Eventual saturation of the climate–carbon cycle feedback studied with a conceptual model

A saturation of climate–carbon cycle feedback was found earlier in the simulations with the IAP RAS climate model of intermediate complexity. Here, this eventual saturation is interpreted by using a conceptual linearised coupled model. It is shown that this saturation is due to weak, logarithmic, dependence of the carbon dioxide radiative forcing on its atmospheric concentration. This eventual saturation leads to the non-monotonic behaviour of climate–carbon cycle parameter f   in time. If the time scale of the atmospheric CO₂${\text{CO}}_2$ build up is _tp$t_{\text{p}}$ then, starting from an initial equilibrium, f   approaches maximum in time ?_tp$?t_{\text{p}}$. Afterwards, climate–carbon cycle parameter decreases and eventually tends to unity. The time scale of the latter decrease is _t1=(1−5)_tp$t_1=(1-5)t_{\text{p}}$. A dependence of _tm$t_{\text{m}}$ and _t1$t_1$ on governing parameters of the conceptual model is studied. It is argued that an eventual saturation of the climate–carbon cycle feedback is expected to occur also in the other integrations of sufficient length with coupled climate–carbon cycle models.     

Description and sensitivity analysis for the LESV model: Water quality variables and the balance of organisms in a fjordic region of restricted exchange

In this paper we describe a new ecological model for Regions of Restricted Exchange (RRE), such as fjords, estuaries, rias and lagoons. The model is intended to simulate the impact of external nutrient input on microplankton (phytoplankton plus pelagic microheterotrophs) in RREs. We have implemented the model with the practical purpose of finding a safe limit to the capacities of RRE to assimilate fish-farm waste. Sea-cage farming of fish is increasing in fjords in northern and southern hemispheres, and its external nutrient input can lead to environmental problems such as eutrophication and deoxygenation. The model includes a physical system of three layers with exchanges driven by tidal movement, freshwater input, wind stirring. The biological part includes two microplankton compartments, each parameterizing a microbial loop and each containing chlorophyll. The first compartment represents diatoms and associated heterotrophs, and the second compartment represents flagellates and associated heterotrophs. As well as the balance of these organisms, the model simulates concentrations of nutrient N, P, and Si, dissolved oxygen, and water transparency. Chlorophyll and nutrient change are linked by yields (q  ). Losses of microplankton to grazing by mesozooplankton or benthos are simulated by a temperature-dependent grazing pressure acting on a mean loss (_L0)$(L_0)$. The model also includes the ability to simulate point source inputs of nutrients or organic matter and a generic tracer with first order decay. Sea-cage fish-farms exemplify such point sources. In order to explore model behaviour, we included inputs from a 1500 tonnes salmon farm multiplied by a factor (γ)$(\gamma )$. We carried out sensitivity analysis to identify the most influential model parameters and forcing variables in the case of the shallow Scottish fjord, Loch Creran, in 1975 before the introduction of salmon farming. We tested the model fit to this pristine state (γ=0)$(\gamma =0)$, using Major Axis Regression of simulated variables on observed variables. The model successfully follows the seasonal cycles of chlorophyll (summer over both microplanktons) and the limiting nutrients (P, N). The sensitivity analysis identified three sets of key parameters: (γ)$(\gamma )$ and other fish-farm coefficients, which control farm waste effects on an RRE; (_L0)$(L_0)$ parameters for each microplankton, which link these to the rest of the ecosystem and which have implications for future inclusion of shellfish farming in the model and, chlorophyll yields from nutrients (q), which are crucial for the predication of eutrophication and the ecological understanding of the model.     

A note on density dependence in population models

One of the most studied phenomena in ecology is density dependent regulation. The model most frequently used to study this behaviour is the theta-logistic model. However, disagreement has developed within the ecology community pertaining to the interpretation of this model’s parameters, and thus as to appropriate values for the parameters to assume. In particular, the parameter θ$\theta$ has been allowed to take negative values, resulting in the ‘growth rate parameter’ estimated to be negative for species which are extant and exhibit no signs of becoming extinct in the short-term. Here we explain this phenomenon by formulating the theta-logistic model in the manner in which the original logistic model was formulated by Verhulst (1838), in doing so providing a simple interpretation of model parameters and thus restrictions on values the parameters may assume. We conclude that θ$\theta$ should (almost always) be restricted to values greater than −1$-1$. This has implications for studies assessing the form of density dependence from data. Additionally, another model appearing in the literature is presented which provides a more flexible model of density dependence at the expense of only one additional parameter.     

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called _R0$R_0$) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) _R0$R_0$ cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.     

