A review of techniques for spatial modeling in geographical, conservation and landscape genetics

Most evolutionary processes occur in a spatial context and several spatial analysis techniques have been employed in an exploratory context. However, the existence of autocorrelation can also perturb significance tests when data is analyzed using standard correlation and regression techniques on modeling genetic data as a function of explanatory variables. In this case, more complex models incorporating the effects of autocorrelation must be used. Here we review those models and compared their relative performances in a simple simulation, in which spatial patterns in allele frequencies were generated by a balance between random variation within populations and spatially-structured gene flow. Notwithstanding the somewhat idiosyncratic behavior of the techniques evaluated, it is clear that spatial autocorrelation affects Type I errors and that standard linear regression does not provide minimum variance estimators. Due to its flexibility, we stress that principal coordinate of neighbor matrices (PCNM) and related eigenvector mapping techniques seem to be the best approaches to spatial regression. In general, we hope that our review of commonly used spatial regression techniques in biology and ecology may aid population geneticists towards providing better explanations for population structures dealing with more complex regression problems throughout geographic space.     

The Ising model in physics and statistical genetics

Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis.     

Grains of connectivity: analysis at multiple spatial scales in landscape genetics

Landscape genetic analyses are typically conducted at one spatial scale. Considering multiple scales may be essential for identifying landscape features influencing gene flow. We examined landscape connectivity for woodland caribou (Rangifer tarandus caribou) at multiple spatial scales using a new approach based on landscape graphs that creates a Voronoi tessellation of the landscape. To illustrate the potential of the method, we generated five resistance surfaces to explain how landscape pattern may influence gene flow across the range of this population. We tested each resistance surface using a raster at the spatial grain of available landscape data (200 m grid squares). We then used our method to produce up to 127 additional grains for each resistance surface. We applied a causal modelling framework with partial Mantel tests, where evidence of landscape resistance is tested against an alternative hypothesis of isolation-by-distance, and found statistically significant support for landscape resistance to gene flow in 89 of the 507 spatial grains examined. We found evidence that major roads as well as the cumulative effects of natural and anthropogenic disturbance may be contributing to the genetic structure. Using only the original grid surface yielded no evidence for landscape resistance to gene flow. Our results show that using multiple spatial grains can reveal landscape influences on genetic structure that may be overlooked with a single grain, and suggest that coarsening the grain of landcover data may be appropriate for highly mobile species. We discuss how grains of connectivity and related analyses have potential landscape genetic applications in a broad range of systems.     

An improved neutral landscape model for recreating real landscapes and generating landscape series for spatial ecological simulations

Many studies have assessed the effect of landscape patterns on spatial ecological processes by simulating these processes in computer‐generated landscapes with varying composition and configuration. To generate such landscapes, various neutral landscape models have been developed. However, the limited set of landscape‐level pattern variables included in these models is often inadequate to generate landscapes that reflect real landscapes. In order to achieve more flexibility and variability in the generated landscapes patterns, a more complete set of class‐ and patch‐level pattern variables should be implemented in these models. These enhancements have been implemented in Landscape Generator (LG), which is a software that uses optimization algorithms to generate landscapes that match user‐defined target values. Developed for participatory spatial planning at small scale, we enhanced the usability of LG and demonstrated how it can be used for larger scale ecological studies. First, we used LG to recreate landscape patterns from a real landscape (i.e., a mountainous region in Switzerland). Second, we generated landscape series with incrementally changing pattern variables, which could be used in ecological simulation studies. We found that LG was able to recreate landscape patterns that approximate those of real landscapes. Furthermore, we successfully generated landscape series that would not have been possible with traditional neutral landscape models. LG is a promising novel approach for generating neutral landscapes and enables testing of new hypotheses regarding the influence of landscape patterns on ecological processes. LG is freely available online.     

EcoGenetics: An R package for the management and exploratory analysis of spatial data in landscape genetics

The integration of ecology and genetics has become established in recent decades, in hand with the development of new technologies, whose implementation is allowing an improvement of the tools used for data analysis. In a landscape genetics context, integrative management of population information from different sources can make spatial studies involving phenotypic, genotypic and environmental data simpler, more accessible and faster. Tools for exploratory analysis of autocorrelation can help to uncover the spatial genetic structure of populations and generate appropriate hypotheses in searching for possible causes and consequences of their spatial processes. This study presents EcoGenetics, an R package with tools for multisource management and exploratory analysis in landscape genetics.     

