Landscape genetics

Instructor: K. McGarigal

Assigned Reading: Manel et al (2003)

Objective: Provide an overview of the consequences of landscape pattern to the spatial geneticstructure of populations. Highlight the role of landscape structure in gene flow and approachesfor 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 landscapes6. Landscape genetics: statistical approaches and examples

Comments: Slides adapted from presentation by Dr. Michael Schwartz, USDA Forest ServiceRocky Mountain Research Station, Missoula, Montana.

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1. What is Landscape Genetics

Landscape genetics is an approach for understanding of how geographical and environmentalfeatures 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; andc. 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 andlandscape ecology.

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2. What is Gene Flow?

Gene flow is the incorporation of genes into the gene pool of one population from otherpopulations. In this regard, it is important to distinguish between the processes of dispersal andmigration 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 newpopulation, since this requires successful reproduction.

• Migration – refers to the movement of genes from one population to another accomplishedby individuals that move and breed in a population other than their birth site. Migration, asdefined here, equals gene flow. Note, migration is defined somewhat differently bybiologists, where it generally refers to the periodic (typically seasonal) movement ofindividuals between geographic locations.

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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) associatedwith small populations, by introducing new genes into a population..

• Prevent depression of population fitness – gene flow functions to increase the heterozygosityof 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 canreduce 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 reductionin fitness due to the loss of heterozygosity, gene flow can serve to decrease the risk ofpopulation extinction.

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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% hatchingsuccess rate, but in 1990 that rate had fallen to 74%. The decrease in fecundity (i.e., fitness) washypothesized to be due to the loss of genetic diversity associated, which declined 30% between1960-1990. To reverse the situation, managers introduced birds from Minnesota and Kansas toinfuse new genes into the population, and hatching rate success increased to 94%. Thepopulation has since recovered from near extinction.

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Example: Scandanavian adder (Maddsen et al. 2001)

An Scandanavian adder population crashed between 1983-1993. The population had very lowgenetic diversity and a large number of stillborn offspring were observed, an indication of lowfitness due to inbreeding depression. To counter the population crash, managers introduced 20males from a larger population for 3 years between 1996-1999. The immediate result was anincrease in male recruitment and a decrease in the number of stillborns. Note, the males werereturned to their native population after performing their duty.

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

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4. How Much Gene Flow is Enough?

So, if gene flow is important, at the very least to reduce the potential for inbreeding depression insmall populations, how much is enough? While this is not an easy question to answer, thegeneral rule of thumb that has been put forth is that one migrant per generation is necessary toprevent the adversities of inbreeding depression, while also allowing for divergence in allelefrequencies among subpopulations. Mills and Allendorf (1996) authors argue that one migrantper generation is an appropriate minimum, but that the “rule” should be broadened to include amaximum of 10 migrants per generation. Vucetich and Waite (2000) question whether that ruleof thumb is sufficient for fluctuation populations, and demonstrate that most populationsfluctuate enough to require >10 migrants per generation and many may even require >20 pergeneration.

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Example: Brassica campestris (Newman and Tallmon 2001)

In this inbreeding experiment involving the mustard Brassica campestris, five of six fitnessrelated components were negatively effected by inbreeding. The researchers experimentallyintroduced migrant treatments of 0, 1, and 2.5. The results were dramatic. The 1 migranttreatment and 2.5 migrant treatment produced higher fitness components than the 0 migranttreatment, and there was no difference between 1 and 2.5 migrant treatments, suggesting that inthis case the 1 migrant per generation rule may be enough to prevent inbreeding depression.

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Example: Peromyscus maniculatus (Schwartz and Mills 2005)

In this study involving Peromyscus maniculatus, the researchers compared survival rates in arelatively isolated control population against two different treatments: a migrant treatment inwhich individuals from another distant source population were introduced to the localpopulation, and an inbreeding treatment in which a population was experimentally inbreed. Themigrant treatment resulted in a dramatic increase in survival. Surprisingly, the inbreedingtreatment also resulted in an increase in survival, which the authors attribute to a number offactors.

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5. Gene Flow in Heterogeneous Landscapes

The question we are most interested in is whether landscape patterns, in particular those createdby human land uses, influence gene flow and to what extent. Consider the following series ofslides and try to answer the question, is gene flow occurring?

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In order to answer the question, is gene flow occurring, we need to sidetrack and do a quickgenetics 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. Optimalsamples (i.e., containing the most DNA) include tissue and blood, but the collection of thesesamples requires invasive sampling. Sub-optimal samples include hair, scat, urine, skins/museumspecimens, feathers and guano, and these can generally be obtained using non-invasive methods.

