Choosing the right sigmoid growth function using the unified‐models approach

Growth of the young is an important part of the life history in birds. However, modelling methods have paid little attention to the choice of regression model used to describe its pattern. The aim of this study was to evaluate whether a single sigmoid model with an upper asymptote could describe avian growth adequately. We compared unified versions of five growth models of the Richards family (the four‐parameter U‐Richards and the three‐parameter U‐logistic, U‐Gompertz, U‐Bertalanffy and U4‐models) for three traits (body mass, tarsus‐length and wing‐length) for 50 passerine species, including species with varied morphologies and life histories. The U‐family models exhibit a unified set of parameters for all models. The four‐parameter U‐Richards model proved a good choice for fitting growth curves to various traits – its extra d‐parameter allows for a flexible placement of the inflection point. Which of the three‐parameter U‐models was the best performing varied greatly between species and between traits, as each three‐parameter model had a different fixed relative inflection value (fraction of the upper asymptote), implying a different growth pattern. Fixing the asymptotes to averages for adult trait value generally shifted the model preference towards one with lower relative inflection values. Our results illustrate an overlooked difficulty in the analysis of organismal growth, namely, that a single traditional three‐parameter model does not suit all growth data. This is mostly due to differences in inflection placement. Moreover, some biometric traits require more attention when estimating growth rates and other growth‐curve characteristics. We recommend fitting either several three‐parameter models from the U‐family, where the parameters are comparable between models, or only the U‐Richards model.     

Adaptive foraging does not always lead to more complex food webs

Recent modeling studies exploring the effect of consumers’ adaptivity in diet composition on food web complexity invariably suggest that adaptivity in foraging decisions of consumers makes food webs more complex. That is, it allows for survival of a higher number of species when compared with non-adaptive food webs. Population-dynamical models in these studies share two features: parameters are chosen uniformly for all species, i.e. they are species-independent, and adaptive foraging is described by the search image model. In this article, we relax both these assumptions. Specifically, we allow parameters to vary among the species and consider the diet choice model as an alternative model of adaptive foraging. Our analysis leads to three important predictions. First, for species-independent parameter values for which the search image model demonstrates a significant effect of adaptive foraging on food web complexity, the diet choice model produces no such effect. Second, the effect of adaptive foraging through the search image model attenuates when parameter values cease to be species-independent. Finally, for the diet choice model we observe no (significant) effect of adaptive foraging on food web complexity. All these observations suggest that adaptive foraging does not always lead to more complex food webs. As a corollary, future studies of food web dynamics should pay careful attention to the choice of type of adaptive foraging model as well as of parameter values.     

Intake rates and the functional response in shorebirds (Charadriiformes) eating macro-invertebrates

