Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models

This article compares a general closed nutrient, stoichiometric producer–consumer model to a two-dimensional ‘quasi-equilibrium’ approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare–Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

Does the environmental background (intensive v. outdoor systems) influence the behaviour of piglets at weaning?

Under intensive pig husbandry, outdoor systems offer a more complex physical and social environment compared with indoor systems (farrowing sheds). As the rearing environment affects behavioural development, it can, therefore, influence behavioural responses of pigs to stressful environments in later stages of production. We tested how the rearing environment influenced behavioural responses to a novel arena test in piglets on the day that they were weaned and mixed into large groups. We recorded video footage and compared the behavioural responses of 30 outdoor-raised and 30 farrowing shed-raised piglets tested in an experimental arena and sequentially exposed to four challenges (each for 5 min) on the day of weaning. Quantitative and qualitative behavioural measures were recorded using time budgets and scoring demeanour or ‘qualitative behavioural expression’ (using Qualitative Behavioural Assessment (QBA)). When held in isolation (challenge 1), both groups were scored as more ‘scared/worried’, while outdoor-raised piglets spent more time eating and jumping against the arena walls. Both groups interacted with a plastic ball (challenge 2: exposure to a novel object) during which they were scored as more ‘playful/curious’ than other challenges. When a food bowl was introduced (challenge 3), farrowing shed-raised piglets were more interested in playing with the food bowl itself, whereas outdoor-raised piglets spent more time eating the feed. Finally, there were no significant differences in social behaviour (challenge 4: introduction of another piglet) between the two groups in terms of the latency to contact each other, amount of time recorded engaged in aggressive/non-aggressive social interactions or QBA scores. Although piglets spent 30% of their time interacting with the other piglet, and half of this time (47%) was engaged in negative interactions (pushing, biting), the levels of aggression were not different between the two groups. Overall, outdoor-raised piglets ate more and were scored as more ‘calm/passive’, whereas farrowing shed-raised piglets spent more time investigating their environment and were scored as more ‘playful/inquisitive’. In conclusion, we did not find differences in behaviour between outdoor-raised and farrowing shed-raised piglets that would highlight welfare issues. The differences found in this study may reflect conflicting affective states, with responses to confinement, neophobia and motivation for exploration evident.     

A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.     

Habitat amount hypothesis and passive sampling explain mammal species composition in Amazonian river islands

Nested structures of species assemblages have been frequently associated with patch size and isolation, leading to the conclusion that colonization–extinction dynamics drives nestedness. The ‘passive sampling’ model states that the regional abundance of species randomly determines their occurrence in patches. The ‘habitat amount hypothesis’ also challenges patch size and isolation effects, arguing that they occur because of a ‘sample area effect’. Here, we (a) ask whether the structure of the mammal assemblages of fluvial islands shows a nested pattern, (b) test whether species’ regional abundance predicts species’ occurrence on islands, and (c) ask whether habitat amount in the landscape and matrix resistance to biological flow predict the islands’ species composition. We quantified nestedness and tested its significance using null models. We used a regression model to analyze whether a species’ relative regional abundance predicts its incidence on islands. We accessed islands’ species composition by an NMDS ordination and used multiple regression to evaluate how species composition responds to habitat amount and matrix resistance. The degree of nestedness did not differ from that expected by the passive sampling hypothesis. Likewise, species’ regional abundance predicted its occurrence on islands. Habitat amount successfully predicted the species composition on islands, whereas matrix resistance did not. We suggest the application of habitat amount hypothesis for predicting species composition in other patchy systems. Although the island biogeography perspective has dominated the literature, we suggest that the passive sampling perspective is more appropriate for explaining the assemblages’ structure in this and other non‐equilibrium patch systems. Abstract in Portuguese is available with online material.     

