Quantitative analyses of observing and attending

We review recent experiments examining whether simple models of the allocation and persistence of operant behavior are applicable to attending. In one series of experiments, observing responses of pigeons were used as an analog of attending. Maintenance of observing is often attributed to the conditioned reinforcing effects of a food-correlated stimulus (i.e., S+), so these experiments also may inform our understanding of conditioned reinforcement. Rates and allocations of observing were governed by rates of food or S+ delivery in a manner consistent with the matching law. Resistance to change of observing was well described by behavioral momentum theory only when rates of primary reinforcement in the context were considered. Rate and value of S+ deliveries did not affect resistance to change. Thus, persistence of attending to stimuli appears to be governed by primary reinforcement rates in the training context rather than conditioned reinforcing effects of the stimuli. An additional implication of these findings is that conditioned "reinforcers" may affect response rates through some mechanism other than response-strengthening. In a second series of experiments, we examined the applicability of the matching law to the allocation of attending to the elements of compound stimuli in a divided-attention task. The generalized matching law described performance well, and sensitivity to relative reinforcement varied with sample duration. The bias and sensitivity terms of the generalized matching law may provide measures of stimulus-driven and goal-driven control of divided attention. Further application of theories of operant behavior to performance on attention tasks may provide insights into what is referred to variously as endogenous, top-down, or goal-directed control of attention.     

Haloperidol, dynamics of choice, and the parameters of the matching law

The idea that dopamine mediates the reinforcing effects of stimuli persists in the field of neurosciences. The present study shows that haloperidol, a dopamine antagonist, does not eliminate the reinforcing value of food reinforcers. The ratio of reinforcers changed seven times across two levers within sessions, modeling a dynamic environment. The magnitude of the reinforcer was manipulated independently of the reinforcer ratio. Four doses of intraperitoneal haloperidol were assessed over periods of 12 daily sessions. Haloperidol did not impair the discrimination that the rats established between rich and lean levers; the response distributions favored the lever associated with the higher probability of reinforcement and the larger pellets. The parameters of the generalized matching law (bias and sensitivity) were used to estimate effects of haloperidol upon the motor system and upon the rats' motivation for food reinforcers.     

Comparing the generalized matching law and contingency discriminability model as accounts of concurrent schedule performance using residual meta-analysis

To compare the generalized matching law (Baum, W.M., 1974b. On two types of deviation from the matching law: bias and undermatching. J. Exp. Anal. Behav. 22, 231-242) and contingency discriminability model (Davison, M., Jenkins, P.E., 1985. Stimulus discriminability, contingency discriminability, and schedule performance. Anim. Learn. Behav. 13, 77-84) as accounts of concurrent schedule performance, we conducted a residual meta-analysis of response- and time-allocation data from 20 studies (n's=886 and 774, respectively). Both models were fitted to the individual-subject data from each study, and residuals were obtained. Polynomial regressions were then performed on the pooled residuals to determine whether systematic trends were present as a function of predicted values. For the contingency discriminability model, the cubic coefficients were positive and statistically significant for both response- and time-allocation data. By contrast, no statistically significant systematic trend was obtained in the residuals for the generalized matching law. These results suggest that the relationship between log response allocation and log reinforcer allocation does not deviate significantly from linearity over an approximate range of +1.25 to -1.25 log units, consistent with the generalized matching law. Although qualitative criteria are also important in comparing models of behavioral phenomena, residual meta-analysis provides a powerful quantitative methodology for model selection and should prove useful in future research.     

Risk-Prone Behaviour Under Rules Which Have Evolved in a Changing Environment

This paper deals with risk sensitivity in amount of food, andis concerned with modelling the risk-sensitive behaviour exhibitedby an animal which is attempting to survive a period such aswinter. I argue that, in maximising survival probability, risk-aversebehaviour is much more important than risk-prone behaviour.I also argue that animals in the laboratory will continue touse rules which are adapted to food sources which change overtime. A model of environmental change is investigated. Thismodel predicts that a consequence of change is that less riskpronebehaviour than that predicted by standard models is to be expectedin laboratory studies. The need to learn about a stochasticfood source in a changing environment is predicted to furtherreduce the incidence of risk-prone behaviour. It is difficultto learn about highly variable food sources. This is shown tolead to risk-aversion even when the optimisation criterion ismaximisation of mean long-term rate of food gain. Implications of the general modelling philosophy are discussed.     

