A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: 1. Estimating parameters of digestion

Parameters related to the microbial digestion of nutrients in the ruminoreticulum have been estimated by fitting mathematical models to degradation profiles generated from kinetic studies. In the present paper, we propose a generalized compartmental model of digestion (GCMD) based on implicit theoretical concepts and the gamma probability density function to estimate fibre digestion parameters. The proposed model is consistent to a broader compartmental model presented in a companion paper that integrates aspects of fibre digestion and passage. Different versions of the GCMD were generated by increasing the integer order of time dependency of the gamma function. These versions were fitted to 192 published fibre degradation profiles that were obtained using an in vitro fermentation technique. The quality of fit was evaluated based on the frequency of minimum sum of squares of errors (SSE), the number of runs of signs of residuals, and its likelihood probability calculated according to the Akaike's Information Criterion. The likelihood of the proposed model was also compared to a discrete lag time model (DLT), which is commonly used to interpret fibre degradation profiles. The GCMD had superior quality of fit compared to the DLT and was considered more likely in describing 68.75% of the profiles evaluated. Only 9.38% of the degradation profiles that were fitted to the DLT model had a lower SSE. Even though the degradation profiles studied were generated by incubating feed samples up to 96 h, the true asymptotic limit of fibre degradation can only be achieved by long-term fermentations. This fact leads to questioning the uniformity of the potentially digestible fibre fraction and a further approach based on GCMD-type model was used to account for its heterogeneous nature.     

A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: 2. Integrating digestion and passage

Models used to predict digestibility and fill of the dietary insoluble fibre (NDF) treat the ruminoreticular particulate mass as a single pool. The underlying assumption is that escape of particles follows first-order kinetics. In this paper, we proposed and evaluated a model of two ruminoreticular sequential NDF pools. The first pool is formed by buoyant particles (raft pool) and the second one by fluid dispersed particles (escapable pool) ventrally to the raft. The transference of particles between these two pools results from several processes that reduce particles buoyancy, assuming the gamma distribution. The exit of escapable pool particles from the ruminoreticulum is exponentially distributed. These concepts were evaluated by comparing ruminoreticular NDF masses as 43 and 27 means from cattle and sheep, respectively, to the same predicted variable using single- and two-pools models. Predictions of the single-pool model were based on lignin turnover and the turnover associated to the descending phase of the elimination of Yb-labelled forage particles in the faeces of sheep. Predictions of the two-pool model were obtained by estimating fractional passage rates associated to the ascending and descending phases of the same Yb excretion profiles in sheep faeces. All turnovers were scaled to the power 0.25 of body mass for interspecies comparisons. Predictions based on lignin turnover (single pool) and the two-pool model presented similar trends, accuracies and precisions. The single-pool approach based solely on the descending phase of the marker yielded biased estimates of the ruminoreticular NDF mass.     

A mathematical model to study the effects of drugs administration on tumor growth dynamics

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.     

Spatial memory shapes migration and its benefits: evidence from a large herbivore

From fine‐scale foraging to broad‐scale migration, animal movement is shaped by the distribution of resources. There is mounting evidence, however, that learning and memory also guide movement. Although migratory mammals commonly track resource waves, how resource tracking and memory guide long‐distance migration has not been reconciled. We examined these hypotheses using movement data from four populations of migratory mule deer (n = 91). Spatial memory had an extraordinary influence on migration, affecting movement 2–28 times more strongly than tracking spring green‐up or autumn snow depth. Importantly, with only an ability to track resources, simulated deer were unable to recreate empirical migratory routes. In contrast, simulated deer with memory of empirical routes used those routes and obtained higher foraging benefits. For migratory terrestrial mammals, spatial memory provides knowledge of where seasonal ranges and migratory routes exist, whereas resource tracking determines when to beneficially move within those areas.     

A hierarchy of conceptual models of red-tide generation: Nutrition,behavior, and biological interactions

