Landscape genetics. Instructor: K. McGarigal. Assigned Reading: Manel et al (2003)

Transcription

1 Landscape genetics Instructor: K. McGarigal Assigned Reading: Manel et al (2003) Objective: Provide an overview of the consequences of landscape pattern to the spatial genetic structure of populations. Highlight the role of landscape structure in gene flow and approaches for examining the relationship between spatial genetic structure and the structure of landscapes. Topics covered: 1. What is landscape genetics? 2. What is gene flow? 3. Why is gene flow important? 4. How much gene flow is enough? 5. Gene flow in heterogeneous landscapes 6. Landscape genetics: statistical approaches and examples Comments: Slides adapted from presentation by Dr. Michael Schwartz, USDA Forest Service Rocky Mountain Research Station, Missoula, Montana. 15.1

2 1. What is Landscape Genetics Landscape genetics is an approach for understanding of how geographical and environmental features structure genetic variation at both the population and individual levels. Importantly, landscape genetics: a. does not require that discrete populations be identified in advance; b. emphasizes the processes and patterns of gene flow and local adaptation; and c. the analysis involves detection of genetic discontinuities and the correlation of these discontinuities with landscape features. Landscape genetics is an emerging discipline that combines the fields of population genetics and landscape ecology. 15.2

3 2. What is Gene Flow? Gene flow is the incorporation of genes into the gene pool of one population from other populations. In this regard, it is important to distinguish between the processes of dispersal and migration as defined from a genetics perspective. Dispersal the permanent movement away from the site where an organism was born (i.e., its natal site). Note dispersal refers to the movement of an individual away from its natal site; it is not necessarily true that the individuals genes will be incorporated into the new population, since this requires successful reproduction. Migration refers to the movement of genes from one population to another accomplished by individuals that move and breed in a population other than their birth site. Migration, as defined here, equals gene flow. Note, migration is defined somewhat differently by biologists, where it generally refers to the periodic (typically seasonal) movement of individuals between geographic locations. 15.3

4 3. Why is Gene Flow Important? Gene flow is important for many reasons, including the following: Prevent inbreeding of populations gene flow reduces the potential for inbreeding, the reduction in fitness due to the random loss of heterozygosity (genetic diversity) associated with small populations, by introducing new genes into a population.. Prevent depression of population fitness gene flow functions to increase the heterozygosity of individuals and populations and thereby increase population fitness. Prevent the suite of demographic problems that arise as a consequence of inbreeding or alone (e.g., allee) gene flow helps to prevent inbreeding depression, as noted above, and can reduce the potential for the Allee effect in small populations the rapid loss of fitness (e.g., fecundity) in very small populations. Decrease extinction risk by functioning to reduce inbreeding depression and the reduction in fitness due to the loss of heterozygosity, gene flow can serve to decrease the risk of population extinction. 15.4

5 Example: Greater prairie chicken (Westemeier et al. 1998) In 1933, the greater prairie chicken in Illinois numbered 25,000; in 1962 it was down to 2,000; and in 1993 it was down to just 50 individuals. Moreover, in 1960 there was a 90% hatching success rate, but in 1990 that rate had fallen to 74%. The decrease in fecundity (i.e., fitness) was hypothesized to be due to the loss of genetic diversity associated, which declined 30% between To reverse the situation, managers introduced birds from Minnesota and Kansas to infuse new genes into the population, and hatching rate success increased to 94%. The population has since recovered from near extinction. 15.5

6 Example: Scandanavian adder (Maddsen et al. 2001) An Scandanavian adder population crashed between The population had very low genetic diversity and a large number of stillborn offspring were observed, an indication of low fitness due to inbreeding depression. To counter the population crash, managers introduced 20 males from a larger population for 3 years between The immediate result was an increase in male recruitment and a decrease in the number of stillborns. Note, the males were returned to their native population after performing their duty. 15.6

7 As this table illustrates (from Manel et al 2003), there are numerous empirical examples of studies showing genetic rescue effects of induced gene flow to small populations. 15.7

8 4. How Much Gene Flow is Enough? So, if gene flow is important, at the very least to reduce the potential for inbreeding depression in small populations, how much is enough? While this is not an easy question to answer, the general rule of thumb that has been put forth is that one migrant per generation is necessary to prevent the adversities of inbreeding depression, while also allowing for divergence in allele frequencies among subpopulations. Mills and Allendorf (1996) authors argue that one migrant per generation is an appropriate minimum, but that the rule should be broadened to include a maximum of 10 migrants per generation. Vucetich and Waite (2000) question whether that rule of thumb is sufficient for fluctuation populations, and demonstrate that most populations fluctuate enough to require >10 migrants per generation and many may even require >20 per generation. 15.8

