Skip to main content Accessibility help
Hostname: page-component-55597f9d44-2qt69 Total loading time: 0.451 Render date: 2022-08-16T19:25:41.141Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Modeling durophagous predation and mortality rates from the fossil record of gastropods

Published online by Cambridge University Press:  13 March 2019

Graham E. Budd
Dept of Earth Sciences, Palaeobiology, Uppsala University, Villavägen 16, Uppsala, Sweden, SE 752 36. E-mail:
Richard P. Mann
Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom; and Alan Turing Institute, London NW1 2DB, United Kingdom. E-mail:


Gastropods often show signs of unsuccessful attacks by durophagous predators in the form of healed scars in their shells. As such, fossil gastropods can be taken as providing a record of predation through geological time. However, interpreting the number of such scars has proved to be problematic—Would a low number of scars mean a low rate of attack or a high rate of success, for example? Here we develop a model of population dynamics among individuals exposed to predation, including both lethal and nonlethal attacks. Using this model, we calculate the equilibrium distributions of ages and healed scars in the population and among fossilized specimens, based on the assumption that predation is independent of age or scar number. Based on these results, we formally show that the rates of attack and success cannot be disambiguated without further information about population structure. Nevertheless, by making the assumptions that the non-durophagous predatory death rate is both constant and low, we show that it is possible to use relatively small assemblages of gastropods to produce accurate estimates of both attack and success rates, if the overall death rate can be estimated. We consider likely violations of the assumptions in our model and what sort of information would be required to solve this problem in these more general cases. However, it is not easy to extract the relevant information from the fossil record: a variety of important biases are likely to intervene to obscure the data that gastropod assemblages may yield. Nonetheless, the model provides a theoretical framework for interpreting summary data, including for comparison between different assemblages.

Copyright © The Paleontological Society. All rights reserved 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Data available from the Dryad Digital Repository:


Abrams, P. A. 1989. The evolution of rates of successful and unsuccessful predation. Evolutionary Ecology 3:157171.CrossRefGoogle Scholar
Alexander, R. R., and Dietl, G. P.. 2003. The fossil record of shell-breaking predation on marine bivalves and gastropods. Pp. 141176 in Kelley, P., Kowalewski, M., and Hansen, T. A., eds. Predator–prey interactions in the fossil record. Springer, New York.CrossRefGoogle Scholar
Andrews, E. 1935. Shell repair by the snail, Neritina. Journal of Experimental Zoology 70:75107.CrossRefGoogle Scholar
Bengtson, S. 2002. Origins and early evolution of predation. Paleontological Society Papers 8:289318.Google Scholar
Bengtson, S., and Zhao, Y.. 1992. Predatorial borings in late Precambrian mineralized exoskeletons. Science 257:367369.CrossRefGoogle ScholarPubMed
Bicknell, R. D., and Paterson, J. R.. 2018. Reappraising the early evidence of durophagy and drilling predation in the fossil record: implications for escalation and the Cambrian Explosion. Biological Reviews 93:754784.CrossRefGoogle ScholarPubMed
Birkeland, C. 1974. Interactions between a sea pen and seven of its predators. Ecological Monographs 44:211232.CrossRefGoogle Scholar
Blundon, J., and Vermeij, G.. 1983. Effect of shell repair on shell strength in the gastropod Littorina irrorata. Marine Biology 76:4145.CrossRefGoogle Scholar
Brey, T. 1999. Growth performance and mortality in aquatic macrobenthic invertebrates. Advances in Marine Biology 35:153223.CrossRefGoogle Scholar
Britton, J. C., and Morton, B.. 1994. Marine carrion and scavengers. Oceanography and Marine Biology: An Annual Review 32:369434.Google Scholar
Budd, G. E. 2000. Ecology of nontrilobite arthropods and lobopods in the Cambrian. Pp. 404427 in Yu. Zhuravlev, A. and Riding, R., eds. The ecology of the Cambrian radiation. Columbia University Press, New York.Google Scholar
