Models of landscape change?

Instructor: K. McGarigal

Assigned Reading: Turner et al. 2001 (Chapter 3); Scheller and Mladenoff (2007)

Objective: Provide an overview of the varied types of dynamic landscape models and theirapplications for examining pattern-process relationships. Highlight the use of stochastic landscapedisturbance-succession simulation models (e.g., LANDIS, LANDSUM, RMLANDS).

Topics covered:1. Purpose of landscape change models2. Change detection: First-order Markov Chains3. Issues in modeling landscape change4. Landscape disturbance-succession models (LDSMs)

4.1. Types and components of LDSM’s4.2. Selecting an LDSM4.3. Applications of LDSM’s

5. Prospectus

Comments: Some material taken from Dean Urban’s Landscape Ecology course notes, DukeUniversity.

There is a spectrum of ways to consider landscape change, ranging from simple and readilyinterpretable, to more realistic (complicated) and less interpretable. We will begin this session byexploring a relatively straightforward (albeit simplistic) method for modeling landscape change,not so much because we believe that landscape dynamics could be represented well by such asimple model, but rather, because this model could provide a reference framework and a point ofdeparture (i.e., a neutral model) for more realistic but more complicated scenarios of landscapechange. We will then consider more complicated methods to get around the limitations imposedby the initial, simple model.

A secondary goal of this session is to develop an appreciation for ways of modeling landscapechange, and the logistical and empirical implications of these approaches. This presumes someappreciation of ecological models in general. The intention here is not so much to provide atutorial in landscape modeling (for that, see Weinstein and Shugart 1983, Baker 1989, Sklar andCostanza 1991, Baker and Mladenoff 1998). Rather, this discussion underscores the morefundamental point that to document these aspects of landscape change, one would need the samesort of conceptual framework and (importantly!) data as if one were actually building a model.Thus, the exercise of formulating the model and gathering data to support it is valuable, even ifthe model is never actually built. We will use models here as vehicles for organizing our thoughtsand data toward a richer understanding of landscape change.

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2. Change Detection

Perhaps the most fundamental data on landscape change arise from observations of the state of alandscape at two time periods. For example, we might have land cover maps classified fromsatellite images obtained fortwo dates ten years apart, andnote that some of the cells(pixels) changed type over thattime interval.

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2.1. First-order MarkovChains: The TransitionMatrix

One way to summarizelandscape change is tosimply tally all theinstances, on a cell-by-cellbasis, in which a cell (pixel)changed cover types overthat time interval. Mostimage-processing packageshave automated algorithmsfor change detection thatprocess maps in this way. Aconcise way ofsummarizing these tallies is

ijthe so-called tally matrix, which for N cover types is an N x N matrix, the elements n of whichtally the number of cells that changed from type i to type j over the time interval. This tallymatrix reflects the size of the images, of course, and so it is convenient to convert the raw talliesinto proportions. This is done by dividing each of the elements by the row total, which generates

ija transition matrix P, the elements of which, p , summarize the proportion of cells of each covertype that changed into each other cover type during that time interval. The diagonal elements of

iithis matrix, p , are the proportions of cells that did not change. The transition matrix P has a timestep defined by the interval between the two images or maps used to tally the transitions. Onecommon way to normalizetransition matrices is toadjust them to an annualtime step. To do this, each

ijelement p , i not equal to j,is divided by the number ofyears in the data record. The

iidiagonal elements p mustthen be adjusted so that theelements of each row sum to

ii j ij1.0, i.e., p = 1.0 - SUM (p )for i not equal to j. Thematrix P is a completedescription of the changes inthe proportions of land covertypes observed over thattime period.

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2.2. State Vector Tallies

The same basic data used to build the transition matrix P also can be used to summarize the stateof the landscape in each time period. This summary takes the form of a vector x, the elements of

iwhich x tally the number of cells in each cover type i at each time period:

tx = [x1, x2, x3, ...]

for i = 1, 2, ... N patch types. As with the transition matrix, it is customary to relativize this statevector into proportions of the landscape, by dividing each element by the number of cells in thelandscape map.

