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.     

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.     

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 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 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 conceptual framework for the spatial analysis of landscape genetic data

Understanding how landscape heterogeneity constrains gene flow and the spread of adaptive genetic variation is important for biological conservation given current global change. However, the integration of population genetics, landscape ecology and spatial statistics remains an interdisciplinary challenge at the levels of concepts and methods. We present a conceptual framework to relate the spatial distribution of genetic variation to the processes of gene flow and adaptation as regulated by spatial heterogeneity of the environment, while explicitly considering the spatial and temporal dynamics of landscapes, organisms and their genes. When selecting the appropriate analytical methods, it is necessary to consider the effects of multiple processes and the nature of population genetic data. Our framework relates key landscape genetics questions to four levels of analysis: (i) node-based methods, which model the spatial distribution of alleles at sampling locations (nodes) from local site characteristics; these methods are suitable for modeling adaptive genetic variation while accounting for the presence of spatial autocorrelation. (ii) Link-based methods, which model the probability of gene flow between two patches (link) and relate neutral molecular marker data to landscape heterogeneity; these methods are suitable for modeling neutral genetic variation but are subject to inferential problems, which may be alleviated by reducing links based on a network model of the population. (iii) Neighborhood-based methods, which model the connectivity of a focal patch with all other patches in its local neighborhood; these methods provide a link to metapopulation theory and landscape connectivity modeling and may allow the integration of node- and link-based information, but applications in landscape genetics are still limited. (iv) Boundary-based methods, which delineate genetically homogeneous populations and infer the location of genetic boundaries; these methods are suitable for testing for barrier effects of landscape features in a hypothesis-testing framework. We conclude that the power to detect the effect of landscape heterogeneity on the spatial distribution of genetic variation can be increased by explicit consideration of underlying assumptions and choice of an appropriate analytical approach depending on the research question.     

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).     

Perspectives and challenges in landscape genetics

A recent workshop held at the University of Grenoble gathered the leading experts in the field of landscape genetics and spatial statistics. Landscape genetics was only recently defined as an independent research field. It aims to understand the processes of gene flow and local adaptation by studying the interactions between genetic and spatial or environmental variation. This workshop discussed the perspectives and challenges of combining emerging molecular, spatial and statistical tools to unravel how landscape and environmental variables affect genetic variation.     

Sample design effects in landscape genetics

An important research gap in landscape genetics is the impact of different field sampling designs on the ability to detect the effects of landscape pattern on gene flow. We evaluated how five different sampling regimes (random, linear, systematic, cluster, and single study site) affected the probability of correctly identifying the generating landscape process of population structure. Sampling regimes were chosen to represent a suite of designs common in field studies. We used genetic data generated from a spatially-explicit, individual-based program and simulated gene flow in a continuous population across a landscape with gradual spatial changes in resistance to movement. Additionally, we evaluated the sampling regimes using realistic and obtainable number of loci (10 and 20), number of alleles per locus (5 and 10), number of individuals sampled (10–300), and generational time after the landscape was introduced (20 and 400). For a simulated continuously distributed species, we found that random, linear, and systematic sampling regimes performed well with high sample sizes (>200), levels of polymorphism (10 alleles per locus), and number of molecular markers (20). The cluster and single study site sampling regimes were not able to correctly identify the generating process under any conditions and thus, are not advisable strategies for scenarios similar to our simulations. Our research emphasizes the importance of sampling data at ecologically appropriate spatial and temporal scales and suggests careful consideration for sampling near landscape components that are likely to most influence the genetic structure of the species. In addition, simulating sampling designs a priori could help guide filed data collection efforts     

Simulating natural selection in landscape genetics

Linking landscape effects to key evolutionary processes through individual organism movement and natural selection is essential to provide a foundation for evolutionary landscape genetics. Of particular importance is determining how spatially-explicit, individual-based models differ from classic population genetics and evolutionary ecology models based on ideal panmictic populations in an allopatric setting in their predictions of population structure and frequency of fixation of adaptive alleles. We explore initial applications of a spatially-explicit, individual-based evolutionary landscape genetics program that incorporates all factors--mutation, gene flow, genetic drift and selection--that affect the frequency of an allele in a population. We incorporate natural selection by imposing differential survival rates defined by local relative fitness values on a landscape. Selection coefficients thus can vary not only for genotypes, but also in space as functions of local environmental variability. This simulator enables coupling of gene flow (governed by resistance surfaces), with natural selection (governed by selection surfaces). We validate the individual-based simulations under Wright-Fisher assumptions. We show that under isolation-by-distance processes, there are deviations in the rate of change and equilibrium values of allele frequency. The program provides a valuable tool (cdpop v1.0; http://cel.dbs.umt.edu/software/CDPOP/) for the study of evolutionary landscape genetics that allows explicit evaluation of the interactions between gene flow and selection in complex landscapes.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.     

A synaptic model for spatial frequency adaptation

A model for visual adaptation to spatial grating is developed based on the assumption that inhibitory synapses within the visual system may be temporarily modified as a function of recent usage. Specifically, it is hypothesized that inhibitory synaptic weights are altered as a function of the correlation between recent presynaptic and postsynaptic activity. When such modifiable synapses are incorporated into a simple neural network model having the spatial filtering properties of the human visual system, two coupled equations are obtained which may be solved analytically. The model accounts for experimental data on adaptation to sinusoidal gratings, square wave gratings, single bars, and tilted gratings. The relationship of the model to single and multiple channel models of the human visual system is discussed.     

A spatial simulation model for vegetation dynamics

A fine-resolution, spatially explicit, stochastic model was developed to simulate the dynamics of species cover abundance and pattern in a single vegetation layer wherein neighbouring individuals are assumed to compete for growing space. Each species in the model is characterized by a small number of morphological and life-history parameters, which enter into equations that stand for a minimal set of vegetation processes. The model performed well in reproducing post-fire successional trends among the three codominant dwarf shrubs in a Dutch heathland community as recorded in an annually mapped permanent quadrat. Program inputs, outputs and an example of sensitivity analysis are illustrated. With suitable changes, the model could potentially describe any plant community in which the vertical structure is simple and community dynamics are determined by spatial interactions among neighbouring plants.Jacques de Smidt provided data, information and stimulus for this project. The model was developed during ICP's visit to Utrecht, arranged by Marinus Werger and financed by The Netherlands Science Research Council (ZWO). We also thank David Glenn-Lewin and Ernst Lippe for discussion and cooperation.