Red tides – discolorations of the sea surface due to dense plankton blooms – occur regularly in coastal and offshore waters along much of the world's coastline. Red tides often cause large-scale mortalities of fish and shellfish and significant losses to the aquaculture and tourist industries of many countries. Therefore, understanding and predicting the mechanisms controlling the outbreak, persistence, spread, and decline of red tides are important concerns to scientists, officials, industry, and the public. With increasing knowledge of red-tide species and red-tide events, new mechanisms have been discovered. Based on the nutrition and behaviors of red-tide organisms and biological interactions among them, red-tide outbreaks can be categorized into a hierarchy of four generation mechanisms (GM1–GM4). In the simplest, GM1, all phototrophic red-tide species were treated as exclusively autotrophic organisms without the ability to swim. However, this GM cannot explain red-tide outbreaks in oligotrophic surface waters offshore. Vertical migration (considered in GM2) and mixotrophy (GM3) enable red-tide flagellates to acquire growth factors from nutrient-rich deep waters or co-occurring prey, respectively. In natural environments, all red tides occur by those species outgrowing co-occurring organisms; red-tide species dominate communities by eliminating other species or reducing their abundances. Thus, GM4 contains the direct biological interactions (i.e., inhibition by physical contact or chemical effects) and indirect biological interactions (i.e., acquiring resources faster than others) that can affect the dominance of red-tide species under given conditions. Correctly choosing one of these four GMs for red tides dominated by one causative species is important because the accuracy of predictions may be outweighed by the costs and time required to acquire the relevant information. In this study, mechanisms describing the outbreak, persistence, and decline of red tides were reviewed, the advantages and limitations of each mechanism were evaluated, and insights about the evolution of the mechanisms were developed.     

Negative feedback of extracellular ADP on ATP release in goldfish hepatocytes: A theoretical study

A mathematical model was built to account for the kinetic of extracellular ATP (ATPe) and extracellular ADP (ADPe) concentrations from goldfish hepatocytes exposed to hypotonicity. The model was based on previous experimental results on the time course of ATPe accumulation, ectoATPase activity, and cell viability [Pafundo et al., 2008].The kinetic of ATPe is controlled by a lytic ATP flux, a non-lytic ATP flux, and ecto-ATPase activity, whereas ADPe kinetic is governed by a lytic ADP flux and both ecto-ATPase and ecto-ADPase activities. Non-lytic ATPe efflux was included as a diffusion equation modulated by ATPe activation (positive feedback) and ADPe inhibition (negative feedback).The model yielded physically meaningful and stable steady-state solutions, was able to fit the experimental time evolution of ATPe and simulated the concomitant kinetic of ADPe. According to the model during the first minute of hypotonicity the concentration of ATPe is mainly governed by both lytic and non-lytic ATP efflux, with almost no contribution from ecto-ATPase activity. Later on, ecto-ATPase activity becomes important in defining the time dependent decay of ATPe levels. ADPe inhibition of the non-lytic ATP efflux was strong, whereas ATPe activation was minimal. Finally, the model was able to predict the consequences of partial inhibition of ecto-ATPase activity on the ATPe kinetic, thus emulating the exposure of goldfish cells to hypotonic medium in the presence of the ATP analog AMP-PCP. The model predicts this analog to both inhibit ectoATPase activity and increase non-lytic ATP release.     

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.     

Predicting fundamental and realized distributions based on thermal niche: A case study of a freshwater turtle

Species distribution models (SDM) have been broadly used in ecology to address theoretical and practical problems. Currently, there are two main approaches to generate SDMs: (i) correlative, which is based on species occurrences and environmental predictor layers and (ii) process-based models, which are constructed based on species' functional traits and physiological tolerances. The distributions estimated by each approach are based on different components of species niche. Predictions of correlative models approach species realized niches, while predictions of process-based are more akin to species fundamental niche. Here, we integrated the predictions of fundamental and realized distributions of the freshwater turtle Trachemys dorbigni. Fundamental distribution was estimated using data of T. dorbigni's egg incubation temperature, and realized distribution was estimated using species occurrence records. Both types of distributions were estimated using the same regression approaches (logistic regression and support vector machines), both considering macroclimatic and microclimatic temperatures. The realized distribution of T. dorbigni was generally nested in its fundamental distribution reinforcing theoretical assumptions that the species' realized niche is a subset of its fundamental niche. Both modelling algorithms produced similar results but microtemperature generated better results than macrotemperature for the incubation model. Finally, our results reinforce the conclusion that species realized distributions are constrained by other factors other than just thermal tolerances.     