With the construction of the transition matrix P and the state vector x, the changes observed onthe landscape have been summarized as a first-order Markov chain, a simple model of landscapechange. All that remains is to evaluate the model.

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2.3. Markov Models: Background and Computational Details

A first-order Markov model assumes that to predict the state of the system at time t+1, you needonly know the state of the system at time t. The heart of a Markov model is the transition matrixP, which summarizes the probability that a cell in cover type i will change to cover type j duringa single time step. Here, the matrix P is as computed from the tally matrix as described above.

Markov models, while simple, have a number of appealing properties (Usher 1992). In particular,they can be solved by iteration to project the state of the system into the future. Writing the stateof the system as the vector x (above), the future state of the system can be projected:

t+1 tx = x P

that is, the state vector post-multiplied by the transition matrix. The next projection, for time t+2is continued:

t+2 t+1 t tx = x P = x P P = x P2

and in general, the state of the system at time t=t+k is given by:

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t+k t x = x Pk

twhere x is the initial condition of the map (i.e., its state at time t). Thus, the model can beprojected into the future simply by iterating through the matrix operation.

The steady-state or equilibrium state of the system (if it exists) is given by the eigenvector of thetransition matrix; thus, there is a closed-form solution to the model. Recall, the eigenvector of thematrix is defined such that the eigenvector multiplied by the transition matrix yields the samevector again:

x* = x*P

That is, the system does not change once it reaches this state. There are computational tricks forestimating steady-state solutions (Usher 1992), or you could use a math package to do this. Butfor simple models, the solution often converges rapidly and you can estimate the solutions simplyby projecting the model a few times.

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2.4. Graphical Representation

The model implied by the transition matrix P can also be represented as a graph (a"box-and-arrow" diagram). For example, a 3-state case could be illustrated where thethickness of the arrows between each state indicates the magnitude of the transition rates.

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2.5. Model analysis: projecting a map

By projecting the state vector x using the transition matrix P, we predict the proportions of thelandscape that might be in each cover state at each iteration of the model. This approachconsiders landscape dynamics as a "compartment flow" problem in which land area "flows" fromone cover type to another (Weinstein and Shugart 1983). In many cases, however, we wouldrather actually project a map into the future, an approach that opens up new realms of possibilitywhile creating some new problems. To project a raster map, the transition matrix is simplyinvoked on a cell-by-cell basis. But because each cell can only change into at most one otherstate (a cell can't change fractionally), this must done probabilistically. Written as pseudo-code:

loop through each cell: check to see what cover type this cell is (call it i) look at the ith row of the transition matrix P draw a uniform-random number y on [0,1] loop through each column j of the ith row of P: if p(i,j-1) < y <= p(i,j), then change the cell to type j go to next type j if the cell hasn't been changed yet go to next cell

When finished, each cell will have been changed (the "change" might have been to remain in thesame state), and there would be a new map. Importantly, this new map is only one of manypossible stochastic realizations of a new map, since the map was created probabilistically. Thus,any comparison to a real map would have to be based on a number of replicate, stochastic maps.

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3. Issues in Modeling Landscape Change

The simple Markov model serves as a useful point of departure for more complicated issues inlandscape modeling. For a Markov model built from data, a projection of the state vector x from

1 2 2t to t should reproduce the state vector at t correctly (i.e., within rounding error). This isbecause the model is defined to summarize these observations. But while verifying the overallchange in proportions of cover types on the landscape, this projection need not verify that thedynamics are actually those of a first-order Markovian process. Nor does the ability to reproduce

2conditions at time t imply that this model will also project conditions reliably into the future.That is, it may still be true that the observed dynamics violate some of the assumptions of afirst-order Markov model. There are three issues of interest here:

5. Nonstationarity The rates or probabilities of transitions among cover types varythrough time, implying that the rules governing landscape changeare themselves changing.

