growth equation
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Close-to-nature management (CTNM) is the most promising option for plantation silviculture and has received widespread attention in recent years. Stand density is a key variable in CTNM, as it directly influences growth and yield. Research for the optimal density that maximizes the total harvest has been ongoing. In this paper, a dynamic programming model was applied to the CTNM of Phoebe bournei plantations for the first time to solve the problem of stand density and target tree density control. This paper took Phoebe bournei plantations in Jindong Forest Farm of Hunan Province as the research object. Based on the data of seven consecutive years from 2015 to 2021, Richard’s growth equation was used to fit the height growth equation and basal area growth equation of Phoebe bournei. Stand growth was divided into five development stages according to the forest growth process and characteristics. Stand density and basal area were selected as two-dimensional state variables, and the maximum total harvest in the entire stand growth process was used as the objective function to establish a dynamic programming model. The optimal stand density and target tree density at each growth stage of the stand under three different site conditions were determined. According to the results obtained, the objective forest shape was designed for the stand under three types of site conditions, which can provide a theoretical basis for the CTNM of Phoebe bournei plantations to make the stand achieve the maximum harvest.

The reservoirs of the K. Satpayev canal are the important fishery water bodies in the Central Kazakhstan. Some of these reservoirs are inhabited by tench, a fish species relatively widely represented in other water systems of the region. In the reservoirs of the canal this species is not the main commercial one but it has a fairly high commercial value due to its popularity with consumers. As part of the research, the growth indicators of Tinca tinca from 4 reservoirs were evaluated, and the data on its growth from 3 more reservoirs were also provided. These samples differ in efficiency and growth rates. It has been found that there is no sexual or generation variability. Growth rates in successive fish generations strongly correlate with each other, which may indirectly indicate the stability of living conditions. The R. Lee’s phenomenon was not marked. In this regard, the calculation of variables of the von Bertalanffy growth equation was carried out without additional data processing. The highest rates of linear growth were characteristic of Tinca tinca from the reservoir of HS No. 9. However, the effectiveness of its growth scheme was the lowest. Population with a longer age range from the reservoir HS No. 3 did not have high linear growth rates, but its growth efficiency was higher. In this case, it is obvious that any assessment of growth will be relative and depend on the goals set for it. In the reservoirs of the canal there are more or less similar conditions for tench populations living due to the specifics of its functioning. The main limiting factor for the growth rate, in our opinion, will be abundance of the species in the reservoir and related trophic factors with a certain influence of withdrawal (fishing, predators).

The growth of GDP is considered as a natural-growth process amenable to description by the logistic-growth equation. The S-shaped logistic pattern provides good descriptions and forecasts for both nominal and real GDP per capita in the US over the last 80 years. This enables the calculation of a long-term forecast for inflation, which is to enter a declining trend not so far in the future. The two logistics are well advanced, more so for nominal GDP. The assumption for logistic growth works even better for Japan whose nominal GDP per capita has already completed tracing out an entire logistic trajectory. The economic woes of industrialized countries could be attributed to the saturation of growth there, as if a niche in nature had been filled to capacity. In contrast, GDP growth in China and India is in the very early stages of logistic growth still indistinguishable from exponential patterns. The ceiling of these logistics can be anywhere between 7 and 15 times today’s levels.

The logistic-growth equation is a special case of the Volterra-Lotka equations. The former describes competition only between members of the same species whereas the latter describes competition also with other species. In the study of US Nobel laureates considering laureates per population improves the quality of the logistic fit but the Volterra-Lotka approach suggests that a logistic description would be a good approximation for data per unit of time rather than cumulative data. Fitting logistic S curves on cumulative data — although proven successful in many business and other applications — constitutes treacherous terrain for inexperienced S-curve enthusiasts. The Volterra-Lotka analysis of Nobel laureates reveals other insights such as that Americans and other nationalities are locked in a win-win struggle with Americans drawing more of a benefit, and also that American Nobel laureates “incubate” new Nobel laureates to a lesser extent than other nationalities.

This article examines the relationship between financial development and economic growth in Mali. The process by which financial development affects economic growth in Mali has been observed: first, by regressing a growth equation, and second, by Granger causality. To do this, the ordinary least squares method is used to estimate an error correction model over the period 1980-2015. The results obtained show that bank deposits and loans to the economy have a negative and significant effect on short-term economic growth. Moreover, the money supply has a negative and significant effect on economic growth in the short and long term. Moreover, public spending and trade openness has a positive and significant effect on economic growth, in the short and long term for the former and, in the long term for the latter. In addition, no Granger causal link was detected. A probable improvement lies in the continuation of the reforms, already undertaken by the CBWAS.

