Publications - Dr. Libby Marschall

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RAD-Seq refines previous estimates of genetic structure in Lake Erie walleye

Abstract
Lake Erie map with sampling sites noted
Lake Erie and locations of the walleye local spawning populations sampled for this study (from Figure 1 of this article).

Delineating population structure helps fishery managers to maintain a diverse “portfolio” of local spawning populations (stocks), as well as facilitate stock‐specific management. In Lake Erie, commercial and recreational fisheries for Walleye Sander vitreus exploit numerous local spawning populations, which cannot be easily differentiated using traditional genetic data (e.g., microsatellites). Here, we used genomic information (12,264 polymorphic loci) generated using restriction site‐associated DNA sequencing to investigate stock structure in Lake Erie Walleye. We found low genetic divergence (genetic differentiation index FST = 0.0006–0.0019) among the four Lake Erie western basin stocks examined, which resulted in low classification accuracies for individual samples (40–60%). However, more structure existed between western and eastern Lake Erie basin stocks (FST = 0.0042–0.0064), resulting in greater than 95% classification accuracy of samples to a lake basin. Thus, our success in using genomics to identify stock structure varied with spatial scale. Based on our results, we offer suggestions to improve the efficacy of this new genetic tool for refining stock structure and eventually determining relative stock contributions in Lake Erie Walleye and other Great Lakes populations.

Citation

Chen, K.Y., P.T. Euclide, S.A. Ludsin, W.A. Larson, M.G. Sovic, H.L. Gibbs, E.A. Marschall. 2020. RAD‐Seq Refines Previous Estimates of Genetic Structure in Lake Erie Walleye. Transactions of the American Fisheries Society 149(2):159-173. doi.org/10.1002/tafs.10215

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Otolith microchemistry shows natal philopatry of walleye in western Lake Erie

Abstract
Otolith
Walleye otolith with annuli visible

Natal philopatry is important to the structure of fish populations because it can lead to local adaptations among component stocks of a mixed population, reducing the risk of recruitment failure. By contrast, straying between component stocks may bolster declining populations or allow for colonization of new habitat. To examine rates of natal philopatry and straying among western Lake Erie walleye (Sander vitreus) stocks, we used the concentration of strontium [Sr] in otolith cores to determine the natal origin of adults captured at three major spawning sites: the Sandusky (n = 62) and Maumee (n = 55) rivers and the Ohio reef complex (n = 50) during the 2012–2013 spawning seasons. Mean otolith core [Sr] was consistently and significantly higher for individuals captured in the Sandusky River than for those captured in the Maumee River or Ohio reef complex. Although logistic regression indicates that no individuals with a Maumee River or Ohio reef complex origin were captured in the Sandusky River, quadratic discriminant analysis suggests low rates of straying of fish between the Maumee and Sandusky rivers. Our results suggest little straying and high rates of natal philopatry in the Sandusky River walleye stock. Similar rates of natal philopatry may also exist across western Lake Erie walleye stocks, demonstrating a need for stock-specific management.

Citation

Chen, K.Y., S.A. Ludsin, B.J. Marcek, J.W. Olesik, E.A. Marschall. 2020. Otolith microchemistry shows natal philopatry of walleye in western Lake Erie. Journal of Great Lakes Research, in pressdoi.org/10.1016/j.jglr.2020.06.006

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Modeling larval American shad recruitment in a large river

