Chemotactic collapse for the Keller-Segel model

 This work is concerned with the system (S) {u _t =Δu − χ∇ (u∇v) for x∈Ω, t>0Γ v _t =Δv+(u−1) for x∈Ω, t>0 where Γ, χ are positive constants and Ω is a bounded and smooth open set in ℝ². On the boundary ∂Ω, we impose no-flux conditions: (N) ∂u∂n =∂v∂n =0 for x∈∂ Ω, t>0 Problem (S), (N) is a classical model to describe chemotaxis corresponding to a species of concentration u(x, t) which tends to aggregate towards high concentrations of a chemical that the species releases. When completed with suitable initial values at t=0 for u(x, t), v(x, t), the problem under consideration is known to be well posed, locally in time. By means of matched asymptotic expansions techniques, we show here that there exist radial solutions exhibiting chemotactic collapse. By this we mean that u(r, t) →Aδ(y) as t→T for some T<∞, where A is the total concentration of the species. Received 9 March 1995; received in revised form 25 December 1995     

Properties of solutions for a chemotaxis system

 We investigate mathematically the system of equations proposed by Chaplain and Stuart [2], to describe the chemotactic response of endothelial cells under the angiogenesis stimulus. In particular, we characterize the steady state endothelial cell density function, and give conditions on the chemotactic parameter k and cell proliferation parameter b that ensure that migration/ proliferation either does or does not occur in steady state. The time dependent problem is also treated. Received 12 September 1995; received in revised form 6 August 1996     

Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations

 In this paper we study the existence of one-dimensional travelling wave solutions u(x, t)=φ(x−ct) for the non-linear degenerate (at u=0) reaction-diffusion equation u _t =[D(u)u _x ] _x +g(u) where g is a generalisation of the Nagumo equation arising in nerve conduction theory, as well as describing the Allee effect. We use a dynamical systems approach to prove: 1. the global bifurcation of a heteroclinic cycle (two monotone stationary front solutions), for c=0, 2. The existence of a unique value c ^*>0 of c for which φ(x−c ^* t) is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts for c≠c ^*. We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation. Received 15 December 1995; received in revised form 14 May 1996     

Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant

We study the effect of noise on the behaviour of a dynamic cell population model in which cell replication and maturation take place simultaneously. We assume that the maximum proliferative potential fluctuates uniformly about a mean value of v, and show that a decrease in v and/or the input flux u _in into the population can lead to an increase in the variance in the cellular efflux u _f. We draw a qualitative correspondence between this behaviour and the commonly observed increase in the variance of circulating blood cell numbers following chemotherapy and radiotherapy, both of which lead to a decrease in v and u _in , and bone marrow transplant which probably corresponds to a decrease in u _in .     

Scattering spectrum properties and their relationship to biogeochemical parameters: a case study in Taihu Lake

The scattering spectrum properties of highly turbid and eutrophic inland case 2 water from Taihu Lake were studied during three cruises from 2006 to 2007. The scattering [b _p(λ)] and backscattering [b _bp(λ)] coefficients and the backscattering probability (B) for Taihu Lake were found to show a clear spectral dependence, and this dependence was well simulated by a power-law function. This dependence, however, became weak when algae dominated the sample points. The mean values of the power-law index for b _p(λ), v, in Oct 2006, Mar 2007 and Nov 2007 were −0.6712, −0.8129 and −0.7600, respectively. To interpret the spectral characteristics and mechanisms of b _p(λ) and b _bp(λ), water samples were collected simultaneously for the biogeochemical characterization of suspended particles. The average values of the specific scattering coefficients for total suspended matter, inorganic suspended matter (ISPM) and organic suspended matter (OSPM) were 0.634 (550 nm), 1.057 (532 nm), and 0.396 g m⁻² (532 nm), respectively. The power-law index of b _bp(λ) (Y) was significantly related to ISPM/OSPM and b _bp(532 nm), but only weakly related to the particle size distribution index. The mean (spatial and wavelength) values of B in Oct 2006, Mar 2007, and Nov 2007 were 0.0108, 0.0138, and 0.0125, respectively. B decreases with increasing ISPM concentration because of the large contribution of ISPM to b _b(λ) and the strong restraint on b _bp(λ) caused by the multi-scattering effect under high-turbidity conditions.     

