Verification of fractal growth models of the sponge Haliclona oculata (Porifera) with transplantation experiments

The growth form of the sponge Haliclona oculata is to a significant extent determined by the environmental conditions in which the form emerges. One of the main environmental parameters affecting the growth form is exposure to water movement. In this study, a morphological growth model is used to simulate the effect on the growth process of a change in exposure to water movement. Predictions based on the model are verified by experiments in which sponges from a sheltered growth site are transplanted to an exposed site, and vice versa. The effect of the transplantation on growth forms is determined by morphological comparisons. By combining the morphological simulation model with interpretation of growth forms, it becomes possible to use the growth form of H. oculata for bio-monitoring purposes. This form reflects the environmental conditions governing the growth process.     

Herbivores enable plant survival under nutrient limited conditions in a model grazing system

We make a theoretical study of nitrogen cycling in a model of a grazing system with five compartments. The rates of uptake of nutrient by plants and herbivores are allowed nonlinear forms which involve no a priori assumptions about whether the system is subject to top-down or bottom-up control. We derive a method of piecewise linear approximation which allows analytical study of the system. We then use this method to investigate the properties of the equilibrium states of the system, and in particular whether the system favours donor- or recipient-control, the grazing optimization problem, and the potential benefits of herbivory to plant growth. We are able to generalise our results to all uptake functions of the same qualitative class as those considered, and to show that in general the system will tend to a stable equilibrium state of donor-controlled herbivory. In this model, the presence of the ‘right’ class of herbivore is not only beneficial to plant growth in certain circumstances, but can be essential to their survival, allowing plants to co-exist with herbivores under conditions in which they would be unable to survive alone.     

Allometry and growth of the green-lipped mussel Perna canaliculus in New Zealand

Length is the most precise (and the most practical) linear measurement for predicting total weight (r>0.98 at P=0.001) in the green-lipped mussel Perna canaliculus Gmelin. The allometry varies with the environmental conditions under which the mussels grow, resulting in morphologically distinct forms of raft- and shore-grown mussels. Mussels grown intertidally are wider, less high and heavier than mussels of similar length grown in suspension. Increase in length and total weight of P. canaliculus grown in suspended cultivation was recorded at 8 experimental sites around New Zealand, during 1973–1975. Comparisons are drawn with growth on an intertidal mussel bed, where length increase was less than half that in the same period in suspension. The growth rate of mussels transferred from intertidal to suspended conditions depends on the size at transfer. Close similarity in growth rate occurred at the majority of sites in spite of a direct correlation between water temperature and length increment and substantial, differences in temperature between sites. Reasons for the uniformity are suggested. Average values for growth at sites over the northern half of New Zealand were 73 mm length (32.5 g weight) after 12 months, 113 mm (110 g) after 2 years. Growth continued throughout the year, highest growth rates corresponding to highest water temperatures. Variation due to depth was not significant. Larger mussels grew more slowly. P. canaliculus can be grown in suspended cultivation in New Zealand at a rate comparable to that in other commercial mussel-farming areas.     

Morphological analysis of growth forms of branching marine sessile organisms along environmental gradients

In this paper a series of growth forms of the sponge Haliclona oculata, the hydrozoan Millepora alcicornis and the scleractinian coral Pocillopora damicornis are morphologically analysed. The growth forms of these species were collected along a gradient of the amount of water movement. In this analysis it is demonstrated that, although these species are from very different taxonomical groups, the degree of compactness of the growth forms shows a similar trend as a response to the exposure to water movement. In all three species the growth forms gradually change from thin-branching to more compact shapes, as evaluated by measurements of various morphological characteristics. Other morphological measurements, in particular the average distance between branch tips and neighbouring branches (“branch spacing”) show a more species-specific pattern. Species in which fusion of branches is almost never observed, as for example P. damicornis, are characterized by a relatively low standard deviation of branch spacing. Species in which anastomosis frequently occurs (H. oculata and M. alcicornis) are characterized by a relatively high standard deviation in branch spacing. The final aim of this research approach is to use the morphological data acquired here in combination with morphological simulation models to gain a better understanding of the growth and form of these organisms and the impact of the physical environment (hydrodynamics and availability of light required for photosynthesis). Received: 8 July 1998 / Accepted: 9 February 1999     