Abstract
American Shad
American Shad

Climate change is altering the spatial and temporal patterns of temperature and discharge in rivers, which is expected to have implications for the life stages of anadromous fish using those rivers. We developed an individual‐based model to track American Shad Alosa sapidissima offspring within a coarse template of spatially and temporally variable habitat conditions defined by a combination of temperature, river velocity, and prey availability models. We simulated spawning at each river kilometer along a 142‐km reach of the Connecticut River on each day (April 1–August 31) to understand how spawning date and location drive larval recruitment differentially across years and decades (1993–2002 and 2007–2016). For both temperature and flow, interannual variation was large in comparison to interdecadal differences. Variation in simulated recruitment was best explained by a combination of season‐specific spawning temperature and location along the course of the river. The greatest potential recruitment occurred during years in which June temperatures were relatively high. In years when June and July were warmer than average, maximum recruitment resulted from spawning taking place at the upstream portion of the modeled reach. Model scenarios (stationary or passive‐drift larvae; and dams or no dams) had predictable effects. We assumed that the pools above dams had negative impacts on eggs and yolk‐sac larvae that may have been deposited there. Allowing eggs and larvae to drift passively with the current reduced spatial differences in recruitment success among spawning sites relative to stationary eggs and larvae. Our results demonstrate the importance of spatiotemporal environmental heterogeneity for producing positive recruitment over the long term. In addition, our results suggest the importance of successful passage of spawners to historical spawning sites in the Connecticut River upstream of Vernon Dam, especially as conditions shift with climate change.

Citation

Marschall, E.A., D.C. Glover, M.E. Mather, D.L. Parrish. 2020. Modeling Larval American Shad Recruitment in a Large River. North American Journal of Fisheries Management, in pressdoi.org/10.1002/nafm.10460

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The influence of larval growth rate on juvenile recruitment in Lake Erie walleye (Sander vitreus)

Abstract
Walleye larva
Walleye larva

Growth-selective mortality as larvae can influence recruitment in marine fishes. Its importance in freshwater fishes, however, remains speculative. We quantified growth trajectories within annual cohorts (2011–2013) of Lake Erie walleye (Sander vitreus) and their relationship with recruitment. We hypothesized that selection against slow or fast growth would be associated with high mortality and poor recruitment, whereas weak or nonexistent growth-selective mortality co-occurring with fast growth would be associated with good recruitment. We used otoliths to reconstruct growth rates during the first 15 days of life from larvae collected during spring and juvenile recruits (survivors) collected during late summer. We documented growth-selective mortality during 2011 and 2013, which exhibited poor recruitment as expected. During 2012, growth selection was absent, but growth was slow when compared to historical averages, resulting in poor recruitment. Growth was also considered slow in 2011 and 2013, due to multiple interacting conditions. Our study indicates that the relationship among larval growth, mortality, and future recruitment is complex, highlighting the need for continued research into how larval processes affect recruitment dynamics in freshwater fishes.

Citation

May, C.J., S.A. Ludsin, D.C. Glover, E.A. Marschall. 2020. The influence of larval growth rate on juvenile recruitment in Lake Erie walleye (Sander vitreus). Canadian Journal of Fisheries and Aquatic Sciences 77(3):548-555. doi.org/10.1139/cjfas-2019-0059

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Challenging life cycles

Long-term data on sockeye salmon in Alaska show how warmer temperatures during the juvenile freshwater stage of this species can drive shifts in later life history patterns.

Citation

Marschall, E.A. 2019. Challenging life cycles. Nature Ecology & Evolution 3(6):875-876. doi.org/10.1038/s41559-019-0920-4

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assignPOP: An R package for population assignment using genetic, non-genetic, or integrated data in a machine-learning framework

Abstract
  1. The use of biomarkers (e.g., genetic, microchemical and morphometric characteristics) to discriminate among and assign individuals to a population can benefit species conservation and management by facilitating our ability to understand population structure and demography.
  2. Tools that can evaluate the reliability of large genomic datasets for population discrimination and assignment, as well as allow their integration with non‐genetic markers for the same purpose, are lacking. Our r package, assignPOP, provides both functions in a supervised machine‐learning framework.
  3. assignPOP uses Monte‐Carlo and K‐fold cross‐validation procedures, as well as principal component analysis, to estimate assignment accuracy and membership probabilities, using training (i.e., baseline source population) and test (i.e., validation) datasets that are independent. A user then can build a specified predictive model based on the relative sizes of these datasets and classification functions, including linear discriminant analysis, support vector machine, naïve Bayes, decision tree and random forest.
  4. assignPOP can benefit any researcher who seeks to use genetic or non‐genetic data to infer population structure and membership of individuals. assignPOP is a freely available r package under the GPL license, and can be downloaded from CRAN or at https://github.com/alexkychen/assignPOP. A comprehensive tutorial can also be found at https://alexkychen.github.io/assignPOP/.
Citation