Photosynthetic apparatus organization and function in the wild type and a chlorophyll b-less mutant of Chlamydomonas reinhardtii. Dependence on carbon source

 The assembly, organization and function of the photosynthetic apparatus was investigated in the wild type and a chlorophyll (Chl) b-less mutant of the unicellular green alga Chlamydomonas reinhardtii, generated via DNA insertional mutagenesis. Comparative analyses were undertaken with cells grown photoheterotrophically (acetate), photomixotrophically (acetate and HCO⁻ ₃) or photoautotrophically (HCO⁻ ₃). It is shown that lack of Chl b diminished the photosystem-II (PSII) functional Chl antenna size from 320 Chl (a and b) to about 95 Chl a molecules. However, the functional Chl antenna size of PSI remained fairly constant at about 290 Chl molecules, independent of the presence of Chl b. Western blot and kinetic analyses suggested the presence of inner subunits of the Chl a-b light-harvesting complex of PSII (LHCII) and the entire complement of the Chl a-b light-harvesting complex of PSI (LHCI) in the mutant. It is concluded that Chl a can replace Chl b in the inner subunits of the LHCII and in the entire complement of the LHCI. Growth of cells on acetate as the sole carbon source imposes limitations in the photon-use efficiency and capacity of photosynthesis. These are manifested as a lower quantum yield and lower light-saturated rate of photosynthesis, and as lower variable to maximal (F_v/F_max) chlorophyll fluorescence yield ratios. This adverse effect probably originates because acetate shifts the oxidation-reduction state of the plastoquinone pool, and also because it causes a decrease in the amount and/or activity of Rubisco in the chloroplast. Such limitations are fully alleviated upon inclusion of an inorganic carbon source (e.g. bicarbonate) in the cell growth medium. Further, the work provides evidence to show that transformation of green algae can be used as a tool by which to generate mutants exhibiting a permanently truncated Chl antenna size and a higher (per Chl) photosynthetic productivity of the cells. Received: 10 November 1999 / Accepted: 22 December 1999     

Kinetic studies of electron transfer in the cyt b 5 : metHb system

 The kinetics of methemoglobin reduction by cytochrome b ₅ has been studied by stopped-flow and saturation transfer NMR. A forward rate constant k _f = 2.44×10⁴ M^–1 s^–1 and a reverse rate constant k _b = 540 M^–1s^–1 have been observed at 10 mm, pH 6.20, 25  °C. The ratio k _f/k _b = k _eq = 43.6 is in good agreement with the equilibrium constant calculated from the electrochemical potential between cyt b ₅ and methemoglobin. A bimolecular collisional mechanism is proposed for the electron transfer from cyt b ₅ to methemoglobin based on the kinetic data analysis. The dependence of the rate constants on ionic strengths supports such collisional mechanism. It is also found that the reaction rate strongly depends on the conformations of methemoglobin. Received: 20 February 1996 / Accepted: 4 June 1996     

On transition bias in mitochondrial genes of pocket gophers

The relative contribution of mutation and purifying selection to transition bias has not been quantitatively assessed in mitochondrial protein genes. The observed transition/transversion (s/v) ratio is (μ _s P _s)/(μ _v P _v), where μ _s and μ _v denote mutation rate of transitions and transversions, respectively, andP _s andP _v denote fixation probabilities of transitions and transversions, respectively. Because selection against synonymous transitions can be assumed to be roughly equal to that against synonymous transversions,P _s/P_v ≈ 1 at fourfold degenerate sites, so that thes/v ratio at fourfold degenerate sites is approximately μ _s /μ _v , which is a measure of mutational contribution to transition bias. Similarly, thes/v ratio at nondegenerate sites is also an estimate of μ _s /μ _v if we assume that selection against nonsynonymous transitions is roughly equal to that against nonsynonymous transversions. In two mitochondrial genes, cytochrome oxidase subunit I (COI) and cytochromeb (cyt-b) in pocket gophers, thes/v ratio is about two at nondegenerate and fourfold degenerate sites for both the COI and the cyt-b genes. This implies that mutation contribution to transition bias is relatively small. In contrast, thes/v ratio is much greater at twofold degenerate sites, being 48 for COI and 40 for cyt-b. Given that the μ _s /μ _v ratio is about 2, theP _s/P_v ratio at twofold degenerate sites must be on the order of 20 or greater. This suggests a great effect of purifying selection on transition bias in mitochondrial protein genes because transitions are synonymous and transversions are nonsynonymous at twofold degenerate sites in mammalian mitochondrial genes. We also found that nonsynonymous mutations at twofold degenerate sites are more neutral than nonsynonymous mutations at nondegenerate sites, and that the COI gene is subject to stronger purifying selection than is the cyt-b gene. A model is presented to integrate the effect of purifying selection, codon bias, DNA repair and GC content ons/v ratio of protein-coding genes. Correspondence to: X. Xia     

