Deconstructing crop processes and models via identities

This paper is part review and part opinion piece; it has three parts of increasing novelty and speculation in approach. The first presents an overview of how some of the major crop simulation models approach the issue of simulating the responses of crops to changing climatic and weather variables, mainly atmospheric CO₂ concentration and increased and/or varying temperatures. It illustrates an important principle in models of a single cause having alternative effects and vice versa. The second part suggests some features, mostly missing in current crop models, that need to be included in the future, focussing on extreme events such as high temperature or extreme drought. The final opinion part is speculative but novel. It describes an approach to deconstruct resource use efficiencies into their constituent identities or elements based on the Kaya‐Porter identity, each of which can be examined for responses to climate and climatic change. We give no promise that the final part is ‘correct’, but we hope it can be a stimulation to thought, hypothesis and experiment, and perhaps a new modelling approach.     

An analysis of biological random processes via optimized statistical models

The concept of a sampled probability-density vector is defined. It is shown that a relationship may be established between this new estimation means and the random process, expressed by its moment vector. This is a linear transformation using invariant matrices i.e. matrices which are independent of the random process. Thus, in deriving biological probability-density models, instead of using an analytical model, to estimate their parameters and to check the distributional assumptions, a single probability-density vector is computed, subject to some constraints. An optimized statistical model is, thus, obtained, by minimizing a certain loss function, which expresses the inaccuracy of the model. The invariant matrices permitting to obtain the optimized model, starting from the moment vector, are given and the procedure is illustrated by examples. Then, the concept of a parametric probability-density space is defined and it is shown that each of the vectors belonging to this space may express the stationary, ergodic, random process equally well. Some typical constraints in the probability-density space are investigated. It is shown that the normal (Gaussian) law may be regarded as a very strong constraint in the probability-density space, while the integral law, expressing the cumulative distribution function, is a weak one. Between these extreme cases, the large class of the usual constraints are examined, which are determined by the prior knowledge of the process, as well as by some desired model features. Thus, the concept of a constrained probability-density vector is introduced. By using a linear-programming procedure and by observing some peak constraints as well as some slope-sign ones, an optimized model with desired shape is obtained, where a certain value of the variable has a very high probability. This leads to a procedure which enables synaptic models to be derived. In such a model, the constraints in the probability-density space may be regarded as a new expression of the information transmitted in the nervous system. Moreover, the loss function may express the aptitude of the random process to realize a given message. Thus, by using the optimized statistical model concept, probabilistic models with desired features for various biological processes may be obtained in a simple and general manner.     

Animal models and conserved processes

Background

The concept of conserved processes presents unique opportunities for using nonhuman animal models in biomedical research. However, the concept must be examined in the context that humans and nonhuman animals are evolved, complex, adaptive systems. Given that nonhuman animals are examples of living systems that are differently complex from humans, what does the existence of a conserved gene or process imply for inter-species extrapolation?

Methods

We surveyed the literature including philosophy of science, biological complexity, conserved processes, evolutionary biology, comparative medicine, anti-neoplastic agents, inhalational anesthetics, and drug development journals in order to determine the value of nonhuman animal models when studying conserved processes.

Results

Evolution through natural selection has employed components and processes both to produce the same outcomes among species but also to generate different functions and traits. Many genes and processes are conserved, but new combinations of these processes or different regulation of the genes involved in these processes have resulted in unique organisms. Further, there is a hierarchy of organization in complex living systems. At some levels, the components are simple systems that can be analyzed by mathematics or the physical sciences, while at other levels the system cannot be fully analyzed by reducing it to a physical system. The study of complex living systems must alternate between focusing on the parts and examining the intact whole organism while taking into account the connections between the two. Systems biology aims for this holism. We examined the actions of inhalational anesthetic agents and anti-neoplastic agents in order to address what the characteristics of complex living systems imply for inter-species extrapolation of traits and responses related to conserved processes.

Conclusion

We conclude that even the presence of conserved processes is insufficient for inter-species extrapolation when the trait or response being studied is located at higher levels of organization, is in a different module, or is influenced by other modules. However, when the examination of the conserved process occurs at the same level of organization or in the same module, and hence is subject to study solely by reductionism, then extrapolation is possible.     