Putting the "landscape" in landscape genetics

Landscape genetics has emerged as a new research area that integrates population genetics, landscape ecology and spatial statistics. Researchers in this field can combine the high resolution of genetic markers with spatial data and a variety of statistical methods to evaluate the role that landscape variables play in shaping genetic diversity and population structure. While interest in this research area is growing rapidly, our ability to fully utilize landscape data, test explicit hypotheses and truly integrate these diverse disciplines has lagged behind. Part of the current challenge in the development of the field of landscape genetics is bridging the communication and knowledge gap between these highly specific and technical disciplines. The goal of this review is to help bridge this gap by exposing geneticists to terminology, sampling methods and analysis techniques widely used in landscape ecology and spatial statistics but rarely addressed in the genetics literature. We offer a definition for the term "landscape genetics", provide an overview of the landscape genetics literature, give guidelines for appropriate sampling design and useful analysis techniques, and discuss future directions in the field. We hope, this review will stimulate increased dialog and enhance interdisciplinary collaborations advancing this exciting new field.     

A quantitative genetics model for viability selection

Viability selection will change gene frequencies of loci controlling fitness. Consequently, the frequencies of marker loci linked to the viability loci will also change. In genetic mapping, the change of marker allelic frequencies is reflected by the departure from Mendelian segregation ratio. The non-Mendelian segregation of markers has been used to map viability loci along the genome. However, current methods have not been able to detect the amount of selection (s) and the degree of dominance (h) simultaneously. We developed a method to detect both s and h using an F2 mating design under the classical fitness model. We also developed a quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individuals. With the liability model, mapping viability loci has been formulated as mapping quantitative trait loci. As a result, nongenetic systematic environmental effects can be easily incorporated into the model and subsequently separated from the genetic effects of the viability loci. The quantitative genetic model has been verified with a series of Monte Carlo simulation experiments.     

A new model system for tomato genetics

The purpose of this study was to develop a model system for studying tomato genetics. Agronomic, genetic, and molecular data are presented which show that the miniature Lycopersicon esculentum cultivar, Micro-Tom (Micro tomato), fulfills the requirements for such a model. It grows at high density (up to 1357 plants/m⁻²); it has a short life cycle (70–90 days from sowing to fruit ripening); and it can be transformed at frequencies of up to 80% through Agrobacterium -mediated transformation of cotyledons. Moreover, it differs from standard tomato cultivars by only two major genes. Therefore, any mutation or transgene can be conveniently studied in Micro-Tom's background and, when needed, transferred into a standard background. We took advantage of Micro-Tom's features to improve the infrastructure for mutagenesis in tomato. A screening of 9000 M1 and 20 000 M2 EMS mutagenized plants is described. Mutants with altered pigmentation or modified shape of leaves, flowers and fruits were found. In addition, an enhancer trapping and a gene trapping system, based on the Ac/Ds maize transposable elements, were transformed into Micro-Tom and found to be active. In summary, Micro-Tom opens new prospects to achieve saturated mutagenesis in tomato, and facilitates the application of transposon-based technologies such as gene tagging, trapping and knockout.     

Habitat-based statistical models for predicting the spatial distribution of butterflies and day-flying moths in a fragmented landscape

1.  Most species' surveys and biodiversity inventories are limited by time and money. Therefore, it would be extremely useful to develop predictive models of animal distributions based on habitat, and to use these models to estimate species' densities and range sizes in poorly sampled regions.
2.  In this study, two sets of data were collected. The first set consisted of over 2000 butterfly transect counts, which were used to determine the relative density of each species in 16 major habitat types in a 35-km² area of fragmented landscape in north-west Wales. For the second set of data, the area was divided into 140 cells using a 500-m grid, and the extent of each habitat and the presence or absence of each butterfly and moth species was determined for each cell.
3.  Logistic regression was used to model the relationship between species' distribution and predicted density, based on habitat extent, in each grid square. The resultant models were used to predict butterfly distributions and occupancy at a range of spatial scales.
4.  Using a jack-knife procedure, our models successfully reclassified the presence or absence of species in a high percentage of grid squares (mean 83% agreement). There were highly significant relationships between the modelled probability of species occurring at regional and local scales and the number of grid squares occupied at those scales.
5.  We conclude that basic habitat data can be used to predict insect distributions and relative densities reasonably well within a fragmented landscape. It remains to be seen how accurate these predictions will be over a wider area.     

