A number of software tools using IBMs have been developed. These include EasyPop, a population genetics simulator to simulate neutral loci datasets under various mating schemes and migration models [52]; IBDSim, a program for simulating isolation by distance between individuals [53]; QuantiNemo, an individual-based model for simulating quantitative traits amongst individuals within heterogeneous “patches” [54]; and SimuPop, a flexible simulator that consists of a library of python functions that are required by the user to be “glued together” within a python script, which again has various different mating schemes and migration models at the users disposal [55,56]. GenomePop [57] is an IBM that utilizes Markovian nucleotide or codon models of DNA mutation, such as the Jukes-Cantor or general time reversible mutation model to generate synonymous and non-synonymous mutations. GenomePop thus provides an IBM that can simulate more information at the nucleotide level. GenomePop can also simulate recombination, allow constant or variable population sizes and provides different migration models such as the Island model and the stepping stone model.

The programs listed in [42,43,52,53,54] have been described as being semi-spatial [58]. However, due to the flexibility of IBMs they can readily have a fully spatial element incorporated within them to become spatially explicit. Broadly speaking, spatially-explicit individual-based models (SIBMs) contain individuals that are distributed across an area, such as a lattice or matrix (although non-lattice models have been proposed [58]) and may interact with other individuals in a spatially constrained way rather than purely at random. A number of plant-based SIBMs simulation studies have also emerged [59,60,61] in which the spatial element of these models is of particular importance, due to the sedentary nature of plants. The spatial element is of increased importance in anemophilous crops and trees due to their limited dispersal, which follows a “leptokurtic” curve [62]. Doligez et al. [59] compared their simulated plant populations, when permitted to form a uniform distribution throughout their matrix, with the clumped populations that readily formed through limited dispersal. They found that the clumped populations exhibited greater spatial genetic structure than the continuously distributed populations, particularly when selfing was allowed. Kitchen and Allaby [60] developed a plant-based SIBM to study the effects of spatial extension between individuals upon the heterozygosity of the plant populations when compared to mean-field HWE expectations. They showed that when plant-mating systems approximated mean-field assumptions (i.e., the density was such that the individuals were approximately randomly mating) the observed and expected heterozygosities were largely equivalent. However, the heterozygosity of individuals decreased from mean-field expectations as sparseness amongst individuals increased. AMELIE [61] is a SIBM with a rather more direct application towards food-security and GM crops, and was used to study the amount of introgression from GM forests to conventional forests. It can also allow various life histories and mating systems and can provide demographic and environmental stochasticity. These simulations, however, are only simulating neutral markers and do not attempt to model selection. It is relatively straightforward to take an IBM or SIBM framework and then hard-code a specific adaptive trait, such as one that may influence selection through the perturbation of mortality, or reproductive rate, at a di-allelic or perhaps even a multi-allelic locus if necessary. However, the goal is to be able to account for a possible continuum in the range of landscape heterogeneity and on the strength of the selection inferred from the landscape. One emergent approach is to utilize the concept of resistance surfaces [63,64] and modify the surface in such a way as to produce a “fitness landscape”.

The activation of some genes within a network may hold certain dependencies with the activities of other genes, such as the “AND” and “OR” behavior described previously. Thus, it is possible to represent genes in a similar manner to logic gates, where a gene may belong to one of two discrete states, namely “ON” or “OFF” and hold a set of discrete dependencies in terms of activation with other genes in the network, such as “AND”, “OR” and “NOT” relationships, Figure 4. Boolean representations of genes were first described by Kauffman [86] and are widely used today. An example piece of software for inference of Boolean network from experimental data is REVEAL (REVerse Engineering Algorithm) [87], which enumerates through all possible Boolean networks from the input data and uses mutual information to score each network, with the most sparse network that best describes the data being given as the optimal network. Boolean networks, which although able to represent dynamical networks, do have quite clear limitations, however. Firstly the transcriptional levels of a gene are continuous values and cannot simply be discretized into a binary variable such as “on” or “off”. Multiple discrete states, however, such as “gene product present” or “gene product absent” as well as “on” or “off” have been proposed [88]. Furthermore, Boolean networks are intrinsically deterministic and may be inadequate for describing the various stochastic effects within a network. To this end, probabilistic [89] and more recently stochastic [90] Boolean network variants have been proposed, which retain the rule-based determinism of Boolean networks yet can better model uncertainty.

