Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-29T15:18:59.569Z Has data issue: false hasContentIssue false

Evaluating hypotheses of instar-grouping in arthropods: a maximum likelihood approach

Published online by Cambridge University Press:  08 April 2016

Gene Hunt
Affiliation:
University of Chicago, Chicago, Illinois 60637. E-mail: eg-hunt@uchicago.edu
Ralph E. Chapman
Affiliation:
Applied Morphometrics Laboratory, ADP, EG-15. NHB: MRC 136, Natural Museum of Natural History. Smithsonian Institution, Washington, D.C. 20560. E-mail: Chapman.Ralph@NMNH.SI.EDU

Abstract

The ontogeny of arthropod exoskeletons is punctuated by short periods of growth following each molt, separated by longer stages of unchanging morphology called instars. The recognition of instar clusters in size distributions has been important in understanding the growth and evolution of fossil arthropods. Generally, these clusters have been identified by inspection, but this approach has been criticized for its subjectivity. In this paper, we describe a statistical framework for evaluating hypotheses of clustering based on maximum likelihood analysis of mixture models. The approach assumes that individuals are normally distributed within instars; thus an arthropod size distribution can be considered a mixture of normal distributions. This methodology provides an objective framework to compare various plausible hypotheses of grouping, including the possibility that there is no significant grouping at all.

We apply this method to evaluate clustering in two trilobite species, Ampyxina bellatula and Piochaspis sellata. Both of these data sets show statistically significant evidence of clustering, a phenomenon rarely documented for holaspid-stage trilobites. After consideration of alternative causes of clustering, we argue that the observed groupings are best explained as instar groups. In these two species, growth increments between molts were similar throughout the observed portion of ontogeny, although subtle yet significant variation can be seen within the ontogeny of Ampyxina bellatula.

Type
Articles
Copyright
Copyright © The Paleontological Society 

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.)

