The effect of periodic habitat fluctuations on a nonlinear insect population model

 Laboratory data show that populations of flour beetles (Tribolium), when grown in a periodically fluctuating volume of flour, can exhibit significant increases in numbers above those attained when grown in a constant volume (of the same average). To analyze and explain this phenomenon a discrete stage-structured model of Tribolium dynamics with periodic environmental forcing is introduced and studied. This model is an appropriately modified version of an experimentally validated model for flour beetle populations growing in a constant volume of flour, in which cannibalism rates are assumed inversely proportional to flour volume. This modeling assumption has been confirmed by laboratory experiments. Theorems implying the existence and stability of periodic solutions of the periodically forced model are proved. The time averages of periodic solutions of the forced model are compared with the equilibrium levels of the unforced model (with the same average flour volume). Parameter constraints are determined for which the average population numbers in the periodic environment are greater than (or less than) the equilibrium population numbers in the associated constant environment. Sample parameter estimates taken from the literature show that these constraints are fulfilled. These theoretical results provide an explanation for the experimentally observed increase in flour beetle numbers as a result of periodically fluctuating flour volumes. More generally, these integrated theoretical and experimental results provide the first convincing example illustrating the possibility of increased population numbers in a periodically fluctuating environment. Received 23 April 1996; received in revised form 28 March 1997     

Family planning inDaphnia: resistance to starvation in offspring born to mothers grown at different food levels

Summary We observed a shift in maternal investment per offspring in clonal cultures of twoDaphnia species. Mothers grown at high food levels produced large clutches of smaller eggs but their offspring could not survive long under starvation conditions. Genetically identical mothers grown at low food levels produced small cultches of larger eggs, and their offspring, albeit low in numbers, were able to survive long periods of starvation. Our data show thatDaphnia mothers are capable of assessing food level and use this information in adjusting their fractional peroffspring allocation of reproductive resources.     

What the hen can tell about her eggs: egg development on the basis of energy budgets

By a simple model involving the state variables size and storage, it is possible to describe a wide variety of observations on the feeding, growth, energy storage and reproduction of animals. The model is based on the assumption that reproduction, growth as well as maintenance depend on the stored energy only and not directly on feeding. If an egg is thought of as a non-feeding animal, the model predicts the respiration ontogeny and growth of the embryo inside the egg. These predictions seem to hold well for published data on the development of eggs of fish and ratite, precocial and altricial birds. The latter two are known to follow different respiration ontogenies, but both are described well, differing only in one (compound) parameter value. The model explains why the incubation times of eggs of different species tend to increase linearly with egg size to the power 1/4, and why kiwis and petrels, which lay relatively large eggs, have to brood them much longer than larger birds with eggs of the same size. Conversely, it explains why the small eggs of the (parasitic) European cuckoo, hatch earlier than the still smaller eggs of their tiny hosts.Furthermore, it has been shown how the maintenance rate constant, which frequently appears in the microbial literature, can be obtained from measurements on the respiration and weight ontogeny in embryos, so linking independent lines of research. Application of the model shows an increase of the maintenance rate constant from bacteria, crustaceans, up to fish and birds, and a decrease from bacteria to green algae, suggesting lines of evolutionary development.     

Effects of habitat drying on size at and time to metamorphosis in the tree hole mosquito Aedes triseriatus

Models of complex life cycles predict that greater mortality of immature stages should induce earlier metamorphosis at smaller sizes. We tested for effects of one source of mortality, habitat drying, on size at and time to metamorphosis of the tree hole mosquito Aedes triseriatus. In a laboratory experiment, we manipulated two variables associated with drying, volume of water and solute concentration, and recorded mean mass at and median days to eclosion for males and females in replicate cohorts. We also tested for treatment effects on the correlation of mass at and time to eclosion. For females, decreasing volume consistently induced metamorphosis at smaller sizes than did constant volume. Decreasing volume also led to earlier metamorphosis of females than did constant volume, but only in one of two experimental runs. For both sexes, increasing concentration led to greater size at metamorphosis and, for males, earlier metamorphosis than did constant volume, but again only in one of two experimental runs. Correlations of size at and time to metamorphosis tended to be positive for females and negative for males, and this difference was significant. For both sexes, decreasing volume led to larger (more positive) correlations than did constant volume, but only in one of two experimental runs. The effects of decreasing volume on females are consistent with the predictions of models of complex life cycles, and suggest that A. triseriatus can perceive volume changes and modify metamorphosis to escape a deteriorating habitat. The effects of increasing concentration are opposite to those predicted, and are consistent with enhanced growth rates, possibly due to enhanced microbial growth, as solutes become concentrated due to drying. The responses of these mosquitoes to habitat drying are complex, and we suggest that habitat drying increases both mortality and growth rates, yielding no simple predictions of how habitat drying will affect these mosquitoes in natural tree holes.     