Multiple identification processes on the Island of Korcula (nested identities)

The aim of this paper is to investigate the ways contemporary identification processes on the island of Korcula take place. The changes in the political situation during 1990s, as well as contemporary context of the accession of the Republic of Croatia into European integration, provided the new "arena" for the expression of different identifications. The positioning of identities into the wider context, either on vertical or horizontal level, is also important in these processes. The research was carried out at all the major settlements on the island of Korcula by qualitative methodological tools and ethnographic approach. The results indicate the existence of nested identities on the island of Korcula (ranging from supranational (European) to national and regional and finally to diverse local identifications and their situational and dynamic character. The nested identities on the island of Korcula demonstrate their mutual compatibility and the fact that not only identities of the higher order (regional, for example) comprise the identities of the lower order (local, for example); the reverse process also takes place. The members of seemingly close and similar island communities in fact have very differentiated local identifications that are very often equally important or even more important than identities of the higher order, such as national.     

Stochastic models for aggregation processes

Three models are presented, which describe the aggregation of objects into groups and the distributions of groups sizes and group numbers within habitats. The processes regarded are pure accumulation processes which involve only formation and invasion of groups. Invasion represents the special case of fusion when only single objects - and not groups - join a group of certain size. The basic model is derived by a single parameter, the formation probability q, which represents the probability of an object to form a new group. A novel, discrete and finite distribution that results for the group sizes is deduced from this aggregation process and it is shown that it converges to a geometric distribution if the number of objects tends to infinity. Two extensions of this model, which both converge to the Waring distribution, are added: the model can be extended either with a beta distributed formation probability or with the assumption that the invasion probability depends on the group size. Relationships between the limiting distributions involved are discussed.     

Chain binomial models and binomial autoregressive processes

Summary We establish a connection between a class of chain‐binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag‐ conditional distribution and related quantities. We focus on two types of chain‐binomial model, extinction–colonization and colonization–extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite‐sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.     

Development of models for specific crop calendar events

In order to test growth prediction and yield prediction equations on historical weather data for areas where planting dates were not published, or for areas where dates of planting will not be as readily accessible as weather data, there is a need for a model to predict the date of planting. Such a model was developed by regressing reported percentages of the wheat crop planted on various weather variables and their transformations. The model for predicting percentage of wheat acreage planted in North Dakota was tested on data not used in formulating the coefficients of the model. Although the predictions may have errors of several days the model is considered to be an improvement over a system utilizing a constant year-to-year average planting date.The research was supported by funds supplied by the National Aeronautics and Space Administration under contract No. NAS 9-14006.Presented at the Seventh International Biometeorological Congress, 17–23 August 1975, College Park, Maryland, USA.     

Differences in diffuse photosynthetically active radiation effects on cropland light use efficiency calculated via contemporary remote sensing and crop production models

Diffuse photosynthetically active radiation (PAR_diff) is instrumental to the light use efficiency (LUE) of vegetation. Accurately assessing the impact of PAR_diff on crop LUE can better our understanding of the carbon cycle in cropland ecosystems. LUE estimates from six remote sensing models (including four big-leaf models and two two-leaf models) and two crop production models were compared with measured FLUXNET LUE data from cropland sites under different PAR_diff fraction (FDIFF_PAR) intervals. Compared with the FLUXNET observations, the Eddy Covariance-Light Use Efficiency (EC-LUEa) model exhibited the best LUE estimation (R² = 0.250, RMSE = 0.868 gC·MJ⁻¹, and Bias = −0.005 gC·MJ⁻¹) owing to the use of more accurate calculation scheme of environmental stress factors. LUEs calculated from FLUXNET observational data were positively correlated with FDIFF_PAR, but only LUEs simulated by the Moderate Resolution Imaging Spectroradiometer Photosynthesis (MOD17) and Two-Leaf Light Use Efficiency (TL-LUE) models increased with increasing FDIFF_PAR. This is attributed to the fact that the MOD17 model divides the crop growth types into cereal and broadleaf, while the TL-LUE model considers the change of light interception with increased FDIFF_PAR. Furthermore, the maximum LUE (LUE_max) increased with FDIFF_PAR at FLUXNET observational sites, but the eight models could not capture the effects of PAR_diff on the crop LUE_max. Among the eight models, the LUE_max–FDIFF_PAR relationship simulated by the two-leaf models fluctuated because the crops were divided into sunlit and shaded leaves, while the big-leaf and crop production models used a constant LUE_max and showed a constant LUE_max–FDIFF_PAR relationship. Additionally, big-leaf models performed better than two-leaf models for gross primary production (GPP) simulation in the cropland ecosystem, which is related to the planting density and vegetation structure. These results demonstrate the importance of considering the impact of FDIFF_PAR on LUE_max in LUE modeling.     

