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.     

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.     

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.     

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.     

Herding tendency as an aggregating factor in a binary mixture of social entities

The role of herding tendency in the group formation of social entities is hereby explored. The herding tendency is quantified by a parameter α∈[0,1]$\alpha \in [0\text{,}1]$. The system consists of a mixture of two types of entities: (i) those with α>0$\alpha >0$ and (ii) those with α=0$\alpha =0$. The latter consist a fraction p   of the entire population. The dynamics of agent interactions leads to the formation of clusters of different sizes. The size distribution D(s)$D(s)$ of these clusters are found to obey a power-law only in the limit that α→1$\alpha \to 1$ and p→0$p\to 0$. Group-size data of several real-world animal systems are fitted with curves generated by the model. This study contributes further to the understanding of group-forming behavior commonly cited in ecological studies.     

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.     

Estimation of winter respiration rates and prediction of oxygen regime in a lake using Bayesian inference

In this paper, we estimate the winter respiration (oxygen depletion per unit area of hypolimnetic surface) in a hyper-eutrophic shallow lake (Tuusulanjärvi) in the northern hemisphere (Finland, northern Europe, latitude 60^∘26′, longitude 25^∘03′) under ice-cover periods in the years 1970–2003. We present a dynamic nonlinear model that can be used for predicting of the oxygen regime in following years and to dimensioning of needed artificial oxygenation efficiency that will prevent fish kills in the lake. We use Bayesian estimation of respiration using Markov chain Monte Carlo (MCMC) method (Adaptive Metropolis–Hastings algorithm). This allows for analysis and predictions that take into account all the uncertainties in the model and the data, pool information from different sources (laboratory experiments and lake data), and to quantify the uncertainties using a full statistical approach. The mean estimated respiration in the study period was $301\pm 105$ mg m⁻² d⁻¹, which is on the upper limit of winter respiration of eutrophic Canadian lakes on the same latitude. The reference rate of the respiration $k$ (d⁻¹) at 4 ^∘C indicated cyclic behavior of about 9-year amplitude and had a statistically significant negative trend through out the study period. The temperature coefficient and respiration rate of the model prove to be highly correlated and unidentifiable with the given data. The future winters can be predicted using the posterior information coming from the past observations. As new observations arrive, they are added to the analysis. Methods are shown to be applicable to the dimensioning of artificial oxygenation devices and to the anticipation of the need for oxygenation during the winter.     

Analytical solution of the system sensitivity equation associated with a linear model

In this paper an analytical derivation of the sensitivity of a linear model to a given parameter is presented. This derivation avoids the numerical solution of the system sensitivity equation associated with the model

$\text{dx/dt=Ax, x(0)=x}{}_0$

and thus reduces the amount of computer time and memory needed to make a comprehensive analysis. Moreover, because of its analytical nature no numerical errors of approximation are made.     

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.