Project Title:
The effects of prescribed burning in grasslands on the population structure of predatory beetles: a spatial modeling approach.

Project Description (short):
The spatial structure of populations and communities has become increasingly important to ecologists because it provides insights into ecological patterns and processes. For example, spatial structure influences parasitism rates in forests, the occurrence of generalist and specialist insect herbivores in agricultural landscapes, and the impact of grazing in desert grasslands. From a practical standpoint, understanding the spatial structure of a population can indicate the proper sampling scheme and statistical protocol.

Given the underlying importance of spatial phenomena in ecological studies, it is imperative that undergraduate students learn the mathematical approaches for quantifying and modeling spatial structure. The emergence of geostatistics (including semivariance, autocorrelation, and kriging) has supported the growing biological interest in spatial structure. Geostatistics is based on the 'general regionalized variable' model and the premise of spatial continuity - that is, sampling points that are closer together are more similar to one another than sampling points that are farther apart. Spatial autocorrelation has been used in a number of biological arenas; it identifies spatial ranges over which variables are similar. Semivariance is more appropriate if the purpose of the study is to model the variance in a dependent variable as a function of space, or lag distance. Finally, kriging represents an extension of both autocorrelation and semivariance in that its main purpose is to interpolate (rather than describe or model) values of a dependent variable between observed data points.

The purpose of the proposed study is to explore the relationship between a disturbance event (prescribed burning and mowing) in grasslands and the distribution and abundance of predatory beetles and grasshoppers as described by mathematical models of spatial structure (e.g., spatial autocorrelation, semivariance, and kriging). The study will take place in six CRP fields in Scotland County, MO. The fields differ in their management techniques (three burned, three mowed). The general approach, which will be modified with student input, will be to develop a spatially explicit, grid-based sampling design that utilizes pitfall traps. Captured beetles and grasshoppers will be identified and counted using resources (identification texts, TSU insect collection, and computer) in Dr. Gering's lab. The students and both professors will then analyze the data using basic statistical methods as well as geostatistical approaches. These approaches, as well as exploratory data analysis and data transformations, will allow the students to apply the techniques they learned in introductory statistics courses.

Skills needed:
Basic familiarity with statistics; comfort with handling and sacrificing insects; ability to work in adverse field conditions (heat and biting insects); enthusiasm.

Start Date:
January 2005

End Date:
December 2005

Mentors:
Prof. Dean DeCock (Biology), decock@truman.edu
Prof. Jon Gering (Mathematics), jgering@truman.edu

Accomplishments:

• Roberta Rader and Mark McKelvey. "The Spatial Ecology of the Ground Beetle Evarthus alternans (Casey 1920) in Burned and Unburned Grasslands" Truman Student Research Conference. April 2006.
• R. Rader, M. Mc Kelvey, J. Gering, and D. De Cock. ”The effects of Management Practices on the Activity Density and Spatial Structure of the Carabid Beetle Evarthus alternans in a Northeast Missouri Grassland” US-IALE Annual Symposium, March 29-31,2006, San Diego, CA.

Past Students:

• Mark McKelvey, 2005 (Mathematics)
• Robbie Rader, 2005 (Biology)

About Prof. DeCock:
Dr. De Cock was born and raised in eastern Iowa and rebelling against his Hawkeye upbringing, he chose to attend Iowa State University where he received a B.S. in Mechanical Engineering. Following several years in the working world as a project engineer he returned to school at the University of Iowa (Go Hawkeyes!) to complete an M.S. in Quality Management and Productivity. He then worked for several years as a Quality Engineer for Maytag before returning to Iowa State to complete a co-major Ph.D. in Statistics and Industrial Engineering. While working on his Ph.D. he spent his summers working for several large corporations (Lennox, 3M, Corning) as a statistical intern.

Dr. De Cock's past research interests include both orthogonal arrays and spatial statistics (kriging). Additionally, in his 4 years at Truman he has mentored capstone students in several different areas of applied statistics including regression, reliability, discriminant analysis, and micro-array analysis.

In his limited free time Dr. De Cock enjoys swimming, reading the Des Moines Register (Sundays at McDonalds), playing Xbox, fishing, and working out at the SRC. He roots for Iowa and Iowa State and watches them anytime they are on television!

About Prof. Gering:
Dr. Gering was born in Ritzville, WA in 1972. He attended Bethel College in Kansas and graduated with honors in 1994. After working for a year at the University of Kansas as a tutor for the athletic department, he left for graduate school at Miami University in Oxford, OH. He completed his M.S. (1997) and Ph.D. (2001) in the Zoology department at Miami University. Both degrees emphasized patterns and processes in ecological communities. He has been at Truman State University since 2001. Dr. Gering's lab uses macroevolutionary approaches to understand the population and community ecology of katydids (Orthoptera: Tettigoniidae).