Genes are not simply active or inactive, yet are transcribed at continuous rates so that the amount of transcript for one gene is dependent upon the rate of transcription of another gene (although this may be discretized through the use of “gene thresholds” for activation in modeling efforts). This lends itself conveniently to using ordinary differential equations (ODE’s) to represent GRNs. The resulting modeling functions used may be linear or non-linear with an example software tool used to infer linear models from expression data being EXAMINE (Expression Array MINing Engine) [91]. Another approach for the mathematical modeling of GRNs is to describe gene expression values as random variables following probability distributions, such as in Bayesian inference [92]. Bayesian networks form a directed-acyclic graph (DAG) and may represent dynamic or static (i.e., representing a GRN once a steady-state has been reached) networks using continuous or discrete data, and are readily able to model the randomness and stochastic effects that may exist amongst GRNs. This makes them more robust in the presence of noise or missing data than Boolean networks. Another benefit of Bayesian networks is that they provide a framework that allows researchers to incorporate prior knowledge for network inference. However, caution should be made when little or no information is available, as the use of uninformative priors (e.g., uniform priors) can make Bayesian network inference inefficient. As Bayesian networks are formed with a DAG, static networks cannot represent cycles such as in feedback loops. However, this limitation is not present with dynamic Bayesian networks [93], as they avoid cyclical representations by using discrete time steps to separate input nodes (e.g., at time t) from output nodes (e.g., at time t + ∆t). BANJO (BAyesian Networks with Java Objects) is a software tool that has been developed for the inference of static and dynamic Bayesian networks [94].

GRNs have so far received little attention within evolutionary studies at the population genetics level [95]. Studies of genotype by phenotype interaction commonly involve the analysis of quantitative traits, such as seed size or petal color that are influenced by one or more loci. Therefore the modeling of quantitative traits or even quantitative trait loci (QTLs) may be a viable alternative to explicitly modeling GRNs and may benefit a model in terms of efficiency or when there is insufficient data in which to infer a GRN. However, QTLs themselves may interact with cis-acting or trans-acting elements on the transcriptomic and proteomic levels, and may code for catalytic proteins that interact with substrates on the metabolomic level, before the quantitative trait is expressed. It has also been suggested that all genes are not equivalent regarding their evolutionary role, as in standard population genetics models, yet it is a gene’s position within a network that determines its evolutionary role [96,97,98]. Therefore differential effects on phenotypic variation may arise from mutation of the genes in a network. For instance, we have already discussed an example found in nature with mutation of the nodes within the photoperiodicity system (Figure 2) causing either late or early flowering times. Allelic variants of these elements may also be under selection: For example, we know that 6% of the human genome is currently under selection, yet only 1.5% of the genome is protein coding [99], with the rest of the purifying selection possibly on regulatory elements. If selection favors co-inheritence of a collection of alleles which interact with each other within a GRN, then these alleles may also be placed under linkage disequilibrium and not become segregated by recombination [100]. Therefore simulation of GRNs may provide researchers with a better understanding of the specific alleles that need to be in a network to fully take advantage of a given set of environmental conditions.