Evidence of a 2-day periodicity of striae formation in the tropical scallop Comptopallium radula using calcein marking

The periodicity of striae formation in the tropical scallop Comptopallium radula (Indo-West Pacific Ocean) was investigated with an in situ marking technique, using the calcein fluorochrome. To minimize scallop stress caused by excessive handling, in situ benthic chambers were used for marking experiments. Once marked, scallops (shell height range: 38.4–75.8 mm) remained on site in a large benthic enclosure and were collected at regular time intervals to count new striae formed after marking, over a period of 3 months. A 3-h exposure period with calcein (150 mg l⁻¹) was sufficiently long to create a detectable mark in nearly all shells. It was, however, impossible to count the striae in 48.2% of the shells (mainly large specimens) because of a very small growth after marking. Lack of significant mortality during the experiments indicated that tested calcein concentrations were not lethal. A decrease in shell growth rate was observed after marking but the respective impacts of calcein toxicity and changes in environmental conditions could not be discriminated. Our results suggest that in situ calcein marking inside benthic chambers is suitable for shell growth studies of scallops, provided the latter are not too old. After marking, the juvenile C. radula formed an average of one stria every 2.1 days in summer. Reports of 2-day periodicity in biological rhythms are rare. Striae formation in C. radula may be controlled by an endogenous oscillator, synchronized by an environmental cue acting as a zeitgeber, such as seawater temperature or sea level pressure, both of which exhibit 2-day variations in the Pacific Ocean. As in many other scallop species, C. radula forms striae periodically under natural conditions, but this study shows that in pectinid juveniles, this periodicity can deviate from a daily cycle. These results suggest that C. radula shells have tremendous potential for recording environmental conditions during periods ranging from months to a few years and with a resolution of 2 days.     

Dynamics and physiology of saxitoxin production by the dinoflagellatesAlexandrium spp.

Toxin content (fmol cell^–1) and a suite of elemental and macromolecular variables were measured in batch cultures of the dinoflagellatesAlexandrium fundyense, A. tamarense andAlexandrium sp. from the southern New England region, USA. A different perspective was provided by semicontinuous cultures which revealed sustained, steady-state physiological adaptations by cells to N and P limitation. Two types of variability were investigated. In batch culture, changes in nutrient availability with time caused growth stage variability in toxin content, which often peaked in mid-exponential growth. A second type of variability that could be superimposed on growth stage differences is best exemplified by the high toxin content of cells grown at suboptimal temperatures. Calculations of the net rate of toxin production (R _tox ; fmol cell^–1 d^–1) for these different culture treatments and modes made it possible to separate the dynamics of toxin production from cell division. Over a wide range of growth rates, cells produced toxin at rates approximating those needed to replace losses to daughter cells during division. The exception to this direct proportionality was with P limitation, which was associated with a dramatic increase in the rate of toxin production as cells stopped dividing due to nutrient limitation in batch culture. Growth stage variability in batch culture thus reflects small imbalances (generally within a factor of two) between the specific rates of toxin production and cell division. N limitation and CO₂ depletion both affect pathways involved in toxin synthesis before those needed for cell division; P limitation does the opposite. The patterns of toxin accumulation were the same as for major cellular metabolites or elemental pools. The highest rates of toxin production appear to result from an increased availability of arginine (Arg) within the cell, due to either a lack of competition for this amino acid from pathways involved in cell division or to increased de novo synthesis. There were no significant changes in toxin content with either acclimated growth at elevated salinity, or with short term increases or decreases of salinity. These results demonstrate that toxin production is a complex process which, under some conditions, is closely coupled to growth rate; under other conditions, these processes are completely uncoupled. Explanations for the observed variability probably relate to pool sizes of important metabolites and to the differential response of key biochemical reactions to these pool sizes and to environmental conditions.     