9 Example: Brassica campestris (Newman and Tallmon 2001) In this inbreeding experiment involving the mustard Brassica campestris, five of six fitness related components were negatively effected by inbreeding. The researchers experimentally introduced migrant treatments of 0, 1, and 2.5. The results were dramatic. The 1 migrant treatment and 2.5 migrant treatment produced higher fitness components than the 0 migrant treatment, and there was no difference between 1 and 2.5 migrant treatments, suggesting that in this case the 1 migrant per generation rule may be enough to prevent inbreeding depression. 15.9

10 Example: Peromyscus maniculatus (Schwartz and Mills 2005) In this study involving Peromyscus maniculatus, the researchers compared survival rates in a relatively isolated control population against two different treatments: a migrant treatment in which individuals from another distant source population were introduced to the local population, and an inbreeding treatment in which a population was experimentally inbreed. The migrant treatment resulted in a dramatic increase in survival. Surprisingly, the inbreeding treatment also resulted in an increase in survival, which the authors attribute to a number of factors

11 5. Gene Flow in Heterogeneous Landscapes The question we are most interested in is whether landscape patterns, in particular those created by human land uses, influence gene flow and to what extent. Consider the following series of slides and try to answer the question, is gene flow occurring? 15.11

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14 In order to answer the question, is gene flow occurring, we need to sidetrack and do a quick genetics primer for those that either haven t had genetics or had it too long ago. Collection of genetic samples The first thing we need to do is collect genetic samples. There are many ways to do this. Optimal samples (i.e., containing the most DNA) include tissue and blood, but the collection of these samples requires invasive sampling. Sub-optimal samples include hair, scat, urine, skins/museum specimens, feathers and guano, and these can generally be obtained using non-invasive methods

15 Types of DNA 1. Mitochondrial DNA (mtdna) is contained (obviously) in the mitochondria of cells and there are thousands of copies per cell (at least 20 times more DNA than in cell nucleus). Mitochondrial DNA is maternally inherited, so it is passed down directly from mother to offspring, and is highly conserved; i.e., it is very stable and does not change much over generations. Thus, the DNA in your mitochondria and very much the same as those that were carried by your great, great, great, great, etc. grandmother. 2. Nuclear DNA is contained (obviously) in the nucleus of cells and there are two copies per cell. Nuclear DNA is inherited from both parents, one copy from each parent. There are highly variable regions called microsatellites that are very useful for distinguishing individuals and for differentiating very recent population divergences

16 Species ID using mtdna mtdna is especially useful for distinguishing among species, which is often the first thing that must be done after collecting non-invasive samples in order to be sure of the species. There are two common approaches for this purpose: 1. Restriction digests (RFLP) in which known genes are extracted using restriction enzymes and the size of the alleles are used to distinguish among species. 2. DNA sequence analysis in which the exact nucleotide sequence for a section of DNA is determined and differences in the sequence are used to distinguish among species

17 Restriction Digests Step 1. The first step is to separate the DNA from other cellular material. Note, at this stage all of the DNA, both nuclear and mitochondrial, is mixed together. Step 2. The next step is to add a primer pair (2 short pieces of DNA, approximately 20 base pairs in length), which latch on to either side of an area of interest (typically a bp length of DNA). Step 3. The next step is to make many copies of the genetic fragment using Polymerase chain reaction (PCR). Step 4. Finally, the last step is to separate the fragments by size using gel electrophoresus. Essentially, this entails putting the genetic material on a gel and passing an electrical current across it. The DNA fragments migrate across the gel according to their size; large fragments only move a short distance, while small fragments move farther across the gel

18 Depending on the gene analyzed, species or groups of related species (e.g., families) can easily be distinguished by the size of the genetic fragment or allele (i.e., alternative form of a gene, varying in length) present. For example, as shown the left, the members of the weasel family are distinguished perfectly from the members of the felid family by this gene. As shown of the right, other genes can be used to distinguish among species of the same family, such as shown here for distinguishing among lynx, bobcat and mountain lion

