Decay of heterogenous detritus: A general model

A new, general model of decay of organic matter assumes that the various constituents of the decaying mass have (1) different rates of decomposition and (2) different rates of transformation to more or less decomposable forms. Existing models of the decay process are special cases of the general model that share three assumptions: (a) no transformation of detrital components, (b) equal rates of decay for one or two homogeneous constituents of the decaying mass, and (6) a uniform distribution of each type of constituent at the beginning of decay. A solution of the general model that relaxes these three assumptions fits previously published data closely. The general model unites existing models, permits comparisons of their assumptions, and provides a theoretical framework for developing and evaluating particular models that embody assumptions more in harmony with empirical knowledge of decay mechanisms.     

Building clone-consistent ecosystem models

Many ecological studies employ general models that can feature an arbitrary number of populations. A critical requirement imposed on such models is clone consistency: If the individuals from two populations are indistinguishable, joining these populations into one shall not affect the outcome of the model. Otherwise a model produces different outcomes for the same scenario. Using functional analysis, we comprehensively characterize all clone-consistent models: We prove that they are necessarily composed from basic building blocks, namely linear combinations of parameters and abundances. These strong constraints enable a straightforward validation of model consistency. Although clone consistency can always be achieved with sufficient assumptions, we argue that it is important to explicitly name and consider the assumptions made: They may not be justified or limit the applicability of models and the generality of the results obtained with them. Moreover, our insights facilitate building new clone-consistent models, which we illustrate for a data-driven model of microbial communities. Finally, our insights point to new relevant forms of general models for theoretical ecology. Our framework thus provides a systematic way of comprehending ecological models, which can guide a wide range of studies.     

Avian SDMs: current state,challenges, and opportunities

Quantifying species distributions using species distribution models (SDMs) has emerged as a central method in modern biogeography. These empirical models link species occurrence data with spatial environmental information. Since their emergence in the 1990s, thousands of scientific papers have used SDMs to study organisms across the entire tree of life, with birds commanding considerable attention. Here, we review the current state of avian SDMs and point to challenges and future opportunities for specific applications, ranging from conservation biology, invasive species and predicting seabird distributions, to more general topics such as modeling avian diversity, niche evolution and seasonal distributions at a biogeographic scale. While SDMs have been criticized for being phenomenological in nature, and for their inability to explicitly account for a variety of processes affecting populations, we conclude that they remain a powerful tool to learn about past, current, and future species distributions – at least when their limitations and assumptions are recognized and addressed. We close our review by providing an outlook on prospects and synergies with other disciplines in which avian SDMs can play an important role.     

Predicting local–regional richness relationships using island biogeography models

Local species richness frequently is linearly related to the richness of the regional species pool from which the local community was presumably assembled. What, if anything, does this pattern imply about the relative importance of species interactions and dispersal as determinants of local species richness? Two recent papers by Hugueny and Cornell and He et al. propose that the classical island biogeography model of MacArthur and Wilson can help answer this question, by serving as a null model of the relationship between local (island) and regional (mainland) species richness in the absence of local species interactions. The two models make very different predictions, despite being derived from apparently‐similar assumptions. Here we reinterpret these two models and show that their contrasting predictions can be regarded as arising from different, implicit assumptions about how species abundances vary with species richness on the mainland. We derive a more general island biogeography model of local–regional richness relationships that explicitly incorporates mainland species abundance and subsumes the two previous models as limiting cases. The new model predicts that the local–regional richness relationship can range from nearly linear to strongly curvilinear, depending on how species abundances on the mainland vary with mainland richness, as well as on rates of immigration to and extinction from islands. Local species interactions are not necessary for producing curvilinear local–regional richness relationships. We discuss the implications of our new model for the interpretation of local–regional richness relationships.     

Towards Predictive Computational Models of Oncolytic Virus Therapy: Basis for Experimental Validation and Model Selection

Oncolytic viruses are viruses that specifically infect cancer cells and kill them, while leaving healthy cells largely intact. Their ability to spread through the tumor makes them an attractive therapy approach. While promising results have been observed in clinical trials, solid success remains elusive since we lack understanding of the basic principles that govern the dynamical interactions between the virus and the cancer. In this respect, computational models can help experimental research at optimizing treatment regimes. Although preliminary mathematical work has been performed, this suffers from the fact that individual models are largely arbitrary and based on biologically uncertain assumptions. Here, we present a general framework to study the dynamics of oncolytic viruses that is independent of uncertain and arbitrary mathematical formulations. We find two categories of dynamics, depending on the assumptions about spatial constraints that govern that spread of the virus from cell to cell. If infected cells are mixed among uninfected cells, there exists a viral replication rate threshold beyond which tumor control is the only outcome. On the other hand, if infected cells are clustered together (e.g. in a solid tumor), then we observe more complicated dynamics in which the outcome of therapy might go either way, depending on the initial number of cells and viruses. We fit our models to previously published experimental data and discuss aspects of model validation, selection, and experimental design. This framework can be used as a basis for model selection and validation in the context of future, more detailed experimental studies. It can further serve as the basis for future, more complex models that take into account other clinically relevant factors such as immune responses.     

