Reply to Sherratt and Holen: Goldilocks and the half-empty glass

Reply to Sherratt and Holen: Goldilocks and the half-empty glass Given the apparent prevalence of multicomponent signals in nature, students of nonhuman signaling have tended to assume that multiple components must confer some pervasive advantage. Hypotheses about the nature of this supposed benefit typically take one of 2 forms: economic or perceptual benefits. Sherratt and Holen’s model considers the economic benefits derived from stimulus combinations. Their model improves upon earlier work by Tricia Rubi and myself (Rubi and Stephens 2016b) which showed that the extent to which receivers can benefit from attending to stimulus combinations depends on the relative frequency of the underlying conditions that are signaled about (e.g. the frequency good vs. bad signalers to use Sherratt and Holen’s example). Our result depended on a simplifying assumption about the underlying payoffs associated with these conditions, Sherratt and Holen’s model removes this restriction, and, in doing so, it provides some valuable insights into the nature of this important problem. I congratulate them on their theoretical achievement. Given the deep connection between their model and our theoretical paper, it seems somewhat surprising that they offer their model as a criticism of our earlier experimental paper (Rubi and Stephens 2016a). In this experimental study, Rubi and I framed our experiments in terms of an even simpler model that not only assumed a simplified “payoff structure” but also a specific base rate of 50%. In these conditions, we predict that it never pays to follow stimulus combinations; instead, receivers should attend to the single most reliable stimulus type. Our empirical results supported this prediction. We felt that these data were important because they suggest the benefits of attending to multiple components may be something less than pervasive. Sherratt and Holen characterize our paper as suggesting that receivers can never benefit from attending to multiple signal components. I have significant cognitive dissonance about this. Not only, do we explicitly say otherwise (“we do not suggest that complex signals are never beneficial for the receiver,” p. 43), but Sherratt and Holen’s paper builds upon work of ours demonstrating exactly this type of economic benefit. Overall, then Sherratt and Holen and I broadly agree: receivers can benefit from attending to stimulus combinations in some conditions but not others. The disagreement, if there is one, would seem to take the form of a dispute about whether the glass is half-empty or half-full. I favor the half-empty view because I am not convinced that one can make a convincing case for an economic account of the “prevalence” of multicomponent signaling. Indeed Sherratt and Holen’s model, itself, illustrates the fragility of economic accounts. To see this, reconsider Sherratt and Holen’s figure 1. The variable β (which differs between the 3 panels) measures the difference between the expected benefits of “accepting” and “rejecting.” So when β>1 as in panel a, the receiver would on average do better by accepting than by rejecting; similarly when β<1 as in panel c, rejecting is on average better than accepting. The central panel β=1 shows the case studied experimentally by Rubi and Stephens, in which accepting and rejecting offer the same expected benefits. In this condition, it never pays to follow stimulus combinations, as explained above. Interestingly, when the benefits of accepting differ from the benefits of rejecting (in either direction), a band emerges along the 1-to-1 line in which it “can” pay to follow stimulus combinations. Since their “multi-componency” band straddles the one-to-one line, Sherratt and Holen predict (as did Rubi and Stephens 2016b) that following multicomponent signals makes the most sense when the components have similar levels of reliability. Outside of this band—when one component is much more reliable than other—they predict that receivers should follow the single most reliable component just as in the equal expected payoff case. Next, observe that the nature of the predicted sensitivity to multiple components is very specific. When the expected benefit of accepting exceeds the benefit of rejecting (panel a), we predict that receivers should normally accept, but reject if and only if the observe a “double negative” signal; similarly, if rejecting is on average better than accepting, we predict a mirror image situation in which receiver should normally reject but accept if and only if they observe a “double positive” signal. This replicates and extends the predictions of Rubi and Stephens (2016b), although Sherratt and Holen make no comment on this parallel. This is a strong and specific prediction about the nature of sensitivity to multiple stimuli, but it is not clear whether this jives with the observed behavioral properties of multicomponent stimuli (cf. Rowe 1999). Finally, there are reasons to doubt the robustness of Sherratt and Holen’s results. They predict that receivers should attend to stimulus combinations when the expected benefit of one action exceeds the expected benefit of the other. However, as we increase this difference (for example, making accepting better than rejecting), we will reach a point where it does not pay to follow signals at all, because receivers can do better by adopting a single fixed action (accepting in this example). So as Sherratt and Holen shift the expected benefits away from equal expected benefit case (panel b), they are creating conditions where it pays to follow stimulus combinations, but they are also reducing the net value of following signals. We see this in the emergence of the “signal ignoring” regions in the lower left corners of panels a and c. Curiously, we need differences in the expected benefits associated with alternative actions to make following multiple components pay off, but these differences can not be too big. Things have to be “just right” for this model to account for the prevalence of naturally occurring multiple componency. The underlying values for alternative actions need to differ, but not by too much. The reliabilities of component stimuli need to be roughly the same. Moreover, it predicts that receiver sensitivity to multiple components should take a very specific form. I would be thrilled to find that most naturally occurring multiple component signals fall into the “just right” region of the parameter space, but it seems like a tall order. REFERENCES Rubi TL , Stephens DW . 2016a . Should Receivers follow multiple signal components? An economic perspective . Behav Ecol . 27 : 36 – 44 . Google Scholar CrossRef Search ADS Rubi TL , Stephens DW . 2016b . Why complex signals matter, sometimes . In: Bee MA , Miller CT , editors. Psychological mechanisms in animal communication . Cham : Springer International Publishing .Vol. 5 , p. 119 – 135 . Google Scholar CrossRef Search ADS Rowe C . 1999 . Receiver psychology and the evolution of multicomponent signals . Anim Behav . 58 : 921 – 931 . Google Scholar CrossRef Search ADS PubMed © The Author(s) 2018. Published by Oxford University Press on behalf of the International Society for Behavioral Ecology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Behavioral Ecology Oxford University Press