19 DNA Sequence Analysis The alternative to restriction digests is complete DNA sequencing, in which the specific nucleotide sequence for a particular segment of DNA is determined. As shown here using sequence chromatographs, in which each base nucleotide (A, C, T, or G) is revealed by a unique florescent signature, the Lynx and the Bobcat have a single nucleotide difference

20 Now back to our original question: Is this river a barrier to gene flow? At this point, using mtdna analysis, let s say that we have confirmed that four of the samples collected are from lynx, and that one of the samples is on the opposite side of the river. Does this suggest gene flow across the river? Yes, IF the samples on opposite sides of the river are from related individuals. But how do we determine if these samples are from the same individuals or from related individuals (as opposed to the same species). This is where nuclear DNA comes in

21 Individual ID using nuclear DNA Nuclear DNA is especially useful for distinguishing among individuals or determining the degree of relatedness among individuals. There are two common approaches for this purpose: 1. Microsatellites highly variable regions of nuclear DNA that diverge rapidly because they are not under selection. Microsatellites have been the mainstay of landscape genetics since inception, but are currently being replaced by the more power analysis of SNPs (below). 2. Single nucleotide polymorphisms (SNPs) DNA sequence variation in which a single nucleotide (A, T, C or G) differs between individuals. Single nucleotides may be changed (substitution), removed (deletion), or added (insertion) to a polynucleotide sequence within a protein coding, non-coding region, or intergenic region between genes, and the magnitude of differences in SNPs between two individuals can be used as a measure of relatedness

22 Microsatellites Here we will focus on microsatellites as they have been the mainstay for landscape genetics work since its inception; only recently have SNPs offered an alternative and potentially more powerful approach for quantifying the genetic differences between individuals. A microsatellite is a highly variable region of nuclear DNA containing mono-, di-, tri- or tetranucleotide units repeated. Importantly, microsatellites are generally referred to as junk DNA because these regions of the genome are presumably non-protein coding and/or not under natural selection. As a result, these regions can change rapidly over time, allowing us to distinguish even relatively recent genetic divergences. The procedure for measuring microsatellites is essentially identical to that described earlier with restriction digests. The DNA material is extracted, segmented into fragments (typically bp in length) at established locations (restriction sites), multiplied using PCR, and measured using gel electrophoresus

23 The resulting gel depicts the allele (alternative form of a gene) size at a specific locus (location of a gene on a chromosome). Diploid individuals containing two homologous chromosomes contain two copies of each gene. If the two copies are the same, the individual is said to by homozygous at this particular locus. If the two copies are different, the individual is said to by heterozygous. In the samples shown here, note that some individuals are homozygous, while others are heterozygous. In addition, note that there are only two different alleles present for this particular gene. Based on the data shown, clearly, samples 4 and 6 cannot be from the same individual, since one is homozygous while the other is heterozygous at this locus. So how many potential individuals to we have represented in this set of 10 samples based on this one locus? 15.23

24 Samples 1, 8, and 9 are all homozygous containing two copies of allele 2, and thus could be from the same individual. Samples 2 and 6 are heterozygous containing a single copy each of allele 1 and 2, and thus could be from the same individual. Samples 3, 4, 7, and 10 are all homozygous containing two copies of allele 1, and thus could be from the same individual. Note, it is not possible to say with any confidence whether any of these samples are from the same individual based on this single locus, but if we evaluate many loci our ability to distinguishing among individuals increases dramatically

25 Back to our question about whether the river is a barrier to gene flow. Let s assume that our analysis of microsatellites allowed us to determine that our 4 samples of lynx represent 3 different individuals, and that the same individual was detected on opposite sides of the river. Given that individual #1 was seen on both sides of the river we now know that the river isn t a complete barrier to movement. Later we will quantify the extent to which rivers and other landscape features act as resistance to movement of genes

26 For gene flow to be occurring there must be reproduction, because that is the only way for genes of one population to migrate to another. So, another question we might be interested in is whether we have both males and females present in our samples. Fortunately, there are specific genes that allow us to determine the sex of an individuals. There are few different genes typically used for this purpose. For example, in the Zf and Amelogenin genes, females are always homozygous and males are always heterozygous, and the SRY gene is only present in males. In our particular example, let s say that we can confirm that we have both males and females present