Random biochemical networks: the probability of self-sustaining autocatalysis

We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient 'food' source. Such systems have previously been investigated for their relevance to origin-of-life models. In this paper we extend earlier work, by finding precisely the order of catalysation required for the emergence of such self-sustaining autocatalytic networks. This answers questions raised in earlier papers, yet also allows for a more general class of models. We also show that a recently described polynomial-time algorithm for determining whether a catalytic reaction system contains an autocatalytic, self-sustaining subsystem is unlikely to adapt to allow inhibitory catalysation--in this case we show that the associated decision problem is NP-complete.     

Dependence of epidemic and population velocities on basic parameters.

This paper describes the use of linear deterministic models for examining the spread of population processes, discussing their advantages and limitations. Their main advantages are that their assumptions are relatively transparent and that they are easy to analyze, yet they generally give the same velocity as more complex linear stochastic and nonlinear deterministic models. Their simplicity, especially if we use the elegant reproduction and dispersal kernel formulation of Diekmann and van den Bosch et al., allows us greater freedom to choose a biologically realistic model and greatly facilitates examination of the dependence of conclusions on model components and of how these are incorporated into the model and fitted from data. This is illustrated by consideration of a range of examples, including both diffusion and dispersal models and by discussion of their application to both epidemic and population dynamic problems. A general limitation on fitting models results from the poor accuracy of most ecological data, especially on dispersal distances. Confirmation of a model is thus rarely as convincing as those cases where we can clearly reject one. We also need to be aware that linear models provide only an upper bound for the velocity of more realistic nonlinear stochastic models and are almost wholly inadequate when it comes to modeling more complex aspects such as the transition to endemicity and endemic patterns. These limitations are, however, to a great extent shared by linear stochastic and nonlinear deterministic models.     

Correlation and process in species distribution models: bridging a dichotomy

Within the field of species distribution modelling an apparent dichotomy exists between process‐based and correlative approaches, where the processes are explicit in the former and implicit in the latter. However, these intuitive distinctions can become blurred when comparing species distribution modelling approaches in more detail. In this review article, we contrast the extremes of the correlative–process spectrum of species distribution models with respect to core assumptions, model building and selection strategies, validation, uncertainties, common errors and the questions they are most suited to answer. The extremes of such approaches differ clearly in many aspects, such as model building approaches, parameter estimation strategies and transferability. However, they also share strengths and weaknesses. We show that claims of one approach being intrinsically superior to the other are misguided and that they ignore the process–correlation continuum as well as the domains of questions that each approach is addressing. Nonetheless, the application of process‐based approaches to species distribution modelling lags far behind more correlative (process‐implicit) methods and more research is required to explore their potential benefits. Critical issues for the employment of species distribution modelling approaches are given, together with a guideline for appropriate usage. We close with challenges for future development of process‐explicit species distribution models and how they may complement current approaches to study species distributions.     

Assessing models of optimal diving

Many birds and mammals forage under water and have to return to the surface to breathe. Models of optimal diving attempt to explain the behaviour of such animals in terms of selection for successful foraging given the constraints imposed by physiology. Several recent papers have questioned the accuracy of both the assumptions and the predictions of these models. Here, I provide a critical review of these papers, arguing that they misrepresent both the models and the data. As a result, they focus on inappropriate tests. I use the debate to suggest various new models and to explore the general relationship between theory and data in behavioural ecology. In particular, I consider the merits of qualitative and quantitative predictions.     