Chen, K.Y., E.A. Marschall, M.G. Sovic, A.C. Fries, H.L. Gibbs, S.A. Ludsin. 2018. assignPOP: An R package for population assignment using genetic, non‐genetic, or integrated data in a machine‐learning framework. Methods in Ecology and Evolution 9(2):439-446. doi.org/10.1111/2041-210X.12897

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Individual behavior and pollination ecology: Implications for the spread of sexually transmitted plant diseases

Citation

Real, L.A., E.A. Marschall, B.M. Roche. 2018. Individual behavior and pollination ecology: implications for the spread of sexually transmitted plant diseases. Pages 492-508. In D.L. DeAngelis (editor), Individual-based models and approaches in ecology, 492-508. Chapman and Hall/CRC, New York. doi.org/10.1201/9781351073462

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Experimental and field evaluation of otolith strontium as a marker to discriminate between river-spawning populations of walleye in Lake Erie

Abstract

Otolith microchemistry is a commonly used tool for stock discrimination in fisheries management. Two key questions remain with respect to its effectiveness in discriminating among river-spawning populations. First, do larvae remain in their natal river long enough for their otoliths to pick up that system’s characteristic chemical signature? Second, are larval otolith microchemical differences between natal rivers sufficiently large to overcome spatiotemporal variation in water chemistry? We quantified how larval age, the ratio of ambient strontium to calcium concentrations (Sr:Ca), and water temperature influence otolith Sr in both lab-reared and wild-collected Lake Erie walleye (Sander vitreus). Otolith microchemistry shows promise as a spawning stock discrimination tool, given that otolith Sr in larval walleye (i) is more strongly influenced by ambient Sr:Ca than by temperature; (ii) reflects Sr:Ca levels in the natal environment, even in larvae as young as 2 days old; and (iii) can effectively discriminate between larvae captured in two key Lake Erie spawning tributaries, even in the face of short larval river residence times and within-year and across-year variation in ambient Sr:Ca.

Citation

Chen, K.Y., S.A. Ludsin, M.M. Corey, P.D. Collingsworth, M.K. Nims, J.W. Olesik, K. Dabrowski, J.J. van Tassell, E.A. Marschall. 2017. Experimental and field evaluation of otolith strontium as a marker to discriminate between river-spawning populations of walleye in Lake Erie. Canadian Journal of Fisheries and Aquatic Sciences 74:693-701. doi.org/10.1139/cjfas-2015-0565

