Spider numeracy
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Ximena J Nelson1*
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Robert R Jackson1,2
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Zealand.
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Mbita Point, Kenya.
School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch, New
International Centre of Insect Physiology and Ecology, Thomas Odhiambo Campus, P.0. Box 30
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*Correspondence: Ximena Nelson, School of Biological Sciences, University of Canterbury,
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Private Bag 4800, Christchurch, New Zealand.
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Email: ximena.nelson@canterbury.ac.nz
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Phone: 64-3-3642987 extn 4050
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Fax: 64-3-3642590
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Although a wide range of vertebrates have been considered in research on numerical competence,
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little is known about the role of number-related decisions in the predatory strategies of
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invertebrates. Here we investigate how numerical competence is expressed in a highly specialized
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predatory strategy adopted by the small juveniles of Portia africana when practicing communal
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predation, with the prey being another spider, Oecobius amboseli. Two or more P. africana
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juveniles sometimes settle by the same oecobiid nest and then share the meal after one individual
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captures the oecobiid. Experiments were designed to clarify how these predators use number-related
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cues in conjunction with non-numerical cues when deciding whether to settle at a nest. We used
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lures (dead spiders positioned in lifelike posture) arranged in a series of 24 different scenes defined
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by the type, configuration and especially number of lures. On the whole, our findings suggest that
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P. africana juveniles base settling decisions on the specific number of already settled conspecific
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juveniles at the nest and express a preference for settling when the number is one instead of zero,
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two or three. By varying the size of the already settled juveniles and their positions around the nest,
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we show that factors related to continuous variables and stimulus configuration are unlikely
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explanations for our findings.
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Keywords: numerosity discrimination, numerical ability, prototype matching, communal predation,
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araneophagy, Salticidae
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Introduction
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Understanding the nature and origin of numerical competence is a primary objective in human and
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animal cognitive science (Carey 1998, 2001; Giaquinto 2001; Feigenson et al. 2004; Shettleworth
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2009). Primates have been prominent in the literature on animal numerical competence, this trend
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being consistent with a tradition of associating numerical competence with advanced human
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language-based cognition (Dehaene 2001; Haun et al. 2010). Yet the once widely accepted view
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that numerical competence is uniquely human and fundamentally dependent on verbal language has
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now been supplanted by a rapidly expanding literature (Wesley 1961; Davis and Memmot 1982;
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Brannon 2002; Cantlon and Brannon 2007; Slaughter et al. 2011) on the numerical competence of
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pre-verbal human infants (hereafter, simply ‘infants’) and on non-human animals (hereafter, simply
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‘animals’), including a wide range of vertebrate species as well as examples from insects (Chittka
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and Geiger 1995; Dacke and Srinivason 2008; Gross et al. 2009; Rezinikova and Ryabko 2011).
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Although research on infants has been based on spontaneous response to number-related
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cues (Wynn 1992, 1998), much of the early animal work depended on extensive training (e.g.,
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Matsuzawa 1985; Boysen and Bernston 1995; Pepperberg 2006) and this encouraged an impression
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that, for animals, numerical competence is a hard-earned ability that is adopted only as a last resort
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(Breukelaar and Dalrymple-Alford 1998; Seron and Pesenti 2001). However, there has been a shift
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toward considering spontaneous expression of numerical competence by animals (Uller et al. 2001;
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Flombaum et al. 2005; Hanus and Call 2007; Wood et al. 2007; Agrillo et al. 2008; Dadda et al.
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2009) and this has, in turn, increased interest in understanding how numerical competence functions
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for particular animals in their natural environments (Hager and Helfman 1991; McComb et al.
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1994; Lyon 2003; Kitchen 2006; Hunt et al. 2008; Benson-Amram et al. 2011).
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In the context of animal-centred research on the expression of numerical competence,
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optimal foraging theory (OFT) has an interesting history. OFT began in a way that could be
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described as decidedly uninterested in cognition (Pyke et al. 1977; Stephens and Krebs 1986). For
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example, terms such as ‘strategy’ have always been prevalent in the OFT literature, but often with
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disclaimers to the effect that nothing cognitive was intended. Yet, from the beginning, OFT was
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relevant to hypotheses about cognitive decision-making and especially numerical cognition
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(Shettleworth 2009). In particular, predictions from OFT (Charnov 1976) often imply considerable
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capacity on the part of the animal to make relative number and relative quantity judgments (see
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Church and Broadbent 1990; Boysen and Bernston 1995; Uller et al. 2003; Brannon 2006; Castelli
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et al. 2006). Animals may sometimes express a go-for-less strategy (e.g., Hoare et al. 2004).