Detection probability in aerial surveys of feral horses

Observation bias pervades data collected during aerial surveys of large animals, and although some sources can be mitigated with informed planning, others must be addressed using valid sampling techniques that carefully model detection probability. Nonetheless, aerial surveys are frequently employed to count large mammals without applying such methods to account for heterogeneity in visibility of animal groups on the landscape. This often leaves managers and interest groups at odds over decisions that are not adequately informed. I analyzed detection of feral horse (Equus caballus) groups by dual independent observers from 24 fixed-wing and 16 helicopter flights using mixed-effect logistic regression models to investigate potential sources of observation bias. I accounted for observer skill, population location, and aircraft type in the model structure and analyzed the effects of group size, sun effect (position related to observer), vegetation type, topography, cloud cover, percent snow cover, and observer fatigue on detection of horse groups. The most important model-averaged effects for both fixed-wing and helicopter surveys included group size (fixed-wing: odds ratio = 0.891, 95% CI = 0.850–0.935; helicopter: odds ratio = 0.640, 95% CI = 0.587–0.698) and sun effect (fixed-wing: odds ratio = 0.632, 95% CI = 0.350–1.141; helicopter: odds ratio = 0.194, 95% CI = 0.080–0.470). Observer fatigue was also an important effect in the best model for helicopter surveys, with detection probability declining after 3 hr of survey time (odds ratio = 0.278, 95% CI = 0.144–0.537). Biases arising from sun effect and observer fatigue can be mitigated by pre-flight survey design. Other sources of bias, such as those arising from group size, topography, and vegetation can only be addressed by employing valid sampling techniques such as double sampling, mark–resight (batch-marked animals), mark–recapture (uniquely marked and identifiable animals), sightability bias correction models, and line transect distance sampling; however, some of these techniques may still only partially correct for negative observation biases. © 2011 The Wildlife Society.     

The bias due to incomplete matching

Observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments. Matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group. In practice, there is a trade-off between the desires to find matches for all treated units and to obtain matched treated-control pairs that are extremely similar to each other. We derive expressions for the bias in the average matched pair difference due to the failure to match all treated units--incomplete matching, and the failure to obtain exact matches--inexact matching. A practical example shows that the bias due to incomplete matching can be severe, and moreover, can be avoided entirely by using an appropriate multivariate nearest available matching algorithm, which, in the example, leaves only a small residual bias due to inexact matching.     

A two-stage model for concurrent sequences

Schneider and Davison [Schneider, S.M., Davison, M., 2005. Demarcated response sequences and the generalised matching law. Behav. Proc. 70, 51–61] showed that the generalised matching law applied to concurrent free-operant two-response sequences. When sufficient temporal spacing is required between the responses, however, neither the response-level nor the sequence-level forms of the generalised matching law provide good fits. An alternative “two-stage sensitivity” model with fewer free parameters features two types of sensitivity to the reinforcement contingencies on sequences. When temporal spacing between the responses is long, the “response distribution sensitivity” parameter describes sensitivity only of the individual responses to the sequence-level contingencies. At a threshold level, this sensitivity reaches a maximum. When spacing is shorter than threshold, the “response order sensitivity” parameter reflects a new sensitivity to the order of the responses within sequences. As this sensitivity approaches its maximum, sequence matching is achieved. For both stages, a changeover parameter describes bias against sequences that require changeovers between the two responses. The model fit data ranging from near-response matching with long minimum inter-response times (IRTs) to sequence matching with no minimum IRTs, using two species and a variety of sequence reinforcer distributions. Rats differed from pigeons in achieving sequence matching only at a nonzero minimum IRT. In a comparison based on pigeon data with no minimum IRT, the two-stage sensitivity model was more efficient than the generalised matching law according to the Akaike criterion. The logic of the model suggests a new way of understanding the mechanisms underlying behavioural units.     

Self-similarity in species–area relationship and in species abundance distribution

In an influential paper, Harte et al. highlighted the scaling or 'self-similar' character of the power law species–area relationship (SAR), and used this feature to derive a species abundance distribution (SAD) and an endemics–area relationship. Here I show that their analysis was incorrect and leads to unrealistic results. I develop a different approach and obtain different results, both for SAD and for endemism. In particular, I show that the power law SAR is naturally associated with the power law statistical distribution, which is the only self-similar distribution and closely matches empirical SADs. The results in this paper shed light on some of the main issues that have been discussed with regard to SARs: their relationship with the lognormal and with the neutral theory, the relative importance of sampling effects vs other mechanisms, and the deviations from a power law. The equations that I develop are simple and easy to apply to field studies.     