Contact,trust and social capital in Northern Ireland: a qualitative study of three mixed communities

In a recent paper, Robert Putnam (2007) challenges the contact hypothesis by arguing that ethnic diversity causes people to ‘hunker down’ and essentially withdraw themselves from society. Drawing on qualitative data collected from three mixed communities in Northern Ireland, this paper explores the extent and quality of contact experienced by Protestants and Catholics in their everyday lives. Themes emerging from our data are generally consistent with the contact hypothesis. There is also some support for Putnam's theory that mixed environments can induce ‘hunkering down’ and that inter-group trust may be compromised. However, our data challenge Putnam's argument that these responses are a consequence of ‘anomie’ or ‘social malaise’. Rather, we find that withdrawal from social activity in the neighbourhoods we observed was a calculated response at times of threat, often aimed at protecting existent positive inter-ethnic relations.     

Cryptic sex? Estimates of genome exchange in unisexual mole salamanders (Ambystoma sp.)

Cryptic sex has been argued to explain the exceptional longevity of certain parthenogenetic vertebrate lineages, yet direct measurements of genetic exchange between sexual and apparently parthenogenetic forms are rare. Female unisexual mole salamanders (Ambystoma sp.) are the oldest known unisexual vertebrate lineage (~5 million years), and one hypothesis for their persistence is that allopolyploid female unisexuals periodically exchange haploid genomes ‘genome exchange’ during gynogenetic reproduction with males from sympatric sexual species. We test this hypothesis by using genome‐specific microsatellite DNA markers to estimate the rates of genome exchange between sexual males and unisexual females in two ponds in NE Ohio. We also test the prediction that levels of gene flow should be higher for ‘sympatric’ (sexual males present) genomes in unisexuals compared to ‘allopatric’ (sexual males absent) unisexual genomes. We used a model testing framework in the coalescent‐based program MIGRATE‐N to compare models where unidirectional gene flow is present and absent between sexual species and unisexuals. As predicted, our results show higher levels of gene flow between sexuals and sympatric unisexual genomes compared to lower (likely artefactual) levels of gene flow between sexuals and allopatric unisexual genomes. Our results provide direct evidence that genome exchange between sexual and unisexual Ambystoma occurs and demonstrate that the magnitude depends on which sexual species are present. The relatively high levels of gene flow suggest that unisexuals must be at a selective advantage over sexual forms so as to avoid extinction due to genetic swamping through genome exchange.     

The Biology of Time and Death

The steady flow of solar energy through prebiotic chemical systems forced them to undergo material cycles, and this cycling was inherited by living organisms. Organisms whose cycling synchronized with periodic phenomena, such as day/night and seasonal variations were favored. At a later stage, evolution also favored organisms that, besides of a synchronized cycling, developed a ‘sense of time’ to cope with non-cyclic and unique events in the environment. In the case of human beings, this ‘sense of time’ was used to detect causal chains (cause → effect), combine them to produce dynamic models of reality, and transform real time scales into mental time scales (it takes a moment to remember a year-long phenomenon). The ‘sense of time’ constituted a decisive evolutive advantage, because it enables humans to analyze a multitude of future possibilities, and choose the most promising one. Yet ‘sense of time’ is just an empty metaphore, because it is not a true ‘sense’, and we ignore what ‘time’ really is. Most scientific disciplines simply take for granted that there is a ‘time flowing from future to past’. Biologists instead, cannot adopt this attitude because ‘time’ may very well be an intrinsic property of our mind, i.e., a peculiar aspect of brain physiology.     

Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models

This article compares a general closed nutrient, stoichiometric producer-consumer model to a two-dimensional 'quasi-equilibrium' approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare-Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

Inferring landscape resistance to gene flow when genetic drift is spatially heterogeneous

In connectivity models, land cover types are assigned cost values characterizing their resistance to species movements. Landscape genetic methods infer these values from the relationship between genetic differentiation and cost distances. The spatial heterogeneity of population sizes, and consequently genetic drift, is rarely included in this inference although it influences genetic differentiation. Similarly, migration rates and population spatial distributions potentially influence this inference. Here, we assessed the reliability of cost value inference under several migration rates, population spatial patterns and degrees of population size heterogeneity. Additionally, we assessed whether considering intra-population variables, here using gravity models, improved the inference when drift is spatially heterogeneous. We simulated several gene flow intensities between populations with varying local sizes and spatial distributions. We then fit gravity models of genetic distances as a function of (i) the ‘true’ cost distances driving simulations or alternative cost distances, and (ii) intra-population variables (population sizes, patch areas). We determined the conditions making the identification of the ‘true’ costs possible and assessed the contribution of intra-population variables to this objective. Overall, the inference ranked cost scenarios reliably in terms of similarity with the ‘true’ scenario (cost distance Mantel correlations), but this ‘true’ scenario rarely provided the best model goodness of fit. Ranking inaccuracies and failures to identify the ‘true’ scenario were more pronounced when migration was very restricted (<4 dispersal events/generation), population sizes were most heterogeneous and some populations were spatially aggregated. In these situations, considering intra-population variables helps identify cost scenarios reliably, thereby improving cost value inference from genetic data.     