Colony expansion model for describing the spatial distribution of populations

Two equations have been used frequently to describe the relation between the sample variance (s ²) and sample mean (m) of the number of individuals per quadrat: Taylor's power law, s ² = am ^b , and Iwao's m ^*−m regression, s ² = cm + dm ², where a, b, c, and d are constants. We can obtain biological information such as colony size and the degree of aggregation of colonies from parameters c and d of Iwao's m ^*−m regression. However, we cannot obtain such biological information from parameters a and b of Taylor's power law because these parameters have not been described by simple functions. To mitigate such in-convenience, I propose a mechanistic model that produces Taylor's power law; this model is called the colony expansion model. This model has the following two assumptions: (1) a population consists of a fixed number of colonies that lie across several quadrats, and (2) the number of individuals per unit occupied area of colony becomes v times larger in an allometric manner when the occupied area of colony becomes h times larger (v≥ 1, h≥ 1). The parameter h indicates the dispersal rate of organisms. We then obtain Taylor's power law with b = {ln[E(h)] + ln[E(v ²)]}/{ln[E(h)] + ln[E(v)]}, where E indicates the expectation. We can use the inverse of the exponent, 1/b, as an index of dispersal of individuals because it increases with increasing E(h). This model also yields a relation, known as the Kono–Sugino relation, between the proportion of occupied quadrats and the mean density per quadrat: −ln(1 −p) = fm ^g , where p is the proportion of occupied quadrats, f is a constant, and g = ln[E(h)]/{ln[E(h)] + ln[E(v)]}. We can use g as an index of dispersal as it increases with increasing E(h). The problem at low densities where Taylor's power law is not applicable is also discussed. Received: January 27, 2000 / Accepted: June 20, 2000     

Effect of gamma radiation on mutant induction of <Emphasis Type="Italic">Fagopyrum dibotrys</Emphasis> Hara

Agronomic traits, photosynthetic pigments, gas exchange, and chlorophyll (Chl) fluorescence parameters of red stem buckwheat (Fagopyrum dibotrys Hara) mutants induced by γ-radiation were compared with green control at seedling stage. Plant height, number of first-class branches, and rhizome biomass were inhibited significantly (p<0.01). Chl a, Chl b, and Chl a+b contents decreased with elevated dose of γ-rays, while increasing carotenoid content indicated that buckwheat was capable of adjusting to the radiation damage. Decrease in net photosynthetic rate was the result of both stomatal and non-stomatal limitations. Fluorescence parameters, such as F₀, F_m, F_v/F_m, F_v/F₀, Φ_PS2, electron transport rate, and photochemical quenching declined significantly (p<0.01) as compared with control due to photoinhibition, while non-photochemical quenching increased to enhance thermal dissipation. Lower parameters implied that leaf tissue was damaged significantly by high dose of γ-radiation and therefore leaf senescence was accelerated.     

Probing the ground state of the purple mixed valence CuA center in nitrous oxide reductase: a CW ENDOR (X-band) study of the 65Cu, 15N-histidine labeled enzyme and interpretation of hyperfine couplings by molecular orbital calculations

