Optimal harvesting strategy based on rearrangements of functions

We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments

A drop of rainwater against a drop of groundwater: does rainwater harvesting really allow us to spare Groundwater?

This paper is concerned with groundwater management issues in the presence of rainwater harvesting (RWH). Namely, we propose a two-state model in order to take into account the standard dynamics of the aquifer and the dynamics of the storage capacity since the collected rainwater reduces the natural recharge. We analyze the trade-off between these two water harvesting techniques in an optimal control model. We notably show that, when these techniques are pure substitutes, the development of RWH conducts in the long run to a depletion of the water table even if pumping is reduced.Rainwater Harvesting, Conjunctive Use, Groundwater Optimal Control Management, Dynamic Model

Light-intensity-dependent regulatory mechanisms in protection of Photosystem I in Arabidopsis

In photosynthetic light reactions, photosystem (PS)II and PSI as well as Cytochrome b6f, which are embedded in the thylakoid membrane of chloroplasts, transfer electrons from water molecules to NADP+ using the light energy collected mostly by light harvesting complexes (LHC)II and LHCI. Simultaneously, an electrochemical gradient is formed across the thylakoid membrane and utilized by ATP synthase to catalyse the synthesis of ATP. With the end products of photosynthetic light reactions, NADPH and ATP, plants bind atmospheric carbon dioxide into organic compounds, which not only support the plants’ growth and development but also nearly all heterotrophic life on Earth. The flow of electrons in the photosynthetic machinery needs to be strictly controlled in order to avoid damage to PSI that, unlike PSII, lacks an efficient repair cycle. To protect PSI, plants are able to control the distribution of energy between the photosystems through phosphorylating and dephosphorylating LHCII, to optimize the electron transfer rate from PSII to PSI through PGR5 protein and to cycle electrons from PSI back to the electron transfer chain through the NDH-1 complex. Here, I applied several biochemical and biophysical approaches to compare the thale cress Arabidopsis thaliana wild type and transgenic lines lacking certain regulatory proteins. I showed that dephosphorylation of LHCII protects PSI from excess electrons by physically separating the complexes but also by regulating the location of Cytochrome b6f and ATP synthase in the thylakoid membrane. Furthermore, I showed that the activation of PGR5 requires light and that when active, the protein controls electron transfer from PSII to PSI but not from PSI onwards. Finally, I demonstrated that in the case of PSI damage, both PGR5 and NDH-1 participate in maintaining the function of the photosynthetic electron transfer chain.Fotosynteesin valoreaktioissa viherhiukkasen tylakoidikalvoon sitoutuneet fotosysteemi (PS)II ja PSI sekä Sytokromi b6f siirtävät elektroneja vesimolekyyliltä NADP+:lle pääasiassa valohaavikompleksien (LHC)II ja LHCI keräämän valoenergian avulla. Samalla tylakoidikalvolle muodostuu elektrokemiallinen gradientti, jonka avulla ATP-syntaasi katalysoi ATP:n muodostumista. Valoreaktioiden lopputuotteita, NADPH:ta ja ATP:ta, kasvi käyttää sitoakseen ilmakehän hiilidioksidia eloperäisiksi yhdisteiksi, jotka ylläpitävät paitsi kasvien kasvua ja kehitystä, myös lähes kaikkea Maan toisenvaraista elämää. Elektronien kulkua valoreaktioissa on ohjattava tarkoin, jotteivät ne vaurioita PSI:tä, jota varten ei ole kehittynyt tehokasta korjauskiertoa kuten PSII:lla. PSI:n suojaamiseksi kasvit kykenevät säätelemään valoenergian jakautumista fotosysteemien välillä fosforyloimalla ja defosforyloimalla LHCII:ta, optimoimaan elektronien kulkunopeutta PSII:lta PSI:lle PGR5-proteiinin avulla sekä kierrättämään elektroneja PSI:ltä takaisin elektroninsiirtoketjuun NDH-1-kompleksin kautta. Tässä väitöskirjaprojektissa vertailin biokemiallisin ja biofysikaalisin menetelmin lituruohon Arabidopsis thaliana villityyppiä ja mutanttilinjoja, joilta on poistettu tunnettu säätelyproteiini. Osoitin, että LHCII:n defosforylaatio suojaa kirkkaassa valossa PSI:tä liiallisilta elektroneilta erottamalla kompleksit fyysisesti toisistaan, mutta säätelee myös Sytokromi b6f:n ja ATP-syntaasin sijaintia tylakoidikalvolla. Osoitin myös, että PGR5-proteiini aktivoituu valossa ja kontrolloi elektroninsiirtoa PSII:lta PSI:lle, mutta ei PSI:ltä eteenpäin. Lisäksi havainnollistin, että mikäli PSI kuitenkin vahingoittuu, sekä PGR5 että NDH-1 osallistuvat fotosynteettisen elektroninsiirtoketjun toiminnan säilyttämiseen

A drop of rainwater against a drop of groundwater: does rainwater harvesting really allow us to spare Groundwater?

This paper is concerned with groundwater management issues in the presence of rainwater harvesting (RWH). Namely, we propose a two-state model in order to take into account the standard dynamics of the aquifer and the dynamics of the storage capacity since the collected rainwater reduces the natural recharge. We analyze the trade-off between these two water harvesting techniques in an optimal control model. We notably show that, when these techniques are pure substitutes, the development of RWH conducts in the long run to a depletion of the water table even if pumping is reduced

Resilience, Uncertainty, and the Role of Economics in Ecosystem Management

Many natural systems have the potential to switch between alternative dynamic behaviors. We consider a system with two distinct equations of motion that are separated by a threshold value of the state variable. We show that utility maximization will give a decision making rule that is consistent with ecosystem-based management objectives that aim to reduce the probability that the system crosses the threshold. Moreover, we find that increasing uncertainty (both uncertainty embedded in the natural system and uncertainty of the decision maker about the location of the threshold) can lead to nonmonotonic changes in precaution. Although small increases in uncertainty may at first increase precaution, large enough increases in uncertainty will lead to a decrease in precaution.Resource /Energy Economics and Policy,