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Full publications list

  1. Chen, K.Y., P.T. Euclide, S.A. Ludsin, W.A. Larson, M.G. Sovic, H.L. Gibbs, E.A. Marschall. 2020. RAD‐Seq Refines Previous Estimates of Genetic Structure in Lake Erie Walleye. Transactions of the American Fisheries Society 149(2):159-173. doi.org/10.1002/tafs.10215
  2. Chen, K.Y., S.A. Ludsin, B.J. Marcek, J.W. Olesik, E.A. Marschall. 2020. Otolith microchemistry shows natal philopatry of walleye in western Lake Erie. Journal of Great Lakes Research, in pressdoi.org/10.1016/j.jglr.2020.06.006
  3. Marschall, E.A., D.C. Glover, M.E. Mather, D.L. Parrish. 2020. Modeling Larval American Shad Recruitment in a Large River. North American Journal of Fisheries Management, in pressdoi.org/10.1002/nafm.10460
  4. May, C.J., S.A. Ludsin, D.C. Glover, E.A. Marschall. 2020. The influence of larval growth rate on juvenile recruitment in Lake Erie walleye (Sander vitreus). Canadian Journal of Fisheries and Aquatic Sciences 77(3):548-555. doi.org/10.1139/cjfas-2019-0059
  5. Marschall, E.A. 2019. Challenging life cycles. Nature Ecology & Evolution 3(6):875-876. doi.org/10.1038/s41559-019-0920-4
  6. Chen, K.Y., E.A. Marschall, M.G. Sovic, A.C. Fries, H.L. Gibbs, S.A. Ludsin. 2018. assignPOP: An R package for population assignment using genetic, non‐genetic, or integrated data in a machine‐learning framework. Methods in Ecology and Evolution 9(2):439-446. doi.org/10.1111/2041-210X.12897
  7. Real, L.A., E.A. Marschall, B.M. Roche. 2018. Individual behavior and pollination ecology: implications for the spread of sexually transmitted plant diseases. Pages 492-508. In D.L. DeAngelis (editor), Individual-based models and approaches in ecology, 492-508. Chapman and Hall/CRC, New York. doi.org/10.1201/9781351073462
  8. Chen, K.Y., S.A. Ludsin, M.M. Corey, P.D. Collingsworth, M.K. Nims, J.W. Olesik, K. Dabrowski, J.J. van Tassell, E.A. Marschall. 2017. Experimental and field evaluation of otolith strontium as a marker to discriminate between river-spawning populations of walleye in Lake Erie. Canadian Journal of Fisheries and Aquatic Sciences 74:693-701. doi.org/10.1139/cjfas-2015-0565
  9. DuFour, M.R., C.J. May, E.F. Roseman, S.A. Ludsin, C.S. Vandergoot, J.J. Pritt, M.E. Fraker, J.J. Davis, J.T. Tyson, J.G. Miner, E.A. Marschall, and C. Mayer. 2015. Portfolio theory as a management tool to guide conservation and restoration of multi‐stock fish populations. Ecosphere, 6(12), pp.1-21. doi.org/10.1890/ES15-00237.1
  10. Farmer, T.M., E.A. Marschall, K. Dabrowski, and S.A. Ludsin. 2015. Short winters threaten temperate fish populations. Nature Communications 6:7724. doi.org/10.1038/ncomms8724
  11. Fraker, M.E., E.J. Anderson, C.J. May, K.Y. Chen, J.J. Davis, K.M. DeVanna, M.R. DuFour, E.A. Marschall, C.M. Mayer, J.G. Miner, K.L. Pangle, J.J. Pritt, E.F. Roseman, J.T. Tyson, Y. Zhao, S.A. Ludsin. 2015. Stock-specific advection of larval walleye (Sander vitreus) in western Lake Erie: Implications for larval growth, mixing, and stock discrimination. Journal of Great Lakes Research 41(3):830–845. doi.org/10.1016/j.jglr.2015.04.008
  12. Gover, T.R., M.K. Nims, J.J. Van Tassell, P.D. Collingsworth, J.W. Olesik, S.A. Ludsin, and E.A. Marschall. 2014. How much cleaning is needed when processing otoliths from fish larvae for microchemical analysis? Transactions of the American Fisheries Society 143(3):779-783. doi.org/10.1080/00028487.2014.889749
  13. Kallis, J.L., and E.A. Marschall. 2014. How body size and food availability influence first-winter growth and survival of a stocked piscivore. Transactions of the American Fisheries Society 143(6):1434-1444. doi.org/10.1080/00028487.2014.945660
