Estimating carnivoran diets using a combination of carcass observations and scats from GPS clusters.

Scat analysis is one of the most frequently used methods to assess carnivoran diets and Global Positioning System (GPS) cluster methods are increasingly being used to locate feeding sites for large carnivorans. However, both methods have inherent biases that limit their use. GPS methods to locate kill sites are biased towards large carcasses, while scat analysis over-estimates the biomass consumed from smaller prey. We combined carcass observations and scats collected along known movement routes, assessed using GPS data from four African lion (Panthera leo) prides in the Kruger National Park, South Africa, to determine how a combination of these two datasets change diet estimates. As expected, using carcasses alone under-estimated the number of feeding events on small species, primarily impala (Aepyceros melampus) and warthog (Phacochoerus africanus), in our case by more than 50% and thus significantly under-estimated the biomass consumed per pride per day in comparison to when the diet was assessed using carcass observations alone. We show that an approach that supplements carcass observations with scats that enables the identification of potentially missed feeding events increases the estimates of food intake rates for large carnivorans, with possible ramifications for predator-prey interaction studies dealing with biomass intake rate.

Superspreading and the effect of individual variation on disease emergence.

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R(0), which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R(0) can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous 'superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R(0) is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

Variation in faecal water content may confound estimates of gastro-intestinal parasite intensity in wild African herbivores.

Estimates of parasite intensity within host populations are essential for many studies of host-parasite relationships. Here we evaluated the seasonal, age- and sex-related variability in faecal water content for two wild ungulate species, springbok (Antidorcas marsupialis) and plains zebra (Equus quagga). We then assessed whether or not faecal water content biased conclusions regarding differences in strongyle infection rates by season, age or sex. There was evidence of significant variation in faecal water content by season and age for both species, and by sex in springbok. Analyses of faecal egg counts demonstrated that sex was a near-significant factor in explaining variation in strongyle parasite infection rates in zebra (P = 0.055) and springbok (P = 0.052) using wet-weight faecal samples. However, once these intensity estimates were re-scaled by the percent of dry matter in the faeces, sex was no longer a significant factor (zebra, P = 0.268; springbok, P = 0.234). These results demonstrate that variation in faecal water content may confound analyses and could produce spurious conclusions, as was the case with host sex as a factor in the analysis. We thus recommend that researchers assess whether water variation could be a confounding factor when designing and performing research using faecal indices of parasite intensity.

Responses of cockroach antennal lobe projection neurons to pulsatile olfactory stimuli.

Behavioral evidence indicates that insects preferentially orient toward pulses of odorants as they occur downwind from a point source. Our recent results have shown that cockroach olfactory receptor neurons are able to reliably resolve 10-Hz pulses of the general "green' odorant 1-hexanol, but it is unknown to what extent the central olfactory pathway is able to resolve temporal aspects of a general odor stimulus. In the present study, temporal response characteristics were measured in antennal lobe projection neurons of female American cockroaches, Periplaneta americana in response to series of short odor pulses (2.5-20 Hz). Odor pulses were delivered to olfactory sensilla in a moving airstream controlled by electromagnetic valves and quantified by replacing the odorant with oil smoke and measuring the concentration of smoke passing through a light beam. The responses of projection neurons were recorded with an intracellular microelectrode placed in the projection neuron cell body. A variety of time courses of responses were recorded. Response patterns were consistent among identical stimuli within a neuron and varied among neurons. Some neurons increased spike frequency with stimulus onset while others decreased spike frequency. The latency to the change in spike frequency and the duration of the response also varied among neurons. Regardless of the temporal characteristics of the responses, nearly all projection neurons were able to resolve pulses of 1-hexanol presented at 5 Hz and some could resolve 10-Hz pulses. Thus, responses of antennal lobe projection neurons can reflect fine structures of non-uniform distributions of general odorants in a turbulent odor plume. In addition, the variety of temporal response characteristics to identical stimuli suggests that odor quality is coded by a temporal code expressed across a population of projection neurons.

Polycondensation and peptide chain-length distribution under prebiotic conditions.

