A model of maximum employment growth with a one-third profit share

Summary Experimental data for maximum growth and food consumption of Atlantic Salmon (Salmo salarL.) parr from five Norwegian rivers situated between 59 and 70°N were analysed and modelled. The growth and feeding models were also applied to groups of Atlantic Salmon growing and feeding at rates below the maximum. The data were fitted to the Ratkowsky model, originally developed for bacterial growth. The rates of growth and food consumption varied significantly among populations but the variation appeared unrelated to thermal conditions in the river of population origins. No correlation was found between the thermal conditions and limits for growth, thermal growth optima or maximum growth, and hypotheses of population‐specific thermal adaptation were not supported. Estimated optimum temperatures for growth were between 16 and 20 °C. Model parameter estimates differed among growth‐groups in that maximum growth and the performance breadth decreased from fast to slow growing individuals. The optimum temperature for growth did not change with growth rate. The model for food consumption (expressed in energy terms) peaked at 19–21 °C, which is only slightly higher than the optimal temperature for growth. Growth appeared directly related to food consumption. Consumption was initiated ≈2 °C below the lower temperature for growth and terminated ≈1·5 °C above the upper critical temperature for growth. Model parameter estimates for consumption differed among growth‐groups in a manner similar to the growth models. By combining the growth and consumption models, growth efficiencies were estimated. The maximum efficiencies were high, 42–58%, and higher in rivers offering hostile than benign feeding and growth opportunities.

Lobster Panulirus polyphagus has a fairly high economic value and is found in the estuary waters of Tarakan City. This research aims to study the growth and mortality model of Lobster P. polyphagus originating in the estuary waters of Tarakan City. The research method was carried out using a quantitative descriptive method. Sampling was conducted 14 times from December 2021-May 2022 using gill nets. The results showed that the male sex ratio was more than the female. Allometric growth of males and females is negative allometric with a thin body shape. The structure of the size obtained was mostly in males ranging from 18.3-20.6 cm, and females around 20.5-22.2 cm. The maximum length growth of P. polyphagus based on von Bertalanffy's growth model was 31.519 cm in males and 31.374 cm in females. The total mortality (Z) of P. polyphagus for males and females was 1.104 and 1.119; catch mortality (F) of 0.106 and 0.253; natural mortality (M) of 0.998 and 0.866; exploitation rate (E) of 0.096 and 0.226, respectively. The high natural mortality causes the extinction of the Lobster species, so good management is needed so that it is sustainable.

Dynamic kinetic analysis of growth of Listeria monocytogenes in a simulated comminuted, non-cured cooked pork product

1. The chief objectives were to analyse and model experimental data for maximum growth and food consumption of Atlantic salmon parr (Salmo salar) collected from a cold glacier fed river in western Norway. The growth and feeding models were also applied to groups of Atlantic salmon growing and feeding at rates below the maximum. The growth models were validated by comparing their predictions with observed growth in the river supplying the experimental fish. 2. Two different models were fitted, one originally developed for British salmon and the other based on a model for bacterial growth. Both gave estimates for optimum temperature for growth at 18–19 °C, somewhat higher than for Atlantic salmon from Britain. Higher optimal temperature for growth in salmon from a cold Norwegian river than from British rivers does not concur with predictions from the thermal adaptation hypothesis. 3. Model parameter estimates differed among growth groups in that the lower critical temperature for growth increased from fast to slow growing individuals. In contrast to findings for brown trout (Salmo trutta), the optimum temperature for growth did not decrease with decreasing levels of food consumption. 4. A new and simple model showed that food consumption (expressed in energy terms) peaked at 19.5–19.8 °C, which is similar to the optimal temperature for growth. Feeding began at a temperature 1.5 °C below the lower temperature for growth and ended about 1 °C above the maximum temperature for growth. Model parameter estimates for consumption differed among growth groups in a manner similar to the growth models. Maximum consumption was lower for Atlantic salmon than for brown trout, except at temperatures above 18 °C. 5. By combining the growth and food consumption models, growth efficiency was estimated and reached a maximum at about 14 °C for fast growing individuals, increasing to nearly 17 °C for slow growing ones, although it was lower overall for the latter group. Efficiency also declined with increasing fish size. Growth efficiency was generally higher for Atlantic salmon than for brown trout, particularly at high temperature.