References

Literature Cited

Adrain, J. M., Fortey, R. A., and Westrop, S. R. 1998. Post-Cambrian trilobite diversity and evolutionary faunas. Science 280:19221925.Google Scholar
Anderson, B. G., Lumer, H., and Zupancic, L. J. 1937. Growth and variability in Daphnia pulex. Biological Bulletin 73:444463.Google Scholar
Andrews, H. E., Brower, J. C., Gould, S. J., and Reyment, R. A. 1974. Growth and variation in Eurypterus remipes DeKay. Bulletin of the Geological Institution of the University of Uppsala, new series 4:81114.Google Scholar
Archie, J. W. 1985. Methods for coding variable morphological features for numerical taxonomic analysis. Systematic Zoology 34:326345.Google Scholar
Basford, K. E., Greenway, D. R., Mclachlan, G. J., and Peel, D. 1997. Standard errors of fitted component means of normal mixtures. Computational Science 12:117.Google Scholar
Brezinski, D. K. 1986. An opportunistic Upper Ordovician trilobite assemblage from Missouri. Lethaia 19:315325.CrossRefGoogle Scholar
Broadbent, S. R. 1955. Quantum hypotheses. Biometrika 42:4557.Google Scholar
Busch, R. M., and Swartz, F. M. 1985. Molting and description of a new homalonotid trilobite from Pennsylvania. Journal of Paleontology 59:10621074.Google Scholar
Chatterton, B. D. E. 1994. Ordovician proetide trilobite Dimeropyge, with a new species from Northwestern Canada. Journal of Paleontology 68:541556.Google Scholar
Chatterton, B. D. E., and Speyer, S. E. 1990. Applications of the study of trilobite ontogeny. In Mikulic, D. G., ed. Arthropod paleobiology. Short Courses in Paleontology 3:116136. Paleontological Society, Knoxville, Tenn.Google Scholar
Chatterton, B. D. E., and Speyer, S. E. 1997. Ontogeny. Pp. 173248in Whittington, H. B. et al. Arthropoda 1, Trilobita. Part O (revised) of R. L. Kaesler. Treatise on invertebrate paleontology. Geological Society of America, Boulder, Colo., and University of Kansas, Lawrence.Google Scholar
Chatterton, B. D. E., Siveter, D. J., Edgecombe, G. D., and Edgecombe, H. A. S. 1990. Larvae and relationships of the Calymenina (Trilobita). Journal of Paleontology 64:255277.CrossRefGoogle Scholar
Chatterton, B. D. E., Edgecombe, G. D., Speyer, S. E., Hunt, A. S., and Fortey, R. A. 1994. Ontogeny and relationships of Trinucleoidea. Journal of Paleontology 68:523540.CrossRefGoogle Scholar
Cisne, J. L. 1973. Life history of an Ordovician trilobite Triarthrus eatoni. Ecology 54:135142.Google Scholar
Clarke, J. S., Fastie, C., Hurtt, G., Jackson, S. T., Johnson, C., King, G. A., Lewis, M., Lynch, J., Pacala, S., Prentice, C., Schupp, E. W., Webb, T. III, and Wyckoff, P. 1998. Reid's paradox of rapid plant migration. Bioscience 48:1324.Google Scholar
Cole, B. J. 1980. Growth ratios in holometabolous and hemimetabolous insects. Annals of the Entomological Society of America 73:489491.Google Scholar
Crônier, C., Renaud, S., Feist, R., and Auffray, J.-C. 1998. Ontogeny of Trimerocephalus lelievrei (Trilobita, Phacopida), a representative of the Late Devonian phacopine paedomorphocline: a morphometric approach. Paleobiology 24:359370.Google Scholar
Daley, H. V. 1985. Insect morphometrics. Annual Review of Entomology 30:415438.CrossRefGoogle Scholar
Dempster, A. P., Laird, N. M., and Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society B 39:138.Google Scholar
Dyar, H. G. 1890. The number of molts of lepidopterous larvae. Psyche 5:420422.CrossRefGoogle Scholar
Edwards, A. W. F. 1992. Likelihood, expanded ed.Johns Hopkins University Press, Baltimore.CrossRefGoogle Scholar
Enders, F. 1976. Size, food-finding, and Dyar's Constant. Environmental Entomology 5:110.CrossRefGoogle Scholar
Fenwick, G. D. 1984. Life history and population biology of the giant ostracod Leuroleberis zealandica (Baird, 1850) (Myodocopida). Journal of Experimental Marine Biology and Ecology 77:255289.Google Scholar
Flury, B. 1997. A first course in multivariate statistics. Springer, New York.Google Scholar
Foote, M. 1996. On the probability of ancestors in the fossil record. Paleobiology 22:141151.CrossRefGoogle Scholar
Gaines, J. C., and Campbell, F. L. 1935. Dyar's Rule as related to the number of instars of the corn ear worm, Heliothis obsoleta (Fab.), collected in the field. Annals of the Entomological Society of America 28:445461.Google Scholar
Hartnoll, R. G. 1982. Growth. Pp. 111196in Abele, L. G., ed. Embryology, morphology, and genetics, Vol. 2. The biology of the Crustacea. Academic Press, New York.Google Scholar
Hartnoll, R. G., and Dalley, R. 1981. The control of size variation within instars of a crustacean. Journal of Experimental Marine Biology and Ecology 53:235239.CrossRefGoogle Scholar
Hughes, N. C., and Chapman, R. E. 1995. Growth and variation in the Silurian proetide trilobite Aulacopleura konincki and its implications for trilobite paleobiology. Lethaia 28:333353.Google Scholar
Hunt, A. S. 1967. Growth, variation, and instar development of an agnostid trilobite. Journal of Paleontology 41:203208.Google Scholar
Hutchinson, G. E., and Tongring, N. 1984. A possible adaptive significance of the Brooks-Dyar rule. Journal of Theoretical Biology 106:437439.CrossRefGoogle Scholar
Hutchinson, J. M. C., McNamara, J. M., Houston, A., and Vollrath, F. 1997. Dyar's Rule and the Investment Principle: optimal moulting strategies if feeding rate is size-dependent and growth is discontinuous. Philosophical Transactions of the Royal Society of London B 352:113138.CrossRefGoogle Scholar
Jones, D. S., and Gould, S. J. 1999. Direct measurements of age in fossil Gryphaea: the solution to a classic problem in heterochrony. Paleobiology 25:158187.Google Scholar
Kado, R., and Kim, M.-H. 1996. Larval development of Octomeris sulcata Nilsson-Cantell (Cirripedia: Thoracica: Chthamalidae). Hydrobiologia 325:6576.Google Scholar
