A new growth model for fishes and the estimation of optimum age of fish populations

Evidence is presented that a simple power equation of the formX _t –X _m =±b(|tࢤt _m|)^B can describe growth in length and weight of fishes, whereX _t denotes fish length or weight at aget, X _m is length or weight (L _m orW _m ) at a reference aget _m , andb andB are parameters to be estimated by the least squares. The optimum age of fish populations (t _y ) may be estimated by the equationMW _m /b=±y ^B (B/y-M) whereM denotes natural mortality and wherey=t _y -t _m .     

A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

A world model of the growth in production and population

A model for the growth in GNP (gross national product) and population has been set up. On the basis of the present data it was found that the growth of a population is a function of GNP, and that GNP seems to follow a logistic growth.     

Effects of kinship on growth of a live-bearing reef fish

The influence of genetic relatedness on the individual performance (e.g. growth, development) of animals is often tied to agonistic or cooperative behaviors among conspecifics, and studies of the effects of kinship have produced mixed results. To explore genetic relatedness independent of these behaviors, we investigated the effects of kinship on the growth of the kelp perch Brachyistius frenatus, a live-bearing, planktivorous marine reef fish that is capable of only limited dispersal. Although juveniles occur in aggregations and compete for food resources, they do not exhibit overt aggressive or cooperative behavioral interactions. We hypothesized that under competition and in the absence of these behaviors, sibling and non-sibling groups of juvenile B. frenatus raised at the same densities in the field would not differ in average growth, but that siblings would exhibit lower variation in growth, simply due to genetic similarities in inherent growth rates. Pregnant, female kelp perch were collected and placed in cages until parturition was complete. Groups of young, recently born from the same mother or from different mothers, were then raised in the field for 9 wk. Our results revealed that average growth rates were similar between sibling and non-sibling treatments. While variation in growth increased initially in non-siblings, siblings showed little such variation. This divergence, however, was not consistent over the duration of the experiment, and variation in the growth of siblings ultimately converged with that of non-siblings. Effects of genetic relatedness would be most likely to manifest themselves early after birth, before environmental factors exert their influence, and this may explain the initial separation but eventual convergence in variation in growth between sibling and non-sibling treatments. For B. frenatus and other organisms that will encounter relatives and compete for resources without overt behavioral interactions, the degree of kinship may play a minor role in the demography of local populations. Received: 26 January 1998 / Accepted: 30 September 1998     

Effects of sheltering fish on growth of their host corals

Stony corals are the foundation species of tropical reefs, and their structures can harbor a diverse range of mutualist taxa that can confer important benefits, including provision of nutrients. Prominent among the associates of branching coral in the genus Pocillopora are groups of zooplanktivorous damselfishes that take refuge in the coral to avoid their predators. In field and laboratory experiments, we explored the effects of colonies of resident damselfishes on growth of their host corals. Laboratory studies revealed a positive relationship between biomass of fish and output of ammonium. In the field, levels of ammonium were significantly elevated in the water surrounding the branches of Pocillopora occupied by colonies of damselfish, particularly in time periods following active feeding by the fish. Experimental manipulation of the presence of fish on host corals during a month-long field experiment revealed that corals hosting fish grew significantly more than those that lacked fish, and coral growth was positively correlated with the biomass of resident fish. The Pocillopora colonies in the field experiment varied in the degree of openness of their branching structure, and dye studies indicated that this affected their ability to retain waterborne nutrients. Together with biomass of resident fish, colony openness explained 76% of the variation in coral growth rate during the experiment. Corals can exhibit considerable morphological variability, and mutualistic fish respond to colony architecture during habitat selection, with some species preferring more open-branched forms. This makes it likely that corals may face tradeoffs in attracting resident fish and in retaining the nutrients they provide.     