Phenotypic plasticity and “cultural transmission” of alternative social organizations in the fire ant Solenopsis invicta

Summary We investigated the process of sexual maturation in winged queens of the fire ant Solenopsis invicta, a species with two distinct forms of social organization. We found that queens of the monogynous social form (single reproductive queen per colony) differ little or not at all from queens of the polygynous form (multiple reproductive queens per colony) in weight and fat content when these are pupae or newly-eclosed adults. Furthermore, the size of a sclerotized region of the adult thorax, which is set during larval growth, does not differ between queens of the two forms. In contrast, winged queens of the two social forms differ dramatically in their physiological phenotypes once they have matured, with monogynous queens weighing more and having greater fat reserves than polygynous queens. A crossfostering experiment revealed that the different maturation processes of queens of the two forms are induced largely by the type of colony in which a queen matures (monogynous or polygynous) rather than being due to intrinsic genetic differences between the forms. However, genetic variation at a single locus does appear to play some role in determining physiological phenotype in queens of the polygynous form, providing an example of genotype-environment interaction in the expression of these physiological traits. Differences between the social forms in the mature phenotypes that are produced constrain the reproductive options of queens, so that the characteristic social organization of a colony is perpetuated by virtue of the social environment in which new queens are reared. Correspondence to: L. Keller     

Do associated zooxanthellae and the nature of the substratum affect survival,attachment and growth of Cliona viridis (Porifera: Hadromerida)? An experimental approach

Massive specimens of Cliona viridis, collected off the coast of Blanes (North-Western Mediterranean Sea) in January 1987, were exposed to different light (natural day-night irradiance/constant darkness) and substrata (calcareous/siliceous) conditions to assess their influence on growth, survival and attachment rates. Sponges cultured under natural irradiance displayed higher growth rates with increasing temperature; those cultured in the dark did not respond to increased temperature, but adapted faster to laboratory conditions. Differences in growth rates between these two culture conditions are ascribed to the presence of a healthy symbiotical zooxanthellae population on individuals cultured under conditions of natural irradiance. Attachment rates of the cut sides of the sponges which were in direct contact with the substratum, also increased with increasing temperature, whilst sponge survival was not significantly dependent on temperature. The chemical nature of the substratum clearly affected survival rates, which were higher on calcified than on siliceous substrata.     

Optimal investment policies with exhaustible resources: An information-based model

An information-based model of the “optimal control” type is developed using concepts from information theory to explore the dynamics of fossil resource exhaustion and the phenomenon of substitution by other forms of capital and technological knowledge. All exhaustible resources stocks and forms of capital (and knowledge) are taken to be equivalent to forms of information in the physical sense. It is shown that, with optimal policies, the planning period, or cycle, has several distinct phases, with different optimal investment patterns. The model has two important qualitative implications: (1) economic growth rates are inherently discontinuous and (2) the model predicts an evolutionary structural change, viz., the creation of a new sector in response to the progressive exhaustion (or obsolescence) of previously essential resources or capital stocks. A multiperiod extension is suggested, leading to a tentative explanation for the Kondratieff long-wave phenomenon.     

Interactive effects of nitrogen and dissolved inorganic carbon on photosynthesis,growth, and ammonium uptake of the macroalgae Cladophora vagabunda and Gracilaria tikvahiae

