Within-Treatments Comparison of Binary and Trinary Choice Trials

<p>The bars show the mean (± s.e.) absolute (FD and FA) and relative (FA*) proportion of choices for each option in the binary (white bars) and trinary (black bars) trials for group NC (A and C) or group C (B and D). Relative preferences were calculated using <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020402#pbio-0020402-e001" target="_blank">equation 1</a> (see text). We compared the preference for the same options between the binary and trinary contexts of the same treatment (when there are no differential energetic effects). There were no violations of either regularity or the constant-ratio rule (<i>p</i> > 0.1).</p

Between-Treatments Comparison in Binary and Trinary Choice Trials

<p>The bars show the mean (± s.e.) absolute (FD and FA: leftmost and centre pairs of columns in each panel, respectively) and relative (FA*: rightmost pair of columns in each panel) proportion of choices for each option in binary (white bars) and trinary (black bars) trials when intake rate is not controlled (group NC: A and C; white background) or is controlled (group C: B and D; grey background). Relative preferences were calculated using <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020402#pbio-0020402-e001" target="_blank">equation 1</a> (see text). We compared the preference between the same two focal options between the binary context of one treatment (e.g., treatment “High Intake”) and the trinary of the other (e.g., treatment “Low Intake”). In group C (B and D), none of the differences between binary and trinary contexts were statistically significant. For group NC (A and C), the asterisk (*) indicates a significant violation of either regularity or the constant-ratio rule at <i>p</i> < 0.05.</p

Discrimination Test

<p>Proportion of choices (± standard error [s.e.]) made by birds for the option offering the largest amount of food when time parameters were held constant. Choice proportions are significantly different from random for all birds (binomial test, <i>p</i> < 0.01). Birds 1, 2, and 3 (white bars) were presented with choices between one and two units of food, and birds 4, 5, and 6 (black bars) with choices between two and five units of food.</p

Individual Proportion of Choices for FA Relative to FD in Treatments “High Intake” and “Low Intake”

<div><p>(A) Effect of intake on choices without decoys. Here, extra food simulates the intake consequences that the two decoys cause when they are present and consumed on 25% of the feeding opportunities (<i>p</i> < 0.01).</p> <p>(B) Results of an experiment with decoys when energetic consequences of the decoys were allowed to take effect (group NC) (<i>p</i> = 0.06).</p> <p>(C) Results of an experiment with decoys, similar to (B), in which the energetic consequences of the decoys were abolished (group C).</p> <p>In (B) and (C), each symbol corresponds to each of the subjects. The dashed lines show the mean values in each of the cases.</p></div

A Functional Model of How State Can Affect Partial Preferences

<div><p>(A) Fitness is plotted as a concave function of the organism's state. Exposure to DD leads to a poorer state (Sd_D) than that reached after exposure to DA (Sd_A) (see also B). Sd_D + FD and Sd_D + FA denote the state reached by subjects under treatment “Low Intake” as a consequence of choosing focal options FD and FA, respectively. Similarly, Sd_A + FD and Sd_A + FA represent the state reached by subjects in treatment “High Intake” after choosing FD and FA, respectively.</p> <p>(B) State is assumed to be a growing, linear function of energy intake. DD and DA represent the average intake rates experienced by subjects that include the decoys with the same names in their diet.</p> <p>Although choosing FA is always better than choosing FD, and the difference between the states caused by this choice is the same under either treatment (Sd_D and Sd_A), the fitness difference between choosing FA and FD is higher under treatment “Low Intake” (δDD) than “High Intake” (δDA). This should lead to a higher level of preference for FA in the former treatment if choices of the low-yielding option were to be reduced in proportion to their cost.</p></div

