The objective of the present study was to evaluate the relationship between body weight (BW) and hip width (HW) in dairy buffaloes (Bubalus bubalis). HW was measured in 215 Murrah buffaloes with a BW of 341 ± 161.6 kg, aged between three months and five years, and raised in southeastern Mexico. Linear and non-linear regressions were used to construct the prediction models. The goodness of fit of the models was evaluated using the Akaike information criterion (AIC), Bayesian information criterion (BIC), coefficient of determination (R2), mean squared error (MSE), and root MSE (RMSE). Additionally, the developed models were evaluated through internal and external cross-validation (k-folds) using independent data. The ability of the fitted models to predict the observed values was assessed based on the root mean square error of prediction (RMSEP), R2, and mean absolute error (MAE). The relationship between BW and HW showed a high correlation coefficient (r = 0.96, P < 0.001). The chosen fitted model to predict BW was: −176.33 (± 40.83***) + 8.74 (± 1.79***) × HW + 0.04 (± 0.01*) × HW2, because it presented the lowest MSE, RMSE, and AIC values, which were 1228.64, 35.05 and 1532.41, respectively. Therefore, with reasonable accuracy, the quadratic model using hip width may be suitable for predicting body weight in buffaloes.

Live weight (LW) is an important piece of information within production systems, as it is related to several other economic characteristics. However, in the main buffalo-producing regions in the world, it is not common to periodically weigh the animals. We develop and evaluate linear, quadratic, and allometric mathematical models to predict LW using the body volume (BV) formula in lactating water buffalo (Bubalus bubalis) reared in southeastern Mexico. The LW (391.5 ± 138.9 kg) and BV (333.62 ± 58.51 dm3) were measured in 165 lactating Murrah buffalo aged between 3 and 10 years. The goodness-of-fit of the models was evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), coefficient of determination (R2), mean-squared error (MSE) and root MSE (RMSE). In addition, the developed models were evaluated through cross-validation (k-folds). The ability of the fitted models to predict the observed values was evaluated based on the RMSEP, R2, and mean absolute error (MAE). LW and BV were significantly positively and strongly correlated (r = 0.81; P < 0.001). The quadratic model had the lowest values of MSE (2788.12) and RMSE (52.80). On the other hand, the allometric model showed the lowest values of BIC (1319.24) and AIC (1313.07). The Quadratic and allometric models had lower values of MSEP and MAE. We recommend the quadratic and allometric models to predict the LW of lactating Murrah buffalo using BV as a predictor.

Human decision-making is affected by a diversity of factors including material cost–benefit considerations, normative and cultural influences, learning and conformity with peers and external authorities (e.g. cultural, religious, political, organisational). Also important are dynamically changing personal perceptions of the situation and beliefs about actions and expectations of others as well as psychological phenomena such as cognitive dissonance and social projection. To better understand these processes, I develop a unifying modelling framework describing the joint dynamics of actions and attitudes of individuals and their beliefs about the actions and attitudes of their groupmates. I consider which norms get internalised and which factors control beliefs about others. I predict that the long-term average characteristics of groups are largely determined by a balance between material payoffs and the values promoted by the external authority. Variation around these averages largely reflects variation in individual costs and benefits mediated by individual psychological characteristics. The efforts of an external authority to change the group behaviour in a certain direction can, counter-intuitively, have an opposite effect on individual behaviour. I consider how various factors can affect differences between groups and societies in the tightness/looseness of their social norms. I show that the most important factors are social heterogeneity, societal threat, effects of authority, cultural variation in the degree of collectivism/individualism, the population size and the subsistence style. My results can be useful for achieving a better understanding of human social behaviour and historical and current social processes, and in developing more efficient policies aiming to modify social behaviour.

In order to determine the sex of Chelonia mydas individuals found within one of the principal foraging areas of the Gulf of California during any given stage of ontogeny, 529 individuals were sampled in Bahía de los Ángeles from 1995–2012, and their morphometric data were collected. A principal component analysis (PCA) was performed for the morphometric variables, and two principal components were obtained that unambiguously separated sexes and ontogenetic stages. The first component was defined by straight carapace length (SCL), curve carapace length (CCL), plastron length (PL) and carapace depth (CD), while the second factor was represented by total tail length (TTL). Allometric models were fitted with the most important variables determined by the PCA. The model PL = αSCLβ was able to distinguish between adults and immature individuals. For adult organisms, the model that best separated males from females was TTL = αSCLβ. Adult females had SCL values of 66–96.7 cm and TTL values of 16.3–25 cm, while adult males had SCL values of 66.4–12.5 cm and TTL values > 25 cm. As the organisms were considered immature only if SCL < 77.3, we were able to determine the TTL values for immature individuals by using elemental mathematics and solving for SCL in the equation TTL = αSCLβ for each group (i.e. adult females, adult males and immatures). So, considering the mathematical approach and acknowledging the lack of background information, immature individuals may be considered potential females if the TTL value is between 7.04–17.8 cm and potential males if the TTL value > 17.8 cm.