6. Spatial dependencies The dynamics depend on spatial covariates (edaphic ormicroclimate variables) or neighborhood effects that influence theprobability of changes among cover types.

7. History matters Antecedent conditions, such as prior land use, leave a legacy orimpart "memory" into landscape dynamics, implying that thedynamics are not first-order.

In each case, the approach to assessing the importance of these factors will be to model landscapechange without including these, and then to examine the model projection for systematic errorsor biases that point to one or more of these factors -- a neutral model approach (Gardner et al.1987).

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3.1. Nonstationarity

For landscapes with well-documented histories, such as manifest in multiple land cover maps, aseries of first-order Markov models could be derived, one of each pair of maps. The questionarises, are the transition rates similar across all of these time periods? If the rates of change (asmatrices P) are the same across time periods, just one matrix would suffice and the matrix is saidto be stationary. Nonstationary transition matrices would suggest that the rules or forcesgoverning landscape change were themselves changing over time. This might be the case inregions driven by historical variation in socioeconomic drivers (true of most of the United Statesover the past several decades).

There is a formal test for stationarity of transition matrices (Usher 1992), but nonstationarity isalso obvious when the projection from one time period does not match the state of the landscape

1 2in the next time period, that is, if the projection based on t and t fails to predict the state at time

3t . This is because the Markov model is a complete empirical description of the observed changesin the proportion of cover types on the landscape, and consequently it must reproduce theaggregate changes for the period for which the model was constructed. Thus, if the model fails at

3 2 3time t , then the transition rates changed between time periods t and t . A lack of stationarity alsois often graphically evident in model projections. Nonstationarity appears as a significant over- orunder-prediction by the model when it is projected to the next period of record.

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There are model extensions that allow one to attend nonstationarity in transitions; but theseextensions render the model non-Markovian and complicate the simulation somewhat. In thecase of nonstationary transition rules, two alternatives are possible. In the discrete case, separatetransition matrices can be computed for each time period of interest. For example, given asequence of aerial photos taken every 10 years for 50 years, one could derive four separatetransition matrices. Each matrix would be used only to project from one time period to the next(one time interval).

Alternatively, the transitions could be specified explicitly as functions of time, so that the rulesgoverning landscape change would vary with time. This approach would generate smootherdynamics, but would require some sort of curve-fitting for the time functions (and also, the datavolume to support that curve-fitting).

This latter approach might provide more confidence in projecting landscape change into thefuture, in that the projections would pose the implicit hypothesis that the trajectory of changewould remain similar into the near-term future. Of course, a clear demonstration of nonstationarypatterns of change should certainly temper any interpretation of projections into the future.

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3.2. Spatial dependencies

Another complication arises if some of the transitions appear to have spatial dependencies. Thereare two general sorts of spatial dependencies in landscape change. One might be termed spatialcovariates, which would encompass dependencies related to soil type, topographic position, orother environmental variables measured at a given point. For example, rates of transition amongvegetation types might depend on edaphic or microclimatic conditions.

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One way to discover whether the model's assumptions hold is to examine the errors made by themodel in projecting a map. If the errors are clustered or aggregated, then it suggests that there issome spatial dependency in the transition probabilities that has not been taken into account.

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These complications drive the modeling approach away from a simple Markov framework,toward models where the transition probabilities depend not only on the current state of thesystem, but also on some other stated conditions. It is easy to envision landscape changes forwhich the rates or probabilities depend not only on the current state of a site, but also onadditional environmental variables at the site. For example, vegetation change is strongly keyedon edaphic factors, topography, and microclimate. Similarly, human land uses are also oftenrelated to topography and soil; for example, many land uses are restricted to certain slopes or soildrainage classes. We can anticipate that a model could be improved by incorporating suchrelationships.

