The psychophysics of uneconomical choice: non-linear reward evaluation by a nectar feeder
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Uneconomical choices by humans or animals that evaluate reward options challenge the expectation that decision-makers always maximize the return currency. One possible explanation for such deviations from optimality is that the ability to sense differences in physical value between available alternatives is constrained by the sensory and cognitive processes for encoding profitability. In this study, we investigated the capacity of a nectarivorous bat species (Glossophaga commissarisi) to discriminate between sugar solutions with different concentrations. We conducted a two-alternative free-choice experiment on a population of wild electronically tagged bats foraging at an array of computer-automated artificial flowers that recorded individual choices. We used a Bayesian approach to fit individual psychometric functions, relating the strength of preferring the higher concentration option to the intensity of the presented stimulus. Psychometric analysis revealed that discrimination ability increases non-linearly with respect to intensity. We combined this result with a previous psychometric analysis of volume perception. Our theoretical analysis of choice for rewards that vary in two quality dimensions revealed regions of parameter combinations where uneconomic choice is expected. Discrimination ability may be constrained by non-linear perceptual and cognitive encoding processes that result in uneconomical choice.
KeywordsNectarivory Bat Psychometric function Uneconomical choice
Value-based decision-making requires that the value of an option can be sensed and stored in memory. This makes a comparison between options possible. Decision-making processes can sometimes lead to outcomes that are not economical (Livnat and Pippenger 2008). This is the case when the decision-maker prefers an option with a lower caloric return over another with a higher caloric return, or when it fails to discriminate between options with different caloric contents. In order to understand how underlying mechanisms can lead to uneconomical choices, it is necessary to have a quantitative understanding of the steps involved in the evaluation process. Sensing the caloric value of a reward, and being able to discriminate between rewards, is the first step in such a process and the objective of our study.
Such considerations about value-based decision-making are also relevant for understanding the co-evolutionary development of energy rewards offered by plants to their pollinators. This is relevant in the context of this study, in which we investigated choice behavior of nectar-feeding bats. The evolution of flower traits in animal-pollinated plants is shaped in part by the selection pressure to offer attractive energy resources to potential pollen vectors (Zimmerman 1983; Real and Rathcke 1991; Sakai 1993). Among pollinator attractants, the most common are simple carbohydrates presented as nectars, i.e., sugar–water solutions (Baker and Baker 1983; Stiles and Freeman 1993). From the pollinators’ perspective, nectars with higher sugar concentrations represent richer energy sources that should be preferred by foragers seeking to optimize their energetic gains. Diverse groups of nectar-feeding animals such as bees (e.g., von Frisch 1927; Cnaani et al. 2006), birds (e.g., Hainsworth and Wolf 1976; Roberts 1996; Nicolson and Fleming 2003), and bats (e.g., Roces et al. 1993; Rodríguez-Peña et al. 2007) show a general pattern of preference for sweeter sugar solutions and more precise discrimination at low concentrations. In the case of nectar-feeding (glossophagine) bats, preference has been estimated by measuring differences in bat visitation and consumption rates at food sources with differing nectar qualities. However, our knowledge on the ability of bats to discriminate between nectar concentrations remains fragmentary and inconclusive, even though this ability has direct consequences on decision-making and on the selection pressures exerted by the bats.
A standardized method for estimating discrimination ability is fitting a psychometric function to data from alternative forced-choice tasks (Treutwein and Strasburger 1999). The psychometric function relates the behavioral response of the animal to the intensities of the physical stimuli. This methodology has been applied to estimate the ability of the flower-visiting and nectar-feeding bat Glossophaga soricina to discriminate between two volumes (Toelch and Winter 2007). Measuring the volume of nectar obtained from a feeding event is one necessary component for reward evaluation. With this study, we determined the second necessary component for a nectar-feeding animal: the ability to evaluate the concentration of sugar in a nectar reward. For this, we performed a psychometric analysis of concentration discrimination ability in a nectarivorous bat species. We obtained our data from a two-alternative free-choice test performed with a group of wild, free-flying Glossophaga commissarisi bats.