27 Given that we have females present, the next question we might want to ask is whether there are related individuals? If we know who the mamma and papa are, we can determine the potential genotypes of their offspring. For example, if mamma is homozygous at a particular locus with allele CA 6 (6 di-nucleotide repeats) and papa is heterozygous at the same locus with alleles CA 4 (4 di-nucleotide repeats) and CA 5 (5 di-nucleotide repeats), then the offspring will all get one allele of CA 6 from their mamma and either CA 4 or CA 5 from their pappa. Thus, the offspring have to either be CA 6 - CA 5 or CA 6 - CA 4. In our particular example, let s say that we can confirm that mamma is found on the opposite side of the river from her son. Relatedness across a potential barrier does suggest gene flow is occurring

28 6. Landscape Genetics: Statistical Approaches and Examples Manel et al. (2003) define the field of landscape genetics and provide a description of the basic approach involving the following key features: The identification of spatial genetic patterns requires the collection of genetic data from many individuals (or populations) whose exact geographical location is known Ideally, the individual is the operational unit of study. However, this can be extended to populations (using allele frequencies) if enough populations can be sampled The advantages of using individuals as the operational unit are to avoid potential bias in identifying populations in advance and to conduct studies at a finer scale After sampling, genetic and statistical tools are used to determine the spatial genetic pattern and to correlate it with landscape or environmental features 15.28

29 The essence of the landscape genetics approach involves three major steps: Step 1 involves identifying/quantifying the spatial genetic structure of the sample. Note, this has been a principal interest of population geneticists for decades and thus is not unique to landscape genetics. There are a variety of approaches for doing this depending, in part, on whether clearly defined and discrete a priori populations exist. In this case, the genetic structure among the prespecified populations can be quantified using a variety of statistical measures, the most common being Fst (see below). An alternative method involves the use of assignment tests (see below). When a priori populations do not exist or there is no reason to expect disjunct population units to be real (e.g., continuously distributed individuals), then there are a wide variety of other statistical approaches for detecting and/or quantifying the spatial genetic structure of the sample. We will discuss the use of Mantel tests below, but see Manel et al. (2003) for a description of the other approaches

30 Step 2 involves quantifying the spatial landscape structure, and this is the purview of landscape ecology. There are a variety of approaches for doing this, but most involve incorporating the notion of landscape resistance (i.e., the impediments to gene flow) caused by landscape features (e.g., land cover, terrain). The most common approach employed involves measuring the cost distance between samples (populations or individuals) based on one or more alternative landscape resistance models. In most cases, the landscape resistance models (and their parameterization) are hypothesize a priori, but in a few rare, recent cases the resistance coefficients for the model have been estimated empirically using maximum likelihood procedures to identify the resistant surface that best explains the spatial genetic structure (from step 1). More on this approach below. In a few cases, instead of measuring the distance between samples, the landscape context is used to derive an index of isolation of each sample unit, and the isolation index is subsequently compared to the spatial genetic structure in step 3. The difference between these approaches is largely whether there is a single observation for each genetic sample (population or individual) - the isolation index approach or whether there is a distance matrix used to represent the distances between all pairs of samples the previous approach

31 Step 3 involves correlating the spatial genetic patterns with the landscape structure and is the cornerstone of landscape genetics which is fundamentally about relating genetic structure to landscape structure. Not surprisingly, there are a variety approaches for doing this. The most common approach involves using Mantel tests and partial Mantel tests to compare a genetic distance matrix (representing the genetic distance between all pairs of samples) to an ecological distance matrix (represent the cost distance between all pairs of samples in a resistant landscape). More on this approach below. An alternative approach involves the use of constrained ordination techniques such as redundancy analysis (RDA) and canonical correspondence analysis (CCA), in which the genetic data is represented as a two-way matrix of samples by loci, and the constraints are landscape variables measures for each sample location. Lastly, in some cases, the approach is simply a visual inspection of the relationships using GIS analysis

32 Example: Population Fst (Spear et al. 2005) When populations are clearly defined and the samples are collected from separate populations, the most common landscape genetic approach involves using a statistic like Fst (there are many variants) to measure the proportion of genetic variation due to among-population differences relative to that due to within-population differences and then comparing the pairwise population Fst values to some measure of ecological distance between populations often based on the least cost path distance between populations. Fst is defined as the proportional reduction in heterozygosity due to population subdivision, and it ranges from 0 to 1. Low levels of gene flow promote genetic divergence among populations and drives Fst to 1. Specifically, Fst=1 happens when two populations share no alleles in common, as shown in the top right-hand figure. Conversely, high levels of gene flow drives Fst to 0. Specifically, Fst=0 happens when two populations have identical allele frequencies; i.e., they share all alleles in the same proportions, as shown in the bottom right-hand figure