In terms of a Markovian transition matrix P, the inclusion of ancillary information converts the

ij ij|ksimple probability of a site changing from type i to type j, p , to the conditional probability p ,where k is some ancillary condition that affects p. It is a relatively straightforward procedure totally transition matrices as conditional probabilities. One simply constructs a multi-layered tallymatrix analogous to the original tally matrix, but incorporating all of the special conditions ofinterest. For example, if we wanted to condition transitions on soil type and we had 3 soils, wecould build a 3-layered tally matrix (dimensioned for cover type i by type j by soil type k), whichis equivalent to building 3 separate transition matrices P -- one for each soil type. For continuous

ijvariables, the elements p might be modeled explicitly as functions of the variable k. Clearly, thiscan become extremely data-hungry.

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A second type of spatial association is neighborhood effects, whereby the transitions at a givenpoint depend on conditions in the cells surrounding that point depends on the condition orbehavior of sites surrounding the site of interest. Examples might include the effects of localspecies composition on species establishment, in which case the neighborhood influence reflectsthe process of seed dispersal. Other examples include contagious processes such as disturbances(fire), pests or disease, or the encroachment of human development into natural habitats.

While it might be enticing to introduce neighborhood effects into a Markov model, there isanother model formalism that is geared toward such applications. Cellular automata (Hogeweg1988, Green 1989) simulate spatial dynamics in raster lattices by conditioning the fate of a focalcell on its state and the states of its neighbor cells. The neighborhood might include 4, 8, or morecells. As a simple example of how an automaton might work, consider a case where the processof interest is the establishment of species into a newly unoccupied grid cell, perhaps one clearedby mortality or disturbance. We wish to estimate the probability of that a particular species willcolonize the central, empty cell, in "competition" with several other species in the model. Onemight tally the number of cells in the 8-cell neighborhood that are occupied by the species. Theprobability of that species colonizing the empty cell is based on its proportional representation inthe 8-cell neighborhood. Each other species would also have its local probability. A randomnumber would "decide" which species actually occupies the cell. Other contagious processes canbe modeled in a similar fashion.

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3.3. The importance of history

The final issue concerns the assumption that, to predict the future state of the system you needonly know its current state. In cases where this is true, the process is truly first-order. In reality,there may be cases where information about additional prior states is needed. For example, ifprior land use has a residual (legacy) effect on future successional dynamics, then the systemretains a "memory" of antecedent conditions; the dynamics are not first-order. These cases wouldlead to higher-order Markov models (e.g., in a second-order model, you would need to know thestate of the system at time t-1 and t-2 to predict its state at time t). Systems with even longer"memory" would require still higher-order models.

Historical legacies or system memory is a bit more complicated to demonstrate empirically,because this requires a more intimate understanding of the data. For example, we might observethat a patch that was clearcut 20 years ago, or farmed for several decades, or was severelyburned, was not projected correctly by the model. This would naturally lead us to examine othersites with known histories, to discover whether other antecedent conditions might also leave alegacy that is manifested in model errors. Of course, it is likely that historical legacies wouldexhibit some sort of detectable spatial pattern that would suggest possible causes. This wouldcertainly be the case if prior land use was the driving factor. Thus, interpretation of the error map

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must be informed by an intimate ground-based appreciation for the factors governing landscapechange.

History comes into landscape dynamics in two general ways. In the first (and simplest) sense,transitions might occur only after a site has been in a particular state for some time. For example,in a successional sequence from old field to pine forest to hardwoods, we would like to delay anytransitions from pine to hardwood until after the pines have "aged" appropriately. Similarly, infire-driven systems, once a fire occurs it may take some time until the system accumulatessufficient fuel to carry a fire again. One solution to this problem of time lags is to introduce themexplicitly into the model, or to otherwise distribute the transitions over time. These approachesrender the model semi-Markovian (Baker 1989, and see, e.g., Acevedo et al. 1995, 1996).