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However, there are also many examples of a go-for-more strategy (e.g., Boysen and Bernston 1995;
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Beran 2008; Beran et al. 2008). These results imply that optimal foraging includes judgments of
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relative number (see Shettleworth 2009).
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Less is known about animals adopting strategies in which specific numbers are innately
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salient and responded to spontaneously (see Tardif et al. 2002). Yet, the distinction between relative
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number judgment and choosing a specific number becomes important when specifying categories of
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numerical competence (Gelman and Gallistel 1978; Dehaene 1992; Gallistel and Gelman 2000).
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Kaufman et al. (1949), for example, distinguished between counting, subitizing and estimating.
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True counting is an iterative process based on assigning a distinct tag to each item, with tags being
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symbols, tokens or physical referents. Counting achieves more than simply detecting a difference
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between two numbers, as it implies that the individual doing the counting has access to
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representations of ordinal and cardinal numbers (Gelman and Gallistel 1978), a phenomenon which
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has been demonstrated especially clearly in primates after varying degrees of training with Arabic
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numerals (Boysen and Bernston 1989, 1995).
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Subitizing is a mechanism by which an individual can, without having access to a
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representation of a specific number, nonetheless make decisions corresponding to specific numbers
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(Trick and Pylyshyn 1994; Railo et al. 2008), with the maximum typically being 3-4 (Cowan 1998,
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2000, 2010). The mechanisms underlying subitizing appear to be related to individuating objects
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(Trick 2005) and assigning them to a limited number of object files (Kahneman et al. 1992) in
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working memory (Baddeley 1986, 2003; Owen 2004; Awh et al. 2007; Anderson et al. 2011;
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Fougnie and Marois 2011). The individual is assumed to form a representation of occupied object
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files, but does not necessarily use these object files as representations of numbers (Trick and
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Pylyshyn 1994; Xu and Spelke 2000; Hauser and Carey 2003).
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When ‘estimating’, an individual might represent an analogue magnitude, or a characteristic
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called the ‘numerousness’ of a set, or the individual might derive a relative number judgment by
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making comparisons (Kobayashi et al. 2004; McCrink and Wynn 2004). This system, known as the
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‘accumulator model’ or ‘analogue-magnitude system’, is used for estimating how different large
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numbers compare to each other (Meck and Church 1983; Gallistel and Gelman 2000) and does not
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require that the individual have access to either a representation of a specific number or to any
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particular information pertaining to a specific number (Le Corre and Carey 2008). This model is
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based on the premise that memory is an inherently noisy medium. According to the accumulator
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model, when non-verbal representations of numerosity are coded into memory, variability increases
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in proportion to the square root of the number targeted for memory (Weber’s Law), with this
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accounting for the seeming discontinuity (≤ 4) in the capacity of animals to perceive number
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directly. However, the accumulator model does not distinguish between the ability to count and
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summation of variables that covary with the counted objects, such as volume or area (Beran 2001).
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Although there has been research on numerical competence in auditory (Starkey et al. 1983),
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tactile (Davis et al. 1989; Riggs et al. 2006) and chemical (Carazo et al. 2009; Thomas and
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Simmons 2010) channels, most of the literature on numerical competence pertains to vision
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(Dehaene 1992; Burr and Ross 2008; Brady et al. 2011). It is striking that the literature on animal
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numerical competence does not include salticid spiders, as these small predators have intricate
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vision-based behaviour and the capacity to classify prey by sight into multiple categories (Nelson
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and Jackson 2011; Harland and Jackson 2001). Salticids belonging to the genus Portia are of
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particular interest because they have often been subjects in research related to animal cognition
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(Jackson and Cross 2011; Jakob et al. 2011).
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Here we consider the role of number-related cues in an especially intricate predatory
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strategy adopted by the small juveniles (body length 1.5-3.0 mm) of P. africana in Kenya (hereafter
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‘Portia’) when preying on Oecobius amboseli (hereafter ‘oecobiid’), a small spider species (adult
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body length, 2-3 mm) that builds tent-like silk nests on boulders, tree trunks and the walls of
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buildings (Jackson et al. 2008).
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A typical oecobiid nest is sparsely woven and only about 5 mm in diameter, with the
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resident oecobiid inside usually remaining visible, although less distinct than when outside. When
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disturbed by a potential predator, the oecobiid runs away from its nest in a straight line and then
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suddenly freezes, but eventually walks back and re-enters the nest. Portia juveniles exploit this
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behaviour by first settling near to the nest and eventually, with its palps and forelegs, initiating
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intermittent probing and striking of the nest silk. Portia may capture the oecobiid as it comes out of
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the nest in an attempt to flee. Alternatively, the oecobiid may escape, but Portia waits at the nest
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and captures it upon its return (Jackson et al. 2008).