Geneland: a computer package for landscape genetics

Geneland is a computer package that allows to make use of georeferenced individual multilocus genotypes for the inference of the number of populations and of the spatial location of genetic discontinuities between those populations. Main assumptions of the method are: (i) the number of populations is unknown and all values are considered a priori equally likely, (ii) populations are spread over areas given by a union of some polygons of unknown location in the spatial domain, (iii) Hardy–Weinberg equilibrium is assumed within each population and (iv) allele frequencies in each population are unknown and treated as random variable either following the so‐called Dirichlet model or Falush model. Different algorithms implemented in Geneland to perform inferences are first briefly presented. Then major running steps and outputs (i.e. histogram of number of populations and map of posterior probabilities of population membership) are illustrated from the analysis of a simulated data set, which was also produced by Geneland.     

On applications of landscape genetics

Recent assertions in the literature (e.g., Keller et al. 2015) suggest that landscape genetic research has been infrequently applied by practitioners. We were interested to test this assertion, which is difficult to assess, since applications may not be detectable through searches of peer-reviewed literature. Producing publications may not be a goal of practitioners. We developed a method to search the internet for evidence of research applications and evaluated 25 different research fields in the natural sciences. We found that fields with more publications also had more applications, but the field of landscape genetics was less applied than expected based on the number of peer-reviewed publications—only about 4 % of landscape genetics articles were applied. In fact, all research fields in genetics or evolutionary biology were under-applied compared to ‘whole organism’, ecological research fields. This result suggests the lack of applications in landscape genetics may be due to a systemic under-application of genetics research, perhaps related to a lack of understanding of genetics by practitioners. We did find some evidence of landscape genetic applications however, which we sorted into 5 categories: (1) identification of evolutionarily significant units for conservation, (2) managing pathogens and invasive species, (3) natural heritage systems planning, (4) assessing population status, and (5) restoration of populations.     

Isolation-by-distance in landscapes: considerations for landscape genetics

In landscape genetics, isolation-by-distance (IBD) is regarded as a baseline pattern that is obtained without additional effects of landscape elements on gene flow. However, the configuration of suitable habitat patches determines deme topology, which in turn should affect rates of gene flow. IBD patterns can be characterized either by monotonically increasing pairwise genetic differentiation (for example, F_ST) with increasing interdeme geographic distance (case-I pattern) or by monotonically increasing pairwise genetic differentiation up to a certain geographical distance beyond which no correlation is detectable anymore (case-IV pattern). We investigated if landscape configuration influenced the rate at which a case-IV pattern changed to a case-I pattern. We also determined at what interdeme distance the highest correlation was measured between genetic differentiation and geographic distance and whether this distance corresponded to the maximum migration distance. We set up a population genetic simulation study and assessed the development of IBD patterns for several habitat configurations and maximum migration distances. We show that the rate and likelihood of the transition of case-IV to case-I F_ST–distance relationships was strongly influenced by habitat configuration and maximum migration distance. We also found that the maximum correlation between genetic differentiation and geographic distance was not related to the maximum migration distance and was measured across all deme pairs in a case-I pattern and, for a case-IV pattern, at the distance where the F_ST–distance curve flattens out. We argue that in landscape genetics, separate analyses should be performed to either assess IBD or the landscape effects on gene flow.     

A statistical model for mapping morphological shape

Background  

Living things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine.     