Multi-metric evaluation of the models WARM,CropSyst, and WOFOST for rice

WARM (Water Accounting Rice Model) simulates paddy rice (Oryza sativa L.), based on temperature-driven development and radiation-driven crop growth. It also simulates: biomass partitioning, floodwater effect on temperature, spikelet sterility, floodwater and chemicals management, and soil hydrology. Biomass estimates from WARM were evaluated and compared with the ones from two generic crop models (CropSyst, WOFOST). The test-area was the Po Valley (Italy). Data collected at six sites from 1989 to 2004 from rice crops grown under flooded and non-limiting conditions were split into a calibration (to estimate some model parameters) and a validation set. For model evaluation, a fuzzy-logic based multiple-metrics indicator (MQI) was used: 0 (best) ≤ MQI ≤ 1 (worst). WARM estimates compared well with the actual data (mean MQI = 0.037 against 0.167 and 0.173 with CropSyst and WOFOST, respectively). On an average, the three models performed similarly for individual validation metrics such as modelling efficiency (EF > 0.90) and correlation coefficient (R > 0.98). WARM performed best in a weighed measure of the Akaike Information Criterion: (worst) 0<wk<1$0<w_k<1$ (best), considering estimation accuracy and number of parameters required to achieve it (mean wk=0.983$w_k=0.983$ against 0.007 and ∼0.000 with CropSyst and WOFOST, respectively). WARM results were sensitive to 30% of the model parameters (ratio being lower with both CropSyst, <10%, and WOFOST, <20%), but appeared the easiest model to use because of the lowest number of crop parameters required (10 against 15 and 34 with CropSyst and WOFOST, respectively). This study provides a concrete example of the possibilities offered using a range of assessment metrics to evaluate model estimates, predictive capabilities, and complexity.     

Mathematical modelling for conservation and management of gorgonians corals: youngs and olds,could they coexist?

Gorgonian corals are long-lived, slow-growing marine species dominating Mediterranean rocky bottoms. Endowed with complex morphologies they give a structure to the whole community, moreover, being efficient suspension feeders, they play a key role in plankton-benthos energy flow and CO₂${\text{CO}}_2$ storage. Thus, the structure and the development of benthic, hard bottom communities are linked to gorgonian survival. The red coral Corallium rubrum (L. 1758) is a precious gorgonian endemic to the Mediterranean Sea. Harvested and traded world-wide since ancient times red coral is a clear example of overexploited marine resource. This species is structured into self-seeding, genetically differentiated populations, some of which, living in the shallower part of the species bathymetric distribution, was recently affected by anomalous mortality events linked to global climate change. The co-occurrence of overharvesting and mass mortality could dramatically affect such populations. Demographic population models, widely applied by conservation biologists to check population viability and to project population trends over time are fundamental to foster survival of such populations matching harvesting to population growth rates. Therefore we set out a dynamic model of a genetically differentiated red coral population living in shallow waters. This population is characterised by small/young, crowded colonies and high recruitment rate. On the basis of the size–age structure determined for this population, a static life-history table, in which survival and reproduction coefficients of the different size–age classes were reported, has been set out. Demographic data were included in a non-linear, discrete, age-structured dynamic model, based on a Leslie-Lewis transition matrix. Our field data indicate that the recruits-to-larvae ratio is actually density-dependent. Such dependence, positive for low and negative for high density values, was included into the model and the effect of colonies of different size–age classes on recruits-to-larvae ratio was considered to be proportional to the number of polyps they have. We applied such model to simulate the trends of the studied population under different increases of survival and life-span. As some populations of gorgonians actually show the dominance of sparse, big/old colonies and low recruitment rate, while others are characterised by crowded, small/young colonies and high recruitment rate, we simulated the shift from the former to the latter structure increasing survival and life-span. Our results suggest that a dramatic mortality increase of bigger–older colonies (due, in the case of red coral to overfishing) could have determined the population structure we found.     

Oligopoly meets oligopsony: The case of permits

This paper derives market equilibria (in demand functions and in bidding strategies) between oligopolists and oligopsonists in a market with intermediates and no competition in final markets. To the best of my knowledge, this theme has not been explored, despite two observations: Firstly, the commonly applied framework of non-competitive and competitive fringe firms has implausible properties for the limit of purely strategic players. Secondly, real world cases correspond at least potentially to such strategic interactions, e.g., non-competitive players selling and buying permits (${\mathrm{CO}}_2$ and ${\mathrm{SO}}_2$). The major implications are that these non-competitive markets are characterized by a kind of double marginalization (on the demand and the supply side) resulting in too little trade and wrong price signals.