A More Realistic Approach to Pest-Management Problem

The paper deals with integrated pest management (IPM) of a single density-dependent pest affecting a single crop. The model is basically a prey–predator model, predator being the natural enemy of the pest. In addition, it also contains the growth equation of the affected crop. This dynamic model is subjected to biological control in the form of release of additional predators and chemical control in the form of spraying of pesticides. To consider the natural side effect of pesticide on fish living in the soil water, the model is further improved to accommodate the growth equation of the fishes in the soil water. The paper considers the optimal analysis of the model under two control parameters, one is the spraying of pesticide and other one is the release of predators; such optimal analysis under multi-control parameters is completely new of its kind. The paper was presented by S. Bhattacharyya in the conference “Joint AMS-India Mathematics Meeting,” 17–20 December 2003, India.     

The periodically forced Droop model for phytoplankton growth in a chemostat

 It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population, to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone growth rate and monotone uptake rate, the latter possibly depending on the cell quota. Received 10 October 1995; received in revised form 26 March 1996     

Population dynamics and competition in chemostat models with adaptive nutrient uptake

 The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative feature of some experimental data which show that the population density of the winning species approaches a positive steady state via transient oscillations while that of the losing species approaches the zero steady state monotonically. Received 4 August 1995; received in revised form 15 December 1995     

Optimal harvesting of stochastically fluctuating populations

 We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under the most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model where there are constraints on the admissible harvesting rates. We use stochastic calculus to derive the optimal population threshold at which individuals are harvested as well as the overall value of the population in the sense of the model. We show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution which we find explicitly. Needless to say, our results prove that any strategy which totally depletes the population is sub-optimal. These results are much more precise than those previously obtained for this problem. Received 24 June 1996; received in revised form 7 April 1997     

Melnikov analysis of chaos in a simple epidemiological model

 Melnikov’s method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model. Received 8 August 1995; received in revised form 21 November 1995     

Effects of arbuscular mycorrhizal fungi and drought stress on growth and nutrient uptake of two wheat genotypes differing in drought resistance

 The effects of an arbuscular mycorrhizal (AM) fungus and drought stress on the growth, phosphorus, and micronutrient uptake of two wheat genotypes exhibiting differences in drought resistance were investigated. Plants were grown on a low P (4 mg kg^–1 soil) silty clay (Typic Xerochrept) soil-sand mix. Mycorrhizal infection was higher under well-watered than under dry soil conditions and the drought-resistant genotype CR057 had a higher mycorrhizal colonization than the drought-sensitive genotype CR006. Total and root dry matter yields and total root length were higher in mycorrhizal than in nonmycorrhizal plants of both genotypes. CR057 had higher total dry matter but not root dry matter than CR006 plants. The enhancement in total dry matter due to AM inoculation was 42 and 39% under well-watered and 35 and 45% under water-stressed for CR057 and and CR006, respectively. For both genotypes, the contents of P, Zn, Cu, Mn, and Fe were higher in mycorrhizal than in nonmycorrhizal plants and higher under well-watered than under dry soil conditions. The enhancement of P, Zn, Cu, Mn, and Fe uptake due to AM inoculation was more pronounced in CR006 than in CR057, particularly under water-stressed conditions. Thus CR006 benefitted from AM infection more than the CR057 under dry soil conditions, despite the fact that CR057 roots were highly infected. It appears that CR006 is more dependent on AM symbiosis than CR057. Accepted: 12 February 1997     

Relationships between fungal uptake of ammonium, fungal growth and nitrogen availability in ectomycorrhizal Pinus sylvestris seedlings