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Types of DNA

1. Mitochondrial DNA (mtDNA) – is contained (obviously) in the mitochondria of cells andthere 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 tooffspring, and is highly conserved; i.e., it is very stable and does not change much overgenerations. Thus, the DNA in your mitochondria and very much the same as those that werecarried by your great, great, great, great, etc. grandmother.

2. Nuclear DNA – is contained (obviously) in the nucleus of cells and there are two copies percell. Nuclear DNA is inherited from both parents, one copy from each parent. There are highlyvariable regions called microsatellites that are very useful for distinguishing individuals and fordifferentiating very recent population divergences.

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Species ID using mtDNA

mtDNA is especially useful for distinguishing among species, which is often the first thing thatmust be done after collecting non-invasive samples in order to be sure of the species. There aretwo common approaches for this purpose:

1. Restriction digests (RFLP) – in which known genes are extracted using restriction enzymesand 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 isdetermined and differences in the sequence are used to distinguish among species.

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Restriction Digests

Step 1. The first step is to separate the DNA from other cellular material. Note, at this stage all ofthe 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 pairsin length), which latch on to either side of an area of interest (typically a 100-800 bp length ofDNA).

Step 3. The next step is to make many copies of the genetic fragment using Polymerase chainreaction (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 currentacross it. The DNA fragments migrate across the gel according to their size; large fragments onlymove a short distance, while small fragments move farther across the gel.

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Depending on the gene analyzed, species or groups of related species (e.g., families) can easilybe 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 aredistinguished 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 fordistinguishing among lynx, bobcat and mountain lion.

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DNA Sequence Analysis

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

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Now back to our original question: Is this river a barrier to gene flow? At this point, usingmtDNA analysis, let’s say that we have confirmed that four of the samples collected are fromlynx, and that one of the samples is on the opposite side of the river. Does this suggest gene flowacross the river?

Yes, IF the samples on opposite sides of the river are from related individuals. But how do wedetermine if these samples are from the same individuals or from related individuals (as opposedto the same species). This is where nuclear DNA comes in.

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Individual ID using nuclear DNA

Nuclear DNA is especially useful for distinguishing among individuals or determining thedegree 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 arenot under selection. Microsatellites have been the mainstay of landscape genetics sinceinception, but are currently being replaced by the more power analysis of SNPs (below).

2. Single nucleotide polymorphisms (SNPs) – DNA sequence variation in which a singlenucleotide (A, T, C or G) differs between individuals. Single nucleotides may be changed(substitution), removed (deletion), or added (insertion) to a polynucleotide sequence within aprotein coding, non-coding region, or intergenic region between genes, and the magnitude ofdifferences in SNPs between two individuals can be used as a measure of relatedness.

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Microsatellites

Here we will focus on microsatellites as they have been the mainstay for landscape geneticswork since its inception; only recently have SNPs offered an alternative and potentially morepowerful approach for quantifying the genetic differences between individuals.

A microsatellite is a highly variable region of nuclear DNA containing mono-, di-, tri- or tetra-nucleotide units repeated. Importantly, microsatellites are generally referred to as “junk” DNAbecause these regions of the genome are presumably non-protein coding and/or not under naturalselection. As a result, these regions can change rapidly over time, allowing us to distinguish evenrelatively recent genetic divergences.

The procedure for measuring microsatellites is essentially identical to that described earlier withrestriction digests. The DNA material is extracted, segmented into fragments (typically 50-300bp in length) at established locations (restriction sites), multiplied using PCR, and measuredusing gel electrophoresus.

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The resulting gel depicts the allele (alternative form of a gene) size at a specific locus (locationof a gene on a chromosome). Diploid individuals containing two homologous chromosomescontain two copies of each gene. If the two copies are the same, the individual is said to byhomozygous at this particular locus. If the two copies are different, the individual is said to byheterozygous. In the samples shown here, note that some individuals are homozygous, whileothers are heterozygous. In addition, note that there are only two different alleles present for thisparticular gene. Based on the data shown, clearly, samples 4 and 6 cannot be from the sameindividual, 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 thisone locus?

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Samples 1, 8, and 9 are all homozygous containing two copies of allele 2, and thus could be fromthe same individual.

Samples 2 and 6 are heterozygous containing a single copy each of allele 1 and 2, and thus couldbe from the same individual.

Samples 3, 4, 7, and 10 are all homozygous containing two copies of allele 1, and thus could befrom the same individual.

Note, it is not possible to say with any confidence whether any of these samples are from thesame individual based on this single locus, but if we evaluate many loci our ability todistinguishing among individuals increases dramatically.