Reply to Sherratt and Holen: Goldilocks and the half-empty glass

Behavioral Ecology , Volume Advance Article (4) – Apr 19, 2018

Loading next page...
 
/lp/ou_press/reply-to-sherratt-and-holen-goldilocks-and-the-half-empty-glass-PYlU0gnGa8
Publisher
Oxford University Press
Copyright
© The Author(s) 2018. Published by Oxford University Press on behalf of the International Society for Behavioral Ecology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
ISSN
1045-2249
eISSN
1465-7279
D.O.I.
10.1093/beheco/ary049
Publisher site
See Article on Publisher Site

Abstract

Given the apparent prevalence of multicomponent signals in nature, students of nonhuman signaling have tended to assume that multiple components must confer some pervasive advantage. Hypotheses about the nature of this supposed benefit typically take one of 2 forms: economic or perceptual benefits. Sherratt and Holen’s model considers the economic benefits derived from stimulus combinations. Their model improves upon earlier work by Tricia Rubi and myself (Rubi and Stephens 2016b) which showed that the extent to which receivers can benefit from attending to stimulus combinations depends on the relative frequency of the underlying conditions that are signaled about (e.g. the frequency good vs. bad signalers to use Sherratt and Holen’s example). Our result depended on a simplifying assumption about the underlying payoffs associated with these conditions, Sherratt and Holen’s model removes this restriction, and, in doing so, it provides some valuable insights into the nature of this important problem. I congratulate them on their theoretical achievement. Given the deep connection between their model and our theoretical paper, it seems somewhat surprising that they offer their model as a criticism of our earlier experimental paper (Rubi and Stephens 2016a). In this experimental study, Rubi and I framed our experiments in terms of an even simpler model that not only assumed a simplified “payoff structure” but also a specific base rate of 50%. In these conditions, we predict that it never pays to follow stimulus combinations; instead, receivers should attend to the single most reliable stimulus type. Our empirical results supported this prediction. We felt that these data were important because they suggest the benefits of attending to multiple components may be something less than pervasive. Sherratt and Holen characterize our paper as suggesting that receivers can never benefit from attending to multiple signal components. I have significant cognitive dissonance about this. Not only, do we explicitly say otherwise (“we do not suggest that complex signals are never beneficial for the receiver,” p. 43), but Sherratt and Holen’s paper builds upon work of ours demonstrating exactly this type of economic benefit. Overall, then Sherratt and Holen and I broadly agree: receivers can benefit from attending to stimulus combinations in some conditions but not others. The disagreement, if there is one, would seem to take the form of a dispute about whether the glass is half-empty or half-full. I favor the half-empty view because I am not convinced that one can make a convincing case for an economic account of the “prevalence” of multicomponent signaling. Indeed Sherratt and Holen’s model, itself, illustrates the fragility of economic accounts. To see this, reconsider Sherratt and Holen’s figure 1. The variable β (which differs between the 3 panels) measures the difference between the expected benefits of “accepting” and “rejecting.” So when β>1 as in panel a, the receiver would on average do better by accepting than by rejecting; similarly when β<1 as in panel c, rejecting is on average better than accepting. The central panel β=1 shows the case studied experimentally by Rubi and Stephens, in which accepting and rejecting offer the same expected benefits. In this condition, it never pays to follow stimulus combinations, as explained