A statistical model for iTRAQ data analysis

We describe biological and experimental factors that induce variability in reporter ion peak areas obtained from iTRAQ experiments. We demonstrate how these factors can be incorporated into a statistical model for use in evaluating differential protein expression and highlight the benefits of using analysis of variance to quantify fold change. We demonstrate the model's utility based on an analysis of iTRAQ data derived from a spike-in study.     

A statistical model for interpreting the antibiogram

Up to now, to interpret antibiotic susceptibility tests, the common practice has been to use: first, breakpoints without any quantitative justification, secondly, concordance curves between the different measurement techniques; these are not well adapted to the heterogeneous character of bacterial populations. We hereby propose another method: it is based on a global data analysis for each bacterial species, each antibiotic family and each measurement technique. So, we have drawn up a new model for the interpretation, both global and data-processed; it is based on qualifying classes, which are obtained and interpreted by hierarchical ascendent classification, principal components analysis, and comparison with pharmacological data. It can be used by any biologist. What is more, justified breakpoints with a numerical risk and quality control are defined. There are also some additional uses: evaluation of the effect of new antibiotics, standardization of new measurement techniques, detection of the emergence of new bacterial resistance in patients, guidance for research into unknown resistance mechanisms and characters.     

A comparison of individual‐based genetic distance metrics for landscape genetics

A major aim of landscape genetics is to understand how landscapes resist gene flow and thereby influence population genetic structure. An empirical understanding of this process provides a wealth of information that can be used to guide conservation and management of species in fragmented landscapes and also to predict how landscape change may affect population viability. Statistical approaches to infer the true model among competing alternatives are based on the strength of the relationship between pairwise genetic distances and landscape distances among sampled individuals in a population. A variety of methods have been devised to quantify individual genetic distances, but no study has yet compared their relative performance when used for model selection in landscape genetics. In this study, we used population genetic simulations to assess the accuracy of 16 individual‐based genetic distance metrics under varying sample sizes and degree of population genetic structure. We found most metrics performed well when sample size and genetic structure was high. However, it was much more challenging to infer the true model when sample size and genetic structure was low. Under these conditions, we found genetic distance metrics based on principal components analysis were the most accurate (although several other metrics performed similarly), but only when they were derived from multiple principal components axes (the optimal number varied depending on the degree of population genetic structure). Our results provide guidance for which genetic distance metrics maximize model selection accuracy and thereby better inform conservation and management decisions based upon landscape genetic analysis.     

Testing evolutionary hypotheses for phenotypic divergence using landscape genetics

Understanding the evolutionary causes of phenotypic variation among populations has long been a central theme in evolutionary biology. Several factors can influence phenotypic divergence, including geographic isolation, genetic drift, divergent natural or sexual selection, and phenotypic plasticity. But the relative importance of these factors in generating phenotypic divergence in nature is still a tantalizing and unresolved problem in evolutionary biology. The origin and maintenance of phenotypic divergence is also at the root of many ongoing debates in evolutionary biology, such as the extent to which gene flow constrains adaptive divergence ( Garant et al. 2007 ) and the relative importance of genetic drift, natural selection, and sexual selection in initiating reproductive isolation and speciation ( Coyne & Orr 2004 ). In this issue, Wang & Summers (2010) test the causes of one of the most fantastic examples of phenotypic divergence in nature: colour pattern divergence among populations of the strawberry poison frog (Dendrobates pumilio) in Panama and Costa Rica ( Fig. 1 ). This study provides a beautiful example of the use of the emerging field of landscape genetics to differentiate among hypotheses for phenotypic divergence. Using landscape genetic analyses, Wang & Summers were able to reject the hypotheses that colour pattern divergence is due to isolation‐by‐distance (IBD) or landscape resistance. Instead, the hypothesis left standing is that colour divergence is due to divergent selection, in turn driving reproductive isolation among populations with different colour morphs. More generally, this study provides a wonderful example of how the emerging field of landscape genetics, which has primarily been applied to questions in conservation and ecology, now plays an essential role in evolutionary research.

Figure 1 Open in figure viewer PowerPoint Divergent colour morphs observed among populations of the strawberry poison frog, Dendrobates pumilio. Frogs are from San Cristobal (upper left), Cerro Brujo (upper right), Bastimentos (lower right), and Agua (lower left).