 Nitrogen deposition and intentional forest fertilisation with nitrogen are known to affect the species composition of ectomycorrhizal fungal communities. To learn more about the mechanisms responsible for these effects, the relations between fungal growth, nitrogen uptake and nitrogen availability were studied in ectomycorrhizal fungi in axenic cultures and in symbiosis with pine seedlings. Effects of different levels of inorganic nitrogen (NH₄) on the mycelial growth of four isolates of Paxillus involutus and two isolates of Suillus bovinus were assessed. With pine seedlings, fungal uptake of ¹⁵N-labelled NH₄ was studied in short-term incubation experiments (72 h) in microcosms and in long-term incubation experiments (3 months) in pot cultures. For P. involutus growing in symbiosis with pine seedlings, isolates with higher NH₄ uptake were affected more negatively at high levels of nitrogen availability than isolates with lower uptake. More NH₄ was allocated to shoots of seedlings colonised by a high-uptake isolate, indicating transfer of a larger fraction of assimilated NH₄ to the host than with isolates showing lower NH₄ uptake rates. Thus low rates of N uptake and N transfer to the host may enable EM fungi avoid stress induced by elevated levels of nitrogen. Seedlings colonised by S. bovinus transferred a larger fraction of the ¹⁵N label to the shoots than seedlings colonised by P. involutus. Seedling shoot growth probably constituted a greater carbon sink in pot cultures than in microcosms, since the mycelial growth of P. involutus was more sensitive to high NH₄ in pots. There was no homology in mycelial growth rate between pure culture and growth in symbiosis, but N uptake in pure culture corresponded to that during growth in symbiosis. No relationship was found between deposition of antropogenic nitrogen at the sites of origin of the P. involutus isolates and their mycelial growth or uptake of inorganic nitrogen. Accepted: 18 September 1998     

Patterns of vegetative growth and reproduction in relation to branch orders: the plant as a spatially structured population

The patterns of vegetative growth and reproduction in relation to orders of terminal branches were examined in the evergreen woody plant, Eurya japonica. The branch order number was determined centrifugally. The trunk was given order number 1; branches issuing directly from the trunk were order 2; branches growing on order 2 branches were order 3, and so on. The results of this study show the differential patterns of vegetative growth and reproduction in relation to the branch orders. Lower-order shoots of terminal branches grew more, but produced few flowers. On the other hand, for the higher-order terminal branches, shoot growth was very limited but flowering was more intense. The results show that a tree can be interpreted not as a mere population of equivalent modules but as a spatially structured population. Thus, it is essential to consider the position of modules within the branch system when patterns of vegetative growth and reproduction are examined. It is hypothesized that the difference in the opportunity cost in relation to the branch orders is the main cause of the spatial structure for patterns of vegetative growth and reproduction. Furthermore, for same-order terminal branches, current-year shoot elongation was independent of flowering intensity. These results suggest that this species only invests resources in reproduction that are surplus to its requirements for the functions associated with survival, such as growth and/or storage. Received: 22 July 1999 / Accepted: 12 January 2000     

Dry matter allocation and nitrogen productivity explain growth responses to photoperiod and temperature in forage grasses

The mechanisms responsible for fluctuations in species composition of semi-natural grassland are not well understood. To identify plant traits that determine the poor competitive ability of Festuca pratensis compared to Dactylis glomerata especially during summer, the growth of both grasses was monitored over time and at different temperatures and photoperiods. Plants of both grasses were grown from seed with non-limiting nutrient supply at three day/night temperatures (11/6, 18/13 and 25/20°C) and two photoperiods (16 and 12 h). F. pratensis had a significantly lower relative growth rate than D. glomerata, mainly due to its lower specific leaf area and reduced nitrogen productivity. At high temperature, F. pratensis had a considerably lower root weight ratio than D. glomerata leading to substantially slower root growth. F. pratensis responded to a shorter photoperiod with an increase in the net assimilation rate, whereas D. glomerata responded with an increase in specific leaf area. The low competitive ability of F. pratensis compared to D. glomerata was mainly associated with its lower specific leaf area and nitrogen productivity. The stronger decline of its competitive ability during summer was probably related to the decreased allocation of dry matter to the roots at higher temperatures which leads to slower root growth compared to D. glomerata. Received: 7 September 1998 / Accepted: 29 July 1999     

Relationships Between Genomic G+C Content,RNA Secondary Structures,and Optimal Growth Temperature in Prokaryotes