A spatial model of growth and competition strategies in coral communities

A discrete spatial simulation model is developed to investigate the type and intensity of biological and physical factors influencing the structure of coral communities. The model represents reproduction, growth, and interspecific competition by coral colonies in terms of “ownership” of space in a plot of reef habitat. Using data for several eastern Pacific coral species, the model reproduces observed changes in species composition and diversity during coral community development. Model results suggest that during early successional stages, or in areas that are frequently disturbed, larval colonization and rapid growth are more important than dominance achieved by extracoelenteric digestion or by growing over another coral in acquiring and maintaining possession of reef substrate. In mature communities that remain undisturbed, dominance is the best competitive strategy. Although the model was developed to study natural and man-induced changes in the community dynamics of coral reefs, it could be adapted to study other sessile organisms where spatial pattern is an important influence on the frequency and outcome of biological interactions.     

A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

Calculation of search volume on cruise-searching planktivorous fish in foraging model

Search volume of cruising planktivorous fish was calculated based on its detailed behavior Th examine the factors influencing search volume, a series of experiments were conducted by varying ambient conditions, such as structural complexity light intensity and turbidity Pseudorasbora parva were used in experiment as predator and Daphnia pulex was selected as prey The shape of scanning area of P parva showed elliptic and the search volume changed drastically depending on ambient conditions. Compared with the results of previous foraging model, the search volumes of the fish under previous study were larger (1.2 to 2.4 times) than those from our study These results on the changes in feeding rate can be useful in determining microhabitat requirement of P parva and othercyprinids with a similar foraging behavior The calculated search volume is compared with other foraging model andthe effect of zooplankton-planktivore interactions on aquatic ecosystem is discussed.     

RNA-DNA ratio: an index of larval fish growth in the sea

Data on water temperature, RNA-DNA ratio, and growth of eight species of temperate marine fish larvae reared in the laboratory were fit to the equation: $$G_{pi} = 0.93{\text{ }}\operatorname{T} + 4.75{\text{ RNA - DNA}} - 18.18$$ where G_pi is the protein growth rate in % d^-1 and T is the water temperature. Water temperature and larval RNA-DNA ratio explained 92% of the variability in growth rate of laboratory-reared larvae. The model is useful over the entire range of feeding levels (starvation to excess), temperatures (2° to 20°C) and fish species studied. Estimates of recent growth of larval cod, haddock, and sand lance caught at sea based on water temperature and RNA-DNA ratio ranged from negative to 26% d^-1. These data demonstrate the importance of food availability in larval fish mortality and suggest that short-term growth under favorable conditions may be considerably higher than expected from long-term indicators. RNA-DNA ratio analysis offers new possibilities for understanding larval growth and mortality, and their relation to environmental variability.     

A Bayesian mixture model for missing data in marine mammal growth analysis

Much of what is known about bottle nose dolphin (Tursiops truncatus) anatomy and physiology is based on necropsies from stranding events. Measurements of total body length, total body mass, and age are used to estimate growth. It is more feasible to retrieve and transport smaller animals for total body mass measurement than larger animals, introducing a systematic bias in sampling. Adverse weather events, volunteer availability, and other unforeseen circumstances also contribute to incomplete measurement. We have developed a Bayesian mixture model to describe growth in detected stranded animals using data from both those that are fully measured and those not fully measured. Our approach uses a shared random effect to link the missingness mechanism (i.e. full/partial measurement) to distinct growth curves in the fully and partially measured populations, thereby enabling drawing of strength for estimation. We use simulation to compare our model to complete case analysis and two common multiple imputation methods according to model mean square error. Results indicate that our mixture model provides better fit both when the two populations are present and when they are not. The feasibility and utility of our new method is demonstrated by application to South Carolina strandings data.     

Linking patch-use behavior, resource density, and growth expectations in fish

Optimality theory rests on the assumptions that short-term foraging decisions are driven by variation in environmental quality, and that these decisions have important implications for long-term fitness. These assumptions, however, are rarely tested in a field setting. We linked behavioral foraging decisions in food patches with measures of environmental quality covering larger spatial (resource density) or temporal (growth parameters) scales. In 10 lakes, we measured the food density at which benthic fish give up foraging in experimental food patches (giving-up density, GUD), quantified the biomass of benthic invertebrates, and calculated the maximum individual size (L(infinity)) of bream (Abramis brama L.), a typical benthivore in these lakes. We found positive relationships between resource density and both GUD and L(infinity), and a positive relationship between L(infinity) and GUD. Prey characterized as vulnerable to predation contributed most to the relationships between resource density and either GUD or L(infinity). A path analysis showed that resource density and L(infinity) directly explained 54% and 28%, respectively, of the variation in GUD, whereas 86% of the variation in L(infinity) was explained by resource density, with mostly indirect contribution from GUD. We conclude that the short-term foraging behavior of benthivores matched our expectations based on optimality theory by being positively linked to variables on environmental quality operating at both a larger spatial scale and a longer temporal scale.     