Dynamics of a simple regulatory switch

We consider the dynamics of a model toggle switch abstracted from the genetic interactions operative in a fungal stress response circuit. The switch transduces an external signal and propagates it forward by mediating the transport between compartments of two interacting gene products. The transport between compartments is assumed to be related to the degree of association between the interacting proteins, a fact for which there exists a wealth of biological evidence. The ubiquity and modularity of this cellular control mechanism warrants a detailed study of the dynamics entailed by various modelling assumptions. Specifically, we consider a general gate model in which both of the associating proteins are freely transportable between compartments. A more restrictive, but biologically supported model, is considered in which only one of the two proteins undergoes transport. Under the strong assumption that the disassociation of the interacting proteins is unidirectional we show that the qualitative dynamics of the two models are similar; that is they both converge to unique periodic orbits. From a biophysical perspective the assumption of unidirectional dissociation is unrealistic. We show that the same result holds for the more restrictive model when one weakens the assumption of unidirectional binding or disassociation. We speculate that this is not true for the more general model. This difference in dynamics may have important biological implications and certainly points to promising avenues of research.     

A log-linear modeling framework for selective mixing.

Nonrandom mixing can significantly alter the diffusion path of an infectious disease such as AIDS that requires intimate contact. Recent attempts to model this effect have sought a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the balancing problem in a nonequilibrium multigroup population. Log-linear models are proposed here as a general framework for solving the first problem. This approach offers several additional benefits: The parameters used to govern the mixing have a simple, intuitive interpretation, the framework provides a statistically sound basis for the estimation of these parameters from mixing-matrix data, and the resulting estimates are easily integrated into compartmental models for diffusion. A modified selection model is proposed to solve the second problem of generalizing the selection process to nonequilibrium populations. The distribution of contacts under this model is derived and is found to satisfy the assumptions of statistical inference for log-linear models. Together these techniques provide an integrated and flexible framework for modeling the role of selective mixing in the spread of disease.     

Replicating and breaking models: good for you and good for ecology

There are two major limitations to the potential of computational models in ecology for producing general insights: their design is path‐dependent, reflecting different underlying questions, assumptions, and data, and there is too little robustness analysis exploring where the model mechanisms explaining certain observations break down. We here argue that both limitations could be overcome if modellers in ecology would more often replicate existing models, try to break the models, and explore modifications. Replication comprises the re‐implementation of an existing model and the replication of its results. Breaking models means to identify under what conditions the mechanisms represented in a model can no longer explain observed phenomena. The benefits of replication include less effort being spent to enter the iterative stage of model development and having more time for systematic robustness analysis. A culture of replication would lead to increased credibility, coherence and efficiency of computational modelling and thereby facilitate theory development.     

An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City

Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and projection with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible–exposed–infectious–recovered (SEIR) model, including new compartments and model vaccination in order to project the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately project the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC’s government’s website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.     

Idealized, Inaccurate but Successful: A Pragmatic Approach to Evaluating Models in Theoretical Ecology

Ecologists attempt to understand the diversity of life with mathematical models. Often, mathematical models contain simplifying idealizations designed to cope with the blooming, buzzing confusion of the natural world. This strategy frequently issues in models whose predictions are inaccurate. Critics of theoretical ecology argue that only predictively accurate models are successful and contribute to the applied work of conservation biologists. Hence, they think that much of the mathematical work of ecologists is poor science. Against this view, I argue that model building is successful even when models are predictively inaccurate for at least three reasons: models allow scientists to explore the possible behaviors of ecological systems; models give scientists simplified means by which they can investigate more complex systems by determining how the more complex system deviates from the simpler model; and models give scientists conceptual frameworks through which they can conduct experiments and fieldwork. Critics often mistake the purposes of model building, and once we recognize this, we can see their complaints are unjustified. Even though models in ecology are not always accurate in their assumptions and predictions, they still contribute to successful science.     

Defining the assumptions underlying modeling of epistatic QTL using variance component methods

Variance component models are commonly used to detect quantitative trait loci (QTL) in general pedigrees. The variance-covariance structure of the random QTL effect is given by the identity by descent (IBD) between genotypes. Epistatic effects have previously been modeled, both for unlinked and linked loci, as a random effect with a variance-covariance structure given by the Hadamard product between the IBD matrices of the direct QTL effects. In the original papers, the model was given but not derived. Here, we identify the underlying assumptions of this previously proposed model. It assumes that either an unlinked QTL or a fully informative marker (i.e., all marker alleles are unique in the base generation) is located between the loci. We discuss the need of developing a general algorithm to estimate the variance-covariance structure of the random epistatic effect for linked loci.     

Some basic elements of continuous selection models

We present a general framework for the discussion of continuous population genetic models of monoecious diploid populations that incorporate one or more of age structure, mortality selection, mating structure, and fertility of matings. Within this framework, we then develop the specific models recently presented by Charlesworth (1970, Models 1 and 2) and Nagylaki and Crow (1974) and establish conditions under which the Malthusian parameters of these papers are equivalent.