An information-theoretical approach to phylogeography

Data analysis in phylogeographic investigations is typically conducted in either a qualitative manner, or alternatively via the testing of null hypotheses. The former, where inferences about population processes are derived from geographical patterns of genetic variation, may be subject to confirmation bias and prone to overinterpretation. Testing the predictions of null hypotheses is arguably less prone to bias than qualitative approaches, but only if the tested hypotheses are biologically meaningful. As it is difficult to know a priori if this is the case, there is the general need for additional methodological approaches in phylogeographic research. Here, we explore an alternative method for analysing phylogeographic data that utilizes information theory to quantify the probability of multiple hypotheses given the data. We accomplish this by augmenting the model‐selection procedure implemented in ima with calculations of Akaike Information Criterion scores and model probabilities. We generate a ranking of 17 models each representing a set of historical evolutionary processes that may have contributed to the evolution of Plethodon idahoensis, and then quantify the relative strength of support for each hypothesis given the data using metrics borrowed from information theory. Our results suggest that two models have high probability given the data. Each of these models includes population divergence and estimates of ancestral θ that differ from estimates of descendent θ, inferences consistent with prior work in this system. However, the models disagree in that one includes migration as a parameter and one does not, suggesting that there are two regions of parameter space that produce model likelihoods that are similar in magnitude given our data. Results of a simulation study suggest that when data are simulated with migration, most of the optimal models include migration as a parameter, and further that when all of the shared polymorphism results from incomplete lineage sorting, most of the optimal models do not. The results could also indicate a lack of precision, which may be a product of the amount of data that we have collected. In any case, the information‐theoretic metrics that we have applied to the analysis of our data are statistically rigorous, as are hypothesis‐testing approaches, but move beyond the ‘reject/fail to reject’ dichotomy of conventional hypothesis testing in a manner that provides considerably more flexibility to researchers.     

Why do some species have geographically varying responses to fire history?

A capacity to predict the effects of fire on biota is critical for conservation in fire‐prone regions as it assists managers to anticipate the outcomes of different approaches to fire management. The task is complicated because species’ responses to fire can vary geographically. This poses challenges, both for conceptual understanding of post‐fire succession and fire management. We examine two hypotheses for why species may display geographically varying responses to fire. 1) Species’ post‐fire responses are driven by vegetation structure, but vegetation – fire relationships vary spatially (the ‘dynamic vegetation’ hypothesis). 2) Regional variation in ecological conditions leads species to select different post‐fire ages as habitat (the ‘dynamic habitat’ hypothesis). Our case study uses data on lizards at 280 sites in a ～ 100 000 km² region of south‐eastern Australia. We compared the predictive capacity of models based on 1) habitat associations, with models based on 2) fire history and vegetation type, and 3) fire history alone, for four species of lizards. Habitat association models generally out‐performed fire history models in terms of predictive capacity. For two species, habitat association models provided good discrimination capacity even though the species showed geographically varying post‐fire responses. Our results support the dynamic vegetation hypothesis, that spatial variation in relationships between fire and vegetation structure results in regional variation in fauna–fire relationships. These observations explain how the widely recognised ‘habitat accommodation’ model of animal succession can be conceptually accurate yet predictively weak.     