As field determinations take much effort, it would be useful to be able to predict easily the coefficients describing the functional response of free-living predators, the function relating food intake rate to the abundance of food organisms in the environment. As a means easily to parameterise an individual-based model of shorebird Charadriiformes populations, we attempted this for shorebirds eating macro-invertebrates. Intake rate is measured as the ash-free dry mass (AFDM) per second of active foraging; i.e. excluding time spent on digestive pauses and other activities, such as preening. The present and previous studies show that the general shape of the functional response in shorebirds eating approximately the same size of prey across the full range of prey density is a decelerating rise to a plateau, thus approximating the Holling type II ('disc equation') formulation. But field studies confirmed that the asymptote was not set by handling time, as assumed by the disc equation, because only about half the foraging time was spent in successfully or unsuccessfully attacking and handling prey, the rest being devoted to searching.A review of 30 functional responses showed that intake rate in free-living shorebirds varied independently of prey density over a wide range, with the asymptote being reached at very low prey densities (<150/m-2). Accordingly, most of the many studies of shorebird intake rate have probably been conducted at or near the asymptote of the functional response, suggesting that equations that predict intake rate should also predict the asymptote.A multivariate analysis of 468 'spot' estimates of intake rates from 26 shorebirds identified ten variables, representing prey and shorebird characteristics, that accounted for 81% of the variance in logarithm-transformed intake rate. But four-variables accounted for almost as much (77.3%), these being bird size, prey size, whether the bird was an oystercatcher Haematopus ostralegus eating mussels Mytilus edulis, or breeding. The four variable equation under-predicted, on average, the observed 30 estimates of the asymptote by 11.6%, but this discrepancy was reduced to 0.2% when two suspect estimates from one early study in the 1960s were removed. The equation therefore predicted the observed asymptote very successfully in 93% of cases. We conclude that the asymptote can be reliably predicted from just four easily measured variables. Indeed, if the birds are not breeding and are not oystercatchers eating mussels, reliable predictions can be obtained using just two variables, bird and prey sizes. A multivariate analysis of 23 estimates of the half-asymptote constant suggested they were smaller when prey were small but greater when the birds were large, especially in oystercatchers. The resulting equation could be used to predict the half-asymptote constant, but its predictive power has yet to be tested. As well as predicting the asymptote of the functional response, the equations will enable research workers engaged in many areas of shorebird ecology and behaviour to estimate intake rate without the need for conventional time-consuming field studies, including species for which it has not yet proved possible to measure intake rate in the field.     

Errors Affect Hypothetical Intertemporal Food Choice in Women

Growing evidence suggests that the ability to control behavior is enhanced in contexts in which errors are more frequent. Here we investigated whether pairing desirable food with errors could decrease impulsive choice during hypothetical temporal decisions about food. To this end, healthy women performed a Stop-signal task in which one food cue predicted high-error rate, and another food cue predicted low-error rate. Afterwards, we measured participants’ intertemporal preferences during decisions between smaller-immediate and larger-delayed amounts of food. We expected reduced sensitivity to smaller-immediate amounts of food associated with high-error rate. Moreover, taking into account that deprivational states affect sensitivity for food, we controlled for participants’ hunger. Results showed that pairing food with high-error likelihood decreased temporal discounting. This effect was modulated by hunger, indicating that, the lower the hunger level, the more participants showed reduced impulsive preference for the food previously associated with a high number of errors as compared with the other food. These findings reveal that errors, which are motivationally salient events that recruit cognitive control and drive avoidance learning against error-prone behavior, are effective in reducing impulsive choice for edible outcomes.     

Assessment and parameter identification of simplified models to describe the kinetics of semi-continuous biomethane production from anaerobic digestion of green and food waste

Biochemical reactions occurring during anaerobic digestion have been modelled using reaction kinetic equations such as first-order, Contois and Monod which are then combined to form mechanistic models. This work considers models which include between one and three biochemical reactions to investigate if the choice of the reaction rate equation, complexity of the model structure as well as the inclusion of inhibition plays a key role in the ability of the model to describe the methane production from the semi-continuous anaerobic digestion of green waste (GW) and food waste (FW). A parameter estimation method was used to investigate the most important phenomena influencing the biogas production process. Experimental data were used to numerically estimate the model parameters and the quality of fit was quantified. Results obtained reveal that the model structure (i.e. number of reactions, inhibition) has a much stronger influence on the quality of fit compared with the choice of kinetic rate equations. In the case of GW there was only a marginal improvement when moving from a one to two reaction model, and none with inclusion of inhibition or three reactions. However, the behaviour of FW digestion was more complex and required either a two or three reaction model with inhibition functions for both ammonia and volatile fatty acids. Parameter values for the best fitting models are given for use by other authors.     