Study site and subjects
Experiments were conducted from February to April 2009, at La Selva Biological Station, Province Heredia, Costa Rica. Wild bats were initially recruited to visit the experimental site by setting up nectar feeders filled with 20% sugar solution and equipped with a dimethyl disulfide reservoir giving off odor plumes to act as a far-range attractant to the bats (von Helversen et al. 2000). Feeders were mounted on an aluminum rectangular frame (2 × 4 m), suspended below a 3 × 6-m steel frame canopy, which provided cover from the rain. The frame was parallel to and 1.6 m above the ground. Using mist-nets we caught and marked 63 adult individuals, 39 males, and 24 females, of the common (Tschapka 1998) nectarivore Glossophaga commissarisi Gardner. Bats were weighed, sexed, marked with RFID collars, and released at the site of capture. Over the course of the study, 54 of these bats were registered visiting the artificial flowers, along with an unknown number of unmarked bats and other visitors. Permission for experimentation and RFID-tagging was obtained from Sistema Nacional de Areas de Conservación (SINAC) at the Ministerio de Ambiente y Energía (MINAE).
Nectar consisted of fructose and sucrose (2:1 parts) dissolved in water, with a hexose to sucrose ratio similar to the ratio in natural nectars of glossophagine-pollinated plants (Baker et al. 1998). Half of the feeders received nectar from one pumping system, and the other half from the other system (Fig. 1). The two systems were filled with nectars with different concentrations. Thus, during a single night, the concentration offered at each feeder was fixed and did not change. In order to prevent bacterial and fungal growth inside the tubing systems, they were rinsed with water and 70% ethanol every 3–4 days.
We recorded data between 18:00 and 06:00 h. The nectar concentrations ranged from 5 to 50% weight/weight (or 148–1,796 mmol L−1 sucrose equivalents, Bolten et al. 1979) and were presented in two series of two-alternative free-choice tests, with 12 feeders per option. The first series of tests consisted of nine different conditions with a difference between the two options of 5% (from 5% vs. 10% to 45% vs. 50%). The second series consisted of seven conditions with a difference of 15% (from 5% vs. 20% to 35% vs. 50%) between options. The sequence of conditions within both series was random. However, every condition was presented twice on consecutive nights on which the feeder positions for each concentration were exchanged (Fig. 1, black and white feeders), as a control for positional biases. The choice of pumping system for the higher nectar concentration during the first night of each condition was random.
Recorded data consisted of the time-stamped visitation events of marked bats and unknown unmarked visitors. Analysis was limited to the hours between 20:00 and 03:00 h. We excluded the hours before 20:00 h in order to focus on plateau performance, after the initial sampling and exploration phase. The visits after 03:00 h were excluded because of unexpectedly high visit numbers and premature depletion of the nectar supply on some nights. (This only occurred during two nights in the 5% series and three nights in the 15% series.) For each bat and each condition, we calculated the stimulus intensity and the discrimination strength. The stimulus intensity was calculated as the absolute difference between the two sugar concentrations, divided by the mean concentration. Over the two presentations of the same condition, discrimination strength was calculated as the number of visits to higher sugar concentration feeders divided by the total number of visits. If a bat showed a perfect “preference” for one feeder type without having made any visits to the other type during a whole night, including the time before 20:00 h, its data for that night were eliminated from the analysis.
