Species distribution models
Habitat suitability models
Habitat suitability models are statistical models that are based on niche theory and fit the link between a species and its environment from occurrence or abundance data and environmental data. They are mainly used to predict patterns of species distribution over space and/or time.
Mechanistic niche models
Mechanistic niche models are based on niche theory and describe the link between a species and its environment from the relationship between species’ characteristics (behaviour, morphology, physiology…) and environmental factors. They are mainly used to predict patterns of species distribution over space and/or time
Models with emergent dynamics
The current typology was taken from Gallien et al (2010):
Matrix population model (MPM): A MPM describes the growth process of individuals or cohorts via life-stages and transition probabilities (e.g. using Leslie matrices) and is analytically solvable (Caswell 2001). Examples of applications are population viability analyses. There is no information on space.
Metapopulation model (MM): A MM describes the demographic dynamics of a population living on suitable habitat patches within a hostile matrix of unsuitable habitat. The main focus is on extinction and colonization of local populations. The simpler metapopulations MMs are analytically solvable (e.g. incident function models). More complex MMs can be spatially explicit and can describe dispersal, reproduction and competition explicitly.
Simple metapopulation models: At one extreme of the spectrum of metapopulation models is the occupancy model of Levins (1970), which is based on the number of occupied populations, ignoring their location. More recent occupancy models incorporate some aspects of spatial structure. For example, incidence function models (Hanski 1994) take into account the sizes of and the distance between, habitat patches. However, occupancy models often make assumptions that are too unrealistic. For example, they assume that local population growth is fast compared to the time scale of dispersal and recolonization, and they ignore local population dynamics. In addition, incidence function models and other occupancy models assume the metapopulation is in equilibrium.
Structured metapopulation models: Between the extremes of individual-based and occupancy models are spatially structured metapopulation models, which describe the dynamics of each population with struc- tured demographic models and incorporate spatial dynamics by modeling dispersal and temporal correlation among populations. Both dispersal and correlation between each pair of populations depend on the location of the popula- tions, making these models spatially structured. However, dispersal is modeled in terms of the proportion of individu- als moving from one population to another, instead of the movement of each individual. The advantage of this approach is that it requires many fewer data than the individual-based modeling approach.
Cellular automaton (CA): CAs are stochastic spatially explicit models that may be used to describe spread and spatial interactions. Each cell on a grid evolves through discrete time steps according to a set of rules based on the states of neighbouring cells. It is typically used to explore colonization processes and patterns.
Individual-based model (IBM): IBMs are models that focus on units (e.g. individuals, populations…) and their interactions. It describes processes at small scales that directly influence the units. IBMs are typically used to investigate patterns emerging at larger scales and to make predictions. Individual-based models often require more data than are available for most species. In addition to demographic data such as survival rates and fecundities, individual-based models require data on behavior of individuals. These types of models are especially sensitive to the dispersal behavior of individuals. Small errors in dispersal mortality, mobility, and habitat suitability resulted in large errors in predicting dispersal success
SHIFT
Overview: SHIFT (Iverson et al. 2004a) is a cellular automata designed for plant migration at coarse scales, in which the landscape is parsed into cells. Each cell is characterized by a unique location, a forest availability scalar, and an initial abundance of the target species. Colonization of initially unoccupied cells is estimated as a function of recipient cell forest availability and the sum of the probability of each occupied cell sending a propagule to that cell.
Details: SHIFT calculates the probability of an unoccupied cell becoming colonized during each generation (also used as one model iteration).
Applications: Iverson et al. (2004b).
PATCH /HEXSIM
Overview: PATCH (program to assist in tracking critical habitat; Schumaker, 1998) is a spatially explicit, individual-based, animal
population simulator. PATCH is currently a females-only model that incorporates demographic stochasticity through the use of a pseudorandom number generator to evaluate the outcome of each individual survival and reproduction event. It reads raster GIS maps of habitat and stressor distributions, and converts these maps into arrays of hexagonal cells. PATCH stores survival
and reproduction rates as Leslie matrices, but it links these values to habitat quality or stressor intensity, which are in turn stored as hexagon-specific attributes. The actual survival and fecundity rates experienced by an individual therefore vary depending on the spatial attributes associated with the territories they occupy. Thus, the flexibility of PATCH allows incorporation of not only of factors that affect populations via habitat modifications, but also those that act directly on the survival, fecundity, or dispersal behavior of individuals at different life stages, in different habitats, or at different time steps. Importantly, model inputs and outputs are all spatially explicit.