Modelling avian growth with the Unified‐Richards: as exemplified by wader‐chick growth

Postnatal growth in birds is traditionally modelled by fitting three‐parameter models, namely the logistic, the Gompertz, or the von Bertalanffy models. The purpose of this paper is to address the utility of the Unified‐Richards (U‐Richards) model. We draw attention to two forms of the U‐Richards and lay down a set of recommendations for the analysis of bird growth, in order to make this model and the methods more accessible. We examine the behaviour of the four parameters in each model form and the four derived measurements, and we show that all are easy to interpret, and that each parameter controls a single curve characteristic. The two parameters that control the inflection point, enable us to compare its placement in two dimensions, 1) inflection value (mass or length at inflection) and 2) inflection time (time since hatching), between data sets (e.g. between biometrics or between species). We also show how the parameter controlling growth rate directly presents us with the relative growth rate at inflection, and we demonstrate how one can compare growth rates across data sets. The three traditional models, where the inflection value is fixed (to a specific percentage of the upper asymptote), provide incompatible growth‐rate coefficients. One of the two forms of the U‐Richards model makes it possible to fix not only the upper asymptote (adult value), but also the intersection with the y‐axis (hatching value). Fitting the new model forms to data validates the usefulness of interpreting the inflection placement in addition to the growth rate. It also illustrated the advantages and limitations of constraining the upper asymptote (adult value) and the y‐axis intersection (hatching value) to fixed values. We show that the U‐Richards model can successfully replace some of the commonly used growth models, and we advocate replacing these with the U‐Richards when modelling bird growth.     

Searching for Food or Hosts: The Influence of Parasitoids Behavior on Host–Parasitoid Dynamics

A host–parasitoid system with overlapping generations is considered. The dynamics of the system is described by differential equations with a control parameter describing the behavior of the parasitoids. The control parameter models how the parasitoids split their time between searching for hosts and searching for non-host food. The choice of the control parameter is based on the assumption that each parasitoid maximizes the instantaneous growth rate of the number of copies of its genotype. It is shown that optimal individual behavior of parasitoids, with respect to time sharing between hosts and food searching, may have a stabilizing effect on the host–parasitoid dynamics.     

A mathematical analysis of the substrate effect observed in 3beta-hydroxysteroid dehydrogenase reactions of rat testicular microsomes.

The substrate effect in enzyme reactions has been explained mostly in terms of an additional substrate binding site on the enzyme other than the catalytic site. A rate equation for the reaction is introduced according to the steady state mechanism as follows: v = (Ps3+Qs2+Rs)/(s3+Ls2+Ms+N), were the six parameters, L,M,N,P,Q, and R, can be determined by the least-squares method from the experimental points. The v vs. s curve has an asymptote parallel to the s abscissa, and can be classified into one of four types. The type A curve has an intersection with the asymptote and an apparent maximum velocity; the curve descends toward the asymptote. Type B has no intersection and no stationary point; the curve ascends toward the asymptote. Type C has two intersections and two stationary points, an apparent maximum velocity and a minimum velocity; the curve ascends toward the asymptote. Type D has no intersection and two stationary points; the curve ascends toward the asymptote. The equation was applied to the 3beta-hydroxysteroid dehydrogenase [EC 1.1.1.145] reaction of rat testicular microsomes. The conversion of 3beta-hydroxyandrost-5-ene-17-one was represented by type C, with an apparent maximum velocity of 0.338 nmole/min/mg protein at 0.912 muM of the substrate concentration, minimum velocity of 0.108 nmole/min at 16.6 muM, and saturating velocity of 0.169 nmole/min at infinite concentration of the substrate. The converson of 3beta-hydroxypregn-5-ene-20-one was of type B, having two inflexion points, 0.320 nmole/min at 2.735 muM and 0.814 nmole/min at 12.39 muM, and a saturating velocity of 3.80 nmoles/min at infinite concentration of the substrate.     