 CW ENDOR (X-band) spectra for the purple mixed-valence [Cu(1.5+)...Cu(1.5+)], S = 1/2, Cu_A site in nitrous oxide reductase were obtained after insertion of ⁶⁵Cu or both ⁶⁵Cu and ¹⁵N-histidine. The ¹⁴N/¹⁵N isotopic substitution allowed for an unambiguous deconvolution of proton and nitrogen hyperfine couplings in the spectra. A single nitrogen coupling with a value of 12.9 ± 0.4 MHz for ¹⁴N was detected. Its anisotropy was characteristic for imidazole bound to copper. A spin density of 3–5% was estimated for the nitrogen donors to Cu_A, indicating that the ground state is ²B_3u. Proton hyperfine structure was detected from four C_β protons of coordinating cysteine residues. Their isotropic and anisotropic parts were deconvoluted by spectral simulation. From the anisotropic couplings a spin density of 16–24% was estimated for each of the cysteine thiolate donors of Cu_A. The [N_HisCu(RS)₂CuN_His]⁺ core structure of Cu_A in nitrous oxide reductase from Pseudomonas stutzeri is predicted to be similar to the crystallographically determined Cu_A* structure (Wilmanns M, Lappalainen P, Kelly M, Sauer-Eriksson E, Saraste M (1995) Proc Natl Acad Sci USA 92 : 11955–11959), but distinct from the Cu_A structure of Paracoccus denitrificans cytochrome c oxidase (Iwata S, Ostermeier C, Ludwig B, Michel H (1995) Nature 376 : 660–669). The angular dependence of the isotropic couplings as a function of the electronic ground state was calculated by the INDO/S method. The Mulliken atomic-spin populations calculated by a gradient-corrected density functional method and the semiempirical INDO/S method were compared with experimentally derived spin populations, and good agreement between theory and experiment was found for both calculations. The ground state of Cu_A is best represented by the resonance structures of the form [Cu^IS^–S^–Cu^II↔ Cu^IS^•S^–Cu^I↔ Cu^IS^–S^•Cu^I↔ Cu^IIS^–S^–Cu^I]. It is proposed that the Cu 4s,p as well as sulfur 3d orbitals play a role in the stabilization of this novel type of cluster. Received: 17 September 1997 / Accepted: 28 October 1997     

Structure and function of a non-interactive, reactive insect-plant system

Rhagoletis alternata is a common tephritid fly in central Europe, whose larvae feed on the hypanthium of rose hips. The resource-consumer system is “non-interactive”, i.e. the insect has little or no impact on host plant fitness and therefore is not able to influence the rate at which larval food resources are renewed. The system is “reactive”, since fluctuations in the carrying capacity (hip density) of the host plant are important for determining year-to-year fluctuations in the insect's population size. Insect fluctuations exceed those of its carrying capacity. The insect's efficient exploitation strategy, maximizing its fitness at high as well as low resource supply, must be attributed to the variable and unpredictable relationship between resource availability and consumer density. The only regulatory mechanism is contest competition when larval densities exceed the carrying capacity. Due to the low impact of the insect, its exploitation strategy is apparently not opposed by mechanisms selecting for defence in the host plant. This lack of defence and the efficient exploitation strategy may be important factors for the frequently observed high degree of the resource utilization by the insect. Received: 3 November 1997 / Accepted: 22 January 1998     

Kinetic processes initiated by a nanosecond high-current discharge in hot air

Results from numerical investigations of kinetic processes initiated by a pulsed nanosecond discharge in hot (T ₀ ≥ 1000 K) air at atmospheric pressure are presented. The calculated results on the dynamics of the electron density, the population of the N₂(B³Π _g ) and N₂(C³Π _u ) states, and the atomic oxygen density in the axial discharge region agree with experiment. The method for determining the gas temperature by measuring the rotational structure of the transitions N₂(C³Π _u , ν) → N₂(B³Π _g , ν′) of the 2⁺ nitrogen system is analyzed. It is shown that, in relatively weak reduced electric fields typical of secondary discharge pulses, the electron impact excitation of the N₂(C³Π _u ) state from the ground state N₂(X¹Σ _g ⁺) can be accompanied by its additional step population from the N₂(B³Π _g ), N₂(a′Σ _u ⁻), and other electronic states. This effect substantially influences the rotational distribution of nitrogen molecules in the N₂(C³Π _u , ν) state; moreover, the temperature determined from this distribution can be substantially higher than the true gas temperature.     

The evolution of resource use

 The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter α quantifies how simultaneous consumption of both resources influences consumer growth; α<0 corresponds to hemi-essential resources, 0<α<1 corresponds to complementary resources, α=1 corresponds to perfectly substitutable resources, and α>1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when α≤1, there is a unique singular strategy x ^* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when α=1, the singular strategy x ^* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when α>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when α is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when α>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited. Received: 8 June 2002 / Revised version: 28 November 2002 / Published online: 23 April 2003 This work was supported by NSF Grant DMS-0077986 Key words or phrases: Consumer-resource interactions – Adaptive dynamics – Evolutionary branching     

