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A POISSON–PARETO MODEL OF CHLOROPHYLL-A FLUORESCENCE SIGNALS IN MARINE ENVIRONMENTS

Part of: Mathematical biology in general

Published online by Cambridge University Press:  02 July 2015

S. WOODCOCK ,
B. MANOJLOVIC ,
M. E. BAIRD  and
P. J. RALPH
S. WOODCOCK*
Affiliation:
School of Mathematical Sciences, University of Technology Sydney, Sydney, Australia email [email protected], [email protected]
B. MANOJLOVIC
Affiliation:
School of Mathematical Sciences, University of Technology Sydney, Sydney, Australia email [email protected], [email protected]
M. E. BAIRD
Affiliation:
CSIRO Oceans and Atmosphere Flagship, GPO Box 1538, Hobart 7001, Australia email [email protected]
P. J. RALPH
Affiliation:
Plant Functional Biology and Climate Change Cluster, University of Technology Sydney, Sydney, Australia email [email protected]
*
✉[email protected]
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Abstract

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Because of its central role in the global carbon cycle, quantifying the biomass of photosynthetic microalgae in the oceans is crucial to our ability to estimate the oceans’ carbon drawdown. Many traditional methods of primary production assessment have proven to be extremely time consuming and, consequently, have handled only very small sample sizes. The recent advent of in situ bio-optical sensors, such as the water quality monitor (WQM), is now providing lower cost and higher throughput data on these crucial biological communities. These WQMs, however, only quantify the total fluorescence of all individual cells within their optical sample windows, irrespective of size. In this paper, we further develop an established model, based on Pareto random variables, of the size structure of the microalgae community to understand the effect of the WQMs’ sampling and data pooling on their estimates of algal biomass. Unfortunately, evaluating sums of Pareto variables is a notoriously difficult problem. Here, we utilize an approximation for the right-tail of the resulting distribution to derive parameter estimates for the underlying size structure of the microalgae community.

Keywords

Poisson–Pareto random variablesshifted Hill’s estimators

MSC classification

Primary: 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 4 , April 2015 , pp. 373 - 380
Copyright
© 2015 Australian Mathematical Society 

