Quantitative Estimates of Visual Performance Features in Fossil Birds Lars Schmitz* Department of Geology, University of California at Davis, Davis, California 95616 ABSTRACT Eyeball structures such as the lens diame- ter (LD) and axial length are generally assumed to be highly correlated with optically meaningful parameters. However, these optical constraints on eyeball macroanat- omy have never been tested explicitly. Tradeoffs between benefits of improved visual performance and cost of ad- aptation from an increase of tissue production predict that when eyeball size increases, optical parameters such as posterior nodal distance and maximum entrance pupil diameter should increase isometrically with eye- ball axial length and LD, respectively. Here I show quantitatively that the interspecific allometry of the avian eye largely follows this predicted isometry. Addi- tionally, I elaborate a method to estimate optically sig- nificant eyeball soft-tissue dimensions from scleral ring and orbit morphology based on analyses of interspecific allometry in Aves. The stringent correlations between avian eyeball morphology and optical function render this system ideal for the analysis of form–function rela- tionships and allow for an accurate estimate of optically significant eyeball soft-tissue dimensions such as diame- ter, axial length, and LD in fossil species. J. Morphol. 270:759–773, 2009. Ó 2009 Wiley-Liss, Inc. KEY WORDS: eye morphology; scleral rings; optical function; visual performance; fossil birds INTRODUCTION Vision has an outstanding function in many in- vertebrate and vertebrate species and serves sev- eral purposes in intra-and interspecific interac- tions (Walls, 1942; Lythgoe, 1979; Land and Nils- son, 2002). Many predatory species rely on visual cues to detect their prey items, and visual informa- tion also helps maintain group cohesion of social foragers. Vision is a primary information source for motion and navigation control needed for pur- suit and capture of actively moving prey. Prey spe- cies detect and avoid predators by sight. Vision is also important in finding and selecting mates. The shape and size of external and internal eye- ball structures are expected to reflect visual charac- teristics of animals. Eyeball morphology is generally assumed to be matched to the physical characteris- tics of the animal’s visual environment (Walls, 1942; Lythgoe, 1979; Land and Nilsson, 2002), which would render the eye ideal for the study of its form– function relationships. Such a study could also es- tablish morphological traits that reflect visual per- formance features, which, in turn, could be used to study fossil specimens. However, neither the corre- lation of morphological features with optical func- tion nor the estimate of eyeball soft-tissue dimen- sions based on osteology has been tested explicitly. Physiological optics predicts two main optical determinants of visual performance: the posterior nodal distance (PND) and the diameter of the max- imum entrance pupil (see Fig. 1). Visual perform- ance is characterized by two main qualities: acuity and light sensitivity. Acuity, usually given as spa- tial sampling frequency, expresses the fineness of detail that can be discriminated (Land, 1981). Spa- tial sampling frequency depends on two variables. The first variable, PND, equals the distance from the posterior nodal point to the retinal surface (see Fig. 1). The posterior nodal point is defined by the intersection of straight lines connecting points on the image on the retina to equivalent points on the imaged objects, accounting for all refractive surfa- ces in the optical system. The second variable is the average distance between adjacent retinal re- ceptor cells (s), assuming a dense hexagonal pack- ing of photoreceptor cells. spatial sampling frequency v s ¼ PND ffiffiffi 3 p  s  180 p ½cycles=deg ðMiller; 1979Þ; ð1Þ Because visual performance is an integrated result of various steps in the visual process (Hung and Ciuffreda, 2002), including the optical and neurological (retina and brain) system, one needs to test whether the anatomical modeling matches behavioral measurements. Behavioral measure- Contract grant sponsor: DAAD (Doctoral stipend, German Aca- demic Exchange Service). *Correspondence to: Lars Schmitz, Department of Geology, Uni- versity of California at Davis, Davis, CA 95616. E-mail: lschmitz@ucdavis.edu Received 18 May 2008; Revised 30 October 2008; Accepted 7 November 2008 Published online 2 January 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/jmor.10720 JOURNAL OF MORPHOLOGY 270:759–773 (2009) Ó 2009 WILEY-LISS, INC.