Budd, G. E., and Mann, R. P.. 2018. History is written by the victors: the effect of the push of the past on the fossil record. Evolution 72:22762291.CrossRefGoogle ScholarPubMed
Caddy, J. F. 1991. Death rates and time intervals: is there an alternative to the constant natural mortality axiom? Reviews in Fish Biology and Fisheries 1:109138.CrossRefGoogle Scholar
Cadée, G. C., Walker, S. E., and Flessa, K. W.. 1997. Gastropod shell repair in the intertidal of Bahia la Choya (N. Gulf of California). Palaeogeography, Palaeoclimatology, Palaeoecology 136:6778.CrossRefGoogle Scholar
Carriker, M. R., and Yochelson, E. L.. 1968. Recent gastropod boreholes and Ordovician cylindrical borings. United States Geological Survey Professional Papers 593-B:B1B26.Google Scholar
Carter, R. M. 1968. On the biology and palaeontology of some predators of bivalved Mollusca. Palaeogeography, Palaeoclimatology, Palaeoecology 4:2965.CrossRefGoogle Scholar
Chase, J. M. 1999. Food web effects of prey size refugia: variable interactions and alternative stable equilibria. American Naturalist 154:559570.CrossRefGoogle ScholarPubMed
Chattopadhyay, D., Rathie, A., and Das, A.. 2013a. The effect of morphology on postmortem transportation of bivalves and its taphonomic implications. Palaios 28:203209.CrossRefGoogle Scholar
Chattopadhyay, D., Rathie, A., Miller, D. J., and Baumiller, T. K.. 2013b. Hydrodynamic effects of drill holes on postmortem transportation of bivalve shells and its taphonomic implications. Palaios 28:875884.CrossRefGoogle Scholar
Cooper, R. A., Maxwell, P. A., Crampton, J. S., Beu, A. G., Jones, C. M., and Marshall, B. A.. 2006. Completeness of the fossil record: estimating losses due to small body size. Geology 34:241244.CrossRefGoogle Scholar
Dietl, G. P., and Kosloski, M. E.. 2013. On the measurement of repair frequency: how important is data standardization? Palaios 28:394402.CrossRefGoogle Scholar
Ebbestad, J. O. R., and Stott, C. A.. 2008. Failed predation in Late Ordovician gastropods (Mollusca) from Manitoulin Island, Ontario, Canada. Canadian Journal of Earth Sciences 45:231241.CrossRefGoogle Scholar
Feder, H. M. 1963. Gastropod defensive responses and their effectiveness in reducing predation by starfishes. Ecology 44:505512.CrossRefGoogle Scholar
Fey, S. B., Siepielski, A. M., Nusslé, S., Cervantes-Yoshida, K., Hwan, J. L., Huber, E. R., Fey, M. J., Catenazzi, A., and Carlson, S. M.. 2015. Recent shifts in the occurrence, cause, and magnitude of animal mass mortality events. Proceedings of the National Academy of Sciences USA 112:10831088.CrossRefGoogle ScholarPubMed
Gosselin, L. A., and Qian, P.-Y.. 1997. Juvenile mortality in benthic marine invertebrates. Marine Ecology Progress Series 146:265282.CrossRefGoogle Scholar
Hallam, A. 1967. The interpretation of size-frequency distributions in molluscan death assemblages. Palaeontology 10:2542.Google Scholar
Harding, J. M. 2003. Predation by blue crabs, Callinectes sapidus, on Rapa whelks, Rapana venosa: possible natural controls for an invasive species? Journal of Experimental Marine Biology and Ecology 297:161177.CrossRefGoogle Scholar
Harper, E. M. 2006. Dissecting post-Palaeozoic arms races. Palaeogeography, Palaeoclimatology, Palaeoecology 232:322343.CrossRefGoogle Scholar
Harper, E. M., and Peck, L. S.. 2016. Latitudinal and depth gradients in marine predation pressure. Global Ecology and Biogeography 25:670678.CrossRefGoogle Scholar
Harper, E. M., Peck, L. S., and Hendry, K. R.. 2009. Patterns of shell repair in articulate brachiopods indicate size constitutes a refuge from predation. Marine Biology 156:19932000.CrossRefGoogle Scholar
Hoenig, J. M. 1983. Empirical use of longevity data to estimate mortality rates. Fishery Bulletin 82:898903.Google Scholar
Hull, P. M. 2017. Emergence of modern marine ecosystems. Current Biology 27:R466R469.CrossRefGoogle ScholarPubMed
Ilano, A. S., Ito, A., Fujinaga, K., and Nakao, S.. 2004. Age determination of Buccinum isaotakii (Gastropoda: Buccinidae) from the growth striae on operculum and growth under laboratory conditions. Aquaculture 242:181195.CrossRefGoogle Scholar
Ishikawa, M., Kase, T., and Tsutsui, H.. 2018. Deciphering deterministic factors of predation pressures in deep time. Scientific Reports 8:17532.CrossRefGoogle ScholarPubMed
Ivany, L. C. 2012. Reconstructing paleoseasonality from accretionary skeletal carbonates—challenges and opportunities. Paleontological Society Papers 18:133166.Google Scholar