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Although most salticids are solitary predators, Portia often practises communal predation,
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especially when the prey is an oecobiid. In typical sequences, two Portia settle alongside each other
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at an oecobiid’s nest and when one Portia captures an oecobiid, it is joined by the other to feed
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alongside it. For the critical decision of whether to settle at an oecobiid nest, variables known to
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matter include whether a nest is present and occupied by an oecobiid instead of a similar-sized
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Portia, whether another Portia is already settled near the nest and is facing toward or away from the
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nest (Jackson and Nelson 2012).
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That number-related cues might be salient is suggested because more than two Portia
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feeding together or settled together alongside the same oecobiid nest are rarely seen (Jackson et al.
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2008). Taking into consideration the non-numerical cues already known to be important (Jackson
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and Nelson 2012), the hypothesis we consider is that Portia bases decisions on the number of
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Portia settled at a nest inside which there is an oecobiid, with the settled Portia being in a particular
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orientation to the nest and within a specific distance range from the nest.
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As in any study designed to consider the role of number-related cues (Clearfield and Mix
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1999; Hurewitz et al. 2006; Franks et al. 2008), we need to consider possibility that non-numerical
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variables alone suffice to explain our findings. Here we consider three alternative hypotheses, each
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of which specifies particular confounding variables: continuous variables such as the area in a scene
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filled by salient already settled Portia (‘Portia-stuff hypothesis’); the amount of free space
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remaining alongside a nest (‘limited-space hypothesis’); the configuration in which already settled
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Portia are arranged at the nest (‘canonical-configuration hypothesis’).
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Methods
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All test subjects were F2-generation juveniles (body length, 2.5 mm) of Portia africana from
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laboratory culture (standard rearing procedures; for details, see Jackson et al. 2008). Here we focus
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on the details that pertain specifically to numerical cues, with only brief descriptions being provided
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for experimental detail shared with the previous study (Jackson Nelson 2012).
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As our goal was to investigate Portia’s innate, spontaneous decisions, we ensured that
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neither the test spiders nor their parents had prior experience with oecobiids. By basing our
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experiments on the reactions of test spiders (living Portia) to stationary lures (dead spiders
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positioned in lifelike posture in ‘scenes’), we avoided confounding variables that can arise when
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testing predators with living prey (see Nelson and Jackson 2011). We minimized the possibility of
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residual odour cues by making lures from spiders that had been kept in ethanol. After being
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positioned in a scene, the lures were sprayed with aerosol plastic for preservation.
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Portia lures were made from juveniles belonging to three size categories (body length: small
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1.5 mm, medium 2.5 mm, and large 3.0 mm). Test spiders were always medium and, unless stated
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otherwise, Portia lures were also medium. The oecobiids used for making lures were field-collected
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adult females (body length 2.5 mm).
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In experiments, each treatment was based on presenting test spiders with a scene. For each
scene, lures were centred in a different arrangement on the flat surface of a 50 mm-wide rubber
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stopper (hereafter referred to simply as the ‘disc’). Scenes were defined by: the number of lures
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present; the type, configuration and orientation of the lures; whether Portia lures were small,
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medium or large; whether there was a spider present in an artificial nest, and the distance between
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lures and the nest (see Table 1). To create artificial nests (diameter 5.0 mm), silk was taken from a
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nest built by an oecobiid that had been kept in the laboratory without prey for the previous 7 days
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and then draped over a lure. No individual test spider, lure or nest was used more than once (N for
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each scene was 100 or 200; see Table 1) and all tests were conducted between 0800 and 1200 hours
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(laboratory photoperiod, 12L-12D, lights on 0700 hours).
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For making a test chamber (for details see Jackson and Nelson 2012), the disc was first
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inserted into a hole centred on bottom of a Petri dish so that it protruded 2 mm into the dish. The lid
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was then put on the Petri dish, creating the test chamber with the scene enclosed. The dish was then
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turned vertical and held in place by clamping the distal end of the disc to a retort stand (lowest point
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of Petri dish 200 mm above bench). After a 5 min settling period within a glass tube, a test spider
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was allowed access to the test chamber through an entry hole directly across from the centre of the
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scene (i.e., through the ‘lid’ of the Petri dish). Tests began when the test spider walked into the test
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chamber.
