Inference and model comparison for species accumulation functions using approximating pure birth processes

Journal of Agricultural, Biological, and Environmental Statistics

Volumn 7, Issue 3, 2002, Pages 335-349

  Díaz Francés, Eloísa ^a   Gorostiza, Luis G ^b  

^a CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Likelihood ratio; Michaelis Menten equation; Model comparison; Nonhomogeneous pure birth processes; Nonlinear regression model; Profile likelihood

Indexed keywords

BIRTH RATE; COMPARATIVE STUDY; MODELING; REGRESSION ANALYSIS; STATISTICAL ANALYSIS;

EID: 5444264916     PISSN: 10857117     EISSN: None     Source Type: Journal    
DOI: 10.1198/108571102294     Document Type: Article

References (31)

1. Bailey, N. T. J. (1964), The Elements of Stochastic Processes, New York: Wiley.
2. Beccaloni, G. W., and Gaston, K. J. (1995), "Predicting the Species Richness of Neotropical Forest Butterflies-Ithomiinae (Lepidoptera Nymphalidae) as Indicators," Biological Conservation, 71, 77-86.
3. Bojorquez Tapia, L. A., Balvanera, P., and Cuarón, A. D. (1994), "Biological Inventories and Computer-Data Bases. Their Role in Environmental Assessments," Environmental Management, 18, 775-785.
4. Changhyuck, O., Severo, N., and Slivka, J. (1991), "Approximations to the Maximum Likelihood Estimate in Some Pure Birth Processes, Biometrika, 78, 295-299.
5. Clench, H. (1979), "How to Make Regional Lists of Butterflies: Some Thoughts," Journal of the Lepidopterists Society, 33, 216-231.
6. Colwell, R. K., and Coddington, J. A. (1994), "Estimating Terrestrial Biodiversity Through Extrapolation," Philosophical Transactions of the Royal Society of London, Series B-Biological Sciences, 345, 101-118.
7. Edwards, A. W. F. (1992), Likelihood (expanded ed.), Baltimore: The Johns Hopkins University Press.
8. Fagan, W. F., and Kareiva, P. M. (1997), "Using Compiled Species Lists to Make Biodiversity Comparisons Among Regions-A Test-Case Using Oregon Butterflies," Biological Conservation, 80, 249-259.
9. Flather, C. H. (1996), "Fitting Species-Accumulation Functions and Assessing Regional Land-Use Impacts on Avian Diversity," Journal of Biogeography, 23, 155-168.
10. Gorostiza, L. G., and E. Díaz-Francés. (2001), "Species Accumulation Functions and Pure Birth Processes," Statistics and Probability Letters, 55, 221-226.
11. Harrison, J. A., and Martínez, P. (1995), "Measurement and Mapping of Avian Diversity in Southern Africa-Implications for Conservation Planning," Ibis, 137, 410-417.
12. Howard, P., Davenport, T., and Kigenyi, F. (1997), "Planning Conservation Areas in Uganda Natural Forests," Oryx, 31, 253-264.
13. Keating, K. A., and Quinn, J. F. (1998), "Estimating Species Richness-The Michaelis-Menten Model Revisited," Oikos, 81, 411-416.
14. Lamas, G., Robbins, R. K., and Harvey, D. J. (1991), "A Preliminary Survey of the Butterfly Fauna of Pakitza, Parque, Nacional del Manú, Perú, With an Estimate of Its Species Richness," Publicaciones del Museo de Historia Natural, Universidad de San Marcos, Perú, 40, 1-19.
15. Lindsey, J. K. (1999), "Statistical Heresies," The Statistician, 48, 1-40.
16. Longino, J. T., and Colwell, R. K. (1997), "Biodiversity Assessment Using Structured Inventory Capturing the Ant Fauna of a Tropical Rain-Forest," Ecological Applications, 7, 1263-1277.
17. Madrid, J., Sánchez, P., and Ruiz, A. A. (1997), "Diversity and Abundance of a Tropical Fishery on the Pacific Shelf of Michoacán, Mexico," Estuarine Coastal and Shelf Science, 45, 485-495.
18. McNeil, D. R., and Schach, S. (1973), "Central Limit Analogues for Markov Population Processes," Journal of the Royal Statistical Society, Series B, 35, 1-15.
19. Mourelle, C., and Ezcurra, E. (1997), "Differentiation Diversity of Argentine Cacti and Its Relationship to Environmental Factors," Journal of Vegetation Science, 8, 547-558.
20. Nelder, J. A., and Mead, R. (1965), "A Simplex Method for Function Minimization," Computer Journal, 7, 308-313.
21. Nelson, S. M., and Epstein, M. E. (1998), "Butterflies (Lepidoptera, Papilonoidea and Hesperioidea) of Roxborough State Park, Colorado, USA-Base-Line Inventory, Community Attributes, and Monitoring Plan," Environmental Management, 22, 287-295.
22. Parzen, E. (1999), Stochastic Processes, Philadelphia: SIAM.
23. Pielou, E. C. (1969), An Introduction to Mathematical Ecology, New York: Wiley.
24. Raaijmakers, J. G. W. (1987), "Statistical Analysis of the Michaelis-Menten Equation," Biometrics, 43, 793-803.
25. Soberón, J., and Llorente, J. (1993), "The Use of Species Accumulation Functions for the Prediction of Species Richness," Conservation Biology, 7, 480-488.
26. Southwood, T. R. E. (1996), "The Croonian Lecture, 1995-Natural Communities-Structure and Dynamics," Philosophical Transactions of the Royal Society of London, Series B-Biological Sciences, 351, 1113-1129.
27. Sprott, D. A. (2000), Statistical Inference in Science, New York: Springer.
28. Stohlgren, T. J., Quinn, J. F., Ruggiero, M., and Waggoner, G. S. (1995), "Status of Biotic Inventories in U.S. National Parks," Biological Conservation, 71, 97-106.
29. Walther, B. A., Cotgreave, P., Price, R. D., Gregory, R. D., and Clayton, D. H. (1995), "Sampling Effort and Parasite Species Richness," Parasitology Today, 11, 306-310.
30. Walther, B. A., and Morand, S. (1998), "Comparative Performance of Species Richness Estimation Methods," Parasitology, 116, 395-405.
31. Williams, M. R. (1995), "An Extreme-Value Function Model of the Species Incidence and Species-Area Relations," Ecology, 76,