  14. Beuchel, J., E.A. Marschall, D.D. Aday. 2013. Energy allocation patterns in a multiple-spawning sunfish: evidence for an income-based reproductive strategy. Fisheries Management and Ecology 20(6):508-517. doi.org/10.1111/fme.12041
  15. Dabrowski, K., M. Korzeniowska, T.M. Farmer, S.A. Ludsin, and E.A. Marschall. 2013. The function of wax esters in larval fish transition from endogenous to exogenous nutrition - are freshwater fish the exception or the rule? Communications in Agricultural and Applied Biological Sciences 78(4):102-103. PMID: 25141637
  16. May, C.J., D.D. Aday, R.S. Hale, J.C. Seiber-Denlinger, and E.A. Marschall. 2012. Modeling habitat selection of a top predator: considering growth and physical environments in a spatial context. Transactions of the American Fisheries Society 141(1):215-223. doi.org/10.1080/00028487.2012.655122
  17. Collingsworth, P.D. and E.A. Marschall. 2011. Identifying relationships between catches of spawning-condition yellow perch and environmental variables in the western basin of Lake Erie. Transactions of the American Fisheries Society 140(1):31-36. doi.org/10.1080/00028487.2011.545018
  18. Collingsworth, P.D. and E.A. Marschall. 2011. Spatial and temporal patterns in maternal energetic traits of yellow perch (Perca flavescens) in Lake Erie. Freshwater Biology 56(12):2500-2513. doi.org/10.1111/j.1365-2427.2011.02675.x
  19. Marschall, E.A., M.E. Mather, D.L. Parrish, G.W. Allison, and J.R. McMenemy. 2011. Migration delays caused by anthropogenic barriers: modeling dams, temperature, and success of migrating salmon smolts. Ecological Applications 21(8):3014–3031. doi.org/10.1890/10-0593.1
  20. Rinchard, J., K. Ware, K. Dabrowski, J.J. Van Tassell, E.A. Marschall, R.A. Stein. 2011. Egg thiamine concentration affects embryo survival in Lake Erie walleye. Environmental Biology of Fishes 90:53-60. doi.org/10.1007/s10641-010-9717-7
  21. Collingsworth, P.D., J.J. Van Tassell, J.W. Olesik, and E.A. Marschall. 2010. Effects of temperature and elemental concentration on the chemical composition of juvenile yellow perch (Perca flavescens) otoliths. Canadian Journal of Fisheries and Aquatic Sciences 67(7):1187-1196. doi.org/10.1139/F10-050
  22. DeVries, D.R., E.A. Marschall, and R.A. Stein. 2009. Exploring the peer review process: what is it, does it work, and can it be improved? Fisheries 34(6):270-279. doi.org/10.1577/1548-8446-34.6.270
  23. Garvey, J.E., R.A. Wright, and E.A. Marschall. 2009. Searching for threshold shifts in spawner-recruit data. Canadian Journal of Fisheries and Aquatic Sciences 66(2):312-320. doi.org/10.1139/F08-212
  24. Spoelstra, J.A., R.A. Stein, J.A. Royle, and E.A. Marschall. 2008. Movement of reservoir-stocked riverine fish between tailwaters and rivers. Transactions of the American Fisheries Society 137(5):1530-1542. doi.org/10.1577/T06-206.1
  25. Steinhart, G.B., E.S. Dunlop, M.S. Ridgway, and E.A. Marschall. 2008. Should I stay or should I go? Optimal parental care decisions of a nest-guarding fish. Evolutionary Ecology Research 10(3):351-371. [pdf]
  26. Southward-Hogan, L., E.A. Marschall, C. Folt, R.A. Stein. 2007. How non-native species in Lake Erie influence trophic transfer of mercury and lead to top predators. Journal of Great Lakes Research 33(1):46-61. doi.org/10.3394/0380-1330(2007)...
  27. Steinhart, G.B., M.E. Sandrene, S. Weaver, R.A. Stein, and E.A. Marschall. 2005. Increased parental care cost for nest-guarding fish in a lake with hyperabundant nest predators. Behavioral Ecology 16(2):427-434. doi.org/10.1093/beheco/ari006
  28. Steinhart, G.B., N.J. Leonard, R.A. Stein, and E.A. Marschall. 2005. Effects of storms, angling, and nest predation during angling on smallmouth bass (Micropterus dolomieu) nest success. Canadian Journal of Fisheries and Aquatic Sciences 62(11):2649-2660. doi.org/10.1139/f05-171