Dr. Gering enjoys spending time with his wife (Deborah) and his 18-month old son (Benjamin). He also enjoys reading, traveling, racquetball, and the fellowship of eating. He roots for the Green Bay Packers and Seattle Seahawks during football season and rarely misses a televised Kansas Jayhawk game during the college basketball season.

Project Description (long):
The spatial structure of populations and communities has become increasingly important to ecologists because it provides insights into ecological patterns and processes (Rossi et al. 1992, Karieva and Wennegren 1995, Koenig 1999). Roland and Taylor (1997), for example, coupled spatial patterns of forest structure to parasitism rates and the distribution of parasitoid body sizes. Jonsen and Fahrig (1997) linked the spatial structure of agricultural landscapes to the occurrence of generalist and specialist insect herbivores. Documenting spatial structure has also enabled ecologists to understand the impact of grazing in desert grasslands (Tracy et al. 1998) as well as the spread of invasive insect species (Speight et al. 1998). From a practical standpoint, understanding the spatial structure of a population can indicate the proper sampling scheme and statistical protocol. In fact, Rossi et al. (1992) suggest a thorough study of the spatial structure of populations and communities to identify ranges of spatial independence and to validate the use of parametric statistics.

Given the underlying importance of spatial phenomena in ecological studies, it is imperative that undergraduate students learn the mathematical approaches for quantifying and modeling spatial structure (Cliff and Ord 1981, Isaaks and Srivastava 1989, Liehbold et al. 1993). Fortunately, the emergence of geostatistics has supported the growing interest in spatial structure and is an appropriate topic for undergraduate research in mathematical biology because it links mathematical concepts such as "moments" and "variation" to spatial data in a biological setting. In general, geostatistics is based on the "general regionalized variable" model, which identifies random and explanatory components of a spatial pattern or process (Rossi et al. 1992, Robertson 1998). Geostatistical approaches include semivariance, autocorrelation, and kriging, among others (Rossi et al. 1992). They are based on the premise of spatial continuity—that is, sampling points that are closer together are more similar to one another than sampling points that are farther apart.

Spatial autocorrelation has been used in a number of biological arenas (see Sokal and Oden 1978a, b); it identifies spatial ranges over which variables are similar. Both it and semivariance—an analytical for modeling spatial dependence—continue to be widely used in ecological applications (e.g., Lobo et al. 1998, Camarero et al. 2000). Although spatial autocorrelation can not be used to model spatial structure, it has certain advantages over semivariance (Meisel and Turner 1998). These advantages include less sensitivity to changes in the local means and variances (the stationarity assumption) (Rossi et al. 1992), , the ability to be standardized across studies (but see Rossi et al. 1992), and—most importantly—the fact that statistical tests can be used to identify spatial ranges of significant positive or negative autocorrelation (Legendre and Fortin 1989). Thus, spatial autocorrelation analysis is an appropriate tool for examining spatial structure when the intent of the study is to identify and describe spatial patterning. Semivariance is more appropriate if the purpose of the study is to model the variance in a dependent variable as a function of space, or lag distance (Jongman et al. 1995). Finally, kriging represents an extension of both autocorrelation and semivariance in that its main purpose is to interpolate (rather than describe or model) values of a dependent variable between observed data points. The interpolation process is based on a semivariogram (i.e., the model resulting from a semivariance analysis) and has been widely used to map ground water and soil conditions. (Jongman et al. 1995).

PURPOSE: The purpose of the proposed study is to explore the relationship between a disturbance event (prescribed burning and mowing) in Conservation Reserve Program (CRP) grasslands and the distribution and abundance of predatory beetles (Order Coleoptera: Family Carabidae) as described by mathematical models of spatial structure (e.g., spatial autocorrelation, semivariance, and kriging). The study is appropriate for joint mathematical and biological inquiry by undergraduates for three reasons. First, the Carabidae are well-studied, easy to collect, and easy to identify. Second, CRP grasslands are prominent in Missouri (0.6 million ha; USDA 2003) and prescribed burning and mowing of these grasslands has significant impacts on insects (e.g., Anderson et al. 1989). Finally, the underlying premise of spatial continuity (mentioned above) is tractable for undergraduates with a basic understanding of mathematics and statistics.

METHODS: The study will take place in six CRP fields in Scotland County, MO. The fields differ in their management approaches (three burned, three mowed) and are part of an ongoing study of insect populations (by Dr. Gering). The fields are mowed in August and burned in April. The general approach, which will be modified with student input, will be to develop a spatially explicit, grid-based sampling design that utilizes pitfall traps. In each field, the pitfall traps will be placed every 5 m in a 50x50-m regular spaced grid (100 traps x 6 fields = 600 traps). Each field will be sampled at least three times between April and September of each year. Captured beetles will be identified and counted using resources (identification texts, TSU insect collection, and computer) in Dr. Gering's lab.