An open-ended system of differential equations is formulated for the number of polymers of length n, n = 1,2,..., under the assumption that all monomers are kinetically equivalent. Although this assumption does not hold in real systems, solutions to the model could provide insights into the processes of polycondensation including polymerizing proteins and polynucleotides. In this paper the equilibrium solution to the system is derived analytically and is used to estimate the concentration of monomers required to obtain a fixed proportion of polymers longer than a given length. Simulation results are also presented to indicate the effects that autocatalytic interactions may have on the dynamics of polycondensation. The results suggest that relatively long-chained peptides (one to several hundred units long) could well have been synthesized under non-template or prebiotic conditions.

Rate code input produces temporal code output from cockroach antennal lobes.

The experiments presented here were designed to determine the origin of the temporally complex activity of antennal lobe projection neurons in the cockroach olfactory system. We determined this through the use of complex chemical stimuli that evoked neural activity recorded extracellularly from olfactory sensory neurons and intracellularly from antennal lobe projection neurons in the cockroach Periplaneta americana. Olfactory information was represented by a simple, short time-scale rate code in the olfactory sensory neurons. This rate code input from the sensory neurons was processed by the antennal lobe and transformed into a longer time-scale, temporally encoded output expressed across a smaller population of antennal lobe projection neurons. The projection neuron responses comprised temporal patterns of increases and decreases in spike frequency that differed among projection neurons and were consistent among repeated presentations of the same stimulus. Presentation of simple and complex chemical stimuli showed that the complexity of projection neuron activity was a product of the antennal lobes and was not associated with the chemical complexity of the stimulus. To characterize the encoding schemes used by each class of neurons, the responses were decomposed into their principal components. The stimulus was correlated with only the first principal component of the activity of sensory neurons, which is consistent with a rate encoding scheme. The stimulus was correlated with higher order principal components of the activity of projection neurons, which is consistent with a temporal encoding scheme.

Coding properties of peak and average response rates in American cockroach olfactory sensory cells.

The response of phasic neurons is often measured in terms of average spiking rates over arbitrarily selected time intervals. Averages taken over inappropriate intervals may severely reduce the information content of data, as we show here using response data from female American cockroach peripheral olfactory cells. We demonstrate that a 100-ms period around the peak response contains the best information for discriminating among odors at moderate to high concentrations. Further, the 100-ms post-peak response period contains the best information at low concentrations, as well as in situations where it is important to minimize errors in misidentifying the quality of an odor. Averaging the data over the full 0.5 s stimulus period degrades the odor separation qualities of the data.

Partitioning non-linearities in the response of honey bee olfactory receptor neurons to binary odors.

In many organisms, of which honey bees are one example, a general (i.e., non-pheromonal) olfactory receptor neuron may respond to some odorants by increasing its firing rate and to others by decreasing its firing rate. In the latter case, this decrease will be with respect to a background firing rate determined by intrinsic (internal noise) and extrinsic (background odors) factors. To analyse receptor neurons of this complexity, we extend Beidler's model of receptor protein activation dynamics to account for the competition between depolarizing and hyperpolarizing pathways and couple the model to a phenomenological description of the non-linear relationship between the proportion of activate membrane receptors and the receptor cell spike generation rates. We then examine the implications of this theory for predicting the response of receptor neurons to odor mixtures based on their response to pure odorants at concentrations matched to the mixture. We derive inequalities that must be satisfied under our normative model, and propose that deviations from the model be designated as synergisms and inhibitions, depending on the direction in which various equalities and inequalities are violated. We then apply our inequalities to identifying synergisms and inhibitions in data analysed in a different way elsewhere (Akers, R.P. and Getz, W.M. Response of olfactory receptor neurons in honey bees to odorants and their binary mixtures. J. Comp. Physiol. (in press)). In these data regarding the response of honey bee placode sensilla to a number of odorants and their binary combinations, we demonstrate the presence of synergisms and inhibitions--that is, elevated or repressed responses that are not due to competitive interactions of mixture component odorants for receptor sites or Beidler (Beidler, L.M., 1962. Taste receptor stimulation. Prog. Biophys. Biophys. Chem. 12, 107-151) saturation mechanisms.