Deconstructing Eurocentrism in skin pigmentation research via the incorporation of diverse populations and theoretical perspectives

The evolution of skin pigmentation has been shaped by numerous biological and cultural shifts throughout human history. Vitamin D is considered a driver of depigmentation evolution in humans, given the deleterious health effects associated with vitamin D deficiency, which is often shaped by cultural factors. New advancements in genomics and epigenomics have opened the door to a deeper exploration of skin pigmentation evolution in both contemporary and ancient populations. Data from ancient Europeans has offered great context to the spread of depigmentation alleles via the evaluation of migration events and cultural shifts that occurred during the Neolithic. However, novel insights can further be gained via the inclusion of diverse ancient and contemporary populations. Here we present on how potential biases and limitations in skin pigmentation research can be overcome with the integration of interdisciplinary data that includes both cultural and biological elements, which have shaped the evolutionary history of skin pigmentation in humans.     

Solvable models of neighbor-dependent substitution processes

We prove that a wide class of Markov models of neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotidic substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotidic frequencies at equilibrium solve some finite-size linear systems. This provides, for the first time up to our knowledge, explicit and algebraic formulas for the stationary frequencies of non-degenerate neighbor-dependent models of DNA substitutions. Furthermore, we show that the dynamics of these stochastic processes and their distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotidic sites at distance at least three evolve independently, and all the sites, when encoded as purines and pyrimidines, evolve independently.     

Landscape level processes driving carabid crop assemblage in dynamic farmlands

Landscape heterogeneity has been shown to be a major factor in the maintenance of biodiversity and associated services in agricultural landscapes. Farmlands are mosaics of fields with various crop types and farming practices. Crop phenology creates asynchrony between fields sown and harvested in different periods (winter vs. spring crops). The present study was conducted to examine the influence of such spatio-temporal heterogeneity on biodiversity, with the hypothesis that it would lead to spatio-temporal redistribution (shifting) of species. Species richness and activity-density of carabid beetles in winter cereal (winter) and maize (spring) crops were compared across 20 landscapes distributed along a double gradient of relative area and spatial configuration of winter and spring crops. Maize fields were sampled in spring and late summer for comparison over time. The response of carabid species richness to landscape heterogeneity was weak in spring, but maize field richness benefited from adjacencies with woody habitat, in late summer. In spring, increased length of interfaces between winter and spring crops lowered carabid activity-density in winter cereal fields, suggesting that maize fields acted as sinks. Interfaces between woody habitats and crops increased activity-density in both crop types. We found no evidence of spatio-temporal complementation, but different species benefited from winter cereals and maize in spring and late summer, increasing overall diversity. These findings confirm the role of adjacencies between woody and cultivated habitats in the conservation of abundant carabid assemblage in winter cereals and maize. We conclude that between-field population movement occurs, and advocate for better consideration of farmland heterogeneity in future research.     

LFT models of continuous biotechnological processes

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.     