G:C pairs are more stable than A:T pairs because they have an additional hydrogen bond. This has led to many studies on the correlation between the guanine+cytosine (G+C) content of nucleic acids and temperature over the last 20 years. We collected the optimal growth temperatures (T_opt) and the G+C contents of genomic DNA; 23S, 16S, and 5S ribosomal RNAs; and transfer RNAs for 764 prokaryotic species. No correlation was found between genomic G+C content and T_opt, but there were striking correlations between the G+C content of ribosomal and transfer RNA stems and T_opt. Two explanations have been proposed—neutral evolution and selection pressure—for the approximate equalities of G and C (respectively, A and T) contents within each strand of DNA molecules. Our results do not support the notion that selection pressure induces complementary oligonucleotides in close proximity and therefore numerous secondary structures in prokaryotic DNA, as the genomic G+C content does not behave in the same way as that of folded RNA with respect to optimal growth temperature. Received: 25 September 1996 / Accepted: 21 January 1997     

Modeling aggregation and growth processes in an algal population model: analysis and computations

 Aggregation, the formation of large particles through multiple collision of smaller ones is a highly visible phenomena in oceanic waters which can control material flux to the deep sea. Oceanic aggregates more than 1 cm in diameter have been observed and are frequently described to consist of phytoplankton cells as well as other organic matter such as fecel pellets and mucus nets from pteropods. Division of live phytoplankton cells within an aggregate can also increase the size of aggregate (assuming some daughter cells stay in the aggregate) and hence could be a significant factor in speeding up the formation process of larger aggregate. Due to the difficulty of modeling cell division within aggregates, few efforts have been made in this direction. In this paper, we propose a size structured approach that includes growth of aggregate size due to both cell division and aggregation. We first examine some basic mathematical issues associated with the development of a numerical simulation of the resulting algal aggregation model. The numerical algorithm is then used to examine the basic model behavior and present a comparison between aggregate distribution with and without division in aggregates. Results indicate that the inclusion of a growth term in aggregates, due to cell division, results in higher densities of larger aggregates; hence it has the impact to speed clearance of organic matter from the surface layer of the ocean. Received 1 July 1994; received in revised form 23 February 1996     

Effects of vesicular-arbuscular mycorrhizal inoculation at different soil P availabilities on growth and nutrient uptake of in vitro propagated coffee (Coffea arabica L.) plants

 In a pot experiment, the growth and the nutrient status of in vitro propagated coffee (Coffea arabica L.) microcuttings were investigated for 5 months following vesicular-arbuscular mycorrhizal (VAM) inoculation with either Acaulospora melleae or Glomus clarum at four soil P availabilities. Control plants remained P-deficient even at the highest soil P availability while mycorrhizal plants were P-sufficient at all soil P availabilities. Growth of control plants was only improved at the highest soil P availability. In P-deficient soil, neither of the two VAM species improved plant growth. Plant growth increased by 50% following inoculation with either A. melleae or G. clarum when P availability went from deficient to low. No further plant growth improvement was induced by either VAM species at intermediate and high soil P levels. Nevertheless, growth of plants inoculated with G. clarum was still significantly greater than that of non-mycorrhizal plants at the highest soil P availability. Root colonization by G. clarum increased with increasing soil P availability while root colonization by A. mellea decreased with soil P level increasing above low P availability. Soil P availability also affected Zn nutrition through its influence on VAM symbiosis. With increasing soil P availability, foliar Zn status increased with G. clarum or decreased with A. mellea in parallel to root colonization by VAM. This study demonstrates the beneficial effects of VAM inoculation on in vitro propagated Arabica coffee microcuttings, as shown previously for seedlings. This study also demonstrates differences in tolerance to soil P availability between VAM species, most likely resulting from their differing abilities to enhance coffee foliar P status. Accepted: 14 November 1996     

Alfin1 transcription factor overexpression enhances plant root growth under normal and saline conditions and improves salt tolerance in alfalfa