Kesling, R. V. 1953. A slide rule for determination of instars in ostracod species. Contributions from the Museum of Paleontology, University of Michigan 11:97109.Google Scholar
Klingenberg, C. P. 1996. Individual variation of ontogenies: a longitudinal study of growth and timing. Evolution 50:24122428.Google Scholar
Kopaska-Merkel, D. 1981. Ontogeny of Ehmaniella: implications for trilobite ecology. In Taylor, M. E., ed. Short papers for the second international symposium on the Cambrian System. U.S. Geological Survey Open-File Report 81–743:111114.Google Scholar
Kopaska-Merkel, D. 1988. Trace-fossil frequency modes and arthropod growth. Northeastern Geology 10:300306.Google Scholar
Lee, D.-C., and Chatterton, B. D. E. 1997. Ontogenies of trilobites from the Lower Ordovician Garden City Formation of Idaho and their implications for the phylogeny of the Cheirurina. Journal of Paleontology 71:683702.CrossRefGoogle Scholar
Levi-Setti, R. 1993. Trilobites, 2d ed.University of Chicago Press, Chicago.Google Scholar
Longhurst, A. R. 1986. Instar increments in copepod growth. Canadian Journal of Fisheries and Aquatic Science 43:16711674.Google Scholar
Maiorana, V. 1978. An explanation of ecological and developmental constants. Nature 273:375377.Google Scholar
McKinney, M. 1999. Heterochrony: beyond words. Paleobiology 25:149153.Google Scholar
McLachlan, G. J., and Basford, K. E. 1988. Mixture models: inference and applications to clustering. Marcel Dekker, New York.Google Scholar
McLachlan, G. J., and Krishnan, T. 1997. The EM algorithm and extensions. Wiley, New York.Google Scholar
McLachlan, G. J., and Peel, D. 1998. MIXFIT: an algorithm for the automatic fitting and testing of normal mixture models. Pp. 553557in Proceedings of the 14th international conference on pattern recognition. IEEE Computer Society, Los Alamitas, Calif.Google Scholar
Olszewski, T. 1999. Taking advantage of time-averaging. Paleobiology 25:226238.CrossRefGoogle Scholar
Palmer, A. R. 1957. Ontogenetic development of two olenellid trilobites. Journal of Paleontology 31:105128.Google Scholar
Palmer, A. R. 1962. Comparative ontogeny of some opisthoparian, gonatoparian, and proparian Upper Cambrian trilobites. Journal of Paleontology 36:8797.Google Scholar
Pearson, J. D., Morrell, C. H., and Brant, L. J. 1992. Mixture models for investigating complex distributions. Journal of Quantitative Anthropology 3:325345.Google Scholar
Poulsen, V. 1974. Olenellacean trilobites from Eastern North Greenland. Bulletin of the Geological Society of Denmark 23:79101.Google Scholar
Quinn, T. J., and Deriso, R. B. 1999. Quantitative fish dynamics. Oxford University Press, New York.CrossRefGoogle Scholar
Raup, D. M., and Sepkoski, J. J. Jr. 1982. Mass extinctions in the marine fossil record. Science 215:15011503.CrossRefGoogle ScholarPubMed
Retallack, G. J., and Feakes, C. R. 1987. Trace fossil evidence for Late Ordovician animals on land. Science 235:6163.Google Scholar
Reyment, R. A. 1963. Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda, Part 2. Danian, Paleocene, and Eocene Ostracoda. Stockholm Contributions in Geology 10:1287.Google Scholar
Rice, A. L. 1968. Growth ‘rules’ and the larvae of decapod crustaceans. Journal of Natural History 2:525530.Google Scholar
Romano, M. 1976. The trilobite genus Placoparia from the Ordovician of the Valongo area, North Portugal. Geological Magazine 113:1128.Google Scholar
Schweitzer, P. N., Kaesler, R. L., and Lohmann, G. P. 1986. Ontogeny and heterochrony in the ostracode Cavellina Coryell from Lower Permian rocks in Kansas. Paleobiology 12:290301.Google Scholar
Sekiguchi, K., Seshimo, H., and Sugita, H. 1988. Post-embryonic development of the horseshoe crab. Biological Bulletin 174:337345.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1981. A factor analytic description of the Phanerozoic marine fossil record. Paleobiology 7:3653.Google Scholar
Sheldon, P. R. 1988. Trilobite size-frequency distributions, recognition of instars, and phyletic size changes. Lethaia 21:293306.Google Scholar
Simpson, G. G., Roe, A., and Lewontin, R. C. 1960. Quantitative zoology, revised ed.Harcourt, Brace, New York.Google Scholar
Smith, B. D., and Jamieson, G. S. 1989. Growth of male and female dungeness crabs near Tofino, British Columbia. Transactions of the American Fisheries Society 118:556563.Google Scholar
Sokal, R. R., and Rohlf, F. J. 1995. Biometry, 3d ed.W. H. Freeman, New York.Google Scholar
Strait, D. S., Moniz, M. A., and Strait, P. T. 1996. Finite mixture coding: a new approach to coding continuous characters. Systematic Biology 45:6778.Google Scholar
Tanaka, A. 1981. Regulation of body size during larval development in the German cockroach, Blattella germanica. Journal of Insect Physiology 27:587592.Google Scholar
Tuck, I. D., Chapman, C. J., and Atkinson, R. J. A. 1997. Population biology of the Norway lobster, Nephrops norvegicus (L.) in the Firth of Clyde, Scotland. I. Growth and density. Journal of Marine Science 54:125135.Google Scholar
Twombly, S., and Burns, C. W. 1996. Exuvium analysis: a nondestructive method of analyzing copepod growth and development. Limnology and Oceanography 41:13241329.Google Scholar
Van Valen, L. M. 1984. A resetting of Phanerozoic community evolution. Nature 307:5052.Google Scholar
West, T. L., and Costlow, J. D. 1987. Size regulation in larvae of the crustacean Balanus eburneus (Cirripedia: Thoracica). Marine Biology 96:4758.Google Scholar
Whittington, H. B. 1997. Mode of life, habits and occurrence. Pp. 137169in Whittington, H. B. et al. Arthropoda 1, Trilobita. Part O (revised) of R. L. Kaesler. Treatise on invertebrate paleontology. Geological Society of America, Boulder, Colo., and University of Kansas, Lawrence.Google Scholar
Zhang, X.-G. 1989. Ontogeny of an Early Cambrian eodiscoid trilobite from Henan, China. Lethaia 22:1329.Google Scholar