Economic weights are obtained for feed intake using a growth model and an economic model. The underlying concept of the growth model is the linear plateau model. Parameters of this model are the marginal ratio (MR) of extra fat and extra protein deposition with increasing feed intake (FI) and the maximum protein deposition (Pd(max)). The optimum feed intake (FI0) is defined as the minimum feed intake that meets energy requirements for Pd(max). The effect of varying FI and MR on performance traits was determined. An increase in FI results in a larger increase in growth rate with lower MR. For a given MR, feed conversion ratio is lowest when FI equals FI0. Lean meat percentage (LMP) is largest for a low MR in combination with a low FI. The decrease in LMP with higher FI islargest when FI exceeds FI0. Economic weights for FI, MR and Pd(max) depend on FI in relation to FI0. Economic weights for FI are positive when FI is less than FI0 and negative when FI is larger than FI0. The MR has only then a negative economic weight, when FI is below FI0. Economic weights of FI and MR have a larger magnitude with lower MR and lower Fl. In contrast, economic weights for growth rate and FI derived from the economic model only change in magnitude and not in sign with different levels of these traits. The economic model always puts a negative economic weight on FI since it expresses profit due to a decrease in FI with constant growth rate and LMP. This holds the risk of continuous decrease in FI in pig breeding programs. In contrast, the use of growth models for genetic improvement allows direct selection for an optimum feed intake which maximizes feed efficiency in combination with maximum lean meat growth. It is concluded that recording procedures have to be adapted to collect the data necessary to implement growth models in practical pig breeding applications.

Summary 1. The objectives were: (i) to check the validity of a new growth model; (ii) to examine the relationship between population density and both mean mass and mean growth rate and (iii) to discover if compensatory growth occurred. First (0+) and second (1+) year-old juvenile sea-trout were sampled by electrofishing at the beginning and end of the summer from 1967 to 2000. Additional samples were taken in some years in winter and in the critical period for survival when the fry first emerge from the gravel. The trout left the stream as pre-smolts in May, soon after their second birthday. 2. A growth model (Elliott, Hurley & Fryer, 1995) estimated the mean mass of the trout over the 2 years spent in fresh water. The date and mean mass at the start of the growth period were defined as the median date for fry emerging from the gravel and their mean mass at emergence, both being estimated from individual-based models (Elliott & Hurley, 1998a, b). 3. The variation in mean mass among year-classes was small for newly-emerged fry (CV = 6.2%), maximum at the start of the first summer of the life cycle (CV = 38.1%), and then decreased gradually for successive life-stages to a low value for pre-smolts (CV = 10.8%). Mean mass was not related to population density and, therefore, mean growth rate was density-independent. Growth in the first, but not the second, winter of the life cycle was lower than model prediction, but when it was assumed in the model that there was no first-winter growth, there was good agreement in most year-classes between model estimated values and observed mean mass. Exceptions were that mean masses and growth rates for 0+ trout after four summer droughts were lower than expected, but compensatory growth followed, so that observed and expected masses were similar for 1+ trout. 4. Pre-smolt mean mass on 30 April measured total growth achieved in the freshwater phase of the life cycle. This was significantly related to mean mass at the end of the first and second summers of the life cycle, but not to the emergence date and mean mass of emerging fry. 5. These juvenile sea-trout were growing at their maximum potential in most year-classes but when this was not achieved, compensatory growth soon restored their mass to values expected from the model. This ensured a low variation in the mean mass of pre-smolts just before they migrated to the sea. However, the latter mass was higher in more recent year-classes (1987–98) than in previous ones (1967–86), demonstrating the effect of slightly higher stream temperature. This study has shown the importance of developing realistic growth models in order to detect departure from maximum potential growth, and the more subtle effects of temperature change, possibly due to the effects of climate change.