33 Spear et al. (2005) used this approach to measure the genetic distance between all pairwise combinations of 10 populations of blotched tiger salamanders associated with discrete breeding sites (seasonal ponds) in the northern Range of Yellowstone National Park. Specifically, they computed the pairwise Fst values between each combination of ponds based on 8 polymorphic microsatellite loci

34 Next, they hypothesized several alternative models of ecological distance among ponds based on prior information about the landscape factors likely to affect salamander movement among sites. For example, the null model was simply the straight-line Euclidean distance between ponds (i.e., isolation by distance). They compared this model to several more complex models in which distance was measured using topographic distance (i.e., isolation by topographic distance), in which individuals dispersed via a pathway moving through proximate wetlands that have historical records of salamander occurrence (i.e., stepping-stone route), or in which least cost paths were based the likelihood of wetlands, slope, or a combination of the two (i.e, isolation by landscape resistance). Next, for each of the routes (excluding the null model), they estimated percent variation in Fst explained by (i) mean wetland likelihood, (ii) percent of each cover type along the route, (iii) elevation, and (iv) number of streams and rivers crossed by each route in addition to topographical distance. Finally, they used a series of Mantel and partial Mantel tests to evaluate the evidence in support of each model based on AIC, and decomposed the variance explained by each model into the landscape variables. Their results indicated that the straight-line route model containing topographical distance, elevational difference, percent open shrub habitat, and number of river and stream crossings explained the most variance and was the best model based on AIC

35 Example: Assignment test (Wang et al. 2009) An alternative to the Fst approach when populations are clearly defined and the samples are collected from separate populations is to use an assignment test to measure the level of gene flow between populations. Assignment tests use the genotype of individuals from several populations and determine from which population each individual is most likely to have originated using an assignment index -- the highest probability of an individual's genotype in any of the populations. The proportion of individuals from population 1 that are assigned to population 2 can be interpreted as an estimate of the gene flow from population 2 to 1. Note, in this fashion gene flow estimates need not be reciprocal; i.e., gene flow from 2 to 1 can be different than from 1 to

36 Wang et al (2009) used this approach to estimate gene flow among 16 populations of California tiger salamanders in grassland vernal pool habitat at the Fort Ord Natural Reserve, Monterey County, California. Specifically, they estimated asymmetrical gene flow rates between each combination of ponds using assignment tests based on 13 polymorphic microsatellite loci

37 Next, they computed the least-cost path distance between each combination of ponds based on resistant surfaces derived from the cost of movement through different habitat types (grassland, chaparral, oak woodland). To infer the appropriate costs for each habitat type, they calculated least-cost distances over a range of values and compared them to those predicted by the genetic analyses. There were essentially three steps to their analysis: (i) assign hypothetical costs to each habitat type, (ii) calculate the least-cost distances between ponds using those costs, and (iii) compare these least-cost distances to those predicted by gene flow estimates. By assigning a range of costs to each habitat type, they were able to construct thousands of cost surfaces representing alternative cost structures. Because the assignment algorithm provides a 95% confidence interval in addition to the mean of gene flow between ponds, they were able to establish a 95% confidence interval of relative rates predicted from the molecular data. For each of the cost structures, they took the least-cost path distances and compared them to the distances expected by the rates of gene flow resulting from the molecular analysis. If all of the least-cost distances fell within their expected ranges, based on the 95% confidence interval, then they accepted the habitat cost values used to generate those paths as reflecting biologically accurate costs of dispersal. This resulted in a range of values for which the habitat costs matched expectations

38 They were only able to infer significant gene flow rates among four of the ponds; the remainder were indistinguishable from uninformative data. The least-cost path analysis involving these four ponds indicated that dispersal through chaparral is the least costly to A. californiense, and that movement through grassland is approximately twice, and through oak woodland roughly five times as costly as movement through chaparral. Specifically, a small range of costs values ( for grassland and for oak woodland) produced cost distances that fell within the 95% confidence interval inferred from the genetic data (Table 4). The inferred dispersal corridors are plotted on the habitat map shown here as least-cost paths