The multidomain xylanase A of the hyperthermophilic bacterium Thermotoga neapolitana is extremely thermoresistant

 The nucleotide sequence of the xynA gene, encoding extracellular xylanase A of Thermotoga neapolitana, was determined. The xynA gene was 3264 base pairs (bp) long and encoded a putative polypeptide of 1055 amino acids. Three different domains were identified by sequence comparison and functional analysis of proteins with N- and/or C-terminal deletions. The core domain displayed significant homology to members of the glycosyl hydrolase family 10. N- and C-terminal domains were dispensable for enzymatic activity and seemed to be responsible for thermostability and cellulose binding, respectively. The intact gene and its truncated variants were expressed in Escherichia coli and purified for biochemical characterization. The enzyme was shown to act as an endo-1,4-β-xylanase, but minor activities against lichenan, barley glucan, methylumbelliferyl cellobioside and p-nitrophenyl xyloside were also detected. The specific activity and pH and temperature optima for hydrolysis of oat xylan were 111.3 U⋅mg^-1, 5.5 and 102^°C, respectively. The endoxylanase was stable at 90^°C and retained 50% activity when incubated for 2 h at 100^°C. Received: 19 May 1995/Received revision: 31 July 1995/Accepted: 7 September 1995     

Photosystem 2 photochemistry and pigment composition of a yellow mutant of rice (<Emphasis Type="Italic">Oryza sativa</Emphasis> L.) under different irradiances

A yellow leaf colouration mutant (named ycm) generated from rice T-DNA insertion lines was identified with less grana lamellae and low thylakoid membrane protein contents. At weak irradiance [50 μmol(photon) m⁻² s⁻¹], chlorophyll (Chl) contents of ycm were ≈20 % of those of WT and Chl a/b ratios were 3-fold that of wild type (WT). The leaf of ycm showed lower values in the actual photosystem 2 (PS2) efficiency (Φ_PS2), photochemical quenching (q_P), and the efficiency of excitation capture by open PS2 centres 1 (F_v′/F_m′) than those of WT, except no difference in the maximal efficiency of PS2 photochemistry (F_v/F_m). With progress in irradiance [100 and 200 μmol(photon) m⁻² s⁻¹], there was a change in the photosynthetic pigment stoichiometry. In ycm, the increase of total Chl contents and the decrease in Chl a/b ratio were observed. Φ_PS2, q_P, and F_v′/F_m′ of ycm increased gradually along with the increase of irradiance but still much less than in WT. The increase of xanthophyll ratio [(Z+A)/(V+A+Z)] associated with non-photochemical quenching (q_N) was found in ycm which suggested that ycm dissipated excess energy through the turnover of xanthophylls. No significant differences in pigment composition were observed in WT under various irradiances, except Chl a/b ratio that gradually decreased. Hence the ycm mutant developed much more tardily than WT, which was caused by low photon energy utilization independent of irradiance.     

A fitness function for optimal life history in relation to density effects,competition, predation and stability of the environment

A fitness function (function maximized under natural selection) is studied in a population model in which the growth of a population is suppressed by crowding, density-independent continuous mortality (by euryphagous predators) and periodic disturbances. The dynamics of the population density between occurrence of disturbance can be expressed as,dN/dt=(F(N/K)−D)N, whereN is the population density,K is the carrying capacity,D is the density-independent continuous mortality, andF is the growth regulation factor described as a function of crowding (N/K). The period of disturbance isS. The survival rate under disturbance isu. It is concluded that the fitness function is (approximately) a product of competitive ability (C), carrying capacity, and degree of saturation, and is given byCKF ⁻¹(D−(lnu)/S). The degree of saturation is the inverse function of regulation factor (F) at the death rate due to predators and disturbance. I assume a population in which density is regulated only through survival. In this case, a low survival rate at the critical age-group means a high value ofCKF ⁻¹(D−(lnu)/S). Therefore, the reciprocal of the density-dependent survival rate at critical age-group is a measure of the fitness function. Using this measure, I predict the optimal age (body size) at first reproduction of a species of salamander. I also found that fitness calculated from observed values ofl(x) andm(x) includes a tautology. When the concept of fitness function is compared with the ESS method, the latter is more flexible. However, there is a possibility that an ESS is at the minimum of fitness function.     