Trophi morphology and its usefulness for identification of formalin-preserved species of Synchaeta Ehrenberg, 1832 (Rotifera: Monogononta: Synchaetidae)

A study of temporal and spatial distribution of zooplankton frequently requires identification to species level. In such studies, samples are usually fixed, but according to different authors rotifer genera such as Synchaeta (Ehrenberg, 1832) can only be identified in live samples. A procedure for the identification of preserved specimens of Synchaeta is presented, permitting ecological studies without the examination of live material. Trophus morphology, investigated by light and scanning electron microscopy, was related to morphological characteristics of preserved specimens. In this way, body length was used to group formalin-preserved specimens into Synchaeta gr. tremula-oblonga sensu Ruttner-Kolisko (1974) (170 μm) or Synchaeta gr. stylata-pectinata sensu Ruttner-Kolisko (1974) (190 μm). Furthermore, body length, colour and shape were used to identify Synchaeta grandis (Zacharias, 1893), Synchaeta pectinata (Ehrenberg, 1832), Synchaeta kitina (Rousselet, 1902) and Synchaeta lakowitziana (Lucks, 1930). It was, however, impossible to distinguish Synchaeta tremula (Müller, 1786) from Synchaeta oblonga (Ehrenberg, 1832) by their trophi because of contradictions in the diagnostic keys and monographs regarding trophus morphology.     

First results from satellite-linked archival tagging of porbeagle shark, Lamna nasus: Area fidelity, wider-scale movements and plasticity in diel depth changes

Understanding the habitat preferences of large marine vertebrates has only recently become tractable with the widespread availability of satellite telemetry for monitoring movements and behaviour. For many species with low population abundances, however, little progress has been made in identifying space use patterns. The endothermic porbeagle shark, Lamna nasus, has declined in the North Atlantic due to severe fishing pressure, with little evidence of recovery. One potential factor exacerbating population decline is area fidelity to coastal waters where fisheries are intensive. We tested for short-term area fidelity by attaching pop-up satellite-linked archival transmitters to four porbeagles in summer 2007, resulting in 175 days total tracking time covering an estimated 10,256 km distance. Throughout July and August the sharks occupied localised areas (8,602 – 90,153 km²) within the Celtic Sea, between the south-west UK, south-west Wales and southern Ireland. Only one shark was tracked into the autumn, when it moved into deep water off the continental shelf, then north towards colder latitudes. Sharks occupied a broad vertical depth range (0 – 552 m) and water temperatures (9° - 19 °C). Dives were made frequently from the surface to near the seabed in shelf areas, however, in shelf edge habitats extended periods of time were spent at depths > 300 m. Porbeagles showed considerable plasticity in diel depth changes within and between individuals and as a function of habitat type. In addition to no obvious day-night difference in depth occupation, some sharks showed reverse diel vertical migration (DVM) (dawn ascent – dusk descent) in well-mixed coastal waters whereas normal DVM (dawn descent – dusk ascent) characterised movements into deeper, thermally well-stratified waters. The variable behaviours may reflect the need for different search strategies depending on habitat and prey types encountered. These results show porbeagles are potentially vulnerable to fisheries throughout the summer when they aggregate, and that large scale movement across national boundaries identifies the need for international conservation measures.     

CellML: its future, present and past

Advances in biotechnology and experimental techniques have lead to the elucidation of vast amounts of biological data. Mathematical models provide a method of analysing this data; however, there are two issues that need to be addressed: (1) the need for standards for defining cell models so they can, for example, be exchanged across the World Wide Web, and also read into simulation software in a consistent format and (2) eliminating the errors which arise with the current method of model publication. CellML has evolved to meet these needs of the modelling community. CellML is a free, open-source, eXtensible markup language based standard for defining mathematical models of cellular function. In this paper we summarise the structure of CellML, its current applications (including biological pathway and electrophysiological models), and its future development—in particular, the development of toolsets and the integration of ontologies.     

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K ⁺)-limited environment. Our both continuous and discrete models illustrate ‘cancer immunoediting’ as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202–206].     

A partial differential equation model of changing sizes and numbers in a cohort of juvenile fish

Synopsis Numbers and lengths of young crappie were measured over a 20-week period in a Tennessee River reservoir. From these data, the average length at the swimming interval and growth rate were computed. A partial differential equation model was formulated for changes in length distribution through time. The equation was solved analytically and this solution used to predict the numbers by length class through time, given an initial known recruitment or swim-up rate. The simulated numbers agreed in considerable detail with the observations, indicating that the model accurately reflected the basic population mechanics involved. This suggests the model can be used to predict impacts to the fish population of size-dependent mortality caused by man, such as impingement on power plant intake screens.     