Analysis of a generalised growth equation shows that both the maximum growth rate of a microbial culture and the duration of the lag phase are related to each other and to the maximum growth. Similar relationships apply to growth expressions, such as the logistic and Gompertz models, that are special cases of the generalised model. Moreover, the same relationships are observed qualitatively in measurements of the growth of Salmonella species. These results may allow the characterisation of microbial growth with fewer parameters than is usually the case and imply the likelihood of a fundamental physiological interdependence between maximum growth rate, the duration of the lag time and the maximum growth.

ABSTRACTThis article sets out a classical model of economic growth in which the distribution of income features the possibility of profit-sharing with workers, as firms choose periodically between two labor-extraction compensation strategies. Workers are homogeneous with regard to labor power, and firms choose to compensate them with either only a conventional wage or a share of profits on top of this conventional wage. Empirical evidence shows that labor productivity (i.e. labor extraction) in profit-sharing firms is higher than labor productivity in non-sharing firms. The frequency distribution of labor-extraction employee compensation strategies and labor productivity across firms is time-variant, being driven by satisficing imitation dynamics from which we derive two significant results. First, heterogeneity in labor-extraction compensation strategies across firms, and hence earnings inequality across workers can be a stable long-run equilibrium outcome. Second, although convergence to a long-run equilibrium may occur with either a falling or increasing proportion of profit-sharing firms, the share of net profits in income and the rates of net profit, capital accumulation and economic growth nevertheless all converge to the highest possible long-run equilibrium values.

Individual trees in natural forests often exhibit complex, inconsistent and variable growth trajectories influenced by genetics, climate change and uneven stand structure. These growth divergences pose a challenge in predicting the overall growth trend of trees at the aggregate level. Here, we propose a radius‐driven metabolic growth model (iterative growth model at the tree‐ring, IGMR) to explain the radial growth of trees. The IGMR suggests that the best radial growth trajectory (BGT) at the aggregate level varies within a predictable range and can be derived from the maximum radius and total growth time of an individual tree. Analyses based on a global database confirmed the applicability of the IGMR and found that the average radial growth trend closely follows half of the BGT, with the strength of this association potentially related to functional trait trade‐offs. Further analyses show that climate change and uneven stand structure may cause the overall growth trajectory to undergo more drifts (changes in growth rate only) than adaptations (changes in maximum size). Synthesis : Our results reveal not only a convergent growth trajectory in tree size (or radius) at the aggregate level, but also suggest that climate regulates the tree growth–climate relationship by influencing the height (i.e. maximum radial growth rate) of this unimodal trajectory, whereas the length (i.e. with maximum tree radius) of the trajectory shows greater dependence on species. These findings further imply that climate change is more likely to affect the forest's maximum carbon sequestration capacity through shifts in community composition, rather than through direct changes in individual tree growth rates.

Pig growth simulation models are used to determine feeding strategies that improve profitability on commercial farms. For a given farm, the number of diets fed, their energy, amino acid content, the quantity fed and the diet period can vary, thus giving a very large number of possible feeding strategies (F, as many as 1050). Adding nonlinear optimisation methods to a growth model allows us to find an Fyielding the maximum for a given objective function, usually the gross margin per pig or per pig place and year. Our simulation program links a linear program for a least-cost diet formulation, a stochastic pig growth model and a genetic algorithm (GA) to find the Fgiving a best solution. When finding Ffor maximum profitability, the gross margin obtained by the GA is higher than that found by random search or by feeding pigs to their maximal lean growth. In the growth model, pig genotypes are characterised by the maximal protein deposition potential (Pdmax), minimum lipid to protein ratio (MinLP) and the energy intake potential (p). In the model, variances and covariances of these quantities are used to grow a population of pigs instead of a single pig. A simulation study was conducted to investigate how different pig genotypes and different relative economic weightings for gross margin and nitrogen excretion affect the nitrogen retention and profitability. It was found that a large increase in nitrogen retention can be achieved through diet optimisation before profitability is compromised and that a lean genotype will have better nitrogen retention. Adding stochasticity to the model for a given population size showed that as the variances increase the variability in gross margin increases and with unchanging variances, the variability in gross margin decreases as the population size increases. Overall, using a feeding schedule which maximises gross margin for a single pig within a population of pigs results in a lower gross margin.