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When a scene included one or more lures positioned outside the nest, with or without a lure
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inside, the ‘already settled Portia’ lures outside were referred to simply as ‘Portia’, with ‘test
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spiders’ being used to differentiate between dead (lures) and live Portia. Depending on the scene,
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three distances of Portia lures from the nest were applicable. These were defined by distance from
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the centre of the already settled spider’s body and the centre of the nest: close (8 mm), far (16 mm)
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and very far (24 mm). ‘Evenly spread around a nest’ refers to scenes in which Portia were
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positioned so as to make an equilateral triangle with the nest at the centre (e.g., Scene 8, Table 1).
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Side by side ‘on an arc’ refers to scenes in which two or more Portia were positioned on an arc with
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each Portia equidistant from the centre of the nest. When there were three Portia on an arc, the
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Portia in the centre was directly below the nest, on an imaginary line drawn straight down from the
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centre of the nest, one of the other two spiders was on an imaginary line running through the centre
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of the nest 45o to the left and the other was on an imaginary line running through the nest 45o to the
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right (e.g., Scene 9, Table 1). There was no Portia in the middle position when only two Portia
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were present, but the left and the right individuals were positioned the same as when three were
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present. ‘In a horizontal line’ refers to scenes similar to placement on an arc except that the Portia
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formed an imaginary straight line alongside the nest instead of an arc centred on the nest (e.g.,
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Scene 16, Table 1). ‘Lined up one behind the other’ refers to scenes in which two or three Portia
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were positioned so that the first individual faced the nest, the second faced the first from the rear
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and the third faced the second Portia, with the first Portia being close to the nest, the second being
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far from nest and, if present, the third very far from nest (e.g., Scene 10, Table 1).
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Tests ended and the test outcome was recorded when the test spider settled (i.e., when the
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test spider walked on to the disc and, without first attacking a lure or a nest, became quiescent for 2
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min), attacked (i.e., without first settling, the test spider leapt, lunged at or struck at a lure or a nest),
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or else neither settled nor attacked within the 60 min test period. Whenever an attack was seen, the
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target was recorded.
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We carried out pairwise comparisons between different scenes using 2 x 2 contingency
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tables (chi-square and Fisher exact tests (FET) of independence). Bonferroni adjustments for
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multiple comparisons were applied and, unless stated otherwise, all results that were significant
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remained so after adjusting alpha. In all comparisons between scenes there was no significant
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difference for the number of attacks, so while we have left the data in Table 1, we have omitted
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attacks from further discussion. We used Kruskal-Wallis tests to analyse the latency to settle in
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different scenes (Dunn’s multiple comparisons used for pairwise comparisons).
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Results and Discussion
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Are test spider decisions influenced by whether the number of Portia already settled close to the
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nest is one or two and, when two, by how the two are spaced with respect to the nest?
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Significantly more test spiders settled when there was only one Portia close to the oecobiid-
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occupied nest (Scene 2) instead of one at each end (Scene 3) (χ2 = 88.62, P < 0.001), two on an arc
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at one end (Scene 4, χ2 = 48.20, P < 0.001) or two one behind the other at one end (Scene 5, χ2 =
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41.70, P < 0.001). Instead of a go-for-more rule, test spiders appear to be adopting a go-for-one
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rule.
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However, when only one Portia was present (Scene 2), the available space near the nest was
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greater than when two Portia juveniles were present equidistant from the nest (Scenes 3 & 4). This
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suggests that our findings might be explained by the limited-space hypothesis (i.e., when deciding
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whether to settle, test spiders attend to available space instead of the number of already settled
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conspecific juveniles present).
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Using the maximum possible distance at which a test spider might position itself from the
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nearest Portia as an index of available space, the predicted trend from the limited-space hypothesis
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is that more test spiders will settle with Scene 4 or Scene 5 than with Scene 3. Additionally, the
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number of test spiders that will settle with Scene 5 will not be significantly different from the
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number that settle with Scene 2, and more test spiders should settle with Scene 1 than with Scene 2.
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Yet none of these predictions were corroborated by our findings. The number of test spiders that
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settled when two Portia were at opposite ends of a nest (Scene 3) was not significantly different
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from that when the two Portia were on an arc (Scene 4) (χ2 = 0.66, P = 0.417) or lined up at one end
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(Scene 5) (χ2 = 1.95, P = 0.163). The number that settled with Scene 5, however, was significantly
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less than the number that settled with Scene 2. Moreover, as shown in the previous study (Jackson
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and Nelson 2012), more test spiders settled with Scene 2 (one Portia present) than with Scene 1
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(Portia absent), despite Scene 1 offering more space near the nest. This combination of findings
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suggests that, when confronted with Scenes 1-5, test spiders did not attend to available space near
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the nest and instead made settling decisions on the basis of the specific number (0, 1 or 2) of Portia
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at the nest, with one being the favoured number.