DATA ANALYSIS: The students and both professors will then analyze the data using geostatistical approaches (see above). The initial analysis of the data will consist of using SPSS (or similar software) to conduct basic statistical methods such as t-tests and one-way ANOVAs to identify differences in the burned and mowed fields. These approaches, as well as exploratory data analysis and data transformations, will allow the students to apply the techniques learned in their introductory statistics courses. The students will then be introduced to the basic premise of spatial continuity through readings and discussions with both faculty mentors. Further analyses (i.e., spatial autocorrelation, semivariance, kriging) will utilize the spatial data fromthe trapping grid to model and map beetle populations within the fields. The spatial analysis of the data will be conducting using existing software on campus (SAS & GS+), but completion of the project may require additional software packages or original programming (e.g., FORTRAN or C++). These techniques are an extension of the required undergraduate coursework at Truman State University, and will be a valuable asset to students who wish to pursue graduate studies in mathematical biology or related fields. The end result of the study will be a model that describes the population structure of the predatory beetles in burned and mowed grasslands and is publishable in a journal such as Landscape Ecology.

REFERENCES CITED

Anderson, R.C., T. Leahy and S.S. Dhillion. 1989.

Numbers and biomass of selected insect groups on burned and unburned sand prairie. American Midland Naturalist 122:151-162.

Camerero, J.J., E. Gutierrez, and M-J. Fortin. 2000.

Spatial pattern of subalpine grassland ecotones in the Spanish Central Pyrenees. Forest Ecology and Management 134: 1-16.

Cliff, A.D. and J.K. Ord. 1981.

Spatial Processes: Models and Applications. Pion Limited, London, UK.

Isaaks, E.H. and R.M. Srivastava. 1989.

An Introduction to Applied Geostatistics. Oxford University Press, New York, NY.

Jongman, R.H.G., C.J.F. Ter Braak, and O.F.R. Van Tongeren. 1995.

Data Analysis in Community and Landscape Ecology. Cambridge University Press, Cambridge, MA.

Jonsen, I.D. and L. Fahrig. 1997.

Response of generalist and specialist herbivores to landscape spatial structure. Landscape Ecology 12: 185-197.

Kareiva, P. and U. Wennegren. 1995.

Connecting landscape patterns to ecosystem and population processes. Nature 373: 299-302.

Koenig, W.D. 1999. Spatial autocorrelation of ecological phenomena.

Trends in Ecology and Evolution 14: 22-26.

Legendre, P. and M-J. Fortin. 1989.

Spatial pattern and ecological analysis. Vegetatio 80: 107- 138.

Liehbold, A.M., R.E. Rossi, and W.P. Kemp. 1993.

Geostatistics and geographic information systems in applied insect ecology. Annual Review of Ecology and Systematics 38: 303-327.

Lobo, A., K. Moloney, O. Chic, and N. Chiariello. 1998.

Analysis of fine-scale spatial pattern of a grassland from remotely-sensed imagery and field collected data. Landscape Ecology 13: 111-131

Meisel, J.E. and M.G. Turner. 1998.

Scale detection in real and artificial landscapes using semivariance analysis. Landscape Ecology 13: 347-362.

Robertson, G.P. 1998.

GS+: Geostatistics for the Environmental Sciences. Gamma Design Software, Plainwell, MI.

Roland, J. and P.D. Taylor. 1997.

Insect parasitoid species respond to forest structure at different spatial scales. Nature 386: 710-713.

Rossi, R.E., D.J. Mulla, A.G. Journel, and E.H. Franz. 1992.

Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs 62: 277-314.

Sokal, R.R. and N.L. Oden. 1978a.

Spatial autocorrelation in biology: 1. Methodology. Biological Journal of the Linnean Society 10: 199-228.

Sokal, R.R. and N.L. Oden. 1978b.

Spatial autocorrelation in biology: 2. Some biological implications and four applications of evolutionary and ecological interest. Biological Journal of the Linnean Society 10: 229-249.

Speight, M.R., R.S. Hails, M. Gilbert, and A. Foggo. 1998.

Horse chestnut scale (Pulvinaria regalis) (Homoptera: Coccidae) and urban host tree environment. Ecology 79: 1503- 1513.

Tracy, K.N., D.M. Golden, and T.O. Crist. 1998.

The spatial distribution of termite activity in grazed and ungrazed Chihuahuan Desert grassland. Journal of Arid Environments 40: 77-89.

USDA. 2003.

U.S. Department of Agriculture Farm Service Agency Conservation Reserve Program monthly CRP acreage report. Report ID: MEPEGG-R1. Accessed 3/21/03. Updated last 2/28/03. Available from URL: http://www.fsa.usda.gov/crpstorpt/02approved/MEPEGGR1.htm