A stochastic model for phytoplankton dynamics in the Tyrrhenian Sea - PowerPoint PPT Presentation

7 th International Conference on Unsolved Problems on Noise Barcelona, Casa Convalescència, Spain, 13-17 July 2015 A stochastic model for phytoplankton dynamics in the Tyrrhenian Sea a Davide Valenti a Davide Valenti Group of Interdisciplinary in in collaboration collaboration with with University of Palermo Theoretical Physics Denaro a a , Bernardo Spagnolo a a , Fabio Conversano b b , Brunet b b Giovanni Denaro Giovanni , Bernardo Spagnolo , Fabio Conversano , Christophe Christophe Brunet a Dipartimento di Fisica e Chimica, Università di Palermo and CNISM, Unità di Palermo, Group of Interdisciplinary Physics, Viale delle Scienze, Ed. 18 - 90128 Palermo, Italy b Stazione Zoologica Anton Dohrn, Villa Comunale - 80121 Napoli, Italy Barcelona, 16 , 16 July July 2015 2015 Barcelona

Outline Outline First we show real data collected in a hydrologically hydrologically stable area of the stable area of the First we show real data collected in a Mediterranean Sea. Mediterranean Sea. As a second step we present a stochastic advection- -reaction reaction- -diffusion diffusion As a second step we present a stochastic advection model for phytoplankton distribution along a water column. model for phytoplankton distribution along a water column. The model consider the growth of phytoplankton as limited by the The model consider the growth of phytoplankton as limited by the intensity of light I I and concentration of nutrients and concentration of nutrients R R ( (Klausmeier Klausmeier and and intensity of light Litchman, 2001; , 2001; Klausmeier Klausmeier et al., 2007). et al., 2007). Litchman Theoretical results are compared with real data. Theoretical results are compared with real data. UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics

More in detail detail More in A stochastic one- -dimensional reaction dimensional reaction- -diffusion diffusion- -taxis model is used to taxis model is used to A stochastic one reproduce the spatio spatio- -temporal dynamics, along a water column, of five temporal dynamics, along a water column, of five reproduce the picophytoplankton populations. populations. picophytoplankton Periodical changes of environmental variables, such as light intensity, ensity, Periodical changes of environmental variables, such as light int vertical turbulent diffusivity, thermocline thermocline depth and upper mixed layer depth and upper mixed layer vertical turbulent diffusivity, thickness are included. thickness are included. Spatio- -temporal temporal behaviour of biomass concentration of each Spatio behaviour of biomass concentration of each picophytoplankton population is calculated by the model. population is calculated by the model. picophytoplankton 2 goodness χ 2 The total equivalent content of chlorophyll is compared ( χ goodness- -of of- -fit fit The total equivalent content of chlorophyll is compared ( test) with experimental data collected in four different periods of the year in of the year in test) with experimental data collected in four different periods a site of the Tyrrhenian Sea, an ideal habitat to study how ecosystem ystem a site of the Tyrrhenian Sea, an ideal habitat to study how ecos characteristics affect the phytoplankton distribution. characteristics affect the phytoplankton distribution. UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics

Some motivations motivations Some New models recently devised to study spatio spatio- -temporal dynamics of temporal dynamics of New models recently devised to study phytoplankton populations along water columns in marine ecosystems. ms. phytoplankton populations along water columns in marine ecosyste Random fluctuations of environmental variables are not included in in Random fluctuations of environmental variables are not included these models. these models. Lack of exhaustive investigations, which include data analysis, Lack of exhaustive investigations, which include data analysis, theoretical predictions, and comparison of theoretical results with ith theoretical predictions, and comparison of theoretical results w experimental data. experimental data. Importance of this studies from the point of view of fishery: abundance undance Importance of this studies from the point of view of fishery: ab of fish species strictly connected with primary production, i.e. of fish species strictly connected with primary production, i.e. phytoplankton biomass, responsible for chlorophyll concentration. phytoplankton biomass, responsible for chlorophyll concentration . UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics

¿¿Advection-Reaction Reaction- -Diffusion Model?? Diffusion Model?? What is this? Description of spatiotemporal dynamics of biological species based on: - local interaction among populations and/or between each population and resources ( reaction ); - mechanism of spatial interaction, e.g., spread of individuals in space random movement of individuals ( diffusion ); - movement of some material dissolved or suspended in the fluid ( advection ). Specifically If you consider the water flowing in a river you will get advection UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics

What we we do do What Phytoplankton distribution distribution is is analyzed analyzed in a site of the in a site of the Tyrrhenian Tyrrhenian Sea Sea, , an an ideal ideal Phytoplankton habitat to to study study how how ecosystem ecosystem hydrodynamics hydrodynamics affects affects the the phytoplankton phytoplankton habitat distribution. . distribution By using a stochastic stochastic reaction- -diffusion diffusion- -taxis model, the taxis model, the spatio spatio- -temporal temporal By using a reaction behaviour of of picophytoplankton picophytoplankton species is reproduced in the site investigated species is reproduced in the site investigated behaviour during the whole solar year. during the whole solar year. The theoretical distributions are obtained for all seasons by considering the nsidering the The theoretical distributions are obtained for all seasons by co seasonal variations of vertical turbulent diffusivity and light intensity. intensity. seasonal variations of vertical turbulent diffusivity and light In order to compare theoretical results with field observations, the In order to compare theoretical results with field observations, the picophytoplankton biomass concentrations, are converted in biomass concentrations, are converted in chl chl- -a concentration. a concentration. picophytoplankton Comparison between numerical results and experimental data is evaluated by aluated by Comparison between numerical results and experimental data is ev performing statistical checks. performing statistical checks. UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics

Geographical area area Geographical Experimental data collected in the period 24 November 2006 -- -- 9 June 2007 in a 9 June 2007 in a Experimental data collected in the period 24 November 2006 sampling site localized in the middle of the Tyrrhenian Sea, a hydrological stable sampling site localized in the middle of the Tyrrhenian Sea, a h ydrological stable area of Mediterranean Sea, with oligotrophic oligotrophic waters mainly populated by waters mainly populated by area of Mediterranean Sea, with picophytoplankton species. species. picophytoplankton The sampling sampling were were performed performed at four different at four different The times of the year, during four different times of the year, during four different oceanographic cruises: (a) VECTOR- -TM1, TM1, oceanographic cruises: (a) VECTOR November 2006; (b) VECTOR- -TM2, February TM2, February November 2006; (b) VECTOR 2007; (c) VECTOR- -TM3, April 2007; (d) TM3, April 2007; (d) 2007; (c) VECTOR VECTOR- -TM4, June 2007. TM4, June 2007. VECTOR VTM-A UPoN 2015 - Barcelona, 16 July 2015 Davide Valenti - University of Palermo Group of Interdisciplinary Theoretical Physics