Copepod feeding in the ocean: scaling patterns,composition of their diet and the bias of estimates due to microzooplankton grazing during incubations

Here, we report insights from the compilation and analysis of data on marine calanoid copepod feeding rates in the ocean. Our study shows that food availability and body weight are major factors shaping copepod feeding rates in the field, with a relatively minor role of temperature. Although the maximal feeding rates of copepods that are observed in the field agree with the well-known 3/4 of body size scaling rule for animals, copepod feeding in the oceans is typically limited and departs from this rule. Ciliates and dinoflagellates appear to be highly relevant in the composition of copepod diets, and this represents an indirect increase in the flux of primary production that is likely to reach the upper trophic levels; this contribution is higher in the less productive systems and may help to explain accounts of proportionally higher standing stocks of copepods supported per unit of primary producer biomass in oligotrophic environments. Contrary to common belief, diatoms emerge from our dataset as small contributors to the diet of copepods, except in some very productive ecosystems. We have also evaluated the bias in the estimation of copepod grazing rates due to within-bottle trophic cascade effects caused by the removal of microheterotrophs by copepods. This release of microzooplankton grazing pressure accounts for a relevant, but moderate, increase in copepod grazing estimates (ca. 20–30%); this bias has an effect on both the carbon flux budgets through copepods and on our view of their diet composition. However, caution is recommended against the indiscriminate use of corrections because they may turn out to be overestimates of the bias. We advise that both uncorrected and corrected grazing rates should be provided in future studies, as they probably correspond to the lower and upper boundaries of the true grazing rates.     

A sample size formula for the supremum log-rank statistic

An advantage of the supremum log-rank over the standard log-rank statistic is an increased sensitivity to a wider variety of stochastic ordering alternatives. In this article, we develop a formula for sample size computation for studies utilizing the supremum log-rank statistic. The idea is to base power on the proportional hazards alternative, so that the supremum log rank will have the same power as the standard log rank in the setting where the standard log rank is optimal. This results in a slight increase in sample size over that required for the standard log rank. For example, a 5.733% increase occurs for a two-sided test having type I error 0.05 and power 0.80. This slight increase in sample size is offset by the significant gains in power the supremum log-rank test achieves for a wide range of nonproportional hazards alternatives. A small simulation study is used for illustration. These results should facilitate the wider use of the supremum log-rank statistic in clinical trials.     

The ideal free distribution of clonal plant's ramets among patches in a heterogeneous environment

The plastic response of clonal plant to different patch quality is not always the same and the degree is different too. So the result of this kind of foraging behaviour is different. In order to make clear whether the ramtes stay in favourable patches and get the quantitative relationship between the ramets distribution among patches and the available resource amount in heterogeneous environment, we develop a theoretical work under ideal free distribution (IFD) theory framework by neglecting some morphological plasticity of the spacer in this article. The results of our general model show that the ramet distribution should obey input matching rule at equilibrium. That means the ratio of ramet number in different patches should be equal to the ratio of available resource amount in these patches. We also use the simulation to predict the distribution pattern under history mattering. The results show that the initial ramets number has significant influence on the final distribution: over matching and under matching both can occur. More initial ramets in favourable patch result in over matching and more initial ramets in unfavourable patch result in under matching. The degree of the deviation from input matching rule is great when the difference of patches is small. These results prove that ideal free distribution theory works the same with animals. The ramets can stay in favourable patches sometimes in spite of the plasticity of the spacer, and the distribution depends on both patch quality and the history factors. But these results are true only when the functional response is type II.     

Momentary maximizing and optimal foraging theories of performance on concurrent VR schedules

Optimal foraging theory proposes that animals obtain the highest rate of reinforcers for the least effort and momentary maximizing theory proposes that animals make the response that at that instant is most likely to be reinforced. While each theory may account for matching on concurrent schedules, the data supporting each theory are weak. Two experiments assessed these theories by considering concurrent choice as consisting of two pairs of stay and switch schedules. Symmetrical arrangements, which are equivalent to standard concurrent schedules, maintained behavior described by the generalized matching law. Weighted arrangements, in which the programmed rate of earning reinforcers was always greater at one alternative, maintained behavior that was biased towards the weighted alternative, yet the bias was less than that predicted by optimal foraging theory. Asymmetrical arrangements, in which the stay and switch schedules operating at an alternative are the same, maintained behavior that favored one alternative, even though momentary maximizing predicted indifference. The generalized matching law poorly described each rat's pooled data from all conditions but these data were described by an equation based on the stay and switch reinforcers earned per-visit and included elements of optimal foraging and momentary maximizing theories of choice.     