Dissolved inorganic carbon (DIC) is rarely considered limiting for macroalgae, but some research suggests that under conditions of N sufficiency, photosynthetic capacity is enhanced with DIC enrichment. During spring (April–May) and summer (July–August) 1993, we investigated the interactive effects of nitrogen (N) and DIC on photosynthetic capacity, growth, and nutrient uptake rates of the macroalgae, Cladophora vagabunda (L.) van den Hoek and Gracilaria tikvahiae (McLachlan), dominant species in a temperate eutrophic estuary (Cape Cod, Massachusetts, USA). Water-column CO₂ concentrations showed significant diurnal fluctuations, ranging from a morning CO₂ peak (21 M) to an afternoon low (13 M) during summer, probably associated with metabolic activities in a thick algal mat. Results from instantaneous photosynthesis measurements and microcosm experiments indicate that DIC limits photosynthetic capacity and growth rates of C. vagabunda during summer, perhaps related to tissue N sufficiency and low water-column CO₂ concentrations. For example, this species showed enhanced growth (F=8.69, P<0.02) under DIC but not N enrichment. G. tikvahiae showed marginal DIC enhancement of maximum photosynthetic rate, while growth was significantly stimulated by addition of N. Reduced thallus N of this species during the summer further identifies N as the primary factor limiting growth. In addition, G. tikvahiae has the ability to use DIC in its several forms, while C. vagabunda primarily uses dissolved CO₂. DIC enrichment resulted in a depression of NH₄ ⁺ uptake rates for both species, particularly during summer at saturating (60 M) ammonium levels, suggesting competition between NH₄ ⁺ uptake and DIC acquisition under conditions of N sufficiency. Dominance of C. vagabunda and G. tikvahiae in areas undergoing eutrophication has been attributed to their successful procurement and storage of N as well as to high growth rates. The present study revealed that under conditions of N sufficiency during summer, DIC may control rates of production of these opportunistic macroalgae.     

Relative growth of different species of marine algae in wasterwater-seawater mixtures

In recent studies, we developed a combined nutrient removal-marine aquaculture process for the tertiary treatment of wastewater and the production of commercially important shellfish. Part of this process consists of an outdoor mass cultivation system for marine algae. During our previous experiments we observed that marine diatoms almost exclusively are the dominant algal species in our outdoor cultures. To better understand this phenomenon of diatom dominance we grew 16 species of marine algae in continuous monoculture under laboratory conditions simulating to some degree the conditions prevailing in our outdoor experiments. Species such as Skeletonema costatum, Monochrysis lutheri and Tetraselmis sp., which were never dominant in our outdoor cultures, grew as well in monoculture, as Phaeodactylum tricornutum, frequently, the prevalent species outdoors. However, when monocultures of Dunaliella tertiolecta and Thalassiosira pseudonana (3H) were purposely contaminated with P. tricornutum, the latter species quickly became dominant. It is suggested that a complex interaction of environmental factors is usually responsible for the dominance of a particular species; one such factor may be the nitrogen source in the growth media. Under conditions of virtually, complete nitrogen assimilation, the carbon: nitrogen ratio in the algae was high (7 to 8) when NO ₃ ^- –N was the source of nitrogen, and low (4 to 6) when NH ₄ ⁺ –N was the prime form of nitrogen. When algal growth was low, resulting in a large inorganic nitrogen residue, the carbon:nitrogen ratio was low regardless of whether NO ₃ ^- –N or NH ₄ ⁺ –N was the main nitrogen source.Contribution No. 3297 from the Woods Hole Oceanographic Institution.     

Blooms of surf-zone diatoms along the coast of the Olympic Peninsula,Washington. I. Physiological investigations of Chaetoceros armatum and Asterionella socialis in laboratory cultures

Two species of diatoms, Chaetoceros armatum T. West and Asterionella socialis Lewin and Norris, which account for virtually all of the plant biomass present in the surf zone along the Olympic Peninsula (USA), have been isolated and grown in culture, and comparisons have been made with respect to their physiological behavior in response to aeration, light, temperature, salinity, and nutrients. A. socialis displayed the greater maximum growth rate under most situations, which would give this species a natural advantage over C. armatum. However, in the natural habitat, C. armalum is by far the more important of the two, since the blooms often consist of almost pure stands of this species. This may be due to its apparent ability to use low light levels more efficiently. The maximum growth rate of C. armatum was reached at light levels of 750 to 1000 lux in cultures, whereas A. socialis required a higher light intensity (4000 lux) for maximum growth. C. armatum did not produce its mucilage envelope under any culture conditions. Such a mucilage envelope, with its accompanying clay particles, is invariably present surrounding the diatom chains when they are collected from the natural habitat. The absence of the mucilage envelope (and clay particles) may explain the peculiarities of iron nutrition which were observed in culture experiments, i.e., a dependence on the presence of iron as NaFe-EDTA or ferric citrate, and failure to utilize ferric choloride as a source of Fe for growth.Contribution No. 652 from the Department of Oceanography, University of Washington.     