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Are test spider decisions influenced by whether the number of Portia close to the nest is two or three
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and, when three, by how the Portia are spaced with respect to the nest?
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Significantly fewer test spiders settled when three Portia were evenly spaced around the nest
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(Scene 8) than when two Portia were spaced maximally apart (Scene 3) (P < 0.001, FET). Fewer
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test spiders settled when there were three (Scene 9) instead of two (Scene 4) Portia positioned on an
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arc at one end of the nest (χ2 = 30.54, P < 0.001). However, contrary to the limited-space
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hypothesis, the number of test spiders that settled when three Portia were evenly spaced around the
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nest (Scene 8) was not significantly different from how many settled when three Portia were on an
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arc at one end of the nest (Scene 9) (P = 0.053, FET).
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When Portia were lined up at one end of the nest, the number of test spiders that settled
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when two were present (Scene 5) was not significantly different from the number that settled when
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three were present (Scene 10) (χ2 = 0.40, P = 0.529) (i.e., in this instance, response to two Portia
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was comparable to response to three). Significantly more test spiders settled when three Portia were
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lined up (Scene 10) rather than evenly spaced around the nest (Scene 8) (P < 0.001, FET) or on an
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arc at one end of the nest (Scene 9) (χ2 = 46.02, P < 0.001), despite the number of Portia in each of
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these scenes being three.
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These findings are as predicted by the limited-space hypothesis because there is more free
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space near the nest in Scene 10 than in Scenes 8 or 9. Yet we know from the previous study
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(Jackson and Nelson 2012) that distance from the nest is important. In Scenes 8 and 9, each Portia
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was close to the nest, but each Portia in Scene 10 was at a different distance from the nest. If test
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spiders ignore Portia that are very far from the nest, then Scene 10 would have been perceived as a
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scene with two, not three, Portia. Other comparisons (see below) allow us to consider this
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hypothesis.
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Are test-spider decisions influenced by the distance between Portia and the nest?
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Significantly more test spiders settled when two Portia that were at opposite ends of a nest were
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very far from (Scene 11), instead of close to (Scene 3), the nest (χ2 = 19.48, P < 0.001).
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Significantly more test spiders settled when three Portia that were spaced evenly around a nest were
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very far from (Scene 12), instead of close to (Scene 8), the nest (P < 0.001, FET). Likewise, more
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test spiders settled when three Portia that were on an arc at one end of the nest were very far from
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(Scene 13), instead of close to, the nest (Scene 9) (χ2 = 55.44, P < 0.001).
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Evidently, when some Portia are very far from the nest and others are close, only those that
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are close influence the test spiders’ settling decisions. When three Portia were present, significantly
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fewer test spiders settled when all three were close to the nest (Scene 9) than when the centrally
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placed Portia was very far from the nest and the other two Portia were close to the nest (Scene 14)
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(χ2 = 22.34, P < 0.001). When the Portia on the left and right were very far from nest and the
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centrally placed Portia was close to the nest (Scene 15), significantly more test spiders settled than
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when all three were close to the nest (Scene 9) (χ2 =154.60). Similarly, significantly more test
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spiders settled (χ2 =47.21, P < 0.001) when two of the three Portia were very far away (Scene 15),
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instead of only one being far away (Scene 14).
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The number of test spiders that settled when there were no Portia present at a nest (Scene 1)
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was not different from when three Portia were surrounding, but very far from, the nest (Scene 12)
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(χ2 = 3.28, P = 0.070) and compared with when there were three Portia on an arc at one end, but
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very far from, the nest (Scene 13) (χ2 = 0.35, P = 0.552).
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When there were three Portia, two of which were very far from the nest (Scene 15), test
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spider decisions were not significantly different from when there was a single Portia close to a nest
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(Scene 2) (χ2 = 0.87, P = 0.351). Additionally, when there were two Portia close to a nest and a
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third present but very far from the nest (Scene 14), test spider decisions were not different from
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when there were only two Portia close to the nest (Scene 4) (χ2 = 0.48, P = 0.487).
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This combination of findings implies that, when test spiders are making settling decisions,
Portia that are very far from the nest are ignored.
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For test spiders, is distinguishing three from two Portia based on discriminating a triangle from a
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straight line?