Habitat matching: Alternatives and implications to populations and communities

Summary I evaluate habitat matching rules based on ideal distribution models of density-dependent habitat use. Recent approaches and the ideal free continuous input matching rule on which they depend, are restricted to only those habitats that are jointly occupied across the full range of population sizes. These assumptions may often be inappropriate to field applications of habitat matching. I develop alternatives that can be applied to a wide array of ideal forms of habitat selection, including the ideal free, continuous input example. Input matching can be distinguished from assumptions of consumer-resource models and preemptive habitat use by regressions of density between paired habitats (isodars). Isodars for continuous input models should be linear on a logarithmic scale, while those for consumer-resource models should be linear on an arithmetic scale. Pre-emptive isodars can be distinguished from the others by dramatic non-linearities at both low and high densities. Field data on white-footed mice support the consumer-resource theory. Implications of the rules for population regulation and community organization are highlighted by new models that specify how the fitness of pre-emptive habitat selectors should decline with increasing density. Strong non-linearities produced by comparisons between variable and homogeneous habitats produce reversing source-sink population regulation and a new form of cyclical community dynamics. Variable habitats act as a source of emigrants at low density and a sink for immigrants at high density. Subordinate species may occupy only the variable habitat at both low and high density.     

A method for estimating population sex ratio for sage‐grouse using noninvasive genetic samples

Population sex ratio is an important metric for wildlife management and conservation, but estimates can be difficult to obtain, particularly for sexually monomorphic species or for species that differ in detection probability between the sexes. Noninvasive genetic sampling (NGS) using polymerase chain reaction (PCR) has become a common method for identifying sex from sources such as hair, feathers or faeces, and is a potential source for estimating sex ratio. If, however, PCR success is sex‐biased, naively using NGS could lead to a biased sex ratio estimator. We measured PCR success rates and error rates for amplifying the W and Z chromosomes from greater sage‐grouse (Centrocercus urophasianus) faecal samples, examined how success and error rates for sex identification changed in response to faecal sample exposure time, and used simulation models to evaluate precision and bias of three sex assignment criteria for estimating population sex ratio with variable sample sizes and levels of PCR replication. We found PCR success rates were higher for females than males and that choice of sex assignment criteria influenced the bias and precision of corresponding sex ratio estimates. Our simulations demonstrate the importance of considering the interplay between the sex bias of PCR success, number of genotyping replicates, sample size, true population sex ratio and accuracy of assignment rules for designing future studies. Our results suggest that using faecal DNA for estimating the sex ratio of sage‐grouse populations has great potential and, with minor adaptations and similar marker evaluations, should be applicable to numerous species.     

The biochemical composition and calorific content of a rotifer and its algal food: comparison of a two stage chemostat and batch culture

It is often assumed that the use of a two-stage chemostat yields algal food with a well-defined nutritional composition that can maintain herbivores in a steady state of growth. In this study I investigated two bacteriafree culture techniques, continuous flow chemostats and batch cultures, to determine whether the biochemical composition of the rotifer Encentrum linnhei differed in the two cultures. Changes in the biochemical composition and calorific content of the algal food were also examined. In the rotifer reaction vessel only the lipid content of the algal food increased significantly with dilution rates, while significant decreases in protein and carbohydrates were detected at increasing algal densities. A different pattern was observed in the response of the unused algal cells to variables such as dilution, algal input and algal densities in the sump of the rotifer chemostat. In the chemostat the biochemical composition of the rotifers varied as expected with dilution rates, algal input and food availability but significant differences were found in the biochemical composition of the animals growing in the reaction vessel and those collected from the sump. In contrast, the biochemical content of batch-grown E. linnhei varied with time in a way that depended upon food availability and also on the biochemical state of the algal food. However, at the end of the exponential phase of growth, when maximum densities had been achieved, batch-grown rotifers were more biochemically nutritious than chemostat-grown animals in their steady-state phase.     

Shared Mycobacterium avium Genotypes Observed among Unlinked Clinical and Environmental Isolates

Our understanding of the sources of Mycobacterium avium infection is partially based on genotypic matching of pathogen isolates from cases and environmental sources. These approaches assume that genotypic identity is rare in isolates from unlinked cases or sources. To test this assumption, a high-resolution PCR-based genotyping approach, large-sequence polymorphism (LSP)-mycobacterial interspersed repetitive unit–variable-number tandem repeat (MIRU-VNTR), was selected and used to analyze clinical and environmental isolates of M. avium from geographically diverse sources. Among 127 clinical isolates from seven locations in North America, South America, and Europe, 42 genotypes were observed. Among 12 of these genotypes, matches were seen in isolates from apparently unlinked patients in two or more geographic locations. Six of the 12 were also observed in environmental isolates. A subset of these isolates was further analyzed by alternative strain genotyping methods, pulsed-field gel electrophoresis and MIRU-VNTR, which confirmed the existence of geographically dispersed strain genotypes. These results suggest that caution should be exercised in interpreting high-resolution genotypic matches as evidence for an acquisition event.     