Development and field validation of a regional,management‐scale habitat model: A koala Phascolarctos cinereus case study

Species distribution models have great potential to efficiently guide management for threatened species, especially for those that are rare or cryptic. We used MaxEnt to develop a regional‐scale model for the koala Phascolarctos cinereus at a resolution (250 m) that could be used to guide management. To ensure the model was fit for purpose, we placed emphasis on validating the model using independently‐collected field data. We reduced substantial spatial clustering of records in coastal urban areas using a 2‐km spatial filter and by modeling separately two subregions separated by the 500‐m elevational contour. A bias file was prepared that accounted for variable survey effort. Frequency of wildfire, soil type, floristics and elevation had the highest relative contribution to the model, while a number of other variables made minor contributions. The model was effective in discriminating different habitat suitability classes when compared with koala records not used in modeling. We validated the MaxEnt model at 65 ground‐truth sites using independent data on koala occupancy (acoustic sampling) and habitat quality (browse tree availability). Koala bellows (n = 276) were analyzed in an occupancy modeling framework, while site habitat quality was indexed based on browse trees. Field validation demonstrated a linear increase in koala occupancy with higher modeled habitat suitability at ground‐truth sites. Similarly, a site habitat quality index at ground‐truth sites was correlated positively with modeled habitat suitability. The MaxEnt model provided a better fit to estimated koala occupancy than the site‐based habitat quality index, probably because many variables were considered simultaneously by the model rather than just browse species. The positive relationship of the model with both site occupancy and habitat quality indicates that the model is fit for application at relevant management scales. Field‐validated models of similar resolution would assist in guiding management of conservation‐dependent species.     

Fire, climate change and biodiversity in Amazonia: a Late-Holocene perspective

Fire is an important and arguably unnatural component of many wet Amazonian and Andean forest systems. Soil charcoal has been used to infer widespread human use of landscapes prior to European Conquest. An analysis of Amazonian soil carbon records reveals that the records have distinct spatial and temporal patterns, suggesting that either fires were only set in moderately seasonal areas of Amazonia or that strongly seasonal and aseasonal areas are undersampled. Synthesizing data from 300 charcoal records, an age–frequency diagram reveals peaks of fire apparently coinciding with some periods of very strong El Niño activity. However, the El Niño record does not always provide an accurate prediction of fire timing, and a better match is found in the record of insolation minima. After the time of European contact, fires became much scarcer within Amazonia. In both the Amazonia and the Andes, modern fire pattern is strongly allied to human activity. On the flank of the Andes, forests that have never burned are being eroded by fire spreading downslope from grasslands. Species of these same forests are being forced to migrate upslope due to warming and will encounter a firm artificial fire boundary of human activity.     

Relationships between urban open spaces and humans’ health benefits from an ecological perspective: a study in an urban campus

The rapid increase in urban population worldwide is one among the important global environmental issues. The urban ecological system is made up of human society and environments. We cannot exclude humans from the urban ecosystem since humans are an integral component of landscape ecology. Bridging humans and landscape ecology is important to sustainable landscape planning and management from a holistic point of view. Humans’ responses to landscape structure are crucial to understand the relationships between humans and nature. In current study, we conducted a field experiment in an urban campus to investigate the relationships between urban open spaces and humans’ health benefits. The landscape structure of urban open spaces were derived from land cover maps. The results show that people’s psycho-physiological responses are correlated with selected landscape metrics of different land cover types. Overall, dense trees and large artificial structures likely have negative effects on humans, while large continuous grassland patches or water patches enhance humans’ positive responses. The findings give some insights into the design and management of urban open spaces that are favorable for ecosystems and the health of urban population. The methodology taken to investigate the relationships between landscape structure and human health in this study may be of value to future efforts in establishing healthy and sustainable urban environments.     

形目鱼类连体胚胎两例

报道了鳉形目鱼类食蚊鱼(Gambusia affinis)和青鳉(Oryzias latipes)的连体胚胎现象各一例.上述连体胚胎均为腹部粘连,内脏各器官分别独立,产出或孵化后短时存活.     

Living krill,zooplankton and experimental investigations: a discourse on the role of krill and their experimental study in marine ecology

Krill occupy critical positions in a many marine ecosystems and have been the subject of a number of concerted studies yet there are large areas of their biology that still remain a mystery. Most species of krill are open ocean animals, which makes direct observation and sampling difficult. Krill also exhibit a number of physiological and behavioural attributes which frustrate attempts to understand their life history. Krill are conceptually difficult to come to terms with; they are obviously different from larger marine organisms such as squid, fish, whales and fish yet they are also quite distinct from those animals classed as zooplankton such as copepods. Despite these differences they have most often been grouped with zooplankton and have been studied using techniques developed for animals which are orders of magnitude smaller than they. This mismatch has affected our view of their interactions with the physical world and also affects their perceived trophic interactions. Their size and mobility also interferes with our ability to sample them effectively and thus to develop our appreciation of their true role in the marine ecosystem. Understanding how intermediate-sized animals, such as krill, function in aquatic ecosystem is critical to better management of the marine environment.