Artificial light affects the foraging behavior in greater white-toothed shrews (CROCIDURA RUSSULA)

Light pollution is one of the forms by which human-induced alterations are changing natural environments. Artificial light at night (ALAN) has been increasing over the past decades and it is already known that ALAN can have a major influence on the ecology, behavior, and physiology of different taxa. Nocturnal small mammals are particularly vulnerable, as ALAN can increase their predation risk while foraging. The aim of this study was to investigate foraging strategies under different light conditions in a nocturnal small insectivore, the greater white-toothed shrew (Crocidura russula). Compared with rodents, shrews have a higher metabolic rate and thus present a good model for a foraging study. In three laboratory experiments with wild-caught shrews we tested (i) food preference under dark conditions as well as the effect of different light conditions on (ii) foraging strategies and (iii) food choice. The results showed that shrews had a clear food preference under dark conditions. They also preferred to forage under dark over light conditions when presented with the same food in both conditions. However, when presented with the choice of foraging their preferred food under illuminated conditions or a lower food quality in the dark, the food preference of shrews overruled their preference for feeding in the dark. It seems that food preference, rather than risk perception, is the main driver determining the foraging strategy of the greater white-toothed shrews. This study suggests that ALAN does not necessarily prevent high-metabolic nocturnal insectivores from achieving their energetic needs, which might help explain their persistence in urban environments.     

Adaptive learning in arthropods: spider mites learn to distinguish food quality

Many herbivorous arthropods have been shown to possess learning capabilities, yet fitness effects of learning are largely unknown. In this paper, we test whether two-spotted spider mites (Tetranychus urticae) learn to distinguish food quality in choice tests, and whether this results in fitness benefits. Food consisted of cucumber plants with one of three degrees of feeding damage: undamaged (no mites), mildly damaged (infested by a mite strain adapted to tomato) and heavily damaged (infested by a mite strain adapted to cucumber). Mites were subjected to one choice test in a greenhouse and three sequential choice tests on leaf disks. Thereafter, individual mite performance was measured as oviposition rate over four days. In the course of the three small-scale choice tests, preference shifted towards less damaged food. The performance tests showed that learning was adaptive: mites learned to prefer the food type that yielded the higher oviposition rate. Interestingly, innate preferences in the greenhouse tests were close to those shown after learning in the small-scale tests. Given that both strains of mites had not experienced cucumber for several years, we hypothesize that the preference in the greenhouse was due to avoidance of mite odours rather than odours of damaged plants. Through its effect on foraging behaviour, adaptive learning may promote the evolution of host plant specialization in herbivorous arthropods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Assessment of the time constant of relaxation: insights from simulations and hemodynamic measurements

The objective of this study was to use high-fidelity animal data and numerical simulations to gain more insight into the reliability of the estimated relaxation constant derived from left ventricular pressure decays, assuming a monoexponential model with either a fixed zero or free moving pressure asymptote. Comparison of the experimental data with the results of the simulations demonstrated a trade off between the fixed zero and the free moving asymptote approach. The latter method more closely fits the pressure curves and has the advantage of producing an extra coefficient with potential diagnostic information. On the other hand, this method suffers from larger standard errors on the estimated coefficients. The method with fixed zero asymptote produces values of the time constant of isovolumetric relaxation (tau) within a narrow confidence interval. However, if the pressure curve is actually decaying to a nonzero pressure asymptote, this method results in an inferior fit of the pressure curve and a biased estimation of tau.     

Oxygen uptake,heart rate and activities of locomotor muscles during a critical swimming speed protocol in the gilthead sea bream Sparus aurata

Oxygen uptake, heart rate and contraction frequencies of slow oxidative (SO) and fast glycolytic (FG) muscle were measured simultaneously in gilthead seabream Sparus aurata submitted to stepwise increases in current speed in a swimming respirometer. Variation in oxygen uptake was closely related to variation in heart rate, over initial steps these rose in concert with an increase in contraction frequency of SO muscle. There was an asymptote in oxygen uptake and heart rate at high speeds that reflected a transition from exclusive use of aerobic SO muscle to a combination of SO and anaerobic FG muscle, and which preceded fatigue.     