Pigs exposed to stressors might change their daily typical feeding intake pattern. The objective of this study was to develop a method for the early identification of deviations from an individual pig’s typical feeding patterns. In addition, a general approach was proposed to model feed intake and real-time individual nutrient requirements for pigs with atypical feeding patterns. First, a dynamic linear model (DLM) was proposed to model the typical daily feed intake (DFI) and daily gain (DG) patterns of pigs. Individual DFI and DG dynamics are described by a univariate DLM in conjunction with Kalman filtering. A standardized tabular cumulative sum (CUMSUM) control chart was applied to the forecast errors generated by DLM to activate an alarm when a pig showed deviations from its typical feeding patterns. The relative feed intake (RFI) during a challenge period was calculated. For that, the forecasted individual pig DFI is expressed as its highest DFI relative to the intake during pre-challenge period. Finally, the DLM and RFI approaches were integrated into the actual precision-feeding model (original model) to estimate real-time individual nutrient requirements for pigs with atypical feeding patterns. This general approach was evaluated with data from two studies (130 pigs, at 35.25 ± 3.9 kg of initial BW) that investigated during 84 days the effect of precision-feeding systems for growing-finishing pigs. The proposed general approach to estimating real-time individual nutrient requirements (updated model) was evaluated by comparing its estimates with those generated by the original model. For 11 individuals out of 130, the DLM did not fit the observed data well in a specific period, resulting in an increase in the sum of standardized forecast errors and in the number of time steps that the model needed to adapt to the new patterns. This poor fit can be identified by the increase in the CUMSUM with a consequent alarm generated. The results of this study show that the updated model made it possible to reduce intra-individual variation for the estimated lysine requirements in comparison with the original model, especially for individuals with atypical feeding patterns. In conclusion, the DLM in conjunction with CUMSUM could be used as a tool for the online monitoring of DFI for growing-finishing pigs. Moreover, the proposed general approach allows the estimation of real-time amino acid requirements and accounts for the reduced feed intake and growth potential of pigs with atypical feeding patterns.

To estimate the nutritional requirements of hair sheep, knowledge about the animal’s weight and its relationships with growth performances is essential. A study was carried with the objective to establish the relationships between BW, fasting BW (FBW), empty BW (EBW), average daily gain (ADG) and empty BW gain (EBWG) for hair sheep in growing and finishing phases in Brazilian conditions. Databases were obtained from 32 studies, for a total of 1145 observations; there were 3 sex classes (non-castrated male, castrated male and female) and 2 feeding systems (pasture and feedlot). The most representative breeds in the database were Santa Ines (n = 473), Morada Nova (n = 70) and Brazilian Somali (n = 47). The other animals in the database were crossbreeds (n = 555). The FBW (kg), EBW and EBWG (kg/day) were estimated according to linear regression. A random coefficient model was adopted, considering the study as a random effect and including the possibility of covariance between the slope and the intercept. The coefficients obtained from the linear regression of the FBW against the BW, EBW against the FBW and EBWG against the ADG did not differ between sex class (P > 0.05) and genotype (P > 0.05). The equations generated to estimate FBW from the BW, EBW from the FBW and EBWG from the ADG are as follows: FBW = −0.5470 (±0.2025) + 0.9313(±0.019) × BW, EBW = −1.4944 (±0.3639) + 0.8816 (±0.018) × FBW and EBWG = 0.906 (±0.019) × ADG, respectively. The low mean squared error values found in the cross-validation confirmed the reliability of these equations. Considering a sheep with a BW of 30 kg and a 100 g ADG, the estimated FBW, EBW and EBWG calculated using the generated equations are 27, 22.65 and 0.090 kg, respectively. In conclusion, the generated equations can be used in growing hair sheep. The validation procedure applied to the generated equations showed that its use for hair sheep seems to be appropriate.