Manipulation of laying effort reveals habitat-specific variation in egg production constraints in Great Tits (Parus major)

It has been suggested that a bird's clutch size is not limited by the amount of resources available at the time of laying but that differences in the availability of food for nestlings is the ultimate underlying factor determining spatio-temporal variations in clutch size. However, habitat-related variations in egg production ability has yet to be investigated explicitly. We studied the breeding of Great Tits Parus major in deciduous and coniferous forests in the same area. The sizes of both the clutches and the eggs were, on average, larger in the former habitat than in the latter. A number of females were induced to lay more eggs than usual by removing four eggs from designated experimental clutches early in the laying period. These manipulated females laid approximately one egg more than control females, with the number of additional eggs laid not differing between the habitats. However, in both study years the relative size of the extra eggs – relative to the mean size of earlier laid eggs of the same clutch – was smaller in the coniferous habitat than in the deciduous habitat, while there was no habitat-related difference in the relative size of the last-laid eggs of control clutches. This result indicates that some form of proximate limitation during egg-laying period can contribute to the relatively small clutches and eggs in the coniferous habitat. Our results emphasize the need to take egg production costs into account when attempting to account for spatial variation in the reproductive behaviour of birds.     

Foraging in a patchy environment by a predatory net-spinning caddis larva: A test of optimal foraging theory

Summary The predatory larvae of the caddis Plectrocnemia conspersa (Curtis) cause significant prey depletion in a habitat in which prey are patchily distributed. Optimal foraging theory predicts that under these circumstances a predator should stay in any given patch until the prey capture rate there drops to a value equal to the average for the habitat as a whole. This was tested using a combination of field and laboratory data and the results were in broad agreement with the prediction. A second prediction is that the marginal capture rate should be higher in a habitat richer in prey and this was not supported. It is argued that by using a simple rule-of-thumb (constant giving-up-time) P. conspersa is able to approach the optimal solution for much of the time.     

Wild Bornean orangutan (Pongo pygmaeus wurmbii) feeding rates and the Marginal Value Theorem

The Marginal Value Theorem (MVT) is an integral supplement to Optimal Foraging Theory (OFT) as it seeks to explain an animal's decision of when to leave a patch when food is still available. MVT predicts that a forager capable of depleting a patch, in a habitat where food is patchily distributed, will leave the patch when the intake rate within it decreases to the average intake rate for the habitat. MVT relies on the critical assumption that the feeding rate in the patch will decrease over time. We tested this assumption using feeding data from a population of wild Bornean orangutans (Pongo pygmaeus wurmbii) from Gunung Palung National Park. We hypothesized that the feeding rate within orangutan food patches would decrease over time. Data included feeding bouts from continuous focal follows between 2014 and 2016. We recorded the average feeding rate over each tertile of the bout, as well as the first, midpoint, and last feeding rates collected. We did not find evidence of a decrease between first and last feeding rates (Linear Mixed Effects Model, n = 63), between a mid-point and last rate (Linear Mixed Effects Model, n = 63), between the tertiles (Linear Mixed Effects Model, n = 63), nor a decrease in feeding rate overall (Linear Mixed Effects Model, n = 146). These findings, thus, do not support the MVT assumption of decreased patch feeding rates over time in this large generalist frugivore.     