Jones, O. R., Scheuerlein, A., Salguero-Gómez, R., Camarda, C. G., Schaible, R., Casper, B. B., Dahlgren, J. P., Ehrlén, J., García, M. B., Menges, E. S., and Quintana-Ascencio, P. F.. 2014. Diversity of ageing across the tree of life. Nature 505:169173.CrossRefGoogle ScholarPubMed
Kenchington, T. J. 2014. Natural mortality estimators for information-limited fisheries. Fish and Fisheries 15:533562.CrossRefGoogle Scholar
Kidwell, S. M. 2002. Time-averaged molluscan death assemblages: palimpsests of richness, snapshots of abundance. Geology 30:803806.2.0.CO;2>CrossRefGoogle Scholar
Kidwell, S. M., and Bosence, D. W. J.. 1991. Taphonomy and time-averaging of marine shelly faunas. 1991. Pp. 115209 in Allison, P. A. and Briggs, D. E. G., eds. Taphonomy: releasing the data locked in the fossil record. Plenum, New York.CrossRefGoogle Scholar
Kosloski, M. E., Dietl, G. P., and Handley, J. C.. 2017. Anatomy of a cline: dissecting anti-predatory adaptations in a marine gastropod along the US Atlantic coast. Ecography 40:12851299.CrossRefGoogle Scholar
Leighton, L. R. 2002. Inferring predation intensity in the marine fossil record. Paleobiology 28:328342.2.0.CO;2>CrossRefGoogle Scholar
Lessios, H. 1988. Mass mortality of Diadema antillarum in the Caribbean: what have we learned? Annual Review of Ecology and Systematics 19:371393.CrossRefGoogle Scholar
Lindstrom, A., and Peel, J. S.. 2005. Repaired injuries and shell form in some Palaeozoic pleurotomarioid gastropods. Acta Palaeontologica Polonica 50:697704.Google Scholar
Linnell, J. D., Aanes, R., and Andersen, R.. 1995. Who killed Bambi? the role of predation in the neonatal mortality of temperate ungulates. Wildlife Biology 1:209223.CrossRefGoogle Scholar
Miranda, R. M., Fujinaga, K., and Nakao, S.. 2008. Age and growth of Neptunea arthritica estimated from growth marks in the operculum. Marine Biology Research 4:224235.CrossRefGoogle Scholar
Molinaro, D. J., Collins, B. M., Burns, M. E., Stafford, E. S., and Leighton, L. R.. 2013. Do predatory drill holes influence the transport and deposition of gastropod shells? Lethaia 46:508517.CrossRefGoogle Scholar
Molinaro, D. J., Stafford, E. S., Collins, B. M., Barclay, K. M., Tyler, C. L., and Leighton, L. R.. 2014. Peeling out predation intensity in the fossil record: a test of repair scar frequency as a suitable proxy for predation pressure along a modern predation gradient. Palaeogeography, Palaeoclimatology, Palaeoecology 412:141147.CrossRefGoogle Scholar
Ottens, K. J., Dietl, G. P., Kelley, P. H., and Stanford, S. D.. 2012. A comparison of analyses of drilling predation on fossil bivalves: bulk-vs. taxon-specific sampling and the role of collector experience. Palaeogeography, Palaeoclimatology, Palaeoecology 319:8492.CrossRefGoogle Scholar
Paine, R. 1976. Size-limited predation: an observational and experimental approach with the Mytilus-Pisaster interaction. Ecology 57:858873.CrossRefGoogle Scholar
Perron, F. E. 1983. Growth, fecundity, and mortality of Conus pennaceus in Hawaii. Ecology 64:5362.CrossRefGoogle Scholar
Perron, F. E. 1986. Life history consequences of differences in developmental mode among gastropods in the genus Conus. Bulletin of Marine Science 39:485497.Google Scholar
Powell, M. P., and Kowaleski, M.. 2002. Increase in evenness and sampled alpha diversity through the Phanerozoic: comparison of early Paleozoic and Cenozoic marine fossil assemblages. Geology 30:331334.2.0.CO;2>CrossRefGoogle Scholar
Purton, L., and Brasier, M.. 1997. Gastropod carbonate δ18O and δ13C values record strong seasonal productivity and stratification shifts during the late Eocene in England. Geology 25:871874.2.3.CO;2>CrossRefGoogle Scholar
Ray, M., and Stoner, A. W.. 1994. Experimental analysis of growth and survivorship in a marine gastropod aggregation: balancing growth with safety in numbers. Marine Ecology Progress Series 105:4759.CrossRefGoogle Scholar
Reise, K. 1977. Predation pressure and community structure of an intertidal soft-bottom fauna. Pp. 513519 in Keegan, B. F., Boaden, P. J. S., and Ceidigh, P. O., eds. Biology of benthic organisms. Elsevier, Amsterdam.CrossRefGoogle Scholar
Richardson, C., Saurel, C., Barroso, C., and Thain, J.. 2005. Evaluation of the age of the red whelk Neptunea antiqua using statoliths, opercula and element ratios in the shell. Journal of Experimental Marine Biology and Ecology 325:5564.CrossRefGoogle Scholar