Defining herbivore assemblages in the Kruger National Park: a correlative coherence approach.

Spatial associations of seven herbivore species in the Kruger National Park, South Africa, are analyzed using a new technique, Correlative Coherence Analysis (CoCA). CoCA is a generalization of the concept of correlation to more than two sequences of numbers. Prior information on the feeding ecology and metabolic requirements of these species is used to contrast spatial scales at which hypothesized guild aggregation or competition occurs. These hypotheses are tested using 13 years of aerial census data collected during the dry season. Our results are consistent with the hypothesis that distributions of large and small species of the same feeding type (i.e., grazers and browsers) overlap in potentially resource-rich areas, but have lower similarity values across all areas because the higher tolerance of large species for low quality foods results in a more even spatial distribution of large species compared to small species.

A neural network for processing olfactory-like stimuli.

Several critical issues associated with the processing of olfactory stimuli in animals (but focusing on insects) are discussed with a view to designing a neural network which can process olfactory stimuli. This leads to the construction of a neural network that can learn and identify the quality (direction cosines) of an input vector or extract information from a sequence of correlated input vectors, where the latter corresponds to sampling a time varying olfactory stimulus (or other generically similar pattern recognition problems). The network is constructed around a discrete time content-addressable memory (CAM) module which basically satisfies the Hopfield equations with the addition of a unit time delay feedback. This modification improves the convergence properties of the network and is used to control a switch which activates the learning or template formation process when the input is "unknown". The network dynamics are embedded within a sniff cycle which includes a larger time delay (i.e. an integer ts greater than 1) that is also used to control the template formation switch. In addition, this time delay is used to modify the input into the CAM module so that the more dominant of two mingling odors or an odor increasing against a background of odors is more readily identified. The performance of the network is evaluated using Monte Carlo simulations and numerical results are presented.

A kinetic model of the transient phase in the response of olfactory receptor neurons.

A model is presented that predicts the instantaneous spike rate of an olfactory receptor neuron (ORN) in response to the quality and concentration of an odor stimulus. The model accounts for the chemical kinetics of ligand-receptor binding and activation processes, and implicitly the initiation of second messenger cascades that lead to depolarization and/or hyperpolarization of the ORN membrane. Both of these polarizing processes are included in the most general form of the model, as well as a process that restores the voltage to its negative resting state. The spike rate is assumed to be linearly proportional to the level of voltage depolarization above a critical negative voltage level. The model includes the simplifying assumption that activation of bound ligand-receptor complexes by G-proteins and other enabling molecules follows a Monod function that has the ratio of enabling molecules to bound unactivated ligand-receptor complexes as its argument. Parameters are selected that provide an excellent fit of the model to previously published empirical data on the response of cockroach ORNs to pulsed 1-hexanol stimuli. The sensitivity of model output to various model parameters is investigated and changes to parameters are discussed that would improve the ability of ORNs to follow rapidly pulsed stimuli.

Invasion and maintenance of alleles that influence mating and parental success.

Here we develop a model of the invasion, polymorphism, fixation and extinction analysis of genes that differentially influence the mating and parenting success of the two sexes. The model could have application, for example, to the maintenance of homosexuality in diploid populations. The analysis focuses on systems in which mating success is density-dependent and contrasts the results with the density-independent case. Five situations are analyzed, including cases where male and female parenting success is affected in the same and in different directions by the alleles in question. As part of the analysis, a technique is outlined for identifying boundaries between regions where polymorphisms occur and regions where the alleles under consideration go either to fixation or extinction. The results indicate that, unlike in the density-independent case, in the density-dependent case the degree of dominance of the types of alleles analyzed here critically determines whether such alleles are able to invade a population, exist as a polymorphism, or go to fixation.

An odor discrimination model with application to kin recognition in social insects.