A more complex case of historical legacies would temper transitions according to particularantecedent events. For example, Foster (1992) found different successional pathways in NewEngland, depending on prior land use (e.g., succession on abandoned pastures was different thansuccession from old fields that had been tilled). Quantifying the effects of antecedent conditionscould follow the same approach as tallying conditional probabilities in the case of spatialcovariates (above). That is, one would tally the instances in which a certain transition wasobserved in conjunction with each enumerated antecedent condition, estimating, as above, the

ij|kconditional probability p of transition from state i to j, given antecedent condition k. Thisresults in a second-order Markov process if conditions from two previous time steps are required(i.e., to predict time t you need times t-1 and t-2). In the extreme case, you might envision thedata intensity needed to document alternate successional pathways as multi-step paths through anN x N hypervolume of N cover types--each transition conditioned on prior states!

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3.4. The Role of Disturbance

Natural and anthropogenic disturbances pose a special case in landscape models, in that theiroccurrence is often the integration of all of the special conditions considered thus far. Forexample, fires may be topographically conditioned, spread contagiously, and be lagged untilsome time after a previous fire.

Disturbances regimes are also a good illustration of nonstationarity in landscape dynamics. Forexample, fire regimes over much of North America have been altered substantially by humanintervention; fire suppression and exclusion have changed fire frequencies as well as firemagnitudes over much of the west (e.g., Skinner and Chang 1996). Even without these humaninfluences, natural variation in climate over long time spans makes it unlikely that disturbanceregimes conditioned by climate would show any semblance of constancy over time (Clark 1988,1990; Swetnam 1993). The specter of anthropogenic global change makes it even more unlikelythat the rules of change in the past will translate readily into the future.

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4. Building a more "complex" landscape model: Landscape disturbance-succession models

Extending a landscape model to attend some or all of the issues above rapidly can lead to anintimidatingly complex model. Landscape disturbance-succession models (LDSMs) are a specialtype of complex landscape change model in which these and other issues are generally addressedin the context of modeling the interplay between disturbance and succession processes. LDSMsare perhaps the leading type of landscape change model in use today.

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4.1. Types and components of LDSMs

There are numerous LDSMs in use today and they vary dramatically in many respects.Surprisingly perhaps, LDSMs can be either spatial or nonspatial. Nonspatial models take eachlandscape element (e.g., patch), in isolation, and model disturbance and succession. The resultsare typically summarized as the composition of the landscape and its change over time.Alternatively, the results of each patch could be portrayed spatially, e.g., as a map, implying thatthe model is spatial when in reality the underlying model processes are nonspatial. Most LDSMs,however, are spatial, in that they implement disturbance and succession as spatial processeswhereby what happens at one location is influenced by its geographic location and perhaps itsneighborhood. In this regard, the various LDSMs vary markedly in the degree of spatialdynamism incorporated. Another major distinction among LDSMs is the manner in which theytreat ecological communities: either as static or dynamic entities. In static models, the communityis a spatially static element that does not move over time during the simulation; only its ‘states’change over time. In dynamic treatments, the community is spatially dynamic and can move overtime as conditions allow. Lastly, LDSMs differ dramatically in how they treat vegetation orcommunity compositional changes. Process-based models actually model vegetation growth as acontinuous process, whereas pathway-based models treat vegetation change as a discrete process,whereby communities shift from one state to another along a predescribed successional pathway(more on this below).

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LDSM’s generally involve trade-offs in the following:

• Extent vs. resolution.–generally, models intended to simulate disturbance and successionprocesses over very large spatial extents do so at coarser spatial resolutions (grain size), bothbecause the computational demands necessitate it and because at coarser spatial extents thecoarser-grained pattern is likely to be more relevant.

• Mechanistic detail vs. spatial extent and dynamism.–generally, models that representprocesses mechanistically with great detail operate over finer spatial extents due to thecomputational challenges of implementing intensive mechanistic processes over greatextents.

• Complexity vs. generality.–generally, increasing model complexity leads to less modelgeneralizability; i.e., as the model increasingly addresses the details needed to realisticallymodel the complexity of one landscape it simultaneously becomes so specific to thatlandscape that it becomes difficult to apply the model elsewhere.