Ecological consequences of body size: a model for patch choice in desert rodents

Summary Recent models exploring the ecological consequences of body size have assumed that its primary effect is to determine how easily individual prey of different sizes can be pursued or handled. However, for predators that eat small, particulate food, size-related costs associated with finding and harvesting prey should be at least as important as those associated with consuming individual prey once thay have been harvested. Such predators should have generalized diets, and body size differences would not be expected to influence substantially the sizes of prey eaten. The effect of body size on spatial patterns of foraging could, however, be substantial for these predators if prey have a patchy distribution.I develop a simple model for a particle feeder foraging in patchy environments and use it to examine the special case of patch choice by seed-eating desert rodents. The model implies that for most parameter values large and small animals should specialize to different extents on the most profitable patches. Size differences among coexisting desert rodents therefore can be expected to promote partitioning of food by differential patch choice. Preliminary observations of desert rodent seed dispersion and microhabitat preferences indicate that interspecific differences in patch choice do exist.The model predicts that the nature of the relationship between size and patch choice depends on the values taken by certain model parameters. Thus, although the model predicts that patch choice generally should vary with body size, the spatial scale of patchiness and the way in which within-patch harvest rates and between-patch travel velocities scale with size determine whether, and in what way, body size should affect patch choice. As yet estimates of these parameters for heteromyid rodents are not precise enough for us to have much confidence in specific model predictions about this system. However, it will only be a matter of time before we can derive better estimates; in principle the model is testable, and when suitably modified should be applicable to many systems.     

Attraction to and learning from social cues in fruitfly larvae

We examined the use of social information in fruitfly larvae, which represent an ideal model system owing to their robust learning abilities, small number of neurons and well-studied neurogenetics. Focal larvae showed attraction to the distinct odour emanating from food occupied by other larvae. In controlled learning experiments, focal larvae preferred novel odours previously paired with food occupied by other larvae over novel odours previously paired with unoccupied food. When we gave groups of larvae a choice between food patches differing in quality, more larvae aggregated on the higher-quality food, suggesting that attraction to and learning about cues associated with other larvae can be beneficial. Furthermore, larvae were more likely to find the best available food patch in trials when that food patch was occupied by other larvae than in trials when that food patch was unoccupied. Our data suggest, however, that the benefits from joining others may be at least partially offset by the fitness costs of increased competition, because larvae reared in isolation did as well as or better than larvae reared in groups on three key fitness parameters: developmental rate, survival rate and adult dry body mass. Our work establishes fruitfly larvae as a highly tractable model species for further research on the mechanisms that modulate behaviour and learning in a social context.     

Adaptive learning in arthropods: spider mites learn to distinguish food quality

Many herbivorous arthropods have been shown to possess learning capabilities, yet fitness effects of learning are largely unknown. In this paper, we test whether two-spotted spider mites (Tetranychus urticae) learn to distinguish food quality in choice tests, and whether this results in fitness benefits. Food consisted of cucumber plants with one of three degrees of feeding damage: undamaged (no mites), mildly damaged (infested by a mite strain adapted to tomato) and heavily damaged (infested by a mite strain adapted to cucumber). Mites were subjected to one choice test in a greenhouse and three sequential choice tests on leaf disks. Thereafter, individual mite performance was measured as oviposition rate over four days. In the course of the three small-scale choice tests, preference shifted towards less damaged food. The performance tests showed that learning was adaptive: mites learned to prefer the food type that yielded the higher oviposition rate. Interestingly, innate preferences in the greenhouse tests were close to those shown after learning in the small-scale tests. Given that both strains of mites had not experienced cucumber for several years, we hypothesize that the preference in the greenhouse was due to avoidance of mite odours rather than odours of damaged plants. Through its effect on foraging behaviour, adaptive learning may promote the evolution of host plant specialization in herbivorous arthropods.     

Does social status within a dominance hierarchy mediate individual growth,residency and relocation?