The problem of discriminating between a number of similar, nonspecific odors is discussed with special reference to the phenomenon of kin and nestmate discrimination in social insects. Guided by the basic physiological and anatomical features of the olfactory sensory receptors and neural pathways in insects, a model is presented for the process of odor discrimination. The model hypothesizes neural processing capabilities that include the logarithmic transformations of electrical potentials to generate a scalar quantity representing the "similarity" of two multivalued signals. The model thereby quantifies the notion of phenotype matching that appears in the kin recognition literature, and makes the concept of a recognition template more precise. The hypotheses underlying the model suggest a number of neurophysiological studies that should be undertaken, while the model itself provides a basis for integrating several areas of research pertaining to kin recognition in particular species of animals.

Receptor dissociation constants and the information entropy of membranes coding ligand concentration.

The binding of ligands to receptor proteins embedded in cell membranes drives cellular responses that involve either second messenger cascades or directly gated ion channels. It is known that a single class of receptor proteins expresses approximately 98% of its graded response to ligand concentrations over four orders of magnitude, where the response is measured by the equilibrium proportion of bound ligand-receptor complexes. This four-decadic concentration range is centered on a logarithmic scale around logK, where K is the dissociation constant defined by the ratio of ligand-receptor unbinding (k-) to binding (k+) rates. Remarkably, this four-decadic concentration range is intrinsic to all homogeneous ligand-receptor (or, equivalently, enzyme-substrate) systems. Thus, adapting the sensitivity of cell membranes to narrower or wider ranges of ligand concentrations, respectively, requires multivalent receptors or heterogeneous populations of receptors. Here we use a normalized Shannon-Weaver measure of information entropy to represent the efficiency of coding over given concentrations for membranes containing a population of univalent receptors with a specified distribution of dissociation constants, or a homogeneous population of strongly cooperative multivalent receptors. Assuming a specified level of resolution in the response of cellular or neural systems downstream from the membrane that 'read' the ligand concentration 'code', we calculate the range of concentrations over which the coding efficiency of the membrane itself is maximized. Our results can be used to hypothesize the number of receptor types associated with the membranes of particular cells. For example, from data in the literature, we conclude that the response of most general olfactory sensory neurons can be explained in terms of a homogeneous population of receptor proteins, while the response of pheromone sensory neurons is satisfactorily explained by the presence of two types of membrane receptor protein with pheromone-binding dissociation constants that have values at least one to two orders of magnitude apart.

Receptor heterogeneity and its effect on sensitivity and coding range in olfactory sensory neurons.

Signal processing in the olfactory system is initiated by binding of odorant molecules to receptor molecules embedded in the membranes of sensory neurons. Most analyses of odorant-receptor interaction focus on one or more types of odorants binding with one type of receptors. Here, two basic models of this first step are investigated under the assumption that the population of receptors is not homogenous and is characterized by different activation/deactivation rates. Both, discrete and continuous variation of the rates are considered. The steady-state characteristics of the models are derived. In addition, time to crossing a threshold, defined as a response time, is also investigated. The achieved results are compared with those valid for models with the homogenous population of receptors and interpreted in terms of information coding. The obvious implications of the modeling study--that the heterogeneity of receptors enlarges the coding range and increases the sensitivity of the system--are quantified.

Honeybee olfactory sensilla behave as integrated processing units.

Honeybee placode sensilla contain 18-35 olfactory receptor neurons. In insects, such neurons are thought to not interact with one another before reaching the central nervous system. Extracellular, multiunit recordings were made from the placodes and separated into spike shape classes, termed subplacode units. An analysis of the response spectra of subplacode units demonstrated that subplacode units with similar response spectra were more likely to be found in different placodes than in the same placode. An analysis was made of the mean interspike intervals and its variation for whole placodes and subplacode units. The coefficient of variation for whole placodes was less than that for subplacode units. Whole placode spike trains are therefore more uniform than subplacode spike trains, indicating that neurons might not be firing independently of each other.

A neural network model of general olfactory coding in the insect antennal lobe.