Linking recruitment to trophic factors: revisiting the Beverton--Holt recruitment model from a life history and multispecies perspective

The Beverton--Holt recruitment model can be derived from arguments about evolution of life history traits related to foraging and predation risk, along with spatially localized and temporarily competitive relationships in the habitats where juvenile fish forage and face predation risk while foraging. This derivation explicitly represents two key biotic factors, food supply (I) and predator abundance (R), which appear as a risk ratio (R/I) that facilitates modelling of changes in trophic circumstances and analysis of historical data. The same general recruitment relationship is expected whether the juvenile life history is simple or involves a complex sequence of stanzas; in the complex case, the Beverton--Holt parameters represent weighted averages or integrals of risk ratios over the stanzas. The relationship should also apply in settings where there is complex, mesoscale variation in habitat and predation risk, provided that animals sense this variation and move about so as to achieve similar survival at all mesoscale rearing sites. The model predicts that changes in food and predation risk can be amplified violently in settings where juvenile survival rate is low, producing large changes in recruitment rates over time.     

Dinosaur Metabolism and the Allometry of Maximum Growth Rate

The allometry of maximum somatic growth rate has been used in prior studies to classify the metabolic state of both extant vertebrates and dinosaurs. The most recent such studies are reviewed, and their data is reanalyzed. The results of allometric regressions on growth rate are shown to depend on the choice of independent variable; the typical choice used in prior studies introduces a geometric shear transformation that exaggerates the statistical power of the regressions. The maximum growth rates of extant groups are found to have a great deal of overlap, including between groups with endothermic and ectothermic metabolism. Dinosaur growth rates show similar overlap, matching the rates found for mammals, reptiles and fish. The allometric scaling of growth rate with mass is found to have curvature (on a log-log scale) for many groups, contradicting the prevailing view that growth rate allometry follows a simple power law. Reanalysis shows that no correlation between growth rate and basal metabolic rate (BMR) has been demonstrated. These findings drive a conclusion that growth rate allometry studies to date cannot be used to determine dinosaur metabolism as has been previously argued.     

Growth responses of littoral mayflies to the phosphorus content of their food

We examined how mayfly growth rates and body stoichiometry respond to changing phosphorus (P) content in food. In two experiments, mayfly nymphs were given high or low quantities of food at different carbon:phosphorus (C:P) ratios and their growth was measured. Low food quantity resulted in negative growth rates in both experiments, regardless of food P content. However, under high food availability, mayfly growth was affected by the type of food eaten, with low C:P ratio food producing more rapid growth. In addition, mayfly growth increased somewhat when P-poor food was artificially enriched with inorganic P although this effect was not statistically significant. Mayfly body P content was inversely related to body size but increased in animals fed artificially P-enriched food. A model was constructed to simulate mass balance constraints on mayfly growth imposed by the relative supply of two elements (C and P) in food. The model shows that mayfly growth should be limited by food P content at moderately low C:P ratios ( c . 120, by mass). Given high C:P ratios (mean c.  270, by mass) in periphyton from oligotrophic boreal lakes, our experimental and theoretical results indicate that stoichiometric constraints are important factors affecting benthic food webs in lakes from the Canadian Shield and perhaps in other systems with similarly high C:P ratios in periphyton.     

Habitat selection by predators and prey in communities with asymmetrical intraguild predation

Competition and predation have broad ecological consequences as they may influence individual behavior and community structure. In some cases, they are linked and predator and prey are also competitors (intraguild predation). I present a game theoretic model of habitat use by predators and prey under conditions of asymmetrical intraguild predation. This model predicts that when the diet of intraguild predators is restricted to intraguild prey and the resource for which predators and prey compete (the basal resource), co-occurrence is only stable when dietary overlap is low and productivity of the basal resource is not high. The addition of alternative resources for predators results in co-occurrence under all conditions. Variation in alternative resource productivity produces a continuum of intraguild prey distributions from matching relative habitat safety, to one that reflects both food and predation risk. When there is a substantial alternative resource for predators, the distribution of predators matches that of alternative resource availability while the distribution of prey is influenced by both habitat riskiness and food availability. The density and distribution of the predator's alternative resource thus influence habitat selection by the intraguild prey. This stresses the importance of indirect interactions in structuring habitat use in communities and the need to view habitat selection in a community context.