The availability of food, and hence energy, is known to influence the abundance, habitat choice and growth of individuals. In contrast, there is a paucity of knowledge on how the interaction of energy supply and social status determines patterns of residency and movement. This study tests whether the presence of conspecifics and an individual’s social status in relation to food supply influence the fitness and movement of a drift-feeding fish (Galaxias fasciatus). Using an information-theoretic approach (AIC), our analysis indicated that the most parsimonious model of fish movement among pools was one that included food supply, social rank and fish relative growth rate. Our results indicated that subordinate fish relocated more frequently compared to dominant fish, most likely as a consequence of intra-specific competition that limited the access of these smaller fish to resources and constrained their growth. Our results suggest that energy constraints may force individuals to explore new habitats in an effort to find more energetically profitable patches. We conclude that intra-specific competition mediated through the social hierarchy amongst closely interacting individuals plays a key role in determining individual growth, residency and relocation.     

Visual discrimination learning in zebrafish (Danio rerio)

Three experiments demonstrated visual discrimination learning in zebrafish (Danio rerio). In each experiment, zebrafish were given a choice between two visually distinct arms of a T-maze. Choice of one stimulus was always followed by a food reward, but choice of the other stimulus was not rewarded. Different colored sleeves fitted around the arms of the T-maze were used in Experiments 1 (green and purple) and 2 (red and blue). The stimuli used in Experiment 3 were white sleeves lined with horizontal or vertical black stripes. In all three experiments, zebrafish acquired a significant preference for the stimulus that led to a food reward. Experiments 1 and 2 also showed that zebrafish could learn a reversal of the discrimination. Finally, the effect of discontinuing food rewards was examined after reversal training in Experiment 2 and after initial discrimination training in Experiments 1 and 3. Non-reinforcement led to a decrease in correct responding in Experiments 2 and 3 independent of stimulus identity, but to an asymmetrical pattern of responding in Experiment 1. The median latency to make a choice response decreased over the course of acquisition in all three experiments; during extinction, median response times did not change at all in Experiment 1 and increased only very slightly in Experiment 2, but showed a substantial increase in Experiment 3. The implications of these results for the zebrafish as a model system for genetic studies of learning and memory are discussed.     

Kinetic modelling of steam gasification of various woody biomass chars: influence of inorganic elements

A study was performed on the influence of wood variability on char steam gasification kinetics. Isothermal experiments were carried out in a thermobalance in chemical regime on various wood chars produced under the same conditions. The samples exhibited large differences of average reaction rate. These differences were linked neither with the biomass species nor age and may be related to the biomass inorganic elements. A modelling approach was developed to give a quantitative insight to these observations. The grain model was used on one biomass of reference for temperatures between 750 and 900 °C and steam partial pressures between 0 and 0.27 bar. The model was applied to the other samples through the addition of an integral parameter specific to each sample. A satisfactory correlation was found between this parameter and the ratio potassium/silicium. This result highlighted the catalytic effect of potassium and inhibitor effect of silicium on the reaction.     

The establishment of a ‘normal’ population and its behavioural maintenance in the guppy—Poecilia reticulata (Peters)*

Populations of the guppy—Poecilia reticulata (Peters)—were established with a single male and female fish per compartment. In spite of excess food, regular water changes, constant temperature and continuous aeration, the populations eventually reached a stable asymptote which was proportional to the size of the compartment, particularly when the populations were visually isolated from other populations. A weight asymptote was achieved some time after the population plateau. There was a tendency for females to exceed the numbers of males at the asymptote. Fish from the asymptotes were rearranged to relatively increase or decrease the populations, on the expectation that the populations would revert to the original asymptote. This did not happen. It was hypothesized that there was a learned behavioural response which prevented reproduction in the altered populations, but not an ovarian ‘carry-over’ for the ovaries of decreased and increased populations were distinguishable. The learning hypothesis was substantiated in fish of a single generation which were crowded, then uncrowded, and continued to show reduced courtship and increased aggressive behaviour.