Lateral inhibition models of developmental processes

Most mathematical models for embryological pattern formation depend on the phenomenon of local autocatalysis with lateral inhibition (LALI). While the underlying physical and chemical mechanisms hypothesized by the models may be quite different, they all predict very similar kinds of spatial patterns. Therefore, since the underlying mechanism cannot in general be deduced from the pattern itself, other criteria must be applied in evaluating the usefulness of pattern formation models. The author points out how LALI is implemented in neural, chemical, and mechanical models of development, and suggests some general properties of LALI models that may impose limitations on organ shapes in ontogeny and phylogeny.     

Stochastic and deterministic processes shape bioenergy crop microbiomes along a vertical soil niche

Sustainable biofuel cropping systems aim to address climate change while meeting energy needs. Understanding how soil and plant-associated microbes respond to these different cropping systems is key to promoting agriculture sustainability and evaluating changes in ecosystem functions. Here, we leverage a long-term biofuel cropping system field experiment to dissect soil and root microbiome changes across a soil-depth gradient in poplar, restored prairie and switchgrass to understand their effects on the microbial communities. High throughput amplicon sequencing of the fungal internal transcribed spacer (ITS) and prokaryotic 16S DNA regions showed a common trend of root and soil microbial community richness decreasing and evenness increasing with depth. Ecological niche (root vs. soil) had the strongest effect on community structure, followed by depth, then crop. Stochastic processes dominated the structuring of fungal communities in deeper soil layers while operational taxonomic units (OTUs) in surface soil layers were more likely to co-occur and to be enriched by plant hosts. Prokaryotic communities were dispersal limited at deeper depths. Microbial networks showed a higher density, connectedness, average degree and module size in deeper soils. We observed a decrease in fungal-fungal links and an increase of bacteria–bacteria links with increasing depth in all crops, particularly in the root microbiome.     

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ‐level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single‐scale models are unable to capture the critical cross‐scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.     

Modelling biological processes using workflow and Petri Net models

MOTIVATION: Biological processes can be considered at many levels of detail, ranging from atomic mechanism to general processes such as cell division, cell adhesion or cell invasion. The experimental study of protein function and gene regulation typically provides information at many levels. The representation of hierarchical process knowledge in biology is therefore a major challenge for bioinformatics. To represent high-level processes in the context of their component functions, we have developed a graphical knowledge model for biological processes that supports methods for qualitative reasoning. RESULTS: We assessed eleven diverse models that were developed in the fields of software engineering, business, and biology, to evaluate their suitability for representing and simulating biological processes. Based on this assessment, we combined the best aspects of two models: Workflow/Petri Net and a biological concept model. The Workflow model can represent nesting and ordering of processes, the structural components that participate in the processes, and the roles that they play. It also maps to Petri Nets, which allow verification of formal properties and qualitative simulation. The biological concept model, TAMBIS, provides a framework for describing biological entities that can be mapped to the workflow model. We tested our model by representing malaria parasites invading host erythrocytes, and composed queries, in five general classes, to discover relationships among processes and structural components. We used reachability analysis to answer queries about the dynamic aspects of the model. AVAILABILITY: The model is available at http://smi.stanford.edu/projects/helix/pubs/process-model/.     

Understanding patterns and processes in models of trophic cascades

Climate fluctuations and human exploitation are causing global changes in nutrient enrichment of terrestrial and aquatic ecosystems and declining abundances of apex predators. The resulting trophic cascades have had profound effects on food webs, leading to significant economic and societal consequences. However, the strength of cascades–that is the extent to which a disturbance is diminished as it propagates through a food web–varies widely between ecosystems, and there is no formal theory as to why this should be so. Some food chain models reproduce cascade effects seen in nature, but to what extent is this dependent on their formulation? We show that inclusion of processes represented mathematically as density‐dependent regulation of either consumer uptake or mortality rates is necessary for the generation of realistic ‘top‐down’ cascades in simple food chain models. Realistically modelled ‘bottom‐up’ cascades, caused by changing nutrient input, are also dependent on the inclusion of density dependence, but especially on mortality regulation as a caricature of, e.g. disease and parasite dynamics or intraguild predation. We show that our conclusions, based on simple food chains, transfer to a more complex marine food web model in which cascades are induced by varying river nutrient inputs or fish harvesting rates.