Effects of feeding history on the growth characteristics of a reef fish at settlement

A feeding experiment was conducted on the pelagic stages of the tropical goatfish Upeneus tragula (family Mullidae) to examine how food quantity affects growth characteristics and potential success at settlement. Pelagic goatfish were collected from aggregation rafts 3 nautical miles west of Lizard Island on the northern Great Barrier Reef during December 1990. Three tanks in each of four feeding regimes were stocked with 25 pelagic goatfish between 20 and 23 mm standard length (SL). The four feeding regimes were: fed ad lib. (fed): fed once per day (f1pd); starved every second day (stld); starved for 3 d and re-fed (st3d). Fishes were fed 36 to 48 h old Artemia sp. nauplii (Ocean Star strain). Fish were removed from tanks when they underwent metamorphosis, changed pigmentation and settled to the bottom of the tanks. Morphology, muscle development, time taken to settle and biochemical condition were examined. Growth attributes of the treated fish were compared to fish which settled within 24 h of capture (field). All attributes examined were significantly influenced by the feeding treatments. Fish within the fed and st3d treatments were significantly larger and heavier than fish in the less well-fed treatments (f1pd, st1d). Similarly, concentrations of total lipid, carbohydrate and protein in the settled fish were significantly higher in the fed and st3d treatments compared with the st1d and f1pd treatments. For all these morphological and biochemical attributes the st1d and f1pd fish did not significantly differ from the field fishes, but did differ from the fed and st3d fishes. Water content was significantly higher in the f1pd, st1d and field fishes compared with the fed and st3d fish. Furthermore, the average time taken to settle followed the pattern: fed (14d)U. tragula are physiologically well suited to exploiting a patchy food source, and that food availability within the pelagic stages can have a major influence on the growth characteristics of this reef fish at settlement. The ramifications of this finding are discussed in relation to survival and success once fish have recruited to the reef population.     

Modeling the refuge effect of submerged macrophytes in ecological dynamics of shallow lakes: A new model of fish functional response

Submerged macrophytes often provide refuge for zooplankton from fish predation in temperate and subtropical shallow lakes. However, since the relationship between submerged macrophyte abundance and its refuge effect has not been well established, the refuge effect is difficult to be simulated. In this paper, we constructed mathematical models to describe the refuge effect of submerged macrophytes on fish foraging activities and ecological dynamics of shallow lakes based on the previous studies. We clarified the underlying behavioral mechanisms of the observed functional responses through analyses of the fish foraging behavior, extracted the affected variables related to the refuge effect, formulized the relationship between the affected variables and submerged vegetation density, and determined parameter values with a compensative procedure. Calibration and validation results indicated that the new functional response model was successful to simulate the refuge effect on interfering with fish foraging behavior. Moreover, the model was cooperated into a minimal ecological model for shallow lakes. Modeling results showed that the model was able to simulate the refuge effect in ecological dynamics, and made the ecological model produce significantly different results from those with the existing functional response models.     

A new model for the CBL growth based on the turbulent kinetic energy equation

Starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the Convective boundary layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum and solve the 3-D EDS equation. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D EDS. Furthermore, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). Currently there are no available experimental data to directly verify our EDS model.     

Integration of a fish bioenergetics model into a spatially explicit water quality model: Application to menhaden in Chesapeake Bay

Although fish are usually thought of as victims of water quality degradation, it has been proposed that some planktivorous species may improve water quality through consumption of algae and sequestering of nutrients via growth. Within most numerical water quality models, the highest trophic level modeled explicitly is zooplankton, prohibiting an investigation of the effect a fish species may be having on its environment. Conversely, numerical models of fish consumption do not typically include feedback mechanisms to capture the effects of fish on primary production and nutrient recycling. In the present study, a fish bioenergetics model is incorporated into CE-QUAL-ICM, a spatially explicit eutrophication model. In addition to fish consumption of algae, zooplankton, and detritus, fish biomass accumulation and nutrient recycling to the water column are explicitly accounted for. These developments advance prior modeling efforts of the impact of fish on water quality, many of which are based on integrated estimates over an entire system and which omit the feedback the fish have through nutrient recycling and excretion. To validate the developments, a pilot application was undertaken for Atlantic menhaden (Brevoortia tyrannus) in Chesapeake Bay. The model indicates menhaden may reduce the algal biomass while simultaneously increasing primary productivity.     