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When test spiders distinguished Scene 3 from Scene 8 and Scene 4 from Scene 9, they distinguished
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scenes containing two from scenes containing three Portia. Here we consider whether this might be
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a distinction between a straight line (defined by two objects) and a triangle (defined by three
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objects). This more or less corresponds to a hypothesis that, when subitizing, individuals pre-
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attentively discriminate two from three objects not by representing number per se but instead by
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identifying canonical configurations, one object corresponding to a dot, two to a straight line and
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three to a triangle (Mandler and Shebo 1982). This hypothesis suggests that three objects on a
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horizontal line will not be distinguished from two objects (see Trick and Pylyshyn 1994), yet the
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number of test spiders that settled was significantly more when there were only two Portia (Scene
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4) rather than three Portia in a horizontal line (Scene 16) (P < 0.001, FET). Additionally, test-spider
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settling decisions when three Portia were in a horizontal line (Scene 16) were not significantly
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different from test-spider decisions when the scene was otherwise identical except that the three
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Portia were positioned on an arc, thereby defining three points on a virtual triangle (Scene 9) (P =
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0.204, FET).
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Perhaps the canonical-configuration hypothesis can be saved by proposing that, while not
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defining an actual triangle, three objects in a straight line at least defines a potential for a triangle
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(see Dehaene 1992; Trick and Pylyshyn 1994), but the more straightforward conclusion is that the
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mechanism underlying Portia’s discrimination between scenes with three versus two already settled
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Portia is based on information pertaining to numbers.
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Are the test-spider decisions influenced by the orientation of the Portia that is already settled at the
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nest?
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In the previous study (Jackson and Nelson 2012), where there was never more than one Portia at
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the nest, test spider settling decisions varied depending on the orientation of the Portia at the nest.
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Attending to orientation appears to be an additional level of information to process when making
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settling decisions. Here we investigated whether test spiders use this additional information when
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confronted by a scene in which more than one Portia is present.
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Test-spider decisions when two (Scene 17) or three (Scene 18) Portia were facing away
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from the nest were not significantly different from when two (Scene 3) or three (Scene 8) Portia
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were facing the nest (two: χ2 =1.13, P = 0.287; three: P = 0.667, FET). These findings suggest that
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orientation, which matters when only one Portia is seen at a nest, is ignored when there are two
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Portia at a nest. We might account for this difference by proposing that Portia is subject to capacity
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limitations that prevent processing information about orientation at the same time as processing
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information about number, but other comparisons (see below) raise doubts about capacity
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limitations being this severe. An alternative hypothesis, which seems more likely, is that test spiders
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are more strongly motivated to process information about the orientation of already settled Portia
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when the preferred number of them (one) is present and less strongly motivated when the number is
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two.
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Besides being influenced by seeing Portia at a nest, are test spiders influenced by seeing and
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identifying the nest inhabitant?
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Test spiders are more inclined to settle when they see specifically an oecobiid in the nest (Jackson
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and Nelson 2012). Under the added load of representing object identity, we might expect numerical
349
competence to suffer (see Schmitt and Fischer 2011), yet we found that the identity of the spider in
350
the nest influenced settling decisions even when two Portia were present. Significantly more test
351
spiders settled when the nest was occupied by an oecobiid (Scene 3) than when the nest was
14
352
unoccupied (Scene 6) (χ2 = 9.00, P =0.003) or occupied by a Portia juvenile instead of an oecobiid
353
(Scene 7) (P < 0.001, FET).
354
355
Are test spider decisions influenced by the size of the already settled Portia?
356
Animals have considerable ability to make decisions on the basis of perceived quantities expressed
357
as continuous variables instead of numbers (e.g., Rodríguez and Gamboa 2000; Beran 2010;
358
Krusche et al. 2010; Rodríguez and Gloudeman 2011), and one of the challenges in research on
359
numerical competence is to minimize the influence of confounding continuous variables (Lipton
360
and Speke 2003; Brannon et al. 2004; Hurewitz et al. 2006; Beran et al. 2008). Communal
361
predation on oecobiids occurs only among Portia juveniles within a specific size range (Jackson et
362
al. 2008), enabling us to test for the influence of a continuous variable (Portia stuff) on spider
363
settling decisions by varying the size of already settled Portia over this range.
364
We found that, when there was one Portia in a scene, the number of test spiders that settled
365
were not significantly different depending on whether the Portia was large (Scene 19) or small
366
(Scene 20) (χ2 = 0.51, P =0.476). This was also the case when there were two (Scene 21 vs. Scene
367
22: χ2 = 0.11, P = 0.744) or three (Scene 23 vs. Scene 24: none settled) Portia at the scene. These
368
data suggest that the number of Portia at a scene, not continuous variables, affected decisions.
369
370
Does Portia estimate or subitize?
371
According to the accumulator model we would predict that the number of already settled Portia at a
372
scene affect the latency to settle. In fact, we did find a significant positive relationship between the
373
number of already settled spiders at a scene and latency to settle (H20 = 37.24, P = 0.011), but
374
where we would predict specific effects, for example between Scenes 2, 4 and 9, we found instead
375
that the median times to settle (Table 1) did not differ.
