Deciphering deterministic factors of predation pressures in deep time

Predation pressure occurs as a result of predation frequency and prey vulnerability. Although quantifying these factors individually is essential to precisely understand predation effects on evolution, they have been generally less accessible. Here, using a modified form of Poisson function, we quantified the frequencies and vulnerabilities, as well as the resulting predation pressures, concerning the shell drillers versus prey interactions from the Eocene and Miocene periods. Our analysis quantitatively revealed that low-spired shells tend to show increased vulnerability except for two planispiral species that exhibit an unexpectedly low vulnerability. We then identified septal structures within the two species that resemble those in nautiloids and ammonoids but which provided a defensive role against the predators, enhancing the mean lifetime by approximately 20%. The current approach enables us to quantitatively trace how predation frequency and prey vulnerability have interacted, been transformed spatio-temporally, and been a driving force of evolution at geological time scales.

shortened by successful predation, the distribution is altered from Poissonian. We determined that the probability for x number of predation attempts is:  (Fig. 1C). We here term this distribution as Sawf (Stochastic attempts with failures) distribution. Sawf distribution smoothly connects to Poisson and Bernoulli distributions at v = 0 and 1, respectively (Figs 1D and S1). When r and v are given, various aspects of predation pressure can be explicitly evaluated. Thus, for example, the expected fraction of prey surviving all the predation attempts (Fs; fraction of survivors), and the normalized lifetime attenuated by predations (Alt; attenuated lifetime) are analytically given by: Fossil data analysis. We analyzed the distributions of numbers of predatory traces in 9,139 gastropod specimens belonging to 39 species, which were collected from middle Eocene beds in Isle-les Meldeuses and Cressay in the Paris Basin, and the lower Miocene Chipola Formation in Florida. Fossil shells from these beds have been the subjects of paleoecological studies on gastropod drilling predation, taking advantage of the excellent preservation of the fossils 22,23 . Although Sawf function has only two independent parameters, it well fitted most of the fossil data studied (36 out of 39 species examined; Fig. 1E and Table S1). Figure 2A shows a scatter plot of frequency versus vulnerability for the 36 species. As an overall feature, there exist two blank zones. Zone I covers the region of high frequency and high vulnerability (r > 1; v > 0.8), whereas Zone II covers that of high frequency and low vulnerability (r ~ 1; v < 0.2). A possible interpretation of this distribution pattern is that in Zone I the high predation pressure restricts continuous existence of species, whereas in Zone II prey preferences of the predators tend to be biased due to the low-return against drilling costs. In this way, the distribution seems to reflect balance between the two counteracting effects. From the summaries for the three assemblages ( Fig. 2B-D), we confirm that the species of the same family in the same assemblage tends to exhibit similar values. One example is a naticid as prey (Cressay, Fig. 2C; red). The predation attempts on naticids were effective with v > 0.85 except for Natica sp.3 from Cressay, which had a large standard deviation. Also, two species of Keilostoma ( Fig. 2C; cyan) and Omalaxis bifrons ( Fig. 2C; purple) from Cressay, respectively, exhibited similar frequencies and vulnerabilities. These results are anticipated and also illustrate stability of the quantification procedure. Furthermore, comparisons of the predation frequencies and vulnerabilities in closely related species between the different localities may highlight environmentally specific features, such as density and ecology of predators. For example, naticids ( Fig. 2B; red) and ampullinids ( Fig. 2B; blue) from Isles-les-Meldeuses, respectively, exhibited frequencies and vulnerabilities similar to those in Cressay ( Fig. 2C; red, blue), indicating comparable predation traits. By contrast, predation frequency in Sigmesalia fasciata from Cressay ( Fig. 2C; green) was almost twice as large as Mesalia sp. from Isles-les-Meldueses ( Fig. 2B; green), suggesting distinct modes of predation on these related species at these two collecting sites.
Shell morphology and vulnerability. It has long been argued that there exists a correlation between the shell morphology and the vulnerability to predators in marine gastropods 24 . In particular, the "Mesozoic Marine Revolution" hypothesis proposes that the rapid co-evolution between predators and their prey, was boosted by the increased predator-prey interactions from the mid-Mesozoic onward 2,24,25 . During this period, vulnerable traits such as planispiral and trochiform shells were replaced with morphologically more resistant traits, including elongated shells, narrowed and thickened apertures, and elaborated sculptures such as spines. We analyzed vulnerabilities of 24 species that had a moderately small standard deviation (S.D. ≤0.25) along with this hypothesis. The shell-shape index was defined as the aperture height/shell height ratio (Table S1). A plot of vulnerability versus the shell-shape index generally confirmed the previously appreciated trend: high-spired shells generally showed reduced vulnerability (Fig. 3A). However, the two species with low-spired shape exhibited an unexpectedly lower vulnerability based on these indices ( Fig. 3A; dotted circles). These species correspond to the small planispiral gastropods Omalaxis bifrons and Omalaxis marginata collected from Eocene beds (Fig. 3B). In order to reveal possible causes for this deviation from the overall trend, we carefully sectioned the shells and closely investigated the internal structures. We then identified numerous septal structures by which the shell is compartmentalized into many small chambers (Fig. 3C). The septa resemble those seen in the nautiloids and ammonoids in which the chambers function to maintain neutral buoyancy by empting/filling cameral liquids through a siphuncle 26 .
Omalaxis does not have the siphuncle, and the predation from naticids by itself thus reveals the benthic ecology of the species. Our hypothesis is that the septa provide defensive role against predation attempts of shell drillers by restricting the soft parts only to the last whorl. In fact, the micrograph in Fig. 3C