• Parameterization vs. analysis of results.–generally, increasing the number of modelparameters does so at the cost of making the results more difficult to interpret due to theincreasing complexity of the model.

• ‘Spatial’ is not the same as ‘spatially dynamic’.–models can be spatial, but still exhibitvarying degrees of spatial dynamism.

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Data Structure.–All LDSMs have a data structure for organizing, storing and managing the site-level vegetation data. They generally adopt one of the following three approaches:

• Classification-based.–in which the vegetation is classified into community types (or landcover types) based on major recognized vegetation types or species associations. This is themost common framework as it is consistent with the conventional use of categorical maps ofvegetation and land cover.

• Species/cohort-based.–in which each species and/or age cohort (of each species) is storedseparately. This approach facilitates treating communities as dynamic entities wherecomposition (and structure) can easily change over time.

• Individual tree-based.–in which each tree is recorded as a separate entity. This approach israrely used in LDSMs because of the prohibitive data storage requirements; it is restricted tomodels that simulate dynamics over relative fine spatial extents, e.g., an individual stand.

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Inputs.–LDSMs require various types of input data, which is generally of two types:

• Maps.–spatial data layers needed to define important attributes of the landscape that affect orare affected by disturbance and succession processes, e.g., land cover maps, land type,topography, etc.

• Parameters.–estimates of model parameters needed to specify model execution. Theseparameters may be needed to describe attributes of species or communities (e.g., speciescomposition of a community, fuel loads associated with a particular vegetation type, etc.), orthey may be needed to control the behavior of various processes (e.g., probability of insectoutbreak, fire size distribution, etc.).

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Succession simulator.–All LDSMs have a succession simulator; i.e., some way to modelvegetation growth or change over time. There are two approaches used:

• Transition-based (pathways).–in which vegetation changes over time are modeled as shiftsfrom one discrete vegetation state (or condition, e.g., seral stage) to another along pre-specified pathways. These pathways can be branching (i.e., one state can shift to two or moredifferent states depending on conditions) or non-branching (i.e., each state always transitionsto one and only one other state) and these transitions can be either stochastic or deterministic.

• Process-based (vital attributes).–in which vegetation changes over time are modeled viademographic processes, such as dispersal, establish, growth and mortality. Given thecomplexity of population demography and biotic interactions, there are numerous factors(such as those listed here) that can be incorporated into these process-based successionalmodels.

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Shown here is an example of a pathway-based successional model (from RMLands) for thenorthern Rocky Mountain dry-mesic montane mixed conifer forest – ponderosa pine-Douglas firbiophysical setting. Note, this is a classified community type based on potential naturalvegetation or biophysical setting in which the community can exist in one of five states overtime. The boxes depict the states (or stand conditions or seral stages) and the arrows depict thesuccessional pathways. Parameters that control the successional process are depicted asannotations. For example, the age at which stand begin to transition from one state to another arelisted as is the probability of following each pathway when there are two alternative pathways.

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Disturbance simulators.–All LDSMs have a disturbance simulator; i.e., some way to modeldisturbances and their effects. There are two common approaches used:

• Process-based.–Most LDSMs use a process-based simulator, in which each disturbance eventis modeled as a process involving initiation, spread, termination, and finally the ecologicaleffect (i.e., severity) of the disturbance. In most cases, each of these components of thedisturbance process are stochastic so that no two events are ever likely to be identical.

• Pattern-based.–Some LDSMs do not model each disturbance event as a process, but ratherplace disturbance events (in final form) on the landscape based on specified characteristics ofthe disturbance regime that control the spatial and temporal distribution of disturbances.

Note, in most cases, the disturbance effects depend on local site conditions (e.g., vegetation type)and disturbance intensity, so that a mosaic of effects are realized.

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Perhaps what distinguishes LDSMs the most is the spatial interactions that are accounted for.Some models treat disturbance (and sometimes succession) as explicitly spatial processes,whereby each disturbance event interacts with the spatial pattern of vegetation and theenvironment to produce the final result. The degree to which the model incorporates interactivitybetween the disturbance process and the landscape is perhaps the most significant distinctionamong LDSMs in use today.