Energetics of swimming at maximal speeds in humans

The energy cost per unit of distance (C _s, kilojoules per metre) of the front-crawl, back, breast and butterfly strokes was assessed in 20 elite swimmers. At sub-maximal speeds (v), C _s was measured dividing steady-state oxygen consumption (V˙O₂) by the speed (v, metres per second). At supra-maximal v, C _s was calculated by dividing the total metabolic energy (E, kilojoules) spent in covering 45.7, 91.4 and 182.9 m by the distance. E was obtained as: E = E _an+V˙O_2max t _p−V˙O_2max(1−e^{−( t p/)}), where E _an was the amount of energy (kilojoules) derived from anaerobic sources, V˙O_2max litres per second was the maximal oxygen uptake, α (=20.9 kJ · l O₂ ⁻¹) was the energy equivalent of O₂, τ (24 s) was the time constant assumed for the attainment of V˙O_2max at muscle level at the onset of exercise, and t _p (seconds) was the performance time. The lactic acid component was assumed to increase exponentially with t _p to an asymptotic value of 0.418 kJ · kg⁻¹ of body mass for t _p ≥ 120 s. The lactic acid component of E _an was obtained from the net increase of lactate concentration after exercise (Δ[La]_b) assuming that, when Δ[La]_b = 1 mmol · l⁻¹ the net amount of metabolic energy released by lactate formation was 0.069 kJ · kg⁻¹. Over the entire range of v, front crawl was the least costly stroke. For example at 1 m · s⁻¹, C _s amounted, on average, to 0.70, 0.84, 0.82 and 0.124 kJ · m⁻¹ in front crawl, backstroke, butterfly and breaststroke, respectively; at 1.5 m · s⁻¹, C _s was 1.23, 1.47, 1.55 and 1.87 kJ · m⁻¹ in the four strokes, respectively. The C _s was a continuous function of the speed in all of the four strokes. It increased exponentially in crawl and backstroke, whereas in butterfly C _s attained a minimum at the two lowest v to increase exponentially at higher v. The C _s in breaststroke was a linear function of the v, probably because of the considerable amount of energy spent in this stroke for accelerating the body during the pushing phase so as to compensate for the loss of v occurring in the non-propulsive phase. Accepted: 14 April 1998     

On periodic cohort solutions of a size-structured population model

 We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable ‘substrate’. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter β. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n≧2) with small size differences will tend to a periodic one-cohort solution as t→∞. Received 16 March 1995; received in revised form 7 January 1997     

Population dynamics of Daphnia spp. and implications for trophic interactions in small, monomictic lake

In Lake Oglethorpe, Georgia, USA, herbivorous crustacean zooplankton are abundant and dominate zooplankton biomass in winter, but are scarce throughout most of the summer. We used a 3.5 year study of Daphnia population dynamics to infer when food, predators or temperature constrained growth of this population. Transitions between winter and summer consumer assemblages are concurrent with seasonal changes in water temperature, thermal structure (stratification/destratification), resources (autotrophic/heterotrophic-domained production), and predator abundance and activity (e.g. Lepomis macrochirus and Chaoborus punctipennis. We sampled at weekly or less intervals from April 1992 to September 1995, and determined population abundances for all cladoceran species. For the Daphnia population (Daphnia ambigua + Daphnia parvula, we measured clutch size and length for all individuals. We used average water column temperature (where dissolved oxygen is >1 mg l^-1) to estimate egg development time from an empirical model. Estimates of Daphnia population birth and death rate were thus generated from abundance, egg ratio and temperature/dissolved oxygen data. We compared observed birth rate (bobs) with expected birth rate (bexp>95% CI; predicted for food-saturated conditions at ambient temperature). For variable (1-13 week) periods between later November and March, 1992-1995, water temperature was the primary factor constraining Daphnia population growth (bobs = bexp). From about April to early November, bobs < bexp suggested food-limited population growth. In spring, summer and early fall (March-October), population densities were several-fold lower than in late fall and winter (November-February). However, all else being equal, egg ratio and population birth rate data would have predicted that Daphnia abundance fluctuates over equivalent ranges in spring and fall. We interpret this discrepancy as evidence for increased rates of extrinsic mortality during the growing season and a seasonal shift in the relative importance of resource and predator regulation. The duration of predator suppression of crustacean population abundance in Lake Oglethorpe and other warm-latitude lakes (36N-27°S) is longer (3-7 months) than that observed in north temperate lakes (1-2.5 months; 41-52°N).