PATCH is now being superceded by HexSim. HexSim is a spatially-explicit, individual-based, multi-species computer model designed for simulating terrestrial wildlife population dynamics and interactions. HexSim is very general, with landscapes, life histories, disturbance regimes, and most other details being supplied by the user at run-time. HexSim also employs a sophisticated graphical user interface. HexSim is freely available, but still under active development.
Details:
Applications: Carroll et al. (2007), McRae et al. (2008).
URL: http://www.epa.gov/wed/pages/models/hexsim/index.htm
MIGRATE
Overview: MIGRATE is a grid-based (spatially-explicit) population model that is spatially explicit and is capable of simulating migration at the landscape scale (Collingham et al. 1996). The environment is represented as a grid of cells cells of arbitrary size, each with an associated carrying capacity that is computed as the proportion of the cell that is available for colonization. Cell size is arbitrary but cells must not be too large for the length of the dispersal function, otherwise the migration rate can be underestimated.
Details: At each time step the total number of propagules produced by mature individuals in each cell is calculated, the number of mature individuals likely to die is then computed, and these are removed. Propagules are dispersed throughout the cells of the grid according to one or more user-defined dispersal functions (e.g., bivariate normal or negative exponential). Finally, those propagules destined to survive to maturity in the absence of self-thinning compete for the available space; those that establish reproduce in the next generation. The model assumes that propagules can pass freely over areas of unsuitable habitat. While this is likely to be a realistic assumption for anemochorous species, the effects of landscape heterogeneity upon the behavior of animal agents of dispersal may need to be considered in the case of zoochorous species.
Applications: MIGRATE was initially developed in order to simulate the pattern and rate of spread of plants in heterogeneous landscapes (Collingham et al. 1996, Collingham & Huntley 2000), but it has also successfully simulated range expansions in birds, mammals and butterflies (Hill et al 2001, Willis et al 2009).
RAMAS GIS
[From Akçakaya (2000)]
Overview: This model is designed to link GIS-generated landscape data with a spatially structured metapopulation model for extinction risk assessment, viability analysis, reserve design, and wildlife management. The model operates in four steps.
(1) Landscape data are analyzed to find the spatial structure of the habitat patches. The spatial structure is then exported to a metapopulation model.
(2) Temporal dynamics of the landscape (e.g., trends due to expected future habitat loss) are incorporated as time series of model parameters based on expected changes in the landscape.
(3) The metapopulation model is built by combining spatial and demographic information.
(4) Simulations are run to estimate risks of extinction or decline and to predict the abundance and distribution of individuals in the metapopulation.
Details:
Spatial Structure: The habitat suitability map can be calculated in a number of different ways, including statistical analyses (such as logistic regression) that find the relationship between the occurrence (or, density) of the species and the independent variables which describe its habitat requirements. The habitat suitability (HS) map is then used to calculate the spatial structure of the metapopulation, based on species-specific characteristics such as the home range size, dispersal distance, and minimum habitat suitability for reproduction. Two important parameters provide the link between the HS map and the spatial structure of the metapopulation model and determine how the species perceives (or reacts to) the patchiness of the habitat. These parameters, threshold HS and neighborhood distance, are used by a patch-recognition process that delineates patches on the HS map. Threshold HS is the minimum HS value below which the habitat is not suitable for reproduction or survival (although individuals may disperse or migrate through habitat that has a lower HS than this threshold); neighborhood distance is used to identify nearby cells that belong to the same patch. For an animal species, the neigh- borhood distance parameter may represent the foraging distance.