Plant root development is an essential determinant of plant growth and crop yield that could be enhanced by induced changes in the expression of root-specific regulatory factors. We reported previously that Alfin1 binds DNA in a sequence-specific manner and that Alfin1 overexpression in transgenic alfalfa (Medicago sativa L.) enhances expression of the salt-inducible MsPRP2 gene in roots, suggesting that Alfin1 functions to regulate gene expression in roots. Here we show that Alfin1 is an essential gene for root growth and that its overexpression in transgenic plants confers a many-fold increase in root growth under normal and saline conditions. Alfin1-binding sites occur in promoters of genes expressed in roots of a wide variety of plant species and we propose that it is a general root growth regulator. Even though Alfin1 overexpression was under the control of the CaMV 35S promoter, plant shoot growth was not adversely affected. We show further that introduction of the Alfin1 transgene in plants confers a dominant characteristic that significantly increases plant growth and salt tolerance.     

Inoculation and nitrate alter phytohormone levels in soybean roots: differences between a supernodulating mutant and the wild type

 The levels of different cytokinins, indole-3-acetic acid (IAA) and abscisic acid (ABA) in roots of Glycine max [L.] Merr. cv. Bragg and its supernodulating mutant nts382 were compared for the first time. Forty-eight hours after inoculation with Bradyrhizobium, quantitative and qualitative differences were found in the root's endogenous hormone status between cultivar Bragg and the mutant nts382. The six quantified cytokinins, ranking similarly in each genotype, were present at higher concentrations (30–196% on average for isopentenyl adenosine and dihydrozeatin riboside, respectively) in mutant roots. By contrast, the ABA content was 2-fold higher in Bragg, while the basal levels of IAA [0.53 μmol (g DW)⁻¹, on average] were similar in both genotypes. In 1 mM NO₃ ⁻-fed Bragg roots 48 h post-inoculation, IAA, ABA and the cytokinins isopentenyl adenine, and isopentenyl adenosine quantitatively increased with respect to uninoculated controls. However, only the two cytokinins increased in the mutant. High NO₃ ⁻ (8 mM) markedly reduced root auxin concentration, and neither genotypic differences nor the inoculation-induced increase in auxin concentration in Bragg was observed under these conditions. Cytokinins and ABA, on the other hand, were little affected by 8 mM NO₃ ⁻. Root IAA/cytokinin and ABA/cytokinin ratios were always higher in Bragg relative to the mutant, and responded to inoculation (mainly in Bragg) and nitrate (both genotypes). The overall results are consistent with the auxin-burst-control hypothesis for the explanation of autoregulation and supernodulation in soybean. However, they are still inconclusive with respect to the inhibitory effect of NO₃ ⁻. Received: 16 April 1999 / Accepted: 13 December 1999     

Early-generation selection between and within pair crosses in a potato (Solanum tuberosum subsp. tuberosum) breeding programme

 In 1992, 72 seedlings from each of 198 pair crosses were grown in a glasshouse, and the tubers produced by each plant were visually assessed on a 1–9 scale of increasing preference. Three groups of four progenies with high, medium and low mean scores were chosen to progress, without selection via tuber progenies and four-plant plots at a high-grade seed site, to replicated yield trials in the third clonal generation. The three groups maintained their high, medium and low scores for visual preference over the three clonal generations and also had high, medium and low scores in the second and third clonal generations for yield, size and appearance of tubers, all of which were components of visual preference. The three groups were predicted to have 13.6%, 1.8% and 0.2% of their clones exceeding the mean of 13 control cultivars for visual preference in the replicated trials, and 12.1%, 4.9% and 1.4% for yield, and 56.8%, 37.1% and 14.8% for appearance. The experiment confirmed that selection for visual preference within crosses in the seedling and first clonal generations is very ineffective, but that worthwhile progress can be made from selection in the second clonal generation, with correlated responses for faster emergence, earlier maturity, higher yield and greater regularity of shape (appearance). Combining selection of the high group of progenies with selection in the second clonal generation of the best 34 out of the 120 clones in this group, produced a response in visual preference in the third clonal generation of 1.00 compared with a maximum possible of 1.74. Ways of achieving further improvements in early-generation selection are discussed. Received: 26 May 1998 / Accepted: 9 June 1998     