Habitat Deterioration, Habitat Destruction, and Metapopulation Persistence in a Heterogenous Landscape

Levins's unstructured metapopulation model predicts that the equilibrium fraction of empty habitat patches is a constant function of the fractionhof suitable patches in the landscape and that this constant equals the threshold value for metapopulation persistence. Levins's model thus suggests that the minimum amount of suitable habitat necessary for metapopulation persistence can be estimated from the fraction of empty patches at steady state. In this paper we construct several more realistic structured metapopulation models that include variation in patch quality and the rescue effect. These models predict both positive and negative correlations between the fractions of suitable patches and empty patches. The type of correlation depends in an intricate manner on the strength of the rescue effect and on the quality distribution of the patches to be destroyed. Empty patches can be considered as the resource limiting metapopulation growth. Our results demonstrate that the correlation between the fractions of suitable patches and empty patches is positive if and only if the average value of the resource decreases as the number of patches increases.     

Morphological and ultrastructural variations inAzotobacter vinelandii growing in oxygen-controlled continous culture

Membrane development as a response to growth at different oxygen tensions (from about 1% to 100% saturation of the medium with air) was determined inAzotobacter vinelandii strain OP. The organisms were grown in a carbonlimited chemostat either on atmospheric nitrogen or on ammonium as nitrogen sources. Both types of cultures increased not only the number of intracytoplasmic membrane vesicles per cell but also the cell volume with aeration. As the ratio of length per width stayed largely constant increases of volume resulted in decreases of the cell surface area, representing the surface area of the peripheral cytoplasmic membrane, per cell volume. While in nitrogen-fixing cells the proportion of intracytoplasmic membrane surface area per cytoplasmic membrane surface area increased from 1:2 to 3:1 the ratio stayed almost constant in ammonium-assimilating cells. The data suggest that oxygen controls changes in the ratio of intracytoplasmic to cytoplasmic membrane surface areas only under conditions of nitrogen fixation.Abbreviations CM Cytoplasmic membrane - ICM intracytoplasmic membrane     

Enhancement of nitrogen fixation inAnabaena flos-aquae (Cyanobacteria) via low-dose ultrasonic treatment

Low-dose (50 W), short-duration (5 min) ultrasonic treatments were delivered to log phase batch cultures of the cyanobacteriumAnabaena flos-aquae grown in nitrogen-free medium. Near the mid-point of nine-day experimental periods, ultrasonically-treated cultures exhibited higher growth rates, enhanced chlorophylla content, and greater acetylene reduction capacity when compared to cultures grown with reciprocal shaking alone. Heterocyst frequency was markedly higher in ultrasonically-treated cultures over the duration of five-day experimental periods.Author for correspondence     

Modeling of the Competitive Growth of Listeria monocytogenes and Lactococcus lactis in Vegetable Broth

Current mathematical models used by food microbiologists do not address the issue of competitive growth in mixed cultures of bacteria. We developed a mathematical model which consists of a system of nonlinear differential equations describing the growth of competing bacterial cell cultures. In this model, bacterial cell growth is limited by the accumulation of protonated lactic acid and decreasing pH. In our experimental system, pure and mixed cultures of Lactococcus lactis and Listeria monocytogenes were grown in a vegetable broth medium. Predictions of the model indicate that pH is the primary factor that limits the growth of L. monocytogenes in competition with a strain of L. lactis which does not produce the bacteriocin nisin. The model also predicts the values of parameters that affect the growth and death of the competing populations. Further development of this model will incorporate the effects of additional inhibitors, such as bacteriocins, and may aid in the selection of lactic acid bacterium cultures for use in competitive inhibition of pathogens in minimally processed foods.     

Amino acid supplementation decreases plasmid retention in Escherichia coli

The effect of amino acid supplementation on plasmid stability in Escherichia coli B/r was tested experimentally. Comparisons of experimental results to computer-predicted values were made using a detailed, structured single-cell model. The plasmid, pDW17 (a pBR322 derivative with a mutated tac promoter controlling the beta-lactamase gene), was used. In chemostat cultures, the amino acid supplemented cultures were always less stable than those grown in minimal medium. This effect was not a growth rate effect, as increasing growth rate imsproves stability for both cultures in minimal medium and in amino acid supplemented medium. The computer model also predicted a decrease in stability due to amino acid supplementation. The model also predicts that amino acid supplementation, combined with moderately strong plasmid-encoded protein expresion, results in a depletion of low-molecular-weight organics compared with plasmid-free cells. In minimal medium the same level of plasmid-encoded protein synthesis results in a strong reduction in amino acid pools compared with plasmid-free cells. With amino acid supplementation the growth differential between plasmid-bearing and plasmid-free cells may be due to an "energy limitation," while in minimal medium the size of the growth rate differential may be due to a "building block" limitation. (c) 1992 John Wiley & Sons, Inc.     