Fertilization and early developmental stages of eggs of Clupea harengus pallasi n. maris-albi under fresh-water conditions

Eggs of the White Sea herring Clupea harengus pallasi Val. are laid in the intertidal zone, where they are liable to come under the influence of fresh water. The present paper deals with the effect of fresh-water influence on the egg of the White Sea herring, under experimental conditions. In fresh water, egg and sperm are in an unactivated state and, after transfer into sea water, are capable of re-activation, even after 212/ h exposure. The treated eggs develop until the hatching of normal and viable larvae. The number of eggs which are able to complete development depends upon the period of freshwater exposure, although the correlation between the length of that period and survival rates is not very close. Apparently, this is due both to the ability of C. harengus pallasi eggs to develop parthenogenetically and different qualities of eggs (which were obtained from different females). The morphological features of White Sea herring eggs, induced by experimental fresh-water influence, are very similar to those typical for herring eggs of the genus Ilisha, obtained from natural brackish waters. However, such changes are not characteristic of the eggs of forms from natural fresh and brackish-waters.     

Climate Change,Multiple Stressors,and the Decline of Ectotherms

Climate change is believed to be causing declines of ectothermic vertebrates, but there is little evidence that climatic conditions associated with declines have exceeded critical (i.e., acutely lethal) maxima or minima, and most relevant studies are correlative, anecdotal, or short‐term (hours). We conducted an 11‐week factorial experiment to examine the effects of temperature (22 °C or 27 °C), moisture (wet or dry), and atrazine (an herbicide; 0, 4, 40, 400 μg/L exposure as embryos and larvae) on the survival, growth, behavior, and foraging rates of postmetamorphic streamside salamanders (Ambystoma barbouri), a species of conservation concern. The tested climatic conditions were between the critical maxima and minima of streamside salamanders; thus, this experiment quantified the long‐term effects of climate change within the noncritical range of this species. Despite a suite of behavioral adaptations to warm and dry conditions (e.g., burrowing, refuge use, huddling with conspecifics, and a reduction in activity), streamside salamanders exhibited significant loss of mass and significant mortality in all but the cool and moist conditions, which were closest to the climatic conditions in which they are most active in nature. A temperature of 27 °C represented a greater mortality risk than dry conditions; death occurred rapidly at this temperature and more gradually under cool and dry conditions. Foraging decreased under dry conditions, which suggests there were opportunity costs to water conservation. Exposure to the herbicide atrazine additively decreased water‐conserving behaviors, foraging efficiency, mass, and time to death. Hence, the hypothesis that moderate climate change can cause population declines is even more plausible under scenarios with multiple stressors. These results suggest that climate change within the noncritical range of species and pollution may reduce individual performance by altering metabolic demands, hydration, and foraging effort and may facilitate population declines of amphibians and perhaps other ectothermic vertebrates. Cambio Climático, Estresantes Múltiples y la Declinación de Ectotermos     

Physioecology of zooplankton. I. Effects of phytoplankton concentration,temperature, and body size on the growth rate of Calanus pacificus and Pseudocalanus sp.