References

Aban, I. B. and Meerschaert, M. M., “Shifted Hill’s estimator for heavy tails”, Comm. Statist. Simulation Comput. 30 (2001) 949–962; doi:10.1081/SAC-100107790.CrossRefGoogle Scholar
Albrecher, H. and Kortschak, D., “On ruin probability and aggregate claim representations for Pareto size distributions”, Insurance Math. Econom. 45 (2009) 362–373; doi:10.1016/j.insmatheco.2009.08.005.CrossRefGoogle Scholar
Baird, M. E. and Suthers, I. M., “A size-resolved pelagic ecosystem model”, Ecol. Model. 203 (2007) 185–203; doi:10.1016/j.ecolmodel.2006.11.025.CrossRefGoogle Scholar
Blum, M., “On the sums of independently distributed Pareto variates”, SIAM J. Appl. Math. 19 (1970) 191–198; doi:10.1137/0119017.CrossRefGoogle Scholar
Carneiro, R. L., da Silva, A. P. R., de Magalhaes, V. F. and de Oliveira e Azevedo, S. M. F., “Use of the cell quota and chlorophyll content for normalization of cylindrospermopsin produced by two Cylindrospermopsis raciborskii strains grown under different light intensities”, Ecotoxicol. Environ. Contam. 8 (2013) 93–100; doi:10.5132/eec.2013.01.013.Google Scholar
Cavender-Bares, K. K., Rinaldo, A. and Chisholm, S. W., “Microbial size spectra from natural and nutrient enriched ecosystems”, Limnol. Oceanogr. 46 (2001) 778–789; doi:10.4319/lo.2001.46.4.0778.CrossRefGoogle Scholar
Falkowski, P. G., “The role of phytoplankton photosynthesis in global biogeochemical cycles”, Photosyn. Res. 39 (1994) 235–258; doi:10.1007/BF00014586.CrossRefGoogle ScholarPubMed
Falkowski, P. G. and Raven, J. A., Aquatic photosynthesis (Princeton University Press, Princeton, NJ, 2007).CrossRefGoogle Scholar
Finkel, Z. V., “Light absorption and size scaling of light limited metabolism in marine diatoms”, Limnol. Oceanogr. 46 (2001) 86–94; doi:10.4319/lo.2001.46.1.0086.CrossRefGoogle Scholar
Goovaerts, M. J., Kaas, R., Laeven, R. J., Tang, Q. and Vernic, R., “The tail probability of discounted sums of Pareto-like losses in insurance”, Scand. Actuar. J. 6 (2005) 446–461; doi:10.1080/03461230500361943.CrossRefGoogle Scholar
Guillard, R. R. and Sieracki, M. S., “Counting cells in cultures with the light microscope”, in: Algal culturing techniques (ed. Andersen, R. A.), (Elsevier, New York, NY, 2005) 239–252; doi:10.1016/B978-012088426-1/50017-2.Google Scholar
Hill, B. M., “A simple general approach to inference about the tail of a distribution”, Ann. Statist. 3 (1975) 1163–1174; doi:10.1214/aos/1176343247.CrossRefGoogle Scholar
Holm-Hansen, O., Lorenzen, C. J., Holmes, R. W. and Strickland, J. D., “Fluorometric determination of chlorophyll”, J. Cons. Int. Explor. Mer 30(1) (1965) 3–15; doi:10.1093/icesjms/30.1.3.CrossRefGoogle Scholar
Mandelbrot, B., “The stable Paretian income distribution when the apparent exponent is near two”, Internat. Econom. Rev. 4 (1963) 111–115; doi:10.2307/2525463.CrossRefGoogle Scholar
Orrico, C. M., Moore, C., Romanko, D., Derr, A., Barnard, A. H., Janzen, C., Larson, N., Murphy, D., Johnson, R. and Bauman, J., “WQM: a new integrated water quality monitoring package for long-term in-situ observation of physical and biogeochemical parameters”, OCEANS 2007 2007 1–9; IEEE, doi:10.1109/OCEANS.2007.4449418.Google Scholar
Philbrick, S. W., “A practical guide to the single parameter Pareto distribution”, PCAS LXXII 44 (1985) 44–77; http://casualtyactuarialsociety.com/pubs/proceed/proceed85/85044.pdf.Google Scholar
Ramsay, C. M., “The distribution of sums of certain i.i.d. Pareto variates”, Comm. Statist. Theory Methods 35 (2006) 395–405; doi:10.1080/03610920500476325.CrossRefGoogle Scholar
Ramsay, C. M., “The distribution of sums of i.i.d. Pareto random variables with arbitrary shape parameter”, Comm. Statist. Theory Methods 37 (2008) 2177–2184; doi:10.1080/03610920701882503.CrossRefGoogle Scholar
Reynolds, C. S., The ecology of freshwater phytoplankton (Cambridge University Press, UK, 1984).Google Scholar
Rodriguez, J., Jimenez, F., Bautista, B. and Rodriguez, V., “Planktonic biomass spectra dynamics during a winter production pulse in Mediterranean coastal waters”, J. Plankton Res. 9 (1987) 1183–1194; doi:10.1093/plankt/9.6.1183.CrossRefGoogle Scholar
Roehner, B. and Winiwarter, P., “Aggregation of independent Paretian random variables”, Adv. Appl. Probab. 17 (1985) 465–469; doi:10.2307/1427153.CrossRefGoogle Scholar
Sheldon, R. W., Prakash, A. and Sutcliffe, W. H. J., “The size distribution of particles in the ocean”, Limnol. Oceanogr. 17 (1972) 327–340; doi:10.4319/lo.1972.17.3.0327.CrossRefGoogle Scholar
Suthers, I. M., Taggart, C. T., Rissik, D. and Baird, M. E., “Day and night ichthyoplankton assemblages and zooplankton biomass size spectrum in a deep ocean island wake”, Mar. Ecol. Prog. Ser. 322 (2006) 225–238; doi:10.3354/meps322225.CrossRefGoogle Scholar
Vidondo, B., Prairie, Y. T., Blanco, J. M. and Duarte, C. M., “Some aspects of the analysis of size spectra in aquatic ecology”, Limnol. Oceanogr. 42 (1997) 184–192; doi:10.4319/lo.1997.42.1.0184.CrossRefGoogle Scholar
Zaliapin, I. V., Kagan, Y. Y. and Schoenberg, F. P., “Approximating the distribution of Pareto sums”, Pure Appl. Geophys. 162 (2005) 1187–1228; doi:10.1007/s00024-004-2666-3.CrossRefGoogle Scholar