Amount and Delay to Food Corresponding to Each Option

<p>The figure shows the parameters of the experiments using the conventional representation used in foraging theory, with energy gains in the ordinate and time in the abscissa. The origin of coordinates is the point of choice, so that time to the right indicates the delay between choice and reward, while time to the left represents all other times in the cycle, in this case the ITI. The options forming the focal choice pair are shown as white circles while those used as decoys are shown by black circles. FA and FD offer the same short-term rate of food intake (slope of the solid lines) of 0.5 units/s, whereas DA and DD offer the same short-term rate of 0.25 units/s. The slopes of the dashed lines (interrupted for space economy) indicate long-term rate of intake, considering the inter-trial interval of 60 s between consecutive feeding opportunities. “High intake” (horizontally adjacent rectangles) and “low intake” (vertically adjacent rectangles) denote the treatments in which decoy DA and DD (or their simulated energetic consequences), respectively, were present in addition to the focal pair. Since DA offers a higher long-term rate of gain than DD, intake is higher in the treatment where DA is present (“High Intake”). The reverse rationale applies to treatment “Low Intake.”</p

Additional file 1: Table S1. of Estimates of hospitalization attributable to influenza and RSV in the US during 1997–2009, by age and risk status

Seasonal burden of hospitalization attributable to influenza and RSV by season in the US, 1997–2009 (respiratory broad outcome, any mention). 1Annual mean rate per 100,000 population; *Data included up to 31st March 2009; CI: confidential interval. Table S2. Number of hospitalizations attributable to influenza and RSV according to risk status and age in the US, 1997–2009 (respiratory broad outcome, any mention). SD: standard deviation; RSV: respiratory syncytial virus. (DOCX 42 kb

Modeling the Impact of Alternative Immunization Strategies: Using Matrices as Memory Lanes

<div><p>Existing modeling approaches are divided between a focus on the constitutive (micro) elements of systems or on higher (macro) organization levels. Micro-level models enable consideration of individual histories and interactions, but can be unstable and subject to cumulative errors. Macro-level models focus on average population properties, but may hide relevant heterogeneity at the micro-scale. We present a framework that integrates both approaches through the use of temporally structured matrices that can take large numbers of variables into account. Matrices are composed of several bidimensional (time×age) grids, each representing a state (e.g. physiological, immunological, socio-demographic). Time and age are primary indices linking grids. These matrices preserve the entire history of all population strata and enable the use of historical events, parameters and states dynamically in the modeling process. This framework is applicable across fields, but particularly suitable to simulate the impact of alternative immunization policies. We demonstrate the framework by examining alternative strategies to accelerate measles elimination in 15 developing countries. The model recaptured long-endorsed policies in measles control, showing that where a single routine measles-containing vaccine is employed with low coverage, any improvement in coverage is more effective than a second dose. It also identified an opportunity to save thousands of lives in India at attractively low costs through the implementation of supplementary immunization campaigns. The flexibility of the approach presented enables estimating the effectiveness of different immunization policies in highly complex contexts involving multiple and historical influences from different hierarchical levels.</p></div

Additional file 1: Table S1. of Modelling estimates of age-specific influenza-related hospitalisation and mortality in the United Kingdom

Outcomes: hospitalisations (HES) and deaths (ONS). Table S2. Definition of risk factors; any mention of any of these codes placed the patient in the “high-risk” category. Table S3. Mean number of other hospitalisations due to non-respiratory diagnoses attributable to influenza in the United Kingdom. Table S4. Mean number of deaths due to respiratory diagnoses attributable to influenza in the United Kingdom. (DOCX 85 kb

Diagram summarizing the events each age cohort can experience in an annual cycle (it can be also understood as the outcomes an individual may experience each year).

<p>The cycle starts (left) and ends (right) with the proportions of susceptible and immune individuals. Events (vaccinations, infections, mortality) during the cycle change the proportions exported for the next cycle and generate intermediate outcomes of interest (proportions of cases and deaths). Each box represents a matrix of 104 age-groups × 71 years. Probabilities are depicted in the small white boxes: C: Vaccine coverage, E: Vaccine efficiency, F: Force of infection, D: Case fatality ratios, and W: waning Immunity probability. The large colored boxes are compartments, and sequences of letters represent sequences of events (e.g. SVSFI blue box: proportion of susceptible individuals S who were vaccinated–SV–but remained susceptible–SVS–were next infected–SVSF–and became immune SVSFI). N stands for non-vaccinated.</p