We present a model to optimise a vaccination campaign aiming to prevent or to curb a Zika virus outbreak. We show that the optimum vaccination strategy to reduce the number of cases by a mass vaccination campaign should start when the Aedes mosquitoes' density reaches the threshold of 1.5 mosquitoes per humans, the moment the reproduction number crosses one. The maximum time it is advisable to wait for the introduction of a vaccination campaign is when the first ZIKV case is identified, although this would not be as effective to minimise the number of infections as when the mosquitoes' density crosses the critical threshold. This suboptimum strategy, however, would still curb the outbreak. In both cases, the catch up strategy should aim to vaccinate at least 25% of the target population during a concentrated effort of 1 month immediately after identifying the threshold. This is the time taken to accumulate the herd immunity threshold of 56.5%. These calculations were done based on theoretical assumptions that vaccine implementation would be feasible within a very short time frame.

Trypanocide resistance remains a huge challenge in the management of animal African trypanosomiasis. Paucity of data on the prevalence of multi-drug resistant trypanosomes has greatly hindered optimal veterinary management practices. We use mathematical model predictions to highlight appropriate drug regimens that impede trypanocide resistance development in cattle. We demonstrate that using drugs in decreasing resistance order results in a negligible increase in number of cattle with resistant infection, in contrast to a more pronounced increase from trypanocide use in increasing resistance order. We demonstrate that the lowest levels of trypanocide resistance are achieved with combination therapy. We also show that increasing the number of cattle treated leads to a progressive reduction in the number of cattle with drug resistant infections for treatments of up to 80% of the cattle population for the combination treatment strategy. Our findings provide an initial evidence-based framework on some essential practices that promote optimal use of the handful of trypanocides. We anticipate that our modest forecasts will improve therapeutic outcomes by appropriately informing on the best choice, and combination of drugs that minimize treatment failure rates.

Penguins are flightless, so they are forced to walk while on land. In particular, they show rather specific behaviours in their homecoming, which are interesting to observe and to describe analytically. We observed that penguins have the tendency to waddle back and forth on the shore to create a sufficiently large group, and then walk home compactly together. The mathematical framework that we introduce describes this phenomenon, by taking into account “natural parameters”, such as the eyesight of the penguins and their cruising speed. The model that we propose favours the formation of conglomerates of penguins that gather together, but, on the other hand, it also allows the possibility of isolated and exposed individuals.

The model that we propose is based on a set of ordinary differential equations. Due to the discontinuous behaviour of the speed of the penguins, the mathematical treatment (to get existence and uniqueness of the solution) is based on a “stop-and-go” procedure. We use this setting to provide rigorous examples in which at least some penguins manage to safely return home (there are also cases in which some penguins remain isolated). To facilitate the intuition of the model, we also present some simple numerical simulations that can be compared with the actual movement of the penguin parade.

Aedes aegypti, historically known as yellow fever (YF) mosquito, transmits a great number of other viruses such as Dengue, West Nile, Chikungunya, Zika, Mayaro and perhaps Oropouche, among others. Well established in Africa and Asia, Aedes mosquitoes are now increasingly invading large parts of the American continent, and hence the risk of urban YF resurgence in the American cities should because of great concern to public health authorities. Although no new urban cycle of YF was reported in the Americas since the end of an Aedes eradication programme in the late 1950s, the high number of non-vaccinated individuals that visit endemic areas, that is, South American jungles where the sylvatic cycle of YF is transmitted by canopy mosquitoes, and return to Aedes-infested urban areas, increases the risk of resurgence of the urban cycle of YF. We present a method to estimate the risk of urban YF resurgence in dengue-endemic cities. This method consists in (1) to estimate the number of Aedes mosquitoes that explains a given dengue outbreak in a given region; (2) calculate the force of infection caused by the introduction of one infective individual per unit area in the endemic area under study; (3) using the above estimates, calculate the probability of at least one autochthonous YF case per unit area produced by one single viraemic traveller per unit area arriving from a YF endemic or epidemic sylvatic region at the city studied. We demonstrate that, provided the relative vector competence, here defined as the capacity to being infected and disseminate the virus, of Ae. aegypti is greater than 0.7 (with respect to dengue), one infected traveller can introduce urban YF in a dengue endemic area.