39 Example: Causal modeling (Cushman et al. 2006) Landscape genetics is perhaps best exemplified by situations in which discrete populations do not exist. In the traditional population genetics approach, discrete populations are presumed to exist, the genetic samples are collected from those discrete units, and gene frequencies are compared among populations. The landscape genetics approach simply relates these genetic differences to landscape structure. In the hypothetical example shown here, the river and the mountain range are presumed to be barriers to gene flow. Individual samples are presumed to be associated with one of the three distinct populations. The typical analysis involves determining if the populations are genetically distinct. This is the so-called isolation by barrier hypothesis

40 But what if selective pressures exist on a simple geographic distance gradient, in which genetic dissimilarities increase with increasing distance. This is the so-called isolation by distance hypothesis, and it is commonly the null model against which more complex models are compared. Note, the isolation by distance and the isolation by barrier models have been the mainstay of spatial population genetics. Incorporating more complex treatments of heterogeneity is the purview of landscape genetics

41 Landscape genetics hypothesizes that selective pressures may exist on complex landscape structure gradients, in which the landscape is perceived as complex resistant surface where the resistance is determined by landscape features (e.g., land cover, terrain). This is the so-called isolation by landscape resistance hypothesis, and it is the mainstay of landscape genetics

42 Cushman et al (2006) used this landscape genetics approach and a method known as causal modeling to examine the landscape factors affecting the spatial genetic structure of black bear populations in the northern Idaho panhandle. The study design included an incomplete systematic distribution of 266 sample plots in the Selkirk and Purcell Mountains spanning the Kootenai River valley. They collected genetic samples using non-invasive hair snares at each of the sample plots, which resulted in samples from 146 individual bears

43 They computed the pairwise genetic differences among bears based on 9 polymorphic microsatellites. They computed an Fst of 0.02 for the differences between the Selkirk and Purcell Mountains, indicating very low levels of genetic differentiation between these two putative populations. However, assignment tests resulted in 74% of the Purcell animals being assigned to the Purcell Mountains and 89% of the Selkirk animals being assigned to the Selkirk Mountains. Thus, there appears to be some spatial genetic structure due to the these gross topographic features. Lastly, the spatial autocorrelation in genetic similarity revealed significantly positive autocorrelation up to a distance of approximately kilometers, indicating an isolation by distance pattern

44 To examine the role of landscape heterogeneity in structuring the genetic dissimilarities among bears, they computed the genetic distance between each pair of bears based on the percentage dissimilarity in alleles across the 9 loci. This resulted in a genetic distance matrix for the 146 bears in which each row and column represents one of the individual bears and the elements are the genetic dissimilarities. Note, this is a square symmetric matrix; i.e., the lower triangle is a mirror image of the upper triangle

45 Next, they built hypothetical landscape resistance surfaces by considering four factors: land cover (3 levels), slope (3 levels), elevation (4 levels) and roads (3 levels). In a full factorial design (3x3x4x3), this resulted in 108 hypothesized landscape resistance models. They combined this with the two traditional models, isolation by distance and isolation by barrier (in which the Kootenai River serve as the barrier between the Selkirk and Purcell Mountains), for a total of 110 landscape models

46 The slope factor included 3 levels and was modeled as a linear relationship between percent slope and landscape resistance, in which the slope of the relationship was zero (null or no resistance) or low or high. The elevation factor included 4 levels and was modeled as an inverse Gaussian relationship between elevation and landscape resistance, in which resistance was minimal a low, intermediate, and high elevations, or in which there was no relationship with elevation (null). The cover factor included 3 levels and was modeled as a categorical relationship between land cover classes and landscape resistance, in which various non-forested cover classes were given relatively low versus high resistance values, or in which all cover types were equally nonresistant (null). The roads factor included 3 levels and was modeled as a categorical relationship between road class (major roads versus others) and landscape resistance, in which major and minor roads were given relatively low versus high resistance values, or in which there was no resistance to roads (null)

47 Next, they created a resistant surface for each landscape model (i.e., factorial combination of resistances associated with each of the four factors) and computed the pairwise least cost path distances among all bear samples. This resulted in a least cost path distance matrix for the 146 bears in which each row and column represents one of the individual bears and the elements are the ecological least cost path distances. Note, this is a square symmetric matrix of the same dimensions as the genetic distance matrix