Habitat dynamics: In cases where the habitat is expected to change in the future, the analysis of landscape structure as described here can be extended to account for these changes. This analysis can be done by calculating the spatial structure of the patches for each future time step and combining them in the form of a time series of demographic parameters. One case in which the future changes in habitat dynamics are important is the assessment of the impact of planned logging of a forest or planned development that will gradually decrease the quality and size of habitat patches. In such a case, one or more of the habitat characteristics (such as amount of old-growth forest) that determine the suitability of habitat for the species in question may change through time in a deterministic way, whereas other characteristics (such as elevation) will remain the same. Using the approach outlined in the previous section for each time step creates a time series of metapopulation models. The changes in these models through time can be summarized as time series of deterministic changes in model parameters.
Metapopulation model: In the third step, the spatial information for the metapopulation is combined with ecological (demographic) parameters of the species.
Age structure or stage structure within populations is modeled by a matrix model (Caswell 2001) that incorporates age- or stage-specific vital rates (survival rates and fecundities). Each population in the model can have a different matrix and different initial number of individuals in each age or stage.
Density dependence in population dynamics is modeled by modifying the mean values of survival rates and fecundities as a function of the population size (N).
Environmental stochasticity is modeled by random fluctuations in vital rates and in carrying capacities. The random fluctuations can be normal- or lognormal distributed, and can be correlated among populations. In addition to random variation, the average values of the vital rates can also change deterministically (e.g., a temporal trend).
Habitat loss and increase are modeled by specifying a rate of change for the carrying capacity through time, or a time series of carrying capacities for the affected populations. Habitat increase, in combination with catastrophes that affect carrying capacities, can be used to model, for instance, forest growth following disturbances such as fire or windfall.
Dispersal (migration) is modeled by specifying the proportion of individuals that move from each population to each other at every time step. These rates are input in the form of a dispersal matrix. In most cases, the rate of dispersal may be a function of the distance between source and target populations.
Correlations among populations describe the similarity of environmental patterns experienced by each population. This factor is important in the “rescue effect” in metapopulations: when fluctuations are spread over a number of separate populations, the overall risk faced by the metapopulation is reduced (see earlier). Correlated dynamics are modeled by sampling the vital rates of each population from a normal or lognormal distribution that is correlated with the vital rates of other populations according to a correlation matrix. Like dispersal rates, correlation may also depend on the distance between populations, because closer populations are more likely to experience similar environmental patterns.
URL: http://www.ramas.com/ramas.htm
MIGCLIM
Overview: MigClim (Engler & Guisan 2009) is a cellular automaton implemented within the ArcGIS software (ESRI Inc., Redlands, CA, USA). The cells are square and record various values such as cell occupancy status, habitat suitability, reproductive potential or when it was last colonized. To simulate dispersal under climate change, MigClim requires the following inputs: a map defining the species’ initial distribution, maps picturing landscape fragmentation (i.e. barriers to dispersal and permanent unfavourable locations), the species’ dispersal parameters and a series of maps indicating how the distribution of potentially suitable habitats evolves as climate changes.
Details: Dispersal is simulated through a number of decisions that are taken, for each cell, during each dispersal event:
1. Does the target pixel represent a suitable habitat? Is it unoccupied?
2. If point 1 is answered positively, the number n of source pixels within the specified dispersal distance is computed. Source pixels are already occupied pixels that can act as seed sources to colonize a target pixel. Optionally, a barrier layer can be given to prevent dispersal through those pixels being part of the barrier. If a barrier pixel is found between the target and a source pixel, the source pixel is ignored. Barriers can be used, e.g. to prevent a strictly grassland species to disperse through forests.
3. If n > 0, the target pixel becomes colonized with the combined probability PCol, where PDispi is a probability function of the distance between the target pixel and source pixel i and reflects the fact that colonization probability decreases over distance. PMati is a probability that is function of the time as the source pixel i became occupied and represents the increase in reproductive potential of source pixel i over time. PMat can be used to represent time for individuals to reach reproductive maturity and, more globally, theincrease ofapopulation’sreproductivepotentialdue to an increase in the number of individual plants within a pixel over time. PDisp and PMat are implemented as discrete functions and can easily be modified to fit any shape of seed dispersal curve and increase of reproductive potential over time.