A central problem in olfaction is understanding how the quality of olfactory stimuli is encoded in the insect antennal lobe (or in the analogously structured vertebrate olfactory bulb) for perceptual processing in the mushroom bodies of the insect protocerebrum (or in the vertebrate olfactory cortex). In the study reported here, a relatively simple neural network model, inspired by our current knowledge of the insect antennal lobes, is used to investigate how each of several features and elements of the network, such as synapse strengths, feedback circuits and the steepness of neural activation functions, influences the formation of an olfactory code in neurons that project from the antennal lobes to the mushroom bodies (or from mitral cells to olfactory cortex). An optimal code in these projection neurons (PNs) should minimize potential errors by the mushroom bodies in misidentifying the quality of an odor across a range of concentrations while maximizing the ability of the mushroom bodies to resolve odors of different quality. Simulation studies demonstrate that the network is able to produce codes independent or virtually independent of concentration over a given range. The extent of this range is moderately dependent on a parameter that characterizes how long it takes for the voltage in an activated neuron to decay back to its resting potential, strongly dependent on the strength of excitatory feedback by the PNs onto antennal lobe intrinsic neurons (INs), and overwhelmingly dependent on the slope of the activation function that transforms the voltage of depolarized neurons into the rate at which spikes are produced. Although the code in the PNs is degraded by large variations in the concentration of odor stimuli, good performance levels are maintained when the complexity of stimuli, as measured by the number of component odorants, is doubled. When excitatory feedback from the PNs to the INs is strong, the activity in the PNs undergoes transitions from initial states to stimulus-specific equilibrium states that are maintained once the stimulus is removed. When this PN-IN feedback is weak the PNs are more likely to relax back to a stimulus-independent equilibrium state, in which case the code is not maintained beyond the application of the stimulus. Thus, for the architecture simulated here, strong feedback from the PNs onto the INs, together with step-like neuronal activation functions, could well be important in producing easily discriminable odor quality codes that are invariant over several orders of magnitude in stimulus concentration.

Variability of chemosensory stimuli within honeybee (Apis mellifera) colonies: Differential conditioning assay for discrimination cues.

Differential training of honeybee workers using the proboscis extension reflex is applied to the problem of evaluating compounds that may potentially provide cues for kin recognition in the honeybeeApis mellifera. These cues were obtained by contaminating glass rods and steel needles with different materials found in the hive. In particular it is shown that workers discriminate between: cuticular waxes from different adult workers; eggs from the same and different hives; similar aged larvae within the same hive; and needles contaminated with the Nasonov gland secretions of different adult workers. It appears that some of these differences are due to phenotypic variation among individuals that cannot be directly attributed to environmental factors.

Host-parasite dynamics and the evolution of host immunity and parasite fecundity strategies.

We explore evolutionarily stable co-evolution of host-macroparasite++ interactions in a discrete-time two-species population dynamics model, in which the dynamics may be stable, cyclic or chaotic. The macroparasites are assumed to harm host individuals through decreased reproductive output. Hosts may develop costly immune responses to defend themselves against parasites. Parasites compete with conspecifics by adjusting their fecundities. Overall, the presence of both parasites and the immune response in hosts produces more stable dynamics and lower host population sizes than that observed in the absence of the parasites. In our evolutionary analyses, we show that maximum parasite fecundity is always an evolutionarily stable strategy (ESS), irrespective of the type of population interaction, and that maximum parasite fecundity generally induces a minimum parasite population size through over-exploitation of the host. Phenotypic polymorphisms with respect to immunity in the host species are common and expected in ESS host strategies: the benefits of immunication depend on the frequency of the immune hosts in the population. In particular, the steady-state proportions of immune hosts depend, in addition to all the parameters of the parasite dynamics only on the cost of immunity and on the virulence of parasites in susceptible hosts. The implicit ecological dynamics of the host-parasite interaction affect the proportion of immune host individuals in the population. Furthermore, when changes in certain population parameters cause the dynamics of the host-parasite interaction to move from stability to cyclicity and then to chaos, the proportion of immune hosts tend to decrease; however, we also detected counter-examples to this result. As a whole, incorporating immunological and genetic aspects, as well as life-history trade-offs, into host-macroparasite dynamics produces a rich extension to the patterns observed in the models of ecological interactions and epidemics, and deserves more attention than is currently the case.