Detecting nonlinear response of spring phenology to climate change by Bayesian analysis

The impact of climate change on the advancement of plant phenological events has been heavily studied in the last decade. Although the majority of spring plant phenological events have been trending earlier, this is not universally true. Recent work has suggested that species that are not advancing in their spring phenological behavior are responding more to lack of winter chill than increased spring heat. One way to test this hypothesis is by evaluating the behavior of a species known to have a moderate to high chilling requirement and examining how it is responding to increased warming. This study used a 60‐year data set for timing of leaf‐out and male flowering of walnut (Juglans regia) cultivar ‘Payne’ to examine this issue. The spring phenological behavior of ‘Payne’ walnut differed depending on bud type. The vegetative buds, which have a higher chilling requirement, trended toward earlier leaf‐out until about 1994, when they shifted to later leaf‐out. The date of male bud pollen shedding advanced over the course of the whole record. Our findings suggest that many species which have exhibited earlier bud break are responding to warmer spring temperatures, but may shift into responding more to winter temperatures (lack of adequate chilling) as warming continues.     

A network-patch methodology for adapting agent-based models for directly transmitted disease to mosquito-borne disease

Mosquito-borne diseases cause significant public health burden and are widely re-emerging or emerging. Understanding, predicting, and mitigating the spread of mosquito-borne disease in diverse populations and geographies are ongoing modelling challenges. We propose a hybrid network-patch model for the spread of mosquito-borne pathogens that accounts for individual movement through mosquito habitats, extending the capabilities of existing agent-based models (ABMs) to include vector-borne diseases. The ABM are coupled with differential equations representing ‘clouds’ of mosquitoes in patches accounting for mosquito ecology. We adapted an ABM for humans using this method and investigated the importance of heterogeneity in pathogen spread, motivating the utility of models of individual behaviour. We observed that the final epidemic size is greater in patch models with a high risk patch frequently visited than in a homogeneous model. Our hybrid model quantifies the importance of the heterogeneity in the spread of mosquito-borne pathogens, guiding mitigation strategies.     

Mapping the complexity of ecological models

We propose to define the complexity of an ecological model as the statistical complexity of the output it produces. This allows for a direct comparison between data and model complexity. Working with univariate time series, we show that this measure ‘blindly’ discriminates among the different dynamical behaviours a model can exhibit. We then search a model parameter space in order to segment it into areas of different dynamical behaviour and calculate the maximum complexity a model can generate. Given a time series, and the problem of choosing among a number of ecological models to study it, we suggest that models whose maximum complexity is lower than the time series complexity should be disregarded because they are unable to reconstruct some of the structures contained in the data. Similar reasoning could be used to disregard models’ subdomains as well as areas of unnecessary high complexity. We suggest that model complexity so defined better captures the difficulty faced by a user in managing and understanding the behaviour of an ecological model than measures based on a model ‘size’.     

The virtual ecologist approach: simulating data and observers

Ecologists carry a well‐stocked toolbox with a great variety of sampling methods, statistical analyses and modelling tools, and new methods are constantly appearing. Evaluation and optimisation of these methods is crucial to guide methodological choices. Simulating error‐free data or taking high‐quality data to qualify methods is common practice. Here, we emphasise the methodology of the ‘virtual ecologist’ (VE) approach where simulated data and observer models are used to mimic real species and how they are ‘virtually’ observed. This virtual data is then subjected to statistical analyses and modelling, and the results are evaluated against the ‘true’ simulated data. The VE approach is an intuitive and powerful evaluation framework that allows a quality assessment of sampling protocols, analyses and modelling tools. It works under controlled conditions as well as under consideration of confounding factors such as animal movement and biased observer behaviour. In this review, we promote the approach as a rigorous research tool, and demonstrate its capabilities and practical relevance. We explore past uses of VE in different ecological research fields, where it mainly has been used to test and improve sampling regimes as well as for testing and comparing models, for example species distribution models. We discuss its benefits as well as potential limitations, and provide some practical considerations for designing VE studies. Finally, research fields are identified for which the approach could be useful in the future. We conclude that VE could foster the integration of theoretical and empirical work and stimulate work that goes far beyond sampling methods, leading to new questions, theories, and better mechanistic understanding of ecological systems.     