4. Optionally, LDD and stochastic extinction events can be added to the simulation. LDD events are generated from source pixels with a probability PLDD · PMat in a random direction and at a random distance within a user-defined range. If the pixel reached by the long dispersing seed is potentially suitable (satisfying point 1), it becomes colonized. LDD events are not affected by barriers. Stochastic extinctions with probability PExt can also be defined to simulate random extinction of colonized pixels.
5. Steps 1–4 are repeated a number of times (nDisp), typically set so that each repetition corresponds to 1 year.
6. Pixels that are no longer suitable due to changes in environmental conditions have their values reset to zero. Pixels that become unsuitable are reset only after the dispersion stage occurred (steps 1–5), because it is assumed that the change of a habitat from suitable to unsuitable is not a discrete but a continuous process. Thus, organisms inhabiting a pixel still have the potential to disperse during the step when the pixel turns unsuitable.
7. Steps 1–6 are repeated nHSmap times. In each repetition, the habitat suitability is updated to reflect environmental change (e.g. climate change). Simulations without environmental change can be performed by setting nHSmap =1. Additional parameters available in MigClim include vegetative and seed bank resilience time, post-dispersal survival and/or habitat invasibility, anisotropic dispersal to simulate dominant winds or slope, as well as specific dispersal along certain features, such as roads and rivers. These options were not used in the present study.
Bibliography
Akçakaya, H. (2000) Viability analyses with habitat-based metapopulation models. Population Ecology, 42, 45-53.
Caswell, H. (2001) Matrix population models: construction, analysis, and interpretation. Sinauer Associates. Sunderland, Massachusetts, USA.
Carroll, C. (2007) Interacting effects of climate change, landscape conversion, and harvest on carnivore populations at the range margin: Marten and Lynx in the northern Appalachians. Conservation Biology, 21, 1092-1104.
Collingham, Y., Hill, M. & Huntley, B. (1996) The migration of sessile organisms: a simulation model with measurable parameters. Journal of Vegetation Science, 7, 831-846.
Collingham, Y. & Huntley, B. (2000) Impacts of habitat fragmentation and patch size upon migration rates. Ecological Applications, 10, 131-144.
Engler, R. & Guisan, A. (2009) MigClim: Predicting plant distribution and dispersal in a changing climate. Diversity and Distributions, 15, 590-601.
Hill, J., Collingham, Y.C. & Thomas, C. (2001) Impacts of landscape structure on butterfly range expansion. Ecology, 4, 313-321.
Iverson, L., Schwartz, M. W. & Prasad, A.M.(2004a) How fast and far might tree species migrate in the eastern United States due to climate change? Global Ecology and Biogeography, 13, 209-219.
Iverson, L.R., Schwartz, M.W. & Prasad, A.M. (2004b) Potential colonization of newly available tree-species habitat under climate change: An analysis for five eastern US species. Landscape Ecology, 19, 787-799.
McRae, B. H., Schumaker, N. H., McKane, R. B., Busing, R. T., Solomon, A. M. & Burdick, C. A. (2008) A multi-model framework for simulating wildlife population response to land-use and climate change Ecological Modelling, 219, 77-91.
Gallien, L., Münkemüller, T., Albert, C.H., Boulangeat, I. & Thuiller, W. (2010) Predicting potential distributions of invasive species: where to go from here? Diversity and Distributions, 16, 331-342.
Schumaker, N. H. 1998. A user’s guide to the PATCH model. EPA/600/R-98/135. U.S. Environmental Protection Agency, Environmental Research Laboratory, Corvallis, Oregon.
Willis, S. G., Thomas, C. D., Hill, J. K., Collingham, Y. C., Telfer, M. G., Fox, R. & Huntley, B. (2009) Dynamic distribution modelling: predicting the present from the past. Ecography, 32, 5-12.