376
377
Being accurate within the range 0-3, Portia’s settling decisions might suggest subitizing, as
this mechanism typically has an upper limit of 3 or 4 (Cowan 2010). However, Portia’s settling
15
378
decisions are also based on considerable classifying of objects in addition to number, such as the
379
distinction between oecobiids and conspecific individuals (even when seen through nest silk),
380
orientation and distance of the already settled Portia with respect to the nest, and nest occupancy. It
381
has been argued that the attention required for extensive classifying is incompatible with subitizing
382
(Treisman and Gelade 1980; Tomonaga 2008; Xu and Chun 2009), which seems to operate at mid-
383
level visual processing (Butterworth 1999, 2008) that functions primarily in individuating items and
384
assigning them to object files (Pylyshyn 1989, 2001) pre-attentively or without making heavy
385
demands on attention (Piazza et al. 2002, 2011; Railo et al. 2008; Burr et al. 2010).
386
387
Does Portia count?
388
When orientation to and distance from the nest were most effectively positioned, as previously
389
determined (Jackson and Nelson 2012), we found different numbers of Portia to be ranked by test
390
spiders when eliciting settling. The strongest stimulus was a single Portia, there being a sharp drop
391
in the number of test spiders that settled when no Portia were present (zero) and in the presence of
392
one more Portia (two). The fewest test spiders settled when there were three Portia present,
393
although it might be more accurate to say ‘more than two’ instead of ‘three’ as we have no evidence
394
to consider whether three is distinguished from four or any other number larger than three.
395
The rationale for the design of our experiments was an understanding of a specific context in
396
which a particular predator deploys a specialized communal predatory strategy. Each individual
397
Portia was tested only once, with no individual having prior experience with the prey or the
398
experimental set up. These methods were appropriate for our objective of determining whether
399
specific numbers are innately salient to this predator based on its specific predatory strategy. This is
400
rather different from typical objectives in the literature on the numerical competence of animals,
401
which aim to test more general-purpose number-based decisions, such as go-for-more rules (Beran
402
2008; Beran et al. 2008).
16
403
Number appears to be a salient cue when Portia makes settling decisions, but there is no
404
basis for proposing that Portia’s decisions are based on anything especially close to true counting.
405
For example, true counting is based on representing numbers as properties of sets that stay the same
406
even when the identity of the particular objects in a set change, but the expression of numerical
407
competence we have investigated seems to be linked tightly to objects with highly specific
408
characteristics (i.e., other Portia already settled at an oecobiid nest).
409
410
Does Portia use prototype-matching when making number-related decisions?
411
Although numerical competence appears to be important in Portia’s communal predatory strategy,
412
variables related to number appear to be one of an assortment of variables that influence settling
413
decisions. Objects belonging to three categories seem to be identified, a nest and two spider
414
categories: the prey (the oecobiid) and other Portia, and how these objects are arranged with respect
415
to each other is also pertinent. We can not rule out that Portia’s numerical competence is expressed
416
in the context of classifying scenes, with Portia’s settling decisions being based on how closely the
417
scene being viewed matches a prototype scene.
418
Prototype-matching is better known as a mechanism by which individuals assign items to
419
non-numerical categories (Rosch 1975; Rosch et al. 1976) and it is in the context of predatory
420
versatility (Curio 1976) that non-numerical categories have been considered in salticid research.
421
Versatile predators adopt conditional predatory strategies, with each individual deploying different
422
capture tactics depending on prey type. By adopting different behaviour in encounters with different
423
prey, these predators reveal the salient prey categories underlying their classification schemes.
424
Species from the genus Portia have a large repertoire of innate prey-specific capture tactics (Nelson
425
and Jackson 2011) possibly based on matching prey exemplars against a collection of prototypes
426
(Jackson and Cross 2011).
427
428
In the context of communal predation by Portia on oecobiids, we may have evidence of an
innately salient category, but in this instance the most relevant exemplars and prototype may be
17
429
scenes instead of individual prey items or individual prey categories. That Portia will decide to
430
settle may become increasingly more likely as exemplar-prototype resemblance becomes closer,
431
with the prototype being defined in part by a number-related factor.
432
Prototype-matching as a mechanism underlying numerical competence has been proposed
433
before (Terrell and Thomas 1990), yet is rarely considered. Like subitizing and estimating, this
434
mechanism does not require that the animal has access to representations of specific numbers in the
435
full abstract meaning of true numbers, but it does imply that information specific to a number rather
436
than, for example, a continuous variable, is salient. For Portia, numerical competence in the context
437
of preying on oecobiids may be a consequence of this predator adopting, as part of a conditional
438
predatory strategy, a highly specialized prototype-matching routine at the level of scenes instead of
439
only at the level of individual prey items.