天然林林龄的模拟估算及案例

林龄是森林生态系统的一个重要特征,具有生态学意义.但是目前生态学调查中对天然林林龄的估算方法有一定缺陷.在特定的环境条件下,森林有着相应的演替过程.已有林窗研究表明.长白山森林是按照一定次序演替,森林的径级结构也是有规律可循的.由于总是缺乏足够的长期系统观测数据,因此作者采用数值模拟作为替代方法.应用校正过的林窗模型模拟0～600 a的森林演替序列,比较对长白山原始天然林的采样的结果,发现目前的林龄最接近400 a.这个估测结果可以从本地区历史资料记载得到印证.     

TELOC: A simulation model of the effects of lead on corn (Zea maize) growth

The simulation model TELOC has been developed to estimate the potential reduction in corn grain yield caused by soil lead. The model uses local weather data to estimate plant uptake of lead, photosynthesis of growth. The rate of photosynthesis begins to decline at 175 ppm Pb in the leaves. If the rate of photosynthesis is sufficiently reduced the carbohydrate reserves will be insufficient to meet growth demands and potential grain yield will decline.TELOC was developed to generalize across soils so that a variety of soil—lead combinations may be investigated. In addition to local weather data, a dry weight estimate of soil Pb and the parameters controlling Pb sorption by the soil must be furnished for a simulation.The model was written to be as versatile as possible. With minor changes of the code, the impact of pollutants that reduce the rate of photosynthesis may be investigated.     

Environmental influences on larval duration,growth and magnitude of settlement of a coral reef fish

The influence of environmental variables on the planktonic growth, pelagic larval duration and settlement magnitude was examined for the coral reef surgeonfish Acanthurus chirurgus. Newly settled fish were collected daily from patch reefs in the San Blas Archipelago, Caribbean Panama for 3.5 years. Environmental influences on growth were examined at three different life history stages: from 0 to 6 days, 7 to 25 days and from 26 to 50 days after hatching. Larval growth was correlated, using multiple regression techniques, with a combination of factors including solar radiation, rainfall, and along-shore winds. Depending on the life history stage, these accounted for 13–38% of the variation in growth rates when all the months were included in the analyses. Correlations between environmental variables and growth also varied among seasons and were stronger in the dry than in the wet season. During the dry season solar radiation, rainfall and along-shore winds described 57%, 86% and 74% of the variability in growth between 0 and 6 days, 7 and 25 days and 26 and 50 days, respectively. During the wet season rainfall, along-shore winds and temperature only described 38% of the variability in early growth and 27% of growth just before settlement. No significant model was found to describe growth 7–25 days after hatching during the wet season. Rainfall, solar radiation and along-shore winds were negatively correlated with growth up to 25 days after hatching but positively correlated as larvae approached settlement at a mean age of 52 days. Over 65% of the variability in pelagic larval duration was accounted for by a regression model that included solar radiation and along-shore winds. When data sets from wet and dry seasons were analysed separately, along-shore winds accounted for 67% of the change in larval duration in the dry season, and solar radiation accounted for 23% of the variation in larval duration in the wet season. Only 22% of the variability in settlement intensity could be described by solar radiation and temperature, when all months of the year were included in the analysis. Solar radiation and rainfall were included in a regression model that accounted for 40% of the variation in numbers of fish settling during the dry season. This study suggests that the levels of solar radiation, along-shore winds and rainfall during the early larval life can have important effects on the growth, larval duration and consequently, the settlement magnitude of marine fishes. Results also highlight the need to account for seasonality and ontogeny in studies of environmental influences.Communicated by G.F. Humphrey, Sydney