Auxin concentration control of the average DNA content in cells of in vitro cultures: a theoretical model and comparison to experimental data for <Emphasis Type="Italic">Allium cepa</Emphasis> and <Emphasis Type="Italic">Allium sativum</Emphasis>

A theoretical model explaining the average DNA content in cells of in vitro cultures as a function of concentration of auxin 2,4-D in medium is provided. The model assumes influence of auxin on the functioning of the main G1/S and G2/M control points of the cell cycle. Theoretical results are compared to experimental data obtained from the callus cultures of Allium sativum and Allium cepa conducted during 18 months. Adaptation of the model to explanation of the shape of the dose–response curves is suggested and successfully verified for the example of Nicotiana tabacum cultures.     

Cybernetic modeling of bacterial cultures at low growth rates: Mixed-substrate systems

A cybernetic model to predict the low-growth-rate behavior of bacteria in mixed-substrate environment is presented. Using only growth and maintenance parameters from single-substrate experiments, the model accurately predicts the simultaneous substrate utilization and maintenance energy effects in constant fed-batch cultures of Klebsiella oxytoca. The robustness of the model was examined more rigorously by perturbing glucose-limited fed-batch cultures with additions of arabinose, xylose, and fructose. In all cases, reasonable agreement of the model prediction with the experimental data was observed.     

Reproductive strategies in rain-pool dwellers and the model freshwater insect

Reproductive strategies of principal rain-pool midges, Chironomus imicola and Chironomus pulcher are investigated in field and laboratory. The two species are able to lay at least one full clutch without access to food in the adult stage. Since females are also capable of flying for extended periods without feeding, they carry out both adult functions (i.e. dispersal and reproduction), without taking energy from the terrestrial environment.We argue that independance of the terrestrial environment is adaptively appropriate to animals able to exploit a larval habitat rich in food and low in interspecific competition. However, there are costs to this strategy because freshwaters, and notably rain-pools, are unpredictable habitats inclined to dry up periodically. These species must, therefore, constantly colonise new pools by laying eggs. We show that adult females can resort to feeding and that if they do so the energy acquired goes to the production of further eggs with a consequent increase in colonizing ability.As a test of this hypothesis that there is a relationship between duration of habitat and the number of eggs layed, we have examined a third rain-pool dwelling chironomid, Polypedilum vanderplanki. This species is unique among insects in that larvae are able to survive desiccation of their tissues. For them there is thus not the same incentive to leave before the home pool dries. So, P. vanderplanki does not need to be a colonizer. Observations confirm this view since P. vanderplanki adult females, even when fed, lay no more than one clutch of eggs. Consequently, reproduction and feeding in the adult female are related to the way in which duration of the habitat is perceived. We suggest that, measured against P. vanderplanki, Chironomus species provide a useful model of the ideal freshwater animal.     

Repeatability of Foreign Egg Rejection: Testing the Assumptions of Co‐Evolutionary Theory

Most theoretical models of coevolution between brood parasites, whether interspecific or conspecific, and their hosts explicitly assume consistent individual behaviour in host egg‐rejection responses. Accordingly, hosts cast as acceptors always accept, whereas ejectors always reject parasitic eggs when exposed to stable ecological conditions. To date, only few studies have attempted to test this critical assumption of individual repeatability in egg‐rejection responses of hosts. Here, we studied the repeatability of egg rejection in blackbirds (Turdus merula) and song thrush (T. philomelos), species in which females are reported to reject simulated, non‐mimetic foreign eggs at intermediate frequencies at the population level. However, intermediate rates of acceptance and rejection can be consistent with either or both intra‐ and interindividual variability in rejection behaviours. Our experiments revealed generally high individual consistency in these hosts’ responses to experimentally introduced non‐mimetic and mimetic model foreign eggs. Individuals also responded faster on average to second than to first trials within the same breeding attempts, but the difference was statistically significant only in blackbirds. These results are consistent with the critical assumption of co‐evolutionary models, that statistically egg rejection is mostly individually repeatable, but also reveal that some individuals in both species change their responses even within the short time‐window of one breeding attempt. The data suggest that individuals reject foreign eggs faster when perceived parasitism risk is greater because of repeated introductions of experimental parasitic eggs. We provide methodological recommendations to facilitate experimental and meta‐analytical studies of individual egg rejection repeatability and discuss how to reduce technical constraints arising from disparate treatments and variable sample sizes for future studies.     