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Back to our question about whether the river is a barrier to gene flow. Let’s assume that ouranalysis of microsatellites allowed us to determine that our 4 samples of lynx represent 3different 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 acomplete barrier to movement. Later we will quantify the extent to which rivers and otherlandscape features act as resistance to movement of genes.

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For gene flow to be occurring there must be reproduction, because that is the only way for genesof one population to migrate to another. So, another question we might be interested in iswhether 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. Thereare few different genes typically used for this purpose. For example, in the Zf and Amelogeningenes, females are always homozygous and males are always heterozygous, and the SRY gene isonly present in males.

In our particular example, let’s say that we can confirm that we have both males and femalespresent.

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Given that we have females present, the next question we might want to ask is whether there arerelated individuals? If we know who the mamma and papa are, we can determine the potentialgenotypes of their offspring. For example, if mamma is homozygous at a particular locus withallele CA6 (6 di-nucleotide repeats) and papa is heterozygous at the same locus with alleles CA4

(4 di-nucleotide repeats) and CA5 (5 di-nucleotide repeats), then the offspring will all get oneallele of CA6 from their mamma and either CA4 or CA5 from their pappa. Thus, the offspringhave to either be CA6 - CA5 or CA6 - CA4.

In our particular example, let’s say that we can confirm that mamma is found on the oppositeside of the river from her son. Relatedness across a potential “barrier” does suggest gene flow isoccurring.

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6. Landscape Genetics: Statistical Approaches and Examples

Manel et al. (2003) define the field of landscape genetics and provide a description of the basicapproach 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

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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 hasbeen a principal interest of population geneticists for decades and thus is not unique to landscapegenetics. There are a variety of approaches for doing this depending, in part, on whether clearlydefined and discrete a priori populations exist. In this case, the genetic structure among the pre-specified populations can be quantified using a variety of statistical measures, the most commonbeing 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 tobe real (e.g., continuously distributed individuals), then there are a wide variety of otherstatistical 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 theother approaches.

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Step 2 involves quantifying the spatial landscape structure, and this is the purview of landscapeecology. There are a variety of approaches for doing this, but most involve incorporating thenotion 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. Inmost 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 estimatedempirically using maximum likelihood procedures to identify the resistant surface that bestexplains 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 isused to derive an index of isolation of each sample unit, and the isolation index is subsequentlycompared to the spatial genetic structure in step 3. The difference between these approaches islargely 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.

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Step 3 involves correlating the spatial genetic patterns with the landscape structure and is thecornerstone of landscape genetics – which is fundamentally about relating genetic structure tolandscape 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 agenetic distance matrix (representing the genetic distance between all pairs of samples) to anecological distance matrix (represent the “cost” distance between all pairs of samples in aresistant landscape). More on this approach below.

An alternative approach involves the use of constrained ordination techniques such asredundancy analysis (RDA) and canonical correspondence analysis (CCA), in which the geneticdata is represented as a two-way matrix of samples by loci, and the constraints are landscapevariables measures for each sample location.

Lastly, in some cases, the approach is simply a visual inspection of the relationships using GISanalysis.

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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 manyvariants) to measure the proportion of genetic variation due to among-population differencesrelative to that due to within-population differences and then comparing the pairwise populationFst values to some measure of ecological distance between populations – often based on the leastcost path distance between populations.

Fst is defined as the proportional reduction in heterozygosity due to population subdivision, andit ranges from 0 to 1. Low levels of gene flow promote genetic divergence among populationsand drives Fst to 1. Specifically, Fst=1 happens when two populations share no alleles incommon, as shown in the top right-hand figure. Conversely, high levels of gene flow drives Fstto 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.

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Spear et al. (2005) used this approach to measure the genetic “distance” between all pairwisecombinations of 10 populations of blotched tiger salamanders associated with discrete breedingsites (seasonal ponds) in the northern Range of Yellowstone National Park. Specifically, theycomputed the pairwise Fst values between each combination of ponds based on 8 polymorphicmicrosatellite loci.

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Next, they hypothesized several alternative models of ecological distance among ponds based onprior 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 whichdistance was measured using topographic distance (i.e., isolation by topographic distance), inwhich individuals dispersed via a pathway moving through proximate wetlands that havehistorical records of salamander occurrence (i.e., stepping-stone route), or in which least costpaths were based the likelihood of wetlands, slope, or a combination of the two (i.e, isolation bylandscape resistance).

Next, for each of the routes (excluding the null model), they estimated percent variation inFst explained by (i) mean wetland likelihood, (ii) percent of each cover type along theroute, (iii) elevation, and (iv) number of streams and rivers crossed by each route in addition totopographical distance.