Antigenic variation in malaria was discovered in Plasmodium knowlesi studies involving longitudinal infections of rhesus macaques (M. mulatta). The variant proteins, known as the P. knowlesi Schizont Infected Cell Agglutination (SICA) antigens and the P. falciparum Erythrocyte Membrane Protein 1 (PfEMP1) antigens, expressed by the SICAvar and var multigene families, respectively, have been studied for over 30 years. Expression of the SICA antigens in P. knowlesi requires a splenic component, and specific antibodies are necessary for variant antigen switch events in vivo. Outstanding questions revolve around the role of the spleen and the mechanisms by which the expression of these variant antigen families are regulated. Importantly, the longitudinal dynamics and molecular mechanisms that govern variant antigen expression can be studied with P. knowlesi infection of its mammalian and vector hosts. Synchronous infections can be initiated with established clones and studied at multi-omic levels, with the benefit of computational tools from systems biology that permit the integration of datasets and the design of explanatory, predictive mathematical models. Here we provide an historical account of this topic, while highlighting the potential for maximizing the use of P. knowlesi – macaque model systems and summarizing exciting new progress in this area of research.

The timing and origin of Zika virus (ZIKV) introduction in Brazil has been the subject of controversy. Initially, it was assumed that the virus was introduced during the FIFA World Cup in June–July 2014. Then, it was speculated that ZIKV may have been introduced by athletes from French Polynesia (FP) who competed in a canoe race in Rio de Janeiro in August 2014. We attempted to apply mathematical models to determine the most likely time window of ZIKV introduction in Brazil. Given that the timing and origin of ZIKV introduction in Brazil may be a politically sensitive issue, its determination (or the provision of a plausible hypothesis) may help to prevent undeserved blame. We used a simple mathematical model to estimate the force of infection and the corresponding individual probability of being infected with ZIKV in FP. Taking into account the air travel volume from FP to Brazil between October 2013 and March 2014, we estimated the expected number of infected travellers arriving at Brazilian airports during that period. During the period between December 2013 and February 2014, 51 individuals travelled from FP airports to 11 Brazilian cities. Basing on the calculated force of ZIKV infection (the per capita rate of new infections per time unit) and risk of infection (probability of at least one new infection), we estimated that 18 (95% CI 12–22) individuals who arrived in seven of the evaluated cities were infected. When basic ZIKV reproduction numbers greater than one were assumed in the seven evaluated cities, ZIKV could have been introduced in any one of the cities. Based on the force of infection in FP, basic reproduction ZIKV number in selected Brazilian cities, and estimated travel volume, we concluded that ZIKV was most likely introduced and established in Brazil by infected travellers arriving from FP in the period between October 2013 and March 2014, which was prior to the two aforementioned sporting events.

The development of weed management systems requires accurate prediction of weed-crop competition. In this paper, simple regression models of crop yield losses based on weed density and weed leaf area are compared. In weed leaf area models, variations in the relative damage coefficient (q) were also analyzed. Finally, three simple methods to assess weed cover were compared: visual, photographic, and optic device assessment. Leaf area models were at least as accurate as weed density models. However, the generality of the leaf area models was restricted by changes in q, according to the date of leaf area evaluation and the year. Although all methods to assess weed cover correlated adequately with weed leaf area, visual estimates were the best to predict crop yield losses perhaps because very low levels of weed leaf area could be distinguished visually better than by other methods.

The classical Ross–Macdonald model is often utilized to model vector-borne infections; however, this model fails on several fronts. First, using measured (or estimated) parameters, which values are accepted from the literature, the model predicts a much greater number of cases than what is usually observed. Second, the model predicts a single large outbreak that is followed by decades of much smaller outbreaks, which is not consistent with what is observed. Usually towns or cities report a number of recurrences for many years, even when environmental changes cannot explain the disappearance of the infection between the peaks. In this paper, we continue to examine the pitfalls in modelling this class of infections, and explain that, if properly used, the Ross–Macdonald model works and can be used to understand the patterns of epidemics and even, to some extent, be used to make predictions. We model several outbreaks of dengue fever and show that the variable pattern of yearly recurrence (or its absence) can be understood and explained by a simple Ross–Macdonald model modified to take into account human movement across a range of neighbourhoods within a city. In addition, we analyse the effect of seasonal variations in the parameters that determine the number, longevity and biting behaviour of mosquitoes. Based on the size of the first outbreak, we show that it is possible to estimate the proportion of the remaining susceptible individuals and to predict the likelihood and magnitude of the eventual subsequent outbreaks. This approach is described based on actual dengue outbreaks with different recurrence patterns from some Brazilian regions.