Aggregation and collapse in a mechanical model of fungal tip growth

 Interconnected hyphal tubes form the mycelia of a fungal colony. The growth of the colony results from the elongation and branching of these single hyphae. The material being incorporated into the extending hyphal wall is supplied by vesicles which are formed further back in the hyphal tip. Such wall-destined vesicles appear conspicuously concentrated in the interior of the hypha, just before the hyphal apex, in the form of an apical body or Spitzenk?rper. The cytoskeleton of the hyphal tube has been implicated in the organisation of the Spitzenk?rper and the transport of vesicles, but as yet there is no postulated mechanism for this. We propose a mechanism by which forces generated by the cytoskeleton are responsible for biasing the movement of vesicles. A mathematical model is derived where the cytoskeleton is described as a viscoelastic fluid. Viscoelastic forces are coupled to the conservation equation governing the vesicle dynamics, by weighting the diffusion of vesicles via the strain tensor. The model displays collapse and aggregation patterns in one and two dimensions. These are interpreted in terms of the formation of the Spitzenk?rper and the initiation of apical branching. Received: 16 September 1996 / Revised version: 20 July 1998     

Observations of pollen tube growth in Nicotiana alata and their implications for the mechanism of self-incompatibility

 Style squashes and stylar grafts were used to examine the growth of Nicotiana alata pollen tubes in self-compatible and self-incompatible styles. Compatible tubes typically showed a uniform layer of callose deposition in the walls and in small plugs spaced at regular intervals within the tube. Incompatible tubes were characterised by the variability of callose deposition in the walls and by larger, closer and more irregularly spaced plugs. There was no difference in the growth rate of compatible and incompatible tubes during growth through the stigma, but within the style most compatible tubes grew 20–25 mm day^-1 (maximum 30 mm day^–1), whereas incompatible tubes grew 1.0–1.5 mm day^-1 (maximum 5 mm day^–1). Many incompatible tubes continued to grow until flowers senesced, and only a small proportion died as a consequence of tip bursting. Grafting compatibly pollinated styles onto incompatible styles showed that the incompatible reaction could occur in pollen tubes between 2 and 50 mm long, and that inhibition of pollen tube growth occurred in both the upper and lower parts of the transmitting tract. Grafting incompatibly pollinated styles onto compatible styles showed that the incompatible reaction was fully reversible in at least a proportion of the pollen tubes. The findings are not consistent with the cytotoxic model of inhibition of self-pollen tubes in solanaceous plants, which assumes that the incompatible response results from the degradation of a finite amount of rRNA present in the pollen tube. However, if pollen tubes do in fact synthesise rRNA, the findings become consistent with this model. Received: 23 May 1996 / Revision accepted: 22 August 1996     

Evidence for covalent linkage between xyloglucan and acidic pectins in suspension-cultured rose cells

 Neutral xyloglucan was purified from the cell walls of suspension-cultured rose (Rosa sp. `Paul's Scarlet') cells by alkali extraction, ethanol precipitation and anion-exchange chromatography on `Q-Sepharose FastFlow'. The procedure recovered 70% of the total xyloglucan at about 95% purity in the neutral fraction. The remaining 30% of the xyloglucan was anionic, as demonstrated both by anion-exchange chromatography at pH 4.7 and by high-voltage electrophoresis at pH 6.5. Alkali did not cause neutral xyloglucan to become anionic, indicating that the anionic nature of the rose xyloglucan was not an artefact of the extraction procedure. Pre-incubation of neutral [³H]xyloglucan with any of ten non-radioactive acidic polysaccharides did not cause the radioactive material to become anionic as judged by electrophoresis, indicating that stable complexes between neutral xyloglucan and acidic polysaccharides were not readily formed in vitro. The anionic xyloglucan did not lose its charge in the presence of 8 M urea or after a second treatment with NaOH, indicating that its anionic nature was not due to hydrogen-bonding of xyloglucan to an acidic polymer. Proteinase did not affect the anionic xyloglucan, indicating that it was not associated with an acidic protein. Cellulase converted the anionic xyloglucan to the expected neutral nonasaccharide and heptasaccharide, indicating that the repeat-units of the xyloglucan did not contain acidic residues. Endo-polygalacturonase converted about 40% of the anionic xyloglucan to neutral material. Arabinanase and galactanase also converted appreciable proportions of the anionic xyloglucan to neutral material. These results show that about 30% of the xyloglucan in the cell walls of suspension-cultured rose cells exists in covalently-linked complexes with acidic pectins. Received: 5 November 1999 / Accepted: 18 January 2000     