Evolution in the context of GRNs has been receiving more interest in recent years [96,101], especially in the field of evolutionary developmental biology [102,103] or Evo-Devo, concerned with the comparative analysis of the developmental processes of species and of the evolutionary relationship between the developmental processes. The bioinformatics community is also becoming increasingly interested with the study of the ancestral relationships between biomolecular networks, with algorithms being developed for network alignment [104,105]. In their review, Knight and Pinney [101] describe seven mechanistic perturbations of biological networks including rewiring, or new edges being introduced between nodes; node duplication; node loss and entire network duplication. It has been shown that a single point mutation is sufficient to induce entire proteomic network rewiring [106]. It is also understood that duplication may lead to sub- and neo-functionalization within networks, where either the resulting paralogs take on separate functions from each other (where the ancestral gene was capable of all functions) or one paralog takes on a new function, respectively. The concept that single gene and whole genome duplication could lead to evolutionary diversification has existed for decades [107] and is still commonly under study [108,109]. We have already discussed the widely documented examples of network motifs found within biological motifs, their potential roles and how their structure may relate to function, if at all. Whether the structure of a motif necessarily relates to function may currently be a topic of debate, however, it is conceivable that selection for a particular phenotype may require a specific structural motif, and this has been suggested for the positive feedback loop [110]. There have also been a number of studies of how motif structure may influence stochastic fluctuations, or noise, from a network motif, and it has been suggested that noise itself can be placed under selection [111]. Noise may control organism stress-responses such as persistence in bacteria, where the cell may enter a state of dormancy in harsh environmental conditions at the cost of cellular growth rate. Through mathematical modeling of the HipBA toxin-antitoxin system in E. coli [112] Koh and Dunlop showed that by altering the architecture of the network (through removing feedback and placing the two genes on separate operons), they were able to alter the frequency of persistence, a trait that could be selected for in different environmental conditions [113]. Interestingly, a study from Tsong et al. [114] demonstrated that for the two species S. cerevisiae and C. albicans, a particular network shared by the two species had been reversed in structure (one regulated by a repressor, the other by an activator). The “logical output” or phenotype, however, remained the same due to several changes in cis- and trans-regulatory elements. Therefore network evolution may converge to the same outcome as well as diverge.

The GRN reverse engineering approaches described in Section 3.2 can be conceptualized as “top-down” processes, where we begin with a phenotype of an individual (i.e., after subjected to stress or after a gene knock-out procedure), observe the expression patterns, and infer a genetic model from the data using statistical and mathematical approaches. However, the inferred networks and the modeling paradigm used to describe it (such as Boolean or continuous GRNs) could readily be used in a “bottom-up” approach to demonstrate the range in expression and/or the resulting phenotype once subjected to different environmental inputs. We therefore believe that SIBMs parameterized with resistance surfaces or landscape patches provide an excellent framework for producing such models. The GRN could be represented using a Boolean network form or as a continuous form, using linear or non-linear ODEs, that would take its input from the surrounding environment, interact with the other nodes in the network and produce a phenotype. Gene threshold parameters could be used to define the criteria needed for activation, and genes at the top of the network could directly interact with the environment. Whereas Boolean or ODE-based GRNs would classically represent deterministic networks, the output on each gene could instead be a random variable generated from a certain probability distribution, providing a network that may more approximate Bayesian networks. A potentially interesting study could be: If given genetic network data within a real environmental system (such as the distribution of flowering times latitudinally across Europe), which GRN model best explains the data and provides the maximum likelihood?

We have described how the resistance surfaces that may be explicitly incorporated into an SIBM may represent climactic or edaphic factors that can impede dispersal or influence selection of the simulated individuals. However, in a similar vein, they may also represent biotic interactions from animals or plants. Biodiversity varies latitudinally across the globe [116], and biotic interaction is thought to be of particular importance in the tropics [117]. One example of biotic interaction is seed predation, and this has famously been proposed in what is collectively termed the Janzen-Connel hypothesis [118,119] to prevent competitive exclusion. Seed predation can be represented in simulations as probabilities of predation for dispersed seeds, either throughout the entirety of the simulation or at individual grid-points, for example. It may be difficult in this approach, however, to simulate the dynamics of predator-prey co-evolution, unless some form of dependency was incorporated between the modeled individuals and the resistance surfaces. Another approach is to have multiple classes of individuals within a simulation that could represent “species”. Individuals belonging to different species could then be modeled with different GRNs, as has been seen in nature with the barley, wheat and the Arabadopsis photoperidocity network. Individuals may then compete for space (in order to germinate). If the model is specific and growth and nutrient uptake are explicitly modeled (see Section 4.6.2 on functional-structural plant modeling), then different species could potentially compete for resources.