Changes in dry weight and in weight-specific growth rates were measured for copepodite stages of Calanus pacificus Brodsky and Pseudocalanus sp. cultured under various combinations of phytoplankton concentration and temperature. Mean dry weight of early copepodites was relatively unaffected by either food concentration or temperature, but mean dry weight of late stages increased hyperbolically with food concentration and was inversely related to temperature. The food concentration at which maximum body weight was attained increased with increasing temperature and body size, and it was considerably higher for C. pacificus than for Pseudocalanus sp. This suggests that final body size of small species of copepods may be determined primarily by temperature, whereas final body size of large species may be more dependent on food concentration than on temperature. Individual body weight increased sigmoidally with age. The weight-specific growth rate increased hyperbolically with food concentration. The maximum growth rate decreased logarithmically with a linear increase in body weight, and the slope of the lines was proportional to temperature. The critical food concentration for growth increased with body size proportionally more at high than at low temperature, and it was considerably higher for C. pacificus than for Pseudocalanus sp. Because of these interactions, early copepodites optimized growth at high temperature, even at low food concentrations, but under similar food conditions late stages attained higher growth at low temperature. The same growth patterns were found for both species, but the rates were significantly higher for the larger species, C. pacificus, than for the smaller one, Pseudocalanus sp. On the basis of findings in this study and of analyses of relationships between the maximum growth rate, body size, and temperature from other studies it is postulated (1) that the extrapolation of growth rates from one species to another on the basis of similarity in body size is not justified, even for taxonomically related species; (2) that the allometric model is inadequate for describing the relationship between the maximum weight-specific growth rate and body size at the intraspecific level; (3) that the body-size dependence of this rate is strongly influenced by temperature; and (4) that species of zooplankton seem to be geographically and vertically distributed, in relation to body size and food availability, to optimize growth rates at various stages of their life cycles.Contribution No. 1127 from the Department of Oceanography, University of Washington, Seattle, Washington 98195, USA     

The effects of temperature on the growth of juvenile scleractinian corals

Tropical reef corals are well known for their sensitivity to rising temperature, yet surprisingly little is known of the mechanisms through which temperature acts on intact coral colonies. One such mechanism recently has been suggested by the association between the growth of juvenile corals and seawater temperature in the Caribbean, which suggests that temperature causes a transition between isometric and allometric growth scaling in warmer versus cooler years, respectively (Edmunds in Proc R Soc B 273:2275–2281, 2006). Here, this correlative association is tested experimentally for a cause-and-effect relationship. During April and May 2006, juvenile colonies (8–35 mm diameter) of massive Porites spp. from Moorea, French Polynesia, were incubated at warm (27.8°C) and cool (25.7°C) temperatures for 15 days, and their response assessed through the scaling of growth (change in weight) with colony size. The results reveal that the scaling of colony-specific growth (mg colony⁻¹ day⁻¹) was unaffected by temperature, although growth absolutely was greater at the cool compared to the warm temperature, regardless of colony size. This outcome was caused by contrasting scaling relationships for area-specific growth (mg cm⁻² day⁻¹) that were negatively allometric under warm conditions, but independent of size under cool conditions. In April 2007, a 22 days field experiment confirmed that the scaling of area-specific growth in juvenile Porites spp. is negatively allometric at a warm temperature of 29.5°C. Based on strong allometry for tissue thickness, biomass, and Symbiodinium density in freshly collected Porites spp., it is hypothesized that the temperature-dependency of growth scaling in these small corals is mediated by the interaction of temperature with biomass.     

Photosynthetic characteristics of marine Synechococcus spp. with special reference to light environments near the bottom of the euphotic zone of the open ocean