Discussion
In three of 39 species analyzed, the observed distributions of predatory traces did not fit well with a single Sawf distribution (P-value < 0.05; Table S1). There are some possibilities that account for deviations from the model. First, as a general premise in this type of analysis, data of a given prey species must reflect spatiotemporally consistent interactions with predators throughout. Otherwise the resulting distribution becomes a linear sum of Sawf functions with different sets of r and v parameters. Second, the Sawf distribution assumes a simple interaction such as random collisions between a given prey species and predators. More complicated interactions 12,[27][28][29][30] would alter the profile. Although these interactions may be also modeled by incorporating additional parameters, significantly larger numbers of samples would be needed to determine the parameters. In our model, the parameter r relates to the first two stages (i.e., recognition and catching the prey) among the major three stages of predation. Its definition is equivalent to the expected number of occurrences of the first two stages during the lifetime in the absence of predation of interest. High value of r indicates situations, for instance, where predator density is high or prey have fewer abilities to avoid the predators. Thus r reflects multiple aspects including ability to escape, camouflage, predator density, and so on. For example, if one finds species with low r value even from an environment of high predator density, some adaptation mechanisms to moderate the first two stages might be expected. Also, incorporating the approaches to analyze prey preferences of predators 18,27,31 may help to address contributions of such aspects to r. On the other hand, the parameter v reflects resistance in the final subjugation stage. With these clues, in this study, the internal septa structures providing a defensive role was revealed from the Eocene gastropod Omalaxis. The original function of the Omalaxis septa structure remains unknown at present. Given that many Palaeozoic gastropods also have septa 32 and that drilling predation by naticids or muricids increased significantly during the Mesozoic 10,24 , the septa might have an original function other than defense.
In this study, we thus showed that analysis of discrete predatory trace records based on a Sawf distribution permits us to quantify the two deterministic factors of predation pressure. While the naticid-gastropod interaction studied here provides rich data on modern and past predation pressures, this mode of interaction appears in various animal and plant taxa 27,28,[33][34][35][36][37] . We believe that quantitative knowledge of predator-prey interactions will help ecologists and paleontologists toward a deeper understanding of predation as a driving force of evolution.   39 , the complete predatory naticid bore holes were identified and counted under a dissecting microscope. A scanning electron microscope (T330A, JOEL, Tokyo, Japan) was used to make micrographs of samples after ultrasonic cleaning and gold sputtering. The internal anatomy of Omalaxis was investigated after grinding the specimen to the middle line using polishing powder on a glass slide. All the specimens examined in this paper are deposited in the Department of Geology and Paleontology, the National Museum of Nature and Science, Tsukuba, Japan.
Data analysis. Derivations of the Sawf, Fs, and Alt functions (Eqs 1-3) are described in the supplementary materials and methods. The fitting of count data with Sawf function was performed using a custom-made code of MATLAB (MathWorks, MA) on a standard PC. The best fit parameters for the predation frequency (r) and prey vulnerability (v) as well as their standard errors, were determined by least squares and bootstrap (n = 1000) methods, respectively. Goodness of Fit (P-value) was evaluated using a "multinomial.test" function of R software (www.r-project.org) in CX250 Cluster. The Monte-Carlo method of 10 7 trials was used for these evaluations. Figure S3 shows sample code for fitting with Sawf function.