GRNs are dynamic, and therewith comes the necessity of incorporating time-dependent environmental variation when GRNs are simulated within the context of SIBMs. A natural extension of this is that it will become convenient to study past shifts in the environment onto the genotypic and phenotypic characteristics of a population (such as through the effects of bottlenecks and migration, for example). Hypothesized future effects could also be studied in a similar manner.

Such example AD studies have the benefit of allowing researchers to quantify the effects of certain trade-offs to an evolutionary system. We believe the modeling framework proposed in this study of coupling GRNs to SIBMs could also allow for such tradeoffs through interactions between one gene and numerous target genes/traits. When considering complex interconnected networks, it becomes clear that potential trade-offs could be programmed into the system. For instance, a simple example may be where mutation of a gene may cause up-regulation of one or more of its target genes with beneficial fitness effects to trait A, whilst this may indirectly negatively impact the fitness provided by trait B. However, as with the AD framework, such interactions have to be hypothesized. This may not be the case, however, if a model is complicated enough to allow for GRN re-wiring. Through stochastic GRN re-wiring through mutation and movement through a heterogeneous landscape, emergent trade-offs may be observed that may not have previously been hypothesized. This may provide opportunities to document such trade-offs and analyze their evolutionary impact.

The complexity of SIBMs is not trivial and development of a large simulation software tool may not be without problems if inadequate care is not put into the development process, or if there is ambiguity in its function, as this may make the tool difficult to communicate or reproduce. To this end a few authors have proposed protocols that can be used in the design and development of IBMs [51,139]. SIBMs are generally less efficient than aspatial IBMs due to the processing of spatial distances or landscape values, if landscape information is incorporated. The use of a quadtree structure [140], which breaks the two-dimensional space down into nodes and are stored in a hierarchical way (as in a tree-like data structure) may provide some optimization over brute-force searches when individuals interact over space. A further approach for optimization in landscape genetics based on the quadtree was to use a hierarchical system of patches within an irregular grid [141]. Although the efficiency of developed software tools poses one problem, the implementation of complex systems within a model can be non-trivial, especially if interacting genes and environmental information are to be incorporated. Software engineering approaches [142] into the design of a system provide a more thoroughly planned design-process that will allow a greater transparency of the system specification to non-developers and may prevent design flaws or other complications during the development phase. These include the use of process-management models including the waterfall or iterative model, analysis and design of behavior using data flow diagrams, and the use of diagrams specified within the unified modeling language (UML) such as class hierarchy diagrams for object design and use-case diagrams for system interaction analysis and design. Object-oriented programming languages, including languages such as C++, Java, C# and Python provide a number of concepts such as object-inheritance, polymorphism, abstraction and interfaces, which can greatly facilitate the design and implementation of IBMs. For example, classes such as Individual, Gene, Genome, Chromosome and Patch could be implemented, and a number of individual-based modeling studies have taken similar object-oriented approaches [54,55,56,60,141,143]. However, it has been suggested that the use of certain features within SIBMs, such as environmental or terrain features, may be best not represented as objects [144]. Furthermore, the implementation of an IBM using an object-oriented approach in Java and C++ was shown to be less efficient than when implemented with a procedural approach in Fortran 95 [145]. Inexorably, object generation can be computationally costly, therefore, excessive use of objects when unnecessary should be cautioned against.