The present study aimed to resolve the question why marine Synechococcus spp. abundantly occur even at the bottom of the euphotic zone in the Kuroshio are. Photosynthesis under such conditions was examined using simulated blue-green model light (BGL). Results indicated that photosynthesis of marine Synechococcus spp. under BGL is as active enough to support growth of these organisms. Examination of light-harvesting under BGL indicated that active photosynthesis is permitted by an unusually high abundance of phycoerythrin (PE), which is the main light-harvesting pigment for photosystem II (PSII), due to a phycobilisome (PBS) structure which is different from ordinary hemidiscoidals. Although the absorption maximum of PE is located at longer wavelengths than the energy maximum of BGL, PE was found to absorb BGL significantly. Thus, BGL cannot be a typical photosystem I (PSI) light. PSII is also significantly excited by BGL. Carotenoids, which largely absorb BGL, were found to be effective in light-harvesting for PSI. Based on the results obtained, possible reasons why marine Synechococcus spp. commonly occur in warm waters were discussed. Two strains of Synechococcus spp. isolated from the Gulf Stream in 1981 and from Kuroshio, Japan in 1983 were used in the present study.     

A simulation model of rhizome networks for Fallopia japonica (Japanese knotweed) in the United Kingdom

Fallopia japonica (Japanese knotweed) is an aggressively invasive herbaceous perennial that causes substantial economic and environmental damage in the United Kingdom (UK). As such, it is of considerable concern to councils, environmental groups, private landowners and property developers. We construct a 3D correlated random walk model of the development of the subterranean rhizome network for a single stand of F. japonica. The formulation of this model uses detailed knowledge of the morphology and physiology of the plant, both of which differ in the UK to that of its native habitat due to factors including a lack of predation and competition, longer growth seasons and favourable environmental conditions in the UK. Field data obtained as a part of this study are discussed and used in the model for parameterisation and validation. The simulation captures the field data well and predicts, for example, quadratic growth in time for the stand area. Furthermore, the role of a selection of parameters on long-term stand development are discussed, highlighting some key factors affecting vegetative spread rates.     

The transition from dirty to clean industries: optimal fiscal policy and the environmental Kuznets curve

This paper investigates privately and socially optimal patterns of economic development in a two-sector endogenous growth model with clean and dirty goods. We consider a second-best fiscal policy framework in which distortionary taxes jointly influence economic growth and environmental quality. In this policy setting, three conditions produce an Environmental Kuznets Curve (EKC): (i) dirty output is bounded; (ii) clean output grows endogenously; and (iii) growth in the dirty sector reduces growth in the clean sector. These conditions do not arise with a consumption externality, but can emerge with a production externality. Endogenous labor supply implications are also investigated. Although not necessary for producing an EKC, endogenous labor supply provides additional linkages that produce an EKC under circumstances in which it would otherwise not appear.     

A mathematical model for the distribution and abundance of benthic algae in a Norwegian fjord

A mathematical model has been developed to study the distribution and abundance of benthic algae species in a Norwegian fjord. The main forcing functions are the physical factors which have well defined gradients in this area, but biotic interactions are also accounted for in the model.The distribution of algae along vertical transects in the intermediate fjord area has been simulated, and the observed distribution is reproduced fairly well. This indicates that the major factors determining the equilibrium elevation between intertidal and subtidal vegetations in this area are adequately represented in the model.Based on observations in a fjord branch with a high level of freshwater influx and polluted by heavy metals, assumptions are made of the combined influence of these contaminants on growth characteristics of the species considered. The resulting effects on community development and community patterns are simulated. For a certain level of contamination, the decrease in abundance, community development rate and species separation have been determined. It is also shown that the fluctuations in biomass during a year are more pronounced than under unaffected conditions.The relative importance of external growth regulating factors and self-shading is demonstrated for different degrees of community development, and we have indicated that this may be an important factor in the assessment of transient and long-term responses to “natural” and man-made influences on the shore-line vegetation.One of the main problems during model development was the formulation of the interaction function for factors influencing growth parameters. Several alternatives were examined.The differences between the most frequently used forms were small with respect to abundance and not very large with respect to possible changes in distribution. It was noted that even by including only the most limiting factor at each instant, (Liebig's form) a high percentage of the potentially limiting factors did actually limit growth during periods of the year.The model is intended as a working tool for the studies of changes in the shore-line vegetation caused by man-made interferences like heavy metal and oil pollution, and we believe that the results presented demonstrate that it can successfully be used for this purpose.