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Primary outputs.–All LDSMs produce some primary outputs, typically including the following:

• Maps of disturbance events• Maps and graphical/tabular statistical summaries of disturbance characteristics, such as

disturbance frequency, size, return interval, severity, etc.• Maps and graphical/tabular statistical summaries of vegetation characteristics, such as species

distributions, seral stage distributions, age distributions, etc.

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Secondary outputs.–Most LDSMseither allow the application ofindependent analytical tools (e.g.,FRAGSTATS) or have built-inanalytical tools for analyzing theprimary outputs. For example, thevegetation map representing someattribute of interest (e.g., seral stage) ateach timestep of the simulation couldbe analyzed with FRAGSTATS toquantify the landscape structure, orserve as input to a wildlife habitatsuitability model.

Tertiary outputs.–Some LDSMsproduce primary outputs that can becoupled with other process simulationmodels, fo example, to model carbonflux, hydrological runoff, ecosystemservices, economics. Here, the LDSMsimulates disturbance and succession,and a secondary model simulates aprocess based on the LDSM outputs.

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4.2. Selecting an LDSM

There are numerous LDSMs that have been developed for various specific applications. SeveralLDSMs have been developed and applied more generically to a variety of landscapes withvarying goals and objectives. Some of these common LDSMs in use today are listed in the tableabove, but this is by no means a complete list. These (and other) LDSMs vary in model structureand reflect both conceptual and technical differences. One way these LDSMs are distinguished ison the basis of the disturbance agents that can be modeled. Most of these models were originallyconceived and developed to model a single disturbance, typically fire, but many have a moregeneric structure that can be applied to other disturbance agents. Another important distinctionamong LDSMs is the way vegetation is characterized and tracked. Some track individual speciesand cohorts, whereas others track “stage” (e.g., seral stages) of entire communities (e.g., covertypes). LDSMs also differ in how the processes of succession and disturbance are modeled. Insome cases, the processes, or at least portions of the process, are modeled mechanistically, inwhich the mathematical formulations are intended to represent the actual real-world processessuch that the parameters of the model have real-world interpretation. However, in most cases, theprocess are modeled phenomenologically, in which the mathematical formulations are arbitraryand merely intended to produce the desired statistical behaviors. Lastly, LDSMs differsubstantially in the degree of spatial dynamism simulated, which reflects how much spatialcontext affects the processes and allows for shifting distributions of attributes in space over time(e.g., shifting distribution of cover types).

Overall, selecting an LDSM is quite challenging given the variability among LDSMs andtherefore the choice should be driven by several questions, including those listed in the slideabove. No one LDSM is going to be best for all applications since they each have strengths andlimitations.

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4.3. Applications of LDSMs

Not surprisingly, LDSMs (and landscape change models in general) have a wide variety ofapplications, including but not limited to the following:

• Historic range of variability.–quantifying the range of variability in landscape structure underhistoric reference conditions to serve as a general reference for understanding the landscapeand/or to help establish targets for desired future conditions (more on this later).

• Climate change.–quantifying the potential impacts of climate change on landscape patternsand processes.

• Alternative disturbance regimes.–quantifying the potential impacts of, say, insect outbreakson landscape patterns and processes.

• Development (urban growth).–quantifying the potential impacts of urban growth onlandscape patterns and processes.

• Policy options.–quantifying the relative impact on landscape pattern and process of variouspolicy alternative.

• Management alternatives.–quantifying the potential impacts of alternative managementtreatments (e.g., fuels treatments, timber harvest strategies) on landscape patterns andprocesses.

