We examine the connection between a hypothetical kin recognition signal available in visual perception and the perceived facial similarity of children. One group of observers rated the facial similarity of pairs of children portrayed in photographs. Half of the pairs were siblings but the observers were not told this. A second group classified the pairs as siblings or nonsiblings. An optimal Bayesian classifier, given the similarity ratings of the first group, was as accurate in judging siblings as the second group. Mean rated similarity was also an accurate linear predictor (*R*^{2} = .96) of the log-odds that the rated pair portrayed were, in fact, siblings. Surprisingly, mean rated similarity did not vary with the age difference or gender difference of the pairs, both of which were counterbalanced across the stimuli. We conclude that the perceived facial similarity of children is little more than a graded kin recognition signal and that this kin recognition signal is effectively an estimate of the probability that two children are close genetic relatives.

*similarity*leads a double life. In one sense, it describes aspects of perceptual and cognitive experience: We perceive that objects are more or less similar. Yet the term

*similarity*has a second, more abstract, employment. In this second sense, the term “similarity” serves as an explanatory construct. In the past half century “abstract similarity” has played a central role in ethology and animal learning (Guttman & Kalish, 1956; Sutherland & Mackintosh, 1971) as well as the study of human cognition (Shepard, 1987; Tversky, 1977). Analogues of similarity play an important role in artificial intelligence (Falkenheimer, Forbus, & Gentner, 1989; Riesbeck & Schank, 1989), in statistical classification algorithms (Duda & Hart, 1973), in formal models of decision making (Gilboa & Schmeidler, 2001) and in models of kin recognition (Chapais & Berman, 2004; Fletcher & Michener, 1987; Hepper, 1991). Similarity in this second sense is the conceptual glue that binds experience together: “From causes which appear

*similar*we expect similar effects” (Hume, 1748/1993).

*The Marsham Children*(Figure 1), for example, it is hard not to register similarities and dissimilarities between the children portrayed. If challenged to pick the most similar pair, viewers may disagree. There is no “right” answer as there would be if we asked the viewer to pick the youngest child. We do not know what objective measurement or rule captures perceived facial similarity.

*in part*on facial characteristics that signal genetic relatedness. However, we find that the perceived facial similarity of children is little more than a graded kin recognition signal, unaffected by age or gender difference. We also find that the kin recognition signal captured by perceived facial similarity is equivalent to a visual estimate of the probability that the children are close genetic relatives.

*all*of the task-relevant information available to the observer for kin recognition. In Figure 2B, we illustrate a model that leads to the latter outcome. Suppose that the observer carries out a kin recognition task, by first forming a measure of similarity. If the value of the similarity measure exceeds a threshold value, the observer responds “yes” (“related”), otherwise “no” (“not related”). For this

*thresholded similarity observer*(TSO) the similarity measure is effectively a graded kin recognition signal.

*s*of each pair on a scale from 0 (not at all similar) to 10 (very similar). We will use the term “related” to mean that two children have the same biological parents. Half of the pairs of children are related (

*R*) and half are not (

*P*[

*R*] that the children in each pair are related is 1/2. We record the frequency of use of each of the ratings, separately for related and for unrelated pairs. Their expected values are proportional to the true underlying conditional probabilities,

*P*[

*s*|

*R*], the likelihood that the observer says “

*s*” when confronted with a related pair of children, and

*P*[

*s*|

*s*” when confronted with an unrelated pair of children. If the distributions

*P*[

*s*|

*R*] and

*P*[

*s*|

*posterior odds*

*P*[

*R*|

*s*] /

*P*[

*s*] that the children are related by Bayes' theorem in odds form (Mood, Graybill, & Boes, 1974),

*P*[

*R*]/

*P*[

*s*are related is equal to the ratio of likelihoods,

*P*[

*R*] =

*P*[

*s,*compute the log posterior odds,

*D*(

*s*) > Δ if and only if the posterior odds

*P*[

*R*|

*s*]/

*P*[

*s*] are greater than 1:1. The decision rule for this choice of Δ can be paraphrased as, “Say yes if the rating

*s*is more likely to have come from a related pair than from an unrelated pair, otherwise say no.” If

*D*(

*s*) < 0, then the posterior odds

*P*[

*R*|

*s*]/

*P*[

*s*] are less than 1:1. Again, we emphasize that this decision rule is not simply plausible or intuitively appealing but also optimal in the sense that you will make the fewest possible classification errors on average (Duda & Hart, 1973).

^{®}to obliterate all background detail, replacing it by a uniform dark grey field (33% of maximum intensity in each of R, G, and B channels). A sample photograph is shown in Figure 3. The ages of the children ranged from 17 months to 15 years. The distribution of age differences for related and unrelated pairs was matched. The distribution of gender was also counterbalanced across related and unrelated pairs. The facial expressions were neutral or close to neutral. All came from three adjacent provinces of Northern Italy: Padova, Mantova, and Vicenza. All were Caucasian in appearance. The parents of each child gave appropriate permission for their child's photograph to be used in scientific experiments. We asked for and received separate parental permission to use the photograph in Figure 3 as an illustration here. For privacy reasons, we did not verify by DNA fingerprinting that sibling pairs shared two parents. Recent research using DNA fingerprinting shows that the median rate of “extrapair paternity” is much lower than previously thought, under 2% (for a review, see Simmons, Firman, Rhodes, & Peters, 2004). In any case, the presence of half-siblings (who share a mother but not a father) would have little effect on the outcome of our experiment. Such half-sibling would have 25% of their DNA in common rather than 50%, but would still be more closely related than nonsibling pairs.

