Landscape Ecology
Neutral models of landscape heterogeneity

Terms/people:

Modelneutral modelCaswell

Staufferneighborhood (movement) rulesNLM

Purposes and Uses of Ecological Models
Ecological models are developed and used for several purposes:
-to explore real or hypothetical scenarios, especially in cases where experiments are not easy to conduct for ethical or logistical reasons;
-to interpolate or extrapolate understanding across scales where direct empirical work may be difficult or impossible;
-to provide a framework for comparison across systems, providing the equivalent of experimental design and control;
-to provide a formal organizing framework for ideas or data (i.e., a framework for synthesis and integration);
-to make predictions about specific scenarios.

Why are models used so frequently in landscape ecology?

Neutral Models in Landscape Ecology

Neutral landscape models (NLMs) are a special class of models that is particularly useful in a discipline where replication and manipulation are logistically problematic. The objective of using neutral landscape models is to provide a neutral benchmark (i.e., a standard of reference, a standard for comparison, a yardstick) that will serve as a framework for the interpretation of real, observed landscape patterns. This neutral model is one that is generated under a neutral (null) scenario (usually randomness). That is, a neutral model is used to generate a pattern in the absence of specific processes that affect the landscape (e.g. topography, disturbance, etc.). Owing to the logistical impossibility of conducting experiments over large areas that may lack true replicates, neutral models provide a very good alternative. These models are used to determine how real landscape properties differ from a theoretical (random) distribution. They can also be used to determine how certain patterns can affect ecological processes such as organism dispersal, disturbance spread, etc. by acting as a null model.

So why the emphasis on having a null (a.k.a. neutral) model? Recall from an earlier lecture that null models in science are extremely important. Science is characterized as a way of gaining knowledge, but unlike intuition, non-science, and pseudo-science (other ways of gaining knowledge), true science asks falsifiable questions (i.e., the questions have "yes" and "no" as possible outcomes). One of those answers will change the status quo whereas the other answer will not (the null). In order to be able to tell the difference in the answers, you need a null.

Examples:

Fahrig (1997)

Fahrig (2001)

Origin of NLMs:
Caswell 1976 - models of community assembly and diversity structure vs. a model that was neutral with respect to species interactions
Stauffer 1985 - use of randomly generated landscape patterns to compare to real patterns

How to construct an NLM:

The approach begins with developing methods for generating expected values for landscape pattern, generated on a grid of n x n cells. You first designate values representing each land cover type of interest (e.g. 1=habitat, 0=nonhabitat; or 1=habitat A, 2=habitat B, 3=habitat C, etc.). Land cover types are assigned with given (or random) probabilities (p) in a distribution (e.g. if you want a landscape that is 60% forest and 40% grassland, pforest=0.6, pgrassland=0.4). Random number tables or random number generators (computer algorithms) are used to generate the assignments. This distribution may be perfectly random or it may be semi-random (e.g. with degrees of contagion, with hierarchical assignments, etc.).

A single NLM is not particularly useful. Why do you need to generate multiple NLMs for a given value of p?

When p of the habitat of interest is = 0 or 1, the NLM is (obviously) the same as the real landscape pattern. The closer p gets to 0 or 1, the more similar an NLM is to a real pattern.

The size of the grid cells obviously has an effect on landscape structure as a whole. Having more but smaller cells takes more computer effort but represents the landscape at a finer grain.

Change over time (e.g. simulating land cover change over time to represent habitat loss) is represented by changing the distribution of cell values.

You can also represent habitat growth outward from a source (e.g. seedling regeneration in a field surrounding a forest patch). Neighborhood rules (a.k.a. movement rules) are important for this effort (e.g. 4-cell rule vs. 8-cell diagonal rule vs. 12-cell leapfrog rule, etc.).

NLMs can also be built to reflect hierarchical structure, which represents changes in pattern with changes in scale. Hierarchical structure has the same or similar pattern at different scales (e.g. fractals). Hierarchical structure is built into an NLM using a recursive procedure (one that references itself at different levels of resolution). Click here for an example of a hierarchical NLM, and here for three examples of different NLMs.

References:

Botkin, D.B. 1993. Forest Dynamics: An Ecological Model. OxfordUniversity Press, Oxford.

Cale, W.G., R.V. O'Neill, and H.H. Shugart. 1983. Development and application of desirable ecological models. Ecol. Modelling 18:171-186.

Caswell, H. 1976. Community structure: a neutral model analysis. Ecol. Monogr. 46:327-354.

Costanza, R. 1989. Model goodness of fit: a multiple resolution procedure. Ecol. Modelling 47:199-215.

Fahrig, L. 1997. Relative effects of habitat loss and fragmentation on species extinction. Journal of Wildlife Management 61:603-610.

Fahrig, L. 2001. How much habitat is enough? Biological Conservation 100:65-74.

Gardner, R.H., B.T. Milne, M.G. Turner, and R.V. O'Neill. 1987. Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecol. 1:19-28.

Gardner, R. H. and D. L. Urban. 2007. Neutral models for testing landscape hypotheses. Landscape Ecology 22:15-29.

Haefner, J.W. 1996. Modeling Biological Systems: Principles and Applications. Chapman and Hall, New York, NY.

Mankin, J.B., R.V. O'Neill, H.H. Shugart, and B.W. Rust. 1975. The importance of validation in ecosystems analysis. In: New Directions in the Analysis of Ecological Systems, Part 1 (G.S. Innis, ed.). Simulation Councils Proceedings Series, vol. 5. Simulation Councils, La Jolla, CA.

Oreskes, N., K. Shrader-Frechette, and K. Belitz. 1994. Verification, validation, and confirmation of numerical models in the earth sciences. Science 263:641-646.

Power, M. 1993. The predictive validation of ecological and environmental models. Ecol. Modelling 68:33-50.

Stauffer, D. 1985. Introduction to Percolation Theory. Taylor and Francis, London.

With, K.A., and A.W. King. 1997. The use and misuse of neutral landscape models in ecology. Oikos 79:219-229.