above. Interestingly, when the benefits of accepting differ from the benefits of rejecting (in either direction), a band emerges along the 1-to-1 line in which it “can” pay to follow stimulus combinations. Since their “multi-componency” band straddles the one-to-one line, Sherratt and Holen predict (as did Rubi and Stephens 2016b) that following multicomponent signals makes the most sense when the components have similar levels of reliability. Outside of this band—when one component is much more reliable than other—they predict that receivers should follow the single most reliable component just as in the equal expected payoff case. Next, observe that the nature of the predicted sensitivity to multiple components is very specific. When the expected benefit of accepting exceeds the benefit of rejecting (panel a), we predict that receivers should normally accept, but reject if and only if the observe a “double negative” signal; similarly, if rejecting is on average better than accepting, we predict a mirror image situation in which receiver should normally reject but accept if and only if they observe a “double positive” signal. This replicates and extends the predictions of Rubi and Stephens (2016b), although Sherratt and Holen make no comment on this parallel. This is a strong and specific prediction about the nature of sensitivity to multiple stimuli, but it is not clear whether this jives with the observed behavioral properties of multicomponent stimuli (cf. Rowe 1999). Finally, there are reasons to doubt the robustness of Sherratt and Holen’s results. They predict that receivers should attend to stimulus combinations when the expected benefit of one action exceeds the expected benefit of the other. However, as we increase this difference (for example, making accepting better than rejecting), we will reach a point where it does not pay to follow signals at all, because receivers can do better by adopting a single fixed action (accepting in this example). So as Sherratt and Holen shift the expected benefits away from equal expected benefit case (panel b), they are creating conditions where it pays to follow stimulus combinations, but they are also reducing the net value of following signals. We see this in the emergence of the “signal ignoring” regions in the lower left corners of panels a and c. Curiously, we need differences in the expected benefits associated with alternative actions to make following multiple components pay off, but these differences can not be too big. Things have to be “just right” for this model to account for the prevalence of naturally occurring multiple componency. The underlying values for alternative actions need to differ, but not by too much. The reliabilities of component stimuli need to be roughly the same. Moreover, it predicts that receiver sensitivity to multiple components should take a very specific form. I would be thrilled to find that most naturally occurring multiple component signals fall into the “just right” region of the parameter space, but it seems like a tall order. REFERENCES Rubi TL , Stephens DW . 2016a . Should Receivers follow multiple signal components? An economic perspective . Behav Ecol . 27 : 36 – 44 . Google Scholar CrossRef Search ADS Rubi TL , Stephens DW . 2016b . Why complex signals matter, sometimes . In: Bee MA , Miller CT , editors. Psychological mechanisms in animal communication . Cham : Springer International Publishing .Vol. 5 , p. 119 – 135 . Google Scholar CrossRef Search ADS Rowe C . 1999 . Receiver psychology and the evolution of multicomponent signals . Anim Behav . 58 : 921 – 931 . Google Scholar CrossRef Search ADS PubMed © The Author(s) 2018. Published by Oxford University Press on behalf of the International Society for Behavioral Ecology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

Journal

Behavioral EcologyOxford University Press

Published: Apr 19, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off