*related*and in the second as

*unrelated*. Within each group of 15, five pairs depicted two boys, five pairs depicted two girls and five pairs depicted a boy and a girl. The twelve nonexperimental photographs were selected at random from the full set, subject to the constraint that they included three pairs of biological siblings.

*Familiarization*: The observer was first asked to perform a simple recognition memory task that involved all of the experimental stimuli. All 72 photographs of faces were shown in groups of six per display in random order. The purpose of this part of the experiment was to familiarize the observer with the range of faces he would see in the main experiment. The observer was asked to study the display and told that, immediately after studying each group, he would be shown a probe photograph and asked to report whether this photograph had been among the group of six just studied. The probe photographs were the nonexperimental photographs described above which were not used in the main part of the experiment. (2)

*Training*: The observer practiced the response for his condition (similarity or kinship) on six pairs of photographs that did not overlap with the photographs used in the main part of the experiment. These pairs were drawn from the nonexperimental photographs organized so that there were three pairs that were biological siblings and three that were not. The purpose of this part of the experiment was simply to let the observer become comfortable with the procedure and response. (3)

*Main*: The observer then performed the task appropriate for his condition (similarity or kinship) on 30 pairs of photographs, presented in random order.

*s,*what has one learned about the condition probability

*P*[

*R*|

*s*] that the children portrayed are siblings? We will find that the relationship is remarkably simple.

*s*|

*R*] of the similarity ratings 0, 1, 2…, 10 evoked by pairs of children who were actually siblings. The blue-filled circles connected by dashed blue lines in Figure 5A are a plot of the relative frequency of occurrence

*s*|

*P*[

*s*|

*R*] and

*P*[

*s*|

*s*are related. We reach Equation 4 by substituting Equation 2 into Equation 3 and then replacing

*P*[

*s*|

*R*]/

*P*[

*s*|

*D*(

*s*).

*D*(

*s*) as defined in Equation 3 versus similarity rating

*s*. The line is the maximum likelihood regression fit to the log-odds. Its equation is,

*R*

^{2}) is .96. The relationship is remarkably linear and can be interpreted as follows. A rating of 4.79 (near the middle of the scale, 5) corresponds to even odds that the children are related. Each increase in rating by one step corresponds to an increase in

*s*) of 0.489 (the slope of Equation 5). That increase is equivalent to a multiplication of the posterior odds by

*e*

^{0.489}= 1.63. Each decrease in rating by one step corresponds to multiplicative increase of 0.61 = 1/1.63. A rating of 8 corresponds to odds of almost 8:1 that the children are related; a rating of 1 corresponds to odds of more than that 6:1 that they are not.

d′ | β | z | p | |
---|---|---|---|---|

TSO | 1.057 ± 0.084 | 0.936 ± 0.044 | 12.642 | <.001 |

Kin recognition | 0.999 ± 0.084 | 0.867 ± 0.039 | 11.926 | <.001 |

*β*in the kin recognition condition is slightly less than 1, indicating that participants have a slight bias to judge pairs of children to be related. The

*d*′ value is significantly greater than 0 (see table). We then computed signal detection measures for the TSO with threshold 4.79 on the similarity scale. This choice of threshold is the threshold estimated by linear regression above and it also resulted in the closest match between

*β*for the kinship condition and the resulting estimate of

*β*for the TSO. With this choice of threshold, the

*d*′ values for the kinship condition and the TSO are very close and that for the TSO is slightly

*higher*than that for the kinship condition, but not significantly so (

*z*= 0.469;

*p*> .05). The TSO, given the participants' ratings in the similarity condition, is as effective in discriminating genetic relatedness as the participants who directly judged the degree of kinship of the children.

*d*′ and

*β*for this new “TSO (gender).” We arbitrarily designated pairs of the same gender as signal. The results of this analysis are shown in Table 2: the estimate of

*d*′ for the TSO (Gender) is small and is not significantly different from 0. We conclude that we cannot use an analogue of the TSO to reliably predict whether children differ in gender given rated similarity.

d′ | β | z | p | |
---|---|---|---|---|

TSO (age) | 0.016 ± 0.083 | 1.001 ± 0.022 | 0.196 | .845 |

TSO (gender) | 0.094 ± 0.082 | 1.004 ± 0.023 | 1.154 | .249 |

*d*′ is also small and is not significantly different from 0. Although similarity ratings can be used to predict genetic relatedness, we cannot reject the hypotheses that they carry no information about gender and age differences.

*An enquiry concerning human understanding*. An enquiry concerning human understanding. Indianapolis, IN: Hackett Publishing.