Status Signalling by Parus major: An Experiment in Deception

The ‘social control’ and ‘incongruence’ hypotheses, first put forward by ROHWER (1977) to explain how attempted ‘deceit’ status signalling is kept in check among winter-flocking birds, were tested under semi-natural conditions for Parus major. This species signals its social status by the width of its breast stripe. The lowest-ranked male in experimental flocks, each made up of four individuals, was manipulated in one of three ways: 1) the status signal was altered by painting the breast stripe to make it broader; 2) agonistic behaviour was altered by injecting testosterone; 3) both status signal and behaviour were manipulated. A study of the outcome of subsequent agonistic encounters by these birds revealed that the status of the manipulated individuals only rose when both their behaviour and status signal were altered. This indicates that the ‘social control’ hypothesis must be rejected, but not the ‘incongruence’ hypothesis.     

Masting,mixtures and modes: are two models better than one?

A key hypothesis in population ecology is that synchronous and intermittent seed production, known as mast seeding, is driven by the alternating allocation of carbohydrates and mineral nutrients between growth and reproduction in different years, i.e. ‘resource switching’. Such behaviour may ultimately generate bimodal distributions of long‐term flower and seed production, and evidence of these patterns has been taken to support the resource switching hypothesis. Here, we show how a widely‐used statistical test of bimodality applied by many studies in different ecological contexts may fail to reject the null hypothesis that focal probability distributions are unimodal. Using data from five tussock grass species in South Island, New Zealand, we find clear evidence of bimodality only when flowering patterns are analyzed with probabilistic mixture models. Mixture models provide a theory oriented framework for testing hypotheses of mast seeding patterns, enabling the different responses underlying medium‐ and high‐ versus non‐ and low‐flowering years to be modelled more realistically by associating these with distinct probability distributions. Coupling theoretical expectations with more rigorous statistical approaches will empower ecologists to reject null hypotheses more often.     

The past,present and future of reproductive skew theory and experiments

A major evolutionary question is how reproductive sharing arises in cooperatively breeding species despite the inherent reproductive conflicts in social groups. Reproductive skew theory offers one potential solution: each group member gains or is allotted inclusive fitness equal to or exceeding their expectation from reproducing on their own. Unfortunately, a multitude of skew models with conflicting predictions has led to confusion in both testing and evaluating skew theory. The confusion arises partly because one set of models (the ‘transactional’ type) answer the ultimate evolutionary question of what ranges of reproductive skew can yield fitness‐enhancing solutions for all group members. The second set of models (‘compromise’) give an evolutionarily proximate, game‐theoretic evolutionarily stable state (ESS) solution that determines reproductive shares based on relative competitive abilities. However, several predictions arising from compromise models require a linear payoff to increased competition and do not hold with non‐linear payoffs. Given that for most species it may be very difficult or impossible to determine the true relationship between effort devoted to competition and reproductive share gained, compromise models are much less predictive than previously appreciated. Almost all skew models make one quantitative prediction (e.g. realized skew must fall within ranges predicted by transactional models), and two qualitative predictions (e.g. variation in relatedness or competitive ability across groups affects skew). A thorough review of the data finds that these three predictions are relatively rarely supported. As a general rule, therefore, the evolution of cooperative breeding appears not to be dependent on the ability of group members to monitor relatedness or competitive ability in order to adjust their behaviour dynamically to gain reproductive share. Although reproductive skew theory fails to predict within‐group dynamics consistently, it does better at predicting quantitative differences in skew across populations or species. This suggests that kin selection can play a significant role in the evolution of sociality. To advance our understanding of reproductive skew will require focusing on a broader array of factors, such as the frequency of mistaken identity, delayed fitness payoffs, and selection pressures arising from across‐group competition. We furthermore suggest a novel approach to investigate the sharing of reproduction that focuses on the underlying genetics of skew. A quantitative genetics approach allows the partitioning of variance in reproductive share itself or that of traits closely associated with skew into genetic and non‐genetic sources. Thus, we can determine the heritability of reproductive share and infer whether it actually is the focus of natural selection. We view the ‘animal model’ as the most promising empirical method where the genetics of reproductive share can be directly analyzed in wild populations. In the quest to assess whether skew theory can provide a framework for understanding the evolution of sociality, quantitative genetics will be a central tool in future research.