We performed individual psychometric analyses on the data from each animal and fitted Weibull psychometric functions using the algorithm proposed by Kuss et al. (2005) using R 2.10.1 (R Development Core Team 2009). A similar application of this method is presented in Toelch and Winter (2007). In this Bayesian approach, Markov Chain Monte Carlo (MCMC) sampling is used to estimate the threshold, slope, and lapse rate of the psychometric functions, along with their confidence intervals. The point on the curve halfway between the lower and upper asymptote (corresponding to a discrimination performance of ca. 75%) is referred to as the threshold. The slope of the function at the threshold is interpreted as a reliability measure of sensory performance (Treutwein and Strasburger 1999). Finally, the lapse rate is a measure of the frequency of errors (in this case, visits to the low concentration feeders) due to distraction, motivational problems, and other factors of a non-perceptual nature. In this particular application, it may also be interpreted as a base rate of exploration. As prior function for the lapse rate, we chose a beta distribution (2; 50). For the threshold we chose a normally distributed prior with a mean of 1 and a standard deviation of 0.5, and for the slope a log-normal prior with a mean of 2 and a standard deviation of 1. We performed 5,000 MCMC sampling runs with a leapfrog step size of 100. From the individual psychometric functions obtained using this method, we calculated the mean and 95% confidence intervals for the threshold, slope, and lapse rate.
Researchers have shown that the fit of the psychometric function is very sensitive to the sampling scheme, i.e., the choice of stimulus intensities and their distribution (Wichmann and Hill 2001). The intensities resulting from the chosen sugar concentrations in the 5% series were clustered in a region of lower to medium intensities without critical values around the threshold. On the other hand, the intensities resulting from the 15% series resulted in a wider range of intensities and included two points around the threshold. The theoretical expectation was that relative differences rather than absolute differences would predict bat choice. This relative difference is captured by our intensity measure expressed in terms of the absolute difference divided by the mean stimulus magnitude. We therefore restricted individual psychometric analysis to the 23 most active bats, which made on average more than 50 visits per night during the 15% series and were absent for no more than a single test condition from that series. With the exception of three bats, these 23 animals were also detected during the 5% series and analysis was performed on the pooled data from both series. From the individually fitted psychometric functions, we calculated the mean of the lapse rate, threshold, and slope across animals. For visualization purposes, we also fitted a psychometric function on the pooled data from all 23 bats.
Our results indicate that the evaluation of sugar concentrations by G. commissarisi is affected by two systematic biases. Discrimination performance improves as the difference between alternative choices increases (distance effect). Discrimination performance declines as distance (the absolute difference between two concentrations) is kept constant but the average concentration of the two options increases (magnitude effect). Stimulus comparison in the case of sugar concentrations cannot occur simultaneously. Instead, the currently experienced concentration must be compared with a sample retrieved from memory. Presumably the distance and magnitude effects are consequences of sensory transfer functions and the memory representation of sweetness or caloric value. In essence, these effects and Eq. 3 above are consistent with Weber-Fechner’s law, which states that physical stimuli are scaled on a logarithmic internal representation over a major part of their perceptible range and that a differential threshold such as the just-noticeable difference (jnd) is a constant fraction of the magnitude of the stimulus (Kacelnik and Brito e Abreu 1998; Deco and Rolls 2006; Kang et al. 2010). We suggest that a non-linear perception and encoding process can also explain the biases described in this study.
Deviations from optimality can be even stronger if evaluation of reward properties takes place sequentially and if one dimension is given priority over the others. For example, Cnaani et al. (2006) suggest that bumble bees perceive sugar concentration first, and may reject a nectar reward if it is too dilute without consuming it completely and obtaining information about the available volume. Similarly, an emptied flower provides no information about its nectar concentration. Since bats’ discrimination of feeders differing in their likelihood of being empty exhibits the same distance and magnitude effects described above (Nachev and Winter, unpubl.), variance-sensitive foraging behavior can also result in non-profitable choices. In summary, because of the shape of the psychometric functions, negative changes in nectar reward properties along one dimension, e.g., concentration, might be masked by positive changes along the remaining dimensions, reward probability, and volume, even when these changes decrease overall profitability.
We thank Arne Jungwirth for fieldwork assistance and Alexej Schatz for software programming. Ulf Toelch and Lutz Wiegrebe gave helpful comments on earlier drafts of the manuscript. During the preparation of this manuscript, V. N. received funding by the Volkswagen Foundation. Field study funded by the National Geographic Society and further support was received by DFG Exc257 and Exc277.
Conflict of interest
The authors declare that they have no conflict of interest.
Treatment of the experimental animals complied with the national laws on animal care and experimentation.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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