Fecundity compromises attractiveness when pigments are scarce

Theory predicts that the trade-off between ornamentation andfecundity limits female attractiveness. However, there is littleevidence on this theoretical trade-off and its proximate background.Our aim was to study whether pigment availability modulatesthis potential relationship in blue-footed booby females. Wesupplemented females with dietary carotenoids after laying thefirst egg and assessed the change in foot color, a carotenoid-basedsexually selected trait in both sexes. We measured the changein body mass and in the levels of plasma antioxidants and carotenoids.Also, we registered the mass and volume of eggs. Surprisingly,experimental females reduced zeaxanthin concentration in plasma,but not other carotenoids or total antioxidant levels. Conversely,they increased foot color intensity and laid heavier secondeggs and larger second and third eggs than controls. Furthermore,under natural conditions (controls), ornamentation was negativelyassociated with the mass and volume of second eggs, but theassociation was reversed under conditions of high carotenoidavailability (experimental females). Results suggest that carotenoidavailability may mediate the theoretical trade-off between ornamentationand fecundity. We highlight that pigment limitation for femalescould represent an evolutionary pathway to male choosiness inthe blue-footed booby.     

Methods for the Large-Scale Cultivation of an Oxytricha (Ciliophora: Hypotrichida)1

ABSTRACT. Oxytricha strains used in biochemical studies have traditionally been grown in unaerated, unagitated culture tubes or Fernbach flasks. These cultures are limited in volume to about one liter and have a very nonuniform distribution of cells, with the majority of the cells at the very top or bottom of the medium. We have found conditions in which Oxytricha can be grown in 50-liter fermentation vats. The cultures grow to a uniform density of about 6000 cells/ml.     

Inert gas diffusion in heterogeneous tissue I: Without perfusion

A mathematical model is proposed to describe transient gas diffusion into a block of heterogenous tissue placed on an impermeable base. The corresponding asymptotic sultion of mass uptake of the gas is derived on the assumption that the diffusion constant is very much smaller in the cellular phase. It is expected that this will be useful in evaluating the diffusion constant in cellular material, and the volume fraction of extracellular fluid, providing the partition coefficient is known. The phenomenon of mutual interaction and multiple feedback between cellular and extracellular fluid is clearly seen in the overall response of the tissue. In this regard it is shown that the extraction of the two least dominant time constants, by backward projection of the experimental data curve of gas uptake, is likely to confuse the numerical evaluation of the physical parameters of the system. In an appendix, the problem of diffusion straight through a tissue slice is solved at the asymptotic stage, before steady state is reached. The resulting expression predicts the by-passing of cells by the diffusing gas and shows how the parameters cannot reliably be, determined.     

Optimal timing of the production of sexuals in bumblebee colonies

Colonies of annual eusocial insects often produce only workers until they switch to the production of sexuals (queens and males). This switch from the ergonomic phase to the reproductive phase has been modelled by Macevicz & Oster (1976). Their model predicts that the production of sexuals should take place approximately one generation (one brood developmental period) before resources are depleted in order to maximise the number of sexuals. Bumblebees, however, produce sexuals early (relative to colony lifetime) when resources are still abundant and thus the model of Macevicz & Oster does not hold for these insects.Here we show that Macevicz & Oster's prediction hinges critically on their assumption that the egg laying rate of the queen is a function of the foraging effort of the workers. This assumption does not hold for bumblebees, where queens lay eggs at a constant rate. Taking this feature of bumblebees into account the model predicts early production of sexuals, since it does not pay to produce more workers and collect more resources than needed to raise sexuals.