  29. Asoh, K., T. Yoshikawa, R. Kosaki, and E.A. Marschall. 2004. Damage to cauliflower coral by monofilament fishing lines in Hawaii. Conservation Biology 18(6):1645-1650. hdl.handle.net/1811/36709
  30. Steinhart, G.B., E.A. Marschall, and R.A. Stein. 2004. Round goby predation on smallmouth bass offspring in nests during experimental catch-and-release angling. Transactions of the American Fisheries Society 133(1):121-131. doi.org/10.1577/T03-020
  31. Steinhart, G.B., R.A. Stein, and E.A. Marschall. 2004. High growth rate of young-of-year smallmouth bass in Lake Erie: a result of the round goby invasion? Journal of Great Lakes Research 30(3):381-389. doi.org/10.1016/S0380-1330(04)70355-X
  32. Yoder, J.A, E.A. Marschall, and D.A. Swanson. 2004. The cost of dispersal: predation as a function of movement and site familiarity in ruffed grouse. Behavioral Ecology 15(3):469-476. doi.org/10.1093/beheco/arh037
  33. Bunnell, D.B. and E.A. Marschall. 2003. Optimal energy allocation to ovaries after spawning. Evolutionary Ecology Research 5(3):439–457. hdl.handle.net/1811/36703
  34. Garvey, J.E. and E.A. Marschall. 2003. Understanding latitudinal trends in fish body size through models of optimal seasonal energy allocation. Canadian Journal of Fisheries and Aquatic Sciences 60(8):938-948. doi.org/10.1139/f03-083
  35. Treydte, A.C., J.B. Williams, E. Bedi, S. Ostrowski, P.J. Seddon, E.A. Marschall, T.A. Waite, and K. Ismail. 2001. In search of the optimal management strategy for Arabian oryx. Animal Conservation 4(3):239-249. doi.org/10.1017/S1367943001001287
  36. Doherty, P.F., E.A. Marschall, and T. Grubb. 1999. Balancing conservation and economic gain: a dynamic programming approach. Ecological Economics 29(3):349-358. doi.org/10.1016/S0921-8009...
  37. Kershner, M.W., D.M. Schael, R.L. Knight, R.A. Stein, and E.A. Marschall. 1999. Modeling sources of variation for growth and predatory demand of Lake Erie walleye, 1986-1995. Canadian Journal of Fisheries and Aquatic Sciences 56(4):527-538. Lead article. doi.org/10.1139/f98-193
  38. Martinez, F.A. and E.A. Marschall. 1999. A dynamic model of group-size choice in the coral reef fish Dascyllus albisella. Behavioral Ecology 10(5):572-577. doi.org/10.1093/beheco/10.5.572
  39. Mauck, R.A., E.A. Marschall, and P.G. Parker. 1999. Adult survival and imperfect assessment of parentage: Effects on male parenting decisions. The American Naturalist 154:99-109. doi.org/10.1086/303216
  40. Garvey, J.E., E.A. Marschall, and R.A. Wright. 1998. From star charts to stoneflies: detecting relationships in continuous bivariate data. Ecology 79(2):442-447. doi.org/10.1890/0012-9658(1998)...
  41. Kershner, M.W. and E.A. Marschall. 1998. Allocating sampling effort to equalize precision of electrofishing catch per unit effort. North American Journal of Fisheries Management 18(4):822–831. doi.org/10.1577/1548-8675(1998)...
  42. Marschall, E.A. and B.M. Roche. 1998. Using models to enhance the value of information from observations and experiments. Pages 281-297. In, W.J. Resetarits and J. Bernardo (editors), Experimental Ecology: Issues and Perspectives. Oxford University Press, New York. ISBN 0-19-510241-X 
  43. Marschall, E.A., D.A. Roff, T.P. Quinn, J.A. Hutchings, N.B. Metcalfe, T.A. Bakke, R.L. Saunders, and L. Poff. 1998. A framework for understanding Atlantic salmon (Salmo salar) life history. Canadian Journal of Fisheries and Aquatic Sciences 55(Supplement 1):48-55. doi.org/10.1139/d98-007