48 Next, they tested the relationship between genetic distance and each of the ecological distance models using Mantel and partial Mantel tests: Spatial Euclidean distance in which the elements represent the Euclidean distance between bears; this is the isolation by distance model Barrier distance in which the elements equal 1 if the samples are on the same side of the Kootenai River and 0 otherwise; this is the isolation by barrier model Least cost path distance in which the elements represent least cost path distances between bears based on one of the 108 landscape resistance models; this is the isolation by landscape resistance model(s) 15.48

49 For this purpose, they used Causal Modeling to examine the support for 7 different organizational models representing alternative hypotheses about the independent and joint affects of Euclidean distance, the Kootenai River barrier and landscape resistance on genetic structure. For each of these organizational models they listed several diagnostic results that would be indicative of consistent support for that model. For example, the model highlighted in red in the figure represents the isolation by landscape resistance model. The diagnostic results include the following: L 108 G.B>0 this indicates a significant partial Mantel test between one or more of the landscape resistance models and genetic distance after accounting for (i.e, partial out) the barrier effect L 108 G.D>0 this indicates a significant partial Mantel test between one or more of the landscape resistance models and genetic distance after accounting for (i.e, partial out) the Euclidean distance effect BG.L 108 ns this indicates a non-significant (ns) partial Mantel test between the barrier model and genetic distance after accounting for (i.e, partial out) each of the landscape resistance models DG.L 108 ns this indicates a non-significant (ns) partial Mantel test between the Euclidean distance model and genetic distance after accounting for (i.e, partial out) each of the landscape resistance models 15.49

50 The results of the Mantel tests for each of the 110 models were ranked in terms of strength of support. The distance model was significant, as was the barrier model, as was all of the landscape resistance models. In other words, there was significant support for all of the 110 alternative models. However, the barrier model was ranked 102 of 110. The Euclidean distance model was ranked 35 of 110. Thus, there were 35 landscape resistance models with larger Mantel r values than the distance model, suggesting that the landscape resistance model was superior. The causal modeling results based on the partial Mantel tests confirmed this relationship. Specifically, the isolation by landscape resistance model was the only organizational model fully supported by all of the diagnostic results. There were 12 landscape resistance models with significant Mantel r statistics after partialling out the distance model. This is shown graphically in the right-side figure, in which the shaded cubes represent the 12 significant partial models and the blue to red gradient represents magnitude of significance

51 One of the products of this sort of analysis is a bear connectivity model that is empirically derived to represent the landscape features that most affect gene flow in black bears at least among the landscape factors considered. In this case, the best landscape mode is one in which there is a strong affinity for forest cover at mid elevations on any slope and where roads have a neutral affect

52 One of the things they have done subsequently is to extrapolate this model to the entire northern Rockies in order to examine potential corridors for connectivity between the greater Yellowstone ecosystem and Canada. Indeed, by applying the landscape resistance model they derived and simulating potential least cost movements between the two region they were able to identify a few potential corridors of expected movement between the two regions. These corridors have been compared to other proposed corridors, including those based entirely on subjective criteria in addition to those empirically derived for other species using similar procedures

53 One of the implications of their work is to cast doubt over the traditional views of populations as discrete entities, especially for species that are continuously distributed across their range (like the black bear). In these situations, there may not be absolute boundaries to any populations. Rather, populations may be better thought of as a moving local neighborhood in which the spatial extent of the population varies with the spatial context of the landscape. The movie shown here illustrates this concept

54 The take home messages from this section on landscape genetics include the following: Landscape genetics offers a cost-effective quantitative approach to empirically measure relatively recent connectivity (i.e., gene flow). This is immensely important for two reasons. First, measuring connectivity by direct observation of movement of individuals is extremely challenging, costly and time-consuming. Second, direct movement studies are unable to address movements integrated over many years to decades and centuries. Genes flow over short and long periods of time, and landscape genetics allows us to assess this movement in a way that direct movement studies can not. Landscape genetic tools can help us evaluate land use impacts (on gene flow) and identify areas of important connectivity (e.g., corridors) for a focal species. This is immensely important as well, as connectivity is the key to the conservation of ecological integrity and there are few methods available that allow us to quantitatively examine connectivity. Synergy of landscape ecology & genetics is just being realized; recent explosion of analytical methods. This is a very exciting time to be a landscape geneticist as the tools of the trade are evolving rapidly and every day brings a new and exciting approach for examining the relationship between spatial genetic structure and landscape structure