The biomass, nutrient content and decomposition rate of shoot sheaths remain unexplored in the study of Moso bamboo forests. The rapid growth of shoots means many bamboo sheaths are produced each year, and therefore should not be neglected in the study of the Moso bamboo ecosystem. In our study, we selected 160 bamboo shoots of different sizes in Yixing forest farm, Jiangsu Province. Our analysis was based on the allometric growth equation, using diameter at breast height (DBH), internode length of bamboo at breast height (IL), and bamboo height (H) as independent variables to establish the biomass model of shoot sheaths using all samples. In addition, we also measured the nutrient content of shoots and estimated the decomposition rate of shoots by setting up litter decomposition bags. Our results found that logarithmic regression should be used to fit the biomass model of shoot sheaths. From the perspective of practical application, model W3 fitting DBH and IL was determined. The order of the nutrient elements in the shoot sheath is C > N > K > P. Decomposition tests showed that it took 0.47 years for 50% of sheaths to decompose, and 3.15 years for all sheaths to decompose.

The dates on back calculation of perch growth from Vyacheslavsky (Astana) reservoir located in the Akmola oblast of the Republic of Kazakhstan are presented. We studied 2 samples, separated by a time interval approximately equal to duration of one generation. The growth rates of perch in this water body are slower in comparison with previously studied populations. The calculated length of perch have changed little for four years. Sexual and generational variability of growth is not observed. There is a fairly high level of correlation between calculated parameters of body length in adjacent generations, which indicates the stability or insignificant variability of the habitat conditions of perch in the reservoir. It can also show of the immutability of the main influencing factors and their vectors of impact. Taking into account the fact that these factors are a negative, the growth rates of perch in reservoir show a tendency to decrease. Von Bertalanffy’s growth equation performed better in the 2015 sample. This was reflected in the coefficient of Poly-Munro growth efficiency and calculated (theoretical) weight growth. The decrease in the “quality” of population biological parameters indicates beginning of degradation within the group, possibly. But, now observed differences are still at an unreliable level and are characterized only as tendencies. Based on the logical analysis, the main reason for decline in growth rate was termination of commercial fishing, which upset the existing balance in the perch population and caused the so-called “neglect of fishing”.

Since the work of Von Bertalanffy (1957), several models have been proposed that relate the ontogenetic scaling of energy assimilation and metabolism to growth, being able to describe ontogenetic growth trajectories for living organisms and collapse them onto a single universal curve (West et al. 2001; Barnavar et al. 2002). Nevertheless, all these ontogenetic growth models critically depends on fitting parameters and on the allometric scaling of the metabolic rate. Using a new metabolic rate relation (Escala 2019) applied to a Bertalanffy-type ontogenetic growth equation, we find that ontogenetic growth can also be described by an universal growth curve for all studied species, but without the aid of any fitting parameters. We find that the inverse of the heart frequency fH, rescaled by the ratio of the specific energies for biomass creation and metabolism, defines the characteristic timescale for ontogenetic growth. Moreover, our model also predicts a generation time and lifespan that explains the origin of several 'Life History Invariants' (Charnov 1993) and predicts that the Mathusian Parameter should be inversely proportional to both the generation time and lifespan, in agreement with the data in the literature (Duncan et al. 1997; Dillingham et. al 2016; Hatton et al 2019). In our formalism, several critical timescales and rates (lifespan, generation time & intrinsic population growth rate) are all proportional to the heart frequency fH, thus their allometric scaling relations comes directly from the allometry of the heart frequency, which is typically fH ∝ M-0.25 under basal conditions.

AbstractOur lives begin with 1 cell, then 2, then 4, then the trillion cell adult, comprised of cell lineages, tissues, organs. How does this occur? Examination in numbers of cells, N, Cellular Phylodynamics, revealed two previously unappreciated processes: UNI-GROWTH, the slowing of growth that occurs as we become larger, caused by fewer cells dividing, captured by the Universal Mitotic Fraction and Universal Growth Equations, with accuracy confirmed for 13 species, including nematodes, mollusks, and vertebrates; and ALLO-GROWTH, the creation of body parts from Founder Cells, captured by the Cellular Allometric Growth Equation, which describes mitotic expansion by Cell-Heritable change in the Cell Cycle Time. These equations can generate cell lineage approximations, bringing the power of coalescent theory to developmental biology.

Abstract This work is one of the first studies on the growth of Poecilia latipinna outside its natural habitat. The objective of our study was to investigate the growth parameters of the population of P. latipinna, which is an alien species in Oman (Wadi Al-Bahayes). The population structure of P. latipinna in Wadi Al-Bahayes (Oman; 23°40′47″N; 58°11′36″E) was studied in June and August 2020, using 124 fish. In the course of this study, the number of individuals of each sex, age, weight and size composition were determined. In addition, the total length–weight relationship (LRW) was calculated, as well as the von Bertalanffy growth equation. The mean growth performance (phi prime) and the condition factor were calculated. Males accounted for 37.10% and females for 62.90% of the population. The length–weight relationship and the von Bertalanffy growth equation were W = 0.0214 × L 2.7889 R2 = 0.9212, Lt = 11.46 (1 − e −0.127 (t + 2.71)) for males and Lt = 14.51 (1 − e−0.072 (t + 3.98)) for females. The mean growth performance and the condition factor were calculated as 1.22 for males and 1.18 for females and 1.54 for all specimens. The study shows that the population of the species is characterized by a wide age range. Consequently, monitoring of this alien species is highly recommended.