Arguably the most obvious pitfall with using such models is the high computational cost associated with the large ranges in scale required, from subcellular processes within the simulated individuals to the dynamical environment in which they reside. It is generally required that SIBM simulations be run with thousands of individuals, therefore, large GRNs with large numbers of nodes and large numbers of edges may become more intractable. Furthermore, sensory based GRNs such as the delay-response element and the persistence detector mentioned in Section 3.1 may become difficult to implement within simulated individuals as they represent time-dependent processes at a microscopic-scale, with a requirement for continuous transcript levels that builds up or breaks down over a period of time. The level of detail required for such processes could greatly slow down the rest of the simulation at the individual, population and environmental scales. If the simulation model was also run using discrete time steps (such as generations or months), a particularly fine-grained time step, such as hours or even minutes, may realistically be required, confounding the tractability of running the simulation for a meaningful length of time at the population level (such as 1,000 generations, for example). However, discrete GRN models such as Boolean networks or discrete Bayesian networks cannot represent these sorts of sensory networks themselves. GRNs representing memory-based motifs used for cell-fate determination as previously described, however, may be more suitable as they could guide differentiation events at the individual-based level. These could act as switches to ensure that individuals change from one life cycle stage to another, and thus would therefore have important implications to the fitness of an individual.

Domestication represents an important model of evolution where all aforementioned levels of regulation played a role, including the interactions at the genic level, the population level and the roles of abiotic and biotic factors (such as local climactic effects on crops and the roles of weeds and pests to crop yield). Through domestication our crops have developed traits that better serve human needs in agriculture. These traits include the non-shattering phenotype within cereals, where wind is insufficient to mediate dispersal of seeds from the ears and human intervention is necessary; increased seed size, which enables seeds to be sown deeper within the soil due to the larger endosperm, therefore preventing seeds from blowing away from the farmers field; a loss of hooks and awns, helping to prevent loss of seed from the field; and enhanced culinary chemistry, allowing superior food products to be produced (for reviews, see [71,100,147,148,149]). All of the aforementioned domestication traits are heavily relied upon today. It is understood that the non-shattering phenotype is a monogenic trait that occurs within double-recessive homozygotes, whereas the larger seed size phenotype is a polygenic trait [71]. Understanding how such genes interact and the evolutionary processes behind the selection of these traits is an area that warrants further study. Intra-annual variation has also played important roles in the domestication process, as crops were sown and harvested at certain times of the year, and some crops have since developed a lack of sensitivity to environmental cues for flowering or germination (hence a loss of dormancy amongst seeds). A meta-analysis conducted by Munguía-Rosa et al. found that flowering time is still under selection in many plants [150] and increased fitness amongst populations has been seen to be associated with local alleles of flowering time in Arabidopsis lyrata [151]. A model for the simulation of vernalization in onion has been developed by Streck [152] which demonstrated a response in flowering to the temperature and to the duration of vernalization (in days), using statistical functions. However, this simulation was not at a population or a genetic level. Developing models that can incorporate a landscape genetics element and a GRN element could greatly improve our understanding on such phenotypic variation. Dormancy and germination are other complex plant-processes where regulation exists on a population genetics level, where periods of dormancy will have important effects on the emergent seedlings fitness, and where regulation exists at a systems-based level. Dormancy has been described as having a number of categories: morphological, physiological deep, physiological non-deep and physical dormancy [153]. Morphological dormancy arises due to an underdeveloped seed embryo that requires time to mature, whereas physical dormancy involves the development of a water impermeable seed coat that requires scarification. Physiological dormancy, however, arises due to an imbalance in the ratio of abscissic acid and giberrellins, with abscissic acid promoting dormancy [154]. Moisture and temperature (specifically thermoinhibition) are important environmental conditions that may induce germination and hydrothermal models have been developed (including one from Watt et al. [155]) for simulation of germination at different environmental conditions. These models lack the population, landscape and genetic elements to selection, however, which could be simulated with the use of SIBMs and incorporated GRNs.