  44. Mion, J.B., R.A. Stein, and E.A. Marschall. 1998. River discharge drives survival of larval walleye. Ecological Applications 8(1):88-103. doi.org/10.1890/1051-0761(1998)...
  45. Rice, J.A., L.B. Crowder, and E.A. Marschall. 1997. Predation on juvenile fishes: dynamic interactions between size‑ structured predators and prey. Pages 333-356. In, R.C. Chambers and E.A. Trippel (editors), Early Life History and Recruitment in Fish Populations. Chapman and Hall, London. doi.org/10.1007/978-94-009-1439-1_12
  46. Marschall, E.A. and L.B. Crowder. 1996. Assessing population responses to multiple anthropogenic effects: A case study with brook trout. Ecological Applications 6:152-167. doi.org/10.2307/2269561
  47. Marschall, E.A. and L.B. Crowder. 1995. Density-dependent survival as a function of size in juvenile salmonids in streams. Canadian Journal of Fisheries and Aquatic Sciences 52:136-140. Erratum: volume 52:2304. doi.org/10.1139/f95-013
  48. Pappas, P.W., E.A. Marschall, S.H. Morrison, G.M. Durka, and C.S. Daniel. 1995. Increased coprophagic activity of the beetle, Tenebrio molitor, on feces containing eggs of the tapeworm, Hymenolepis diminuta. International Journal for Parasitology 25(10):1179-1184. doi.org/10.1016/0020-7519(95)00051-3
  49. DeAngelis, D.L, K.A. Rose, L.B. Crowder, E.A. Marschall, and D. Lika. 1993. Fish cohort dynamics: application of complementary modeling approaches. The American Naturalist 142(4):604-622. doi.org/10.1086/285560
  50. Rice, J.R., T.J. Miller, K.A. Rose, L.B. Crowder, E.A. Marschall, A. Trebitz, and D.L. DeAngelis. 1993. Growth rate variation and larval survival: inferences of an individual-based size-dependent predation model. Canadian Journal of Fisheries and Aquatic Sciences 50:133-142. doi.org/10.1139/f93-015
  51. Bronmark, C., S.P. Klosiewski, and R.A. Stein. 1992. Indirect effects of predation in a freshwater, benthic food chain. Ecology 73(5):1662-1674. doi.org/10.2307/1940018
  52. Crowder, L.B., J.A. Rice, T.J. Miller, and E.A. Marschall. 1992. Empirical and theoretical approaches to size-based interactions and recruitment variability in fishes. Pages 237-255 in D.L. DeAngelis and L.J. Gross (editors), Individual-Based Models and Approaches in Ecology: Populations, Communities, and Ecosystems. Routledge, Chapman, and Hall: New York. doi.org/10.1201/9781351073462
  53. Real, L.A., E.A. Marschall, and B.M. Roche. 1992. Individual behavior and pollination ecology: implications for the spread of sexually transmitted plant diseases. Pages 492-508 in D.L. DeAngelis and L.J. Gross (editors), Individual-Based Models and Approaches in Ecology: Populations, Communities, and Ecosystems. Routledge, Chapman, and Hall: New York. doi.org/10.1201/9781351073462
  54. Savino, J.F., E.A. Marschall, and R.A. Stein. 1992. Bluegill growth as modified by plant density: an exploration of underlying mechanisms. Oecologia 89:153-160. doi.org/10.1007/BF00317212
  55. Marschall, E.A., P.L. Chesson, and R.A. Stein. 1989. Foraging in a patchy environment: prey-encounter rate and residence time distributions. Animal Behaviour 37(3):444-454. doi.org/10.1016/0003-3472(89)90091-2
  56. Miller, T.J., L.B. Crowder, J.A. Rice, and E.A. Marschall. 1988. Larval size and recruitment mechanisms in fishes: toward a conceptual framework. Canadian Journal of Fisheries and Aquatic Sciences 45(9):1657-1670. doi.org/10.1139/f88-197
  57. Stein, R.A., C.G. Goodman, and E.A. Marschall. 1984. Using time and energetic measures of cost in estimating prey value for fish predators. Ecology 65(3):702-715. doi.org/10.2307/1938042
  58. Gross, K.L., T. Berner, E.A. Marschall, and C. Tomcko. 1983. Patterns of resource allocation among five herbaceous perennials. Bulletin of the Torrey Botanical Club 110(3):345-352. doi.org/10.2307/2996188