Finally, they used a series of Mantel and partial Mantel tests to evaluate the evidence in supportof each model based on AIC, and decomposed the variance explained by each model into thelandscape variables. Their results indicated that the straight-line route model containingtopographical distance, elevational difference, percent open shrub habitat, and number of riverand stream crossings explained the most variance and was the best model based on AIC.

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Example: Assignment test (Wang et al. 2009)

An alternative to the Fst approach when populations are clearly defined and the samples arecollected from separate populations is to use an assignment test to measure the level of gene flowbetween populations.

Assignment tests use the genotype of individuals from several populations and determine fromwhich 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 ofindividuals from population 1 that are assigned to population 2 can be interpreted as an estimateof the gene flow from population 2 to 1. Note, in this fashion gene flow estimates need not bereciprocal; i.e., gene flow from 2 to 1 can be different than from 1 to 2.

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

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Next, they computed the least-cost path distance between each combination of ponds based onresistant surfaces derived from the cost of movement through different habitat types (grassland,chaparral, oak woodland). To infer the appropriate costs for each habitattype, they calculated least-cost distances over a range of values and compared them to thosepredicted by the genetic analyses. There were essentially three steps to their analysis: (i) assignhypothetical costs to each habitat type, (ii) calculate the least-cost distances between ponds usingthose costs, and (iii) compare these least-cost distances to those predicted by gene flowestimates.

By assigning a range of costs to each habitat type, they were able to construct thousands of costsurfaces representing alternative cost structures. Because the assignment algorithm provides a95% confidence interval in addition to the mean of gene flow between ponds, they were able toestablish a 95% confidence interval of relative rates predicted from the molecular data. For eachof the cost structures, they took the least-cost path distances and compared them to the distancesexpected by the rates of gene flow resulting from the molecular analysis. If all of the least-costdistances fell within their expected ranges, based on the 95% confidence interval, then theyaccepted the habitat cost values used to generate those paths as reflecting biologically accuratecosts of dispersal. This resulted in a range of values for which the habitat costs matchedexpectations.

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They were only able to infer significant gene flow rates among four of the ponds; the remainderwere indistinguishable from “uninformative” data. The least-cost path analysis involving thesefour ponds indicated that dispersal through chaparral is the least costly to A. californiense, andthat movement through grassland is approximately twice, and through oak woodland roughlyfive times as costly as movement through chaparral. Specifically, a small range of costs values(1.7–2.2 for grassland and 4.6–5.30 for oak woodland) produced cost distances that fell withinthe 95% confidence interval inferred from the genetic data (Table 4).

The inferred dispersal corridors are plotted on the habitat map shown here as least-costpaths.

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Example: Causal modeling (Cushman et al. 2006)

Landscape genetics is perhaps best exemplified by situations in which discrete populations donot exist. In the traditional population genetics approach, discrete populations are presumed toexist, the genetic samples are collected from those discrete units, and gene frequencies arecompared among populations. The landscape genetics approach simply relates these geneticdifferences to landscape structure.

In the hypothetical example shown here, the river and the mountain range are presumed to bebarriers to gene flow. Individual samples are presumed to be associated with one of the threedistinct populations. The typical analysis involves determining if the “populations” aregenetically distinct. This is the so-called “isolation by barrier” hypothesis.

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But what if selective pressures exist on a simple geographic distance gradient, in which geneticdissimilarities 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 arecompared. Note, the isolation by distance and the isolation by barrier models have been themainstay of spatial population genetics. Incorporating more complex treatments of heterogeneityis the purview of landscape genetics.

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Landscape genetics hypothesizes that selective pressures may exist on complex landscapestructure gradients, in which the landscape is perceived as complex resistant surface where theresistance 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.

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Cushman et al (2006) used this landscape genetics approach and a method known as causalmodeling to examine the landscape factors affecting the spatial genetic structure of black bearpopulations in the northern Idaho panhandle. The study design included an incompletesystematic distribution of 266 sample plots in the Selkirk and Purcell Mountains spanning theKootenai River valley.

They collected genetic samples using non-invasive hair snares at each of the sample plots, whichresulted in samples from 146 individual bears.

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They computed the pairwise genetic differences among bears based on 9 polymorphicmicrosatellites. They computed an Fst of 0.02 for the differences between the Selkirk and PurcellMountains, indicating very low levels of genetic differentiation between these two putativepopulations. However, assignment tests resulted in 74% of the Purcell animals being assigned tothe 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 topographicfeatures. Lastly, the spatial autocorrelation in genetic similarity revealed significantly positiveautocorrelation up to a distance of approximately 10-14 kilometers, indicating an isolation bydistance pattern.