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Example 1. Quantifying HRV

One of the major uses of LDSMs today is for quantifying the range of variation in landscapestructure under historic reference conditions to serve as a general reference for understanding thelandscape and/or to help establish targets for desired future conditions (more on this topic later).In the example shown here, RMLands was used to simulate dynamics in vegetation patterns forthe pre-European settlement period on the San Juan National Forest in southwest Colorado. Themajor disturbance processes were wildfire and a variety of major insect/pathogens. At eachtimestep of the simulation, the structure of the landscape can be analyzed using FRAGSTATS.The resulting trajectory in landscape structure can be summarized to describe the historic rangeof variation in landscape structure – subject to the limitations of the model.

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Example 2. Evaluating alternative future scenarios Another common application of LDSMs is to evaluate alternative future management or policyscenarios; i.e., to evaluate a series of “what if” scenarios and estimate the relative impact onlandscape structure (and species resources such as wildlife). In the example shown here, alandscape change model was used to simulate five different policy options in Lookout Creekwatershed in the Cascades Mountains in western Oregon. The historic conditions werereconstructed using dendrochronology and the model was used to forecast future conditionsunder different disturbance regimes. The alternatives considered here represent a range from anemphasis on old-growth protection to intensive timber harvesting.

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Example 3. Species conservation

A final example involves using a LDSM in combination with a wildlife habitat relationships orpopulation viability model to evaluate the potential fate of a species of conservation concern,perhaps under various management/policy alternatives. For example, what is the likely relativeimpact of different levels of timber harvesting on spotted owl habitat suitability or populationviability?

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5. Prospectus on Applying LDSMs

One of the great challenges in applying LDSMs is validation of the model. Unfortunately, it iseffectively impossible to truly validate predictions made over large areas and very long timescales. The best that we can do is verify that behavior is within empirically known bounds(backcasting), verify that modeled behavior is consistent with known ecological system behavior, validate individual process components, or conduct cross-model comparisons (which is rarelydone). One of the next big challenges is to corroborate interactions of components.

It is easy to become a bit disillusioned about the role of LDSMs in landscape ecology.Ultimately, it is important to keep in mind the following about LDSM models:• Not magic bullets • Not substitutes for unclear goals and assumptions• Premise, intent, scale, assumptions of application must be unequivocal a priori• Models could be black boxes (logic may not be clear)• Clarity and transparency essential

The development and application of models of landscape change certainly evokes a deeperappreciation for the trade-offs between realism and analytic tractability. In the extreme, modelsthat are sufficiently simple to be readily tractable are not realistic enough to be applicable to reallandscapes; conversely, models realistic enough to be interesting and applicable are unlikely tobe readily tractable or interpretable. In this latter case, the more realistic model will almostcertainly be data-limited in its parameterization and its testing. Indeed, for models describinglandscape dynamics that play out over large areas and long time spans, data will always belimiting. This certainly will be frustrating.

When applying LDSMs it is important to be aware of false precision, which results from variabledata accuracy and resolution, fuzzy parameters, and inconsistent assumptions. Unfortunately,error propagation is not accounted for yet. This largely stems from the complexity of the modelsand the difficulties of trying to account for error in the myriad steps of the processes.Nevertheless, despite the unknown error, the spatial, temporal, and stochastic variability capturedby LDSMs can be highly informative (more valuable than central tendencies).

But this perspective overlooks some of the greatest benefits of developing models in the firstplace. One important benefit of model-building is that the process forces us to organize ourhypotheses about how a system works, identifying the primary processes and constraints thatdefine the system. Formalizing these hypotheses also helps to specify and prioritize the dataneeded to implement and parameterize the model.

This task of using a model to marshal those observations, as field measurements or remotelysensed data, that are most crucial to quantifying a hypothesis (parameterizing a model) iscompletely consistent with our overall strategy for landscape analysis. Again, the task is toisolate the definitive observations that will test the hypothesis, and then to tactically pursue these

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observations. That is, exactly which data will be needed to demonstrate that history matters, thatspatial dependencies influence the dynamics, or that the trajectory of change is itself changing?This strategy will be productive, leading to a richer understanding of landscape dynamics, even ifthe model is never actually implemented into computer code. In cases where models are built andapplied, an appreciation for these issues will focus model development and temper theinterpretation of model projections.

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