Multiple activities of a novel substance,dictyopyrone C isolated from Dictyostelium discoideum,in cellular growth and differentiation

Summary.  We report that a novel substance named dictyopyrone C (DPC) has remarkable effects on growth and differentiation of Dictyostelium discoideum Ax-2 cells, in a dose-dependent manner. In the presence of 3–15 μM DPC, differentiation of starving Ax-2 (clone MS) cells was greatly enhanced in submerged culture, when vegetative MS cells were harvested at the mid-late-exponential growth phase (>3 × 10⁶ cells per ml) and starved. In contrast, DPC above 30 μM markedly impaired the progression of differentiation including cell aggregation, most of starved cells being round after 3–4 h of DPC application and then lysed during further incubation. In the presence of 30 μM DPC however, MS cells that had been harvested at the early exponential growth phase (<5 × 10⁵ cells per ml) and starved became neither round nor lysed and exhibited rather enhanced differentiation. Essentially the same results were obtained in cultures of starved cells on nonnutrient agar. With respect to the DPC effect on MS cells growing in axenic medium, cell lysis and growth inhibition by DPC at concentrations higher than 15 μM were realized in the mid-late-exponential-growth-phase cells (>3 × 10⁶ cells per ml) but not in the early-exponential-growth-phase cells (<5 × 10⁵ cells per ml). Moreover, analysis using synchronized MS cells has demonstrated that the DPC effect changes in a cell-cycle-dependent manner. In contrast to such unique DPC actions, the pyrone ring of DPC had no effects on growth and differentiation within the range of 3–120 μM tested. These findings strongly suggested the importance of the combined structure of the pyrone ring and the linear carbon chain in revelation of the DPC activities. Received August 5, 2002; accepted November 11, 2002; published online April 8, 2003 RID="*" ID="*" Correspondence and reprints: Department of Developmental Biology and Neurosciences, Graduate School of Life Sciences, Tohoku University, Aoba, Sendai 980-8578, Japan. E-mail: ymaeda@mail.cc.tohoku.ac.jp     

Inheritance of caffeine and heteroside contents in an interspecific cross between a cultivated coffee species Coffea liberica var dewevrei and a wild species caffeine-free C. pseudozanguebariae

 Coffee species originating from Africa, in particular the two major cultivated species C. arabica and C. canephora, usually contain caffeine in their beans, whereas almost all Malagasy coffee species are caffeine-free. However, one wild coffee species C. pseudozanguebariae, collected near the coast in south Kenya, is also caffeine-free. Beans of this species contain a specific heteroside diterpene (hereinafter referred to simply as heteroside) and give a bitter coffee beverage. We have investigated the inheritance of the caffeine and heteroside contents in the first and second generations of an interspecific cross between C. pseudozanguebariae and C. liberica var. dewevrei, for which the caffeine content is about 1% dmb (dry matter basis). The caffeine content of F₁ hybrids (0.2% dmb) was lower than the parental average (0.47% dmb). Caffeine and heteroside contents appeared to be under polygenic control with a strong genetic effect. Nevertheless, one major gene with two alleles seemed to be involved in the control of both compounds. Absence of caffeine was apparently controlled by one recessive gene. Heteroside content seemed to be controlled by one co-dominant gene, heterozygotes being intermediate between the two different groups of homozygotes. Received: 15 September 1997 / Accepted: 6 October 1997