440
18
441
Acknowledgements
442
Godfrey Otieno Sune, Stephen Aluoch and Jane Atieno Obonyo provided invaluable technical
443
assistance. We acknowledge financial support from the National Geographic Society (RRJ), the
444
Royal Society of New Zealand (Marsden Fund; RRJ; James Cook Fellowship, RRJ).
445
446
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27
Table 1 Data from testing Portia africana juveniles with ‘scenes’ made from lures (dead spiders mounted in lifelike posture) and silken nests. See text
for details. Radiating lines: nest. Black polygon: lure made from adult Oecobius amboseli (Oa) female (always in nest). Grey polygon: lure made from
Portia africana (Pa) juvenile (body length 2mm, unless stated otherwise). White circles (‘eyes’) represent direction in which lure faced. When more
than one lure was in a scene the centre-to-centre distances of all lures was 8 mm unless stated otherwise. Q1 and Q3: 1st and 3rd quartile, respectively.
1
Data from Jackson and Nelson (In Press). *N = 200; all other N = 100.
Scene
Scene description
No.
Diagram
Attacked
Attacked
Settled
Median latency to settle
nest (N)
already settled
(N)
(min) (Q1, Q3)
spider (N)
11*
Oa in nest
9
na
75
22 (13, 31)
21*
Pa and Oa facing each other
1
0
131
26 (15, 36)
3*
Two Pa at opposite ends of nest, one facing Oa
5
2
38
25 (14.5, 29)
head-on and other facing rear of Oa
28
4
Two Pa side-by-side in front of and facing Oa
4
0
23
20 (10, 40)
5
Two Pa lined up one behind the other at one end
1
2
26
28.5 (18.75, 47.5)
0
0
6
22.5 (16.25, 34.25)
0
0
4
23.5 (16.75, 30.25)
0
2
1
39 (39, 39)
3
0
6
21.5 (13.5, 26.25)
of nest. Pa head-on to Oa
6
Two Pa. Each Pa at opposite end of nest. Both
facing empty nest
7
Two Pa at opposite ends of a nest. Both facing
nest. Pa in nest
8*
Three Pa surrounding nest, forming triangle with
Oa at centre. Each Pa facing Oa. Pa in lower
position head-on to Oa
9*
Three Pa side-by-side in front of and facing Oa
29
10
Three Pa lined up one behind the other. Pa head-
4
0
30
18 (11.5, 34.25)
2
0
43
28 (24, 36)
5
0
27
28 (21, 36)
5
0
34
28 (16.5, 39.25)
on to Oa. 1st Pa juvenile close to, 2nd far & 3rd
very far from nest
11
Oa and one Pa facing each other. Other Pa
opposite, facing rear of Oa. Both Pa very far
from nest
12
Three Pa surrounding nest, forming triangle with
Oa at centre. Pa in lower position facing Oa
head-on. All Pa very far from nest
13
Three Pa side-by-side facing Oa (one head-on).
All Pa very far from nest
30
14
Three Pa side-by-side facing Oa. One Pa head-
1
0
19
31 (26, 40)
0
0
122
29 (22, 36.25)
1
2
1
43 (43, 43)
0
3
30
27 (18.5, 36.25)
2
2
0
na
on to Oa, very far from nest and positioned
between other two Pa. Each of other two Pa
close to nest
15*
Three Pa side-by-side facing Oa. One Pa headon to Oa, close to nest and positioned between
other two Pa which are very far from nest
16
Three Pa directly to the side of another facing
Oa (one head-on)
17*
Two Pa at opposite end of nest, both facing away
from Oa
18
Three Pa surrounding nest. Each Pa facing away
from Oa
31
19
Pa (large) and Oa, facing each other
0
0
59
25 (16, 31)
20
Pa (small) and Oa, facing each other
2
0
54
24 (17, 33.75)
21
Two large Pa at opposite end of nest, one facing
0
0
24
27.5 (22.5, 35)
1
1
27
31 (19, 36)
0
1
0
na
Oa head-on and other facing rear of Oa
22
Two small Pa at opposite end of nest, one facing
Oa head-on and other facing rear of Oa
23
Three large Pa surrounding nest, forming
triangle with Oa at centre. Pa in lower position
head-on to Oa
32
24
Three small Pa surrounding nest, forming
0
2
0
na
triangle with Oa at centre. Each Pa facing Oa.
Pa in lower position head-on to Oa
33