Este trabalho objetivou avaliar o crescimento e a produtividade de grãos da cultura do milho, submetida a diferentes doses de nitrogênio. O experimento foi conduzido com a cultura do milho híbrido Pioneer 30F35, no período de 25/06 a 28/10/2009, na região de Rio Largo, AL. O delineamento experimental foi em blocos casualizados e os tratamentos consistiram em seis doses de nitrogênio (0, 50, 100, 150, 200 e 250 kg ha-1 de N), com a fonte ureia, e cinco repetições. Os modelos logístico e pico log normal apresentaram ajustes estatísticos significativos (p<0,05) das variáveis de crescimento e coeficientes de determinação máximo de 0,994 e 0,990, respectivamente. Os valores observados e estimados pelos modelos apresentaram alta associação pelo índice de concordância de Willmott, com valores superiores a 0,953. As plantas apresentaram diferenças estatísticas significativas pelo teste F (p<0,05), entre os tratamentos, para altura e índice de área foliar, com crescimento máximo para a dose de 100 kg ha-1 de N. Os tratamentos mostraram diferenças estatísticas significativas (p<0,05) para a produtividade, sobressaindo-se a dose de 200 kg ha-1, que proporcionou maior produtividade de grãos (5,45 t ha-1). Os modelos de crescimento podem ser utilizados para auxiliar a análise de crescimento.

Growth functions frequently used in forestry have in common that among the model parameters to be estimated, only the asymptote is expressed in the dimensions of the input data. By contrast, parameters determining rate and shape of the curve often exhibit indefinite scales. This might cause problems in specifying adequate starting values and in parameter interpretation. We present a mathematical derivation to obtain a modified growth function based on the four-parameter Richards function. Two of the rate and shape parameters were replaced by new parameters directly related to the growth process: time of maximum growth and maximum growth rate. Both the original model and its modified form were fitted to individual-tree height–age data from the National Forest Inventory in Germany. The modified function has several advantages: (i) easier interpretability of model parameters, (ii) easier specification of starting values, (iii) improved linear behavior allowing for more reliable asymptotic inferences and for better convergence, and (iv) reduced correlation between model parameters. As a further benefit, the presented model allows for deriving biologically interpretable forms of the Gompertz function, the von Bertalanffy function, and the logistic function. Based on the results, we suggest using the modified function provided for further applications in growth modeling.

Microbial growth and isothermal microcalorimetry: Growth models and their application to microcalorimetric data

Production of Crassostrea gigas in hatcheries may be affected by different factors influencing spat quality; this will be reflected during its cultivation in the field. The main indicator of quality is growth. Growth modeling is a form of determining individual growth patterns in bivalves. In this study, multi-model inference (MMI) and the Akaike information criterion (AIC) were employed to identify differences in growth patterns of distinct C. gigas stocks. The experiment used spat produced in four different hatcheries (A, B, C, and D), which were cultivated under identical conditions. The stocks showed similar growth patterns but the best growth models to describe every case were different; hatchery A—von Bertalanffy (AIC = − 15.27), hatchery B—Schnute model case 3 (AIC = − 0.46), and hatcheries C and D—Schnute model case 1 (AIC = 233.4 and − 73.3, respectively). According to the models, oysters from hatchery B did not reach their maximum growth while the rest did it. Differences may be attributed to stock origin while the spat quality seems associated with production protocols. Results showed that growth patterns of C. gigas can be variable under the same cultivation conditions but the differences are difficult to detect. We demonstrated that the only way to find such differences was via MMI, and this approach should be used for any aquaculture resource.

Editor's evaluation: Resource allocation accounts for the large variability of rate-yield phenotypes across bacterial strains