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

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Next, they built hypothetical landscape resistance surfaces by considering four factors: landcover (3 levels), slope (3 levels), elevation (4 levels) and roads (3 levels). In a full factorialdesign (3x3x4x3), this resulted in 108 hypothesized landscape resistance models. Theycombined this with the two traditional models, isolation by distance and isolation by barrier (inwhich the Kootenai River serve as the barrier between the Selkirk and Purcell Mountains), for atotal of 110 landscape models.

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The slope factor included 3 levels and was modeled as a linear relationship between percentslope and landscape resistance, in which the slope of the relationship was zero (null or noresistance) or low or high.

The elevation factor included 4 levels and was modeled as an inverse Gaussian relationshipbetween 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 landcover classes and landscape resistance, in which various non-forested cover classes were givenrelatively low versus high resistance values, or in which all cover types were equally non-resistant (null).

The roads factor included 3 levels and was modeled as a categorical relationship between roadclass (major roads versus others) and landscape resistance, in which major and minor roads weregiven relatively low versus high resistance values, or in which there was no resistance to roads(null).

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

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Next, they tested the relationship between genetic distance and each of the ecological distancemodels 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 landscaperesistance model(s)

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For this purpose, they used Causal Modeling to examine the support for 7 differentorganizational models representing alternative hypotheses about the independent and jointaffects of Euclidean distance, the Kootenai River barrier and landscape resistance on geneticstructure. For each of these organizational models they listed several diagnostic results thatwould be indicative of consistent support for that model. For example, the model highlighted inred in the figure represents the isolation by landscape resistance model. The diagnostic resultsinclude the following:• L108G.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) thebarrier effect

• L108G.D>0 – this indicates a significant partial Mantel test between one or more of thelandscape resistance models and genetic distance after accounting for (i.e, partial out) theEuclidean distance effect

• BG.L108 ns – this indicates a non-significant (ns) partial Mantel test between the barriermodel and genetic distance after accounting for (i.e, partial out) each of the landscaperesistance models

• DG.L108 ns – this indicates a non-significant (ns) partial Mantel test between the Euclideandistance model and genetic distance after accounting for (i.e, partial out) each of thelandscape resistance models

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The results of the Mantel tests for each of the 110 models were ranked in terms of strength ofsupport. The distance model was significant, as was the barrier model, as was all of thelandscape resistance models. In other words, there was significant support for all of the 110alternative models. However, the barrier model was ranked 102 of 110. The Euclidean distancemodel was ranked 35 of 110. Thus, there were 35 landscape resistance models with largerMantel r values than the distance model, suggesting that the landscape resistance model wassuperior.

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 fullysupported by all of the diagnostic results. There were 12 landscape resistance models withsignificant Mantel r statistics after partialling out the distance model. This is shown graphicallyin the right-side figure, in which the shaded cubes represent the 12 significant partial models andthe blue to red gradient represents magnitude of significance.

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One of the products of this sort of analysis is a bear connectivity model that is empiricallyderived to represent the landscape features that most affect gene flow in black bears – at leastamong the landscape factors considered.

In this case, the best landscape mode is one in which there is a strong affinity for forest cover atmid elevations on any slope and where roads have a neutral affect.

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One of the things they have done subsequently is to extrapolate this model to the entire northernRockies in order to examine potential corridors for connectivity between the greater Yellowstoneecosystem and Canada. Indeed, by applying the landscape resistance model they derived andsimulating potential least cost movements between the two region they were able to identify afew potential corridors of expected movement between the two regions. These corridors havebeen compared to other proposed corridors, including those based entirely on subjective criteriain addition to those empirically derived for other species using similar procedures.

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One of the implications of their work is to cast doubt over the traditional views of populations asdiscrete entities, especially for species that are continuously distributed across their range (likethe 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 thespatial extent of the “population” varies with the spatial context of the landscape. The movieshown here illustrates this concept.

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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 extremelychallenging, costly and time-consuming. Second, direct movement studies are unable toaddress movements integrated over many years to decades and centuries. Genes flow overshort and long periods of time, and landscape genetics allows us to assess this movement in away that direct movement studies can not.

• Landscape genetic tools can help us evaluate land use impacts (on gene flow) and identifyareas of important connectivity (e.g., corridors) for a focal species. This is immenselyimportant as well, as connectivity is the key to the conservation of ecological integrity andthere are few methods available that allow us to quantitatively examine connectivity.

• Synergy of landscape ecology & genetics is just being realized; recent explosion of analyticalmethods. This is a very exciting time to be a landscape geneticist as the tools of the trade areevolving rapidly and every day brings a new and exciting approach for examining therelationship between spatial genetic structure and landscape structure.

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