It is not uncommon for flowering plants to exhibit polyploidy [156]. Examples of triploid plants are apple and banana, tetraploids include durum and cotton, and bread wheat is an example of a hexaploid. Polyploidy of many flowering plants are relatively recent events whereas some flowering plants, such as tetraploid brassicas, are paleopolyploids after ancient genome duplication events [157]. Simulation models that simulate independent assortment of chromosomes may not be able to accurately reflect the gametogenesis of allopolyploids, as there is a tendency there for homoeologous chromosomes to preferentially pair during meiosis. However, a recent simulation model of meiosis developed by Voorips and Maliepard [158], called PedigreeSim, allows varying degrees of preferential pairing and the formation of different quadrivalent chromosomal configurations, which can be used for the study of allotetraploids. Future simulation studies will have to take into account similar approaches if polyploid plants or other organisms are to be accurately simulated.

Understanding plant growth habit and morphology is of particular importance to agronomic and ecological studies, as plants react to their environment by adjusting their growth and morphology to maximize their gained benefits from nutrient acquisition. Thus modeling efforts that take plant growth and morphology according to simulated environmental conditions could be useful for determining the impact of changes to the availability of light, temperature or moisture, etc. A currently developing field within the plant science and computational biology disciplines is the field of functional-structural plant modeling (FSPM) [159,160,161]. Modeling efforts within this field are concerned with the acquisition of nutrients from sources such as light, carbon, water and soil minerals and how this impacts upon the growth and morphology of the resulting plants. Complex plant architectures comprising organs such as stalks, leaves and meristems are simulated, often in three dimensions, which take on mass and form complex morphologies. Widely-used algorithmic concepts behind these models are fractal-like rewriting systems called L-systems [162], where in the case of plants, the plant architecture is represented by a text string of components (or phytomers) which represent building blocks that comprise the plant, such as the stalks, branches, flowers and meristems. This systematic approach enables virtual plants to be simulated with realistic morphologies that grow and develop new morphologies over time. Such studies have been used to simulate leaf development according to light input in Arabidopsis thaliana [163], carbon-water acquisition in orange trees [164], carbon and nitrogen acquisition [165] and light competition [166] in general virtual plants, and hormone biosynthesis and photosynthetate of Poplar [167]; where graph-rewriting systems called relational growth grammars (RGGs) [168] based on L-systems were used to model a metabolic regulatory network to simulate biosynthesis. The aforementioned studies do not attempt to simulate the population genetics of these plants. However, a notable study by Buck-Sorlin et al. developed a FSPM of barley using RGGs, where a GRN of seven genes was used to synthesize giberrellic acid, which played a role in the growth and morphology of the virtual barley plants [169]. The genes were able to crossover, therefore sexual reproduction was simulated, allowing the resulting genotypes to influence the resultant barley phenotypes. Only five individuals were simulated per generation, however. A follow-up study used simulated rice morphologies, and the model was parameterized with quantitative trait loci taken from a cultivated population, allowing the phenotypic effects of the morphologies to be influenced by the input genotypes [170]. Another more recent rice FSPM study simulated growth rates and was parameterized with different genotypes, with different effects towards the growth rate [171]. These studies represent important modeling efforts with application towards G × E interactions. Bornhofen et al. [172] provided an interesting FSPM study that utilized an evolutionary L-Systems approach that allowed plant strategies to evolve. Their simulations began with distribution of 1,000 seed individuals throughout a heterogeneous environment (consisting of five patches) that grew into mature virtual plants according to procurement of biomass from the surrounding environment. Their individuals contained a mutating genotype that comprised a set of parameters involved with the life history of the individuals, their dispersal and the system rules concerned with biomass acquisition and distribution. The individuals were able to reproduce asexually. Interdisciplinary work involving FSPM and evolutionary biology or landscape genetics is an interesting avenue of research, although due to the scale required by landscape genetics studies it could be that computational costs involved may impede development of such models at present, as is a limitation discussed by Bornhofen. However, assuming that computational power increases in the future, larger populations of simulated plants within FSPM studies may provide an interesting insight into the demography and adaptation of a population according to nutrient resource availability. They may also provide an important way to study biotic interactions from competitors such as weeds.