Rigby, J. K. 1958. Frequency curves and death relationships among fossils. Journal of Paleontology 32:10071009.Google Scholar
Rocha, F., Guerra, Á., and González, Á. F.. 2001. A review of reproductive strategies in cephalopods. Biological Reviews 76:291304.CrossRefGoogle ScholarPubMed
Rumrill, S. S. 1990. Natural mortality of marine invertebrate larvae. Ophelia 32:163198.CrossRefGoogle Scholar
Schindler, D. E., Johnson, B. M., MacKay, N. A., Bouwes, N., and Kitchell, J. F.. 1994. Crab: snail size-structured interactions and salt marsh predation gradients. Oecologia 97:4961.CrossRefGoogle ScholarPubMed
Schmidt, N. 1989. Paleobiological implications of shell repair in Recent marine gastropods from the northern Gulf of California. Historical Biology 3:127139.Google Scholar
Schoener, T. W. 1979. Inferring the properties of predation and other injury-producing agents from injury frequencies. Ecology 60:11101115.CrossRefGoogle Scholar
Shimoyama, S. 1985. Size-frequency distribution of living populations and dead shell assemblages in a marine intertidal sand snail, Umbonium (Suchium) moniliferum (Lamarck), and their palaeoecological significance. Palaeogeography, Palaeoclimatology, Palaeoecology 49:327353.CrossRefGoogle Scholar
Shoup, J. B. 1968. Shell opening by crabs of the genus Calappa. Science 160:887888.CrossRefGoogle ScholarPubMed
Signor, P. W., and Brett, C. E.. 1984. The mid-Paleozoic precursor to the Mesozoic marine revolution. Paleobiology 10:229245.CrossRefGoogle Scholar
Sih, A. 1987. Prey refuges and predator-prey stability. Theoretical Population Biology 31:112.CrossRefGoogle Scholar
Sih, S., Englund, G., and Wooster, D.. 1998. Emergent impacts of multiple predators on prey. Trends in Ecology and Evolution 13:350355.CrossRefGoogle ScholarPubMed
Stafford, E. S., Tyler, C. L., and Leighton, L. R.. 2015. Gastropod shell repair tracks predator abundance. Marine Ecology 36:11761184.CrossRefGoogle Scholar
Stanley, S. M. 1973. An ecological theory for the sudden origin of multicellular life in the late Precambrian. Proceedings of the National Academy of Sciences USA 70:14861489.CrossRefGoogle ScholarPubMed
Suzuki, K., Hiraishi, T., Yamamoto, K., and Nashimoto, K.. 2002. Estimation of natural mortality and exploitation rates of whelk Neptunea arthritica by multiple tagging experiment. Fisheries Science 68:8794.CrossRefGoogle Scholar
Vermeij, G. J. 1976. Interoceanic differences in vulnerability of shelled prey to crab predation. Nature 260:135.CrossRefGoogle Scholar
Vermeij, G. J. 1977. The Mesozoic marine revolution: evidence from snails, predators and grazers. Paleobiology 3:245258.CrossRefGoogle Scholar
Vermeij, G. J. 1982. Unsuccessful predation and evolution. American Naturalist 120:701720.CrossRefGoogle Scholar
Vermeij, G. J. 1983. Shell-breaking predation through time. Pp. 649669 in Tevesz, M. J. S. and McCall, P. L., eds. Biotic interactions in recent and fossil benthic communities. Springer, New York.CrossRefGoogle Scholar
Vermeij, G. J. 1993. Evolution and escalation: an ecological history of life. Princeton University Press, Princeton, N.J.Google Scholar
Vermeij, G. J., Schindel, D. E., and Zipser, E.. 1981. Predation through geological time: evidence from gastropod shell repair. Science 214:10241026.CrossRefGoogle ScholarPubMed
Walker, S. E. 1989. Hermit crabs as taphonomic agents. Palaios 4:439452.CrossRefGoogle Scholar
Walker, S. E., and Yamada, S. Behrens. 1993. Implications for the gastropod fossil record of mistaken crab predation on empty mollusc shells. Palaeontology 36:735741.Google Scholar
Wang, Y. and Wang, J.. 2012. Influence of prey refuge on predator–prey dynamics. Nonlinear Dynamics 67:191201.CrossRefGoogle Scholar
Wefer, G., and Berger, W. H.. 1991. Isotope paleontology: growth and composition of extant calcareous species. Marine Geology 100:207248.CrossRefGoogle Scholar
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Modeling durophagous predation and mortality rates from the fossil record of gastropods
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Modeling durophagous predation and mortality rates from the fossil record of gastropods
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Modeling durophagous predation and mortality rates from the fossil record of gastropods
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *