## Landscape Ecology Chapter 3: Intro to Models all q…

Landscape Ecology

Chapter 3: Intro to Models

all quotes obtained from Landscape Ecology, Turner et al., 2001

‘a model is an abstract representation of a system or process.’

as landscape ecology is a new field, the bulk of knowledge is incomplete – there are still many holes left making generalizations and predictions difficult. models help to fill this gap by allowing ecologists to use a variety of modeling methods to more accurately predict the outcomes of various interactions. models are used for the same purpose in every field, not just landscape ecology – to help visualize an unknown. ‘…models are employed to explore the consequences of our hypotheses regarding system structure and dynamics.’

as physically modeling landscapes at full scale is near impossible due to the intricacies of and multitude of interactions, ecologists emply experimental manipulations of microlandscapes. these microlandscapes may be completely hypothetical, or they may be physically modeled in the real world. extrapolation of results from microlandscapes to large regions remains a perplexing problem b/c as the size of the model or landscape grows, so too do the amount of interactions. what may be predicted on a small scale may not necessarily correlate on a large scale. ‘models may generate testable hypotheses that can be used to guide field studies by exploring conditions that cannot be manipulated in the field.’

model classification:

deterministic: if the outcome is always the same once all inputs have been assigned

stochastic: if there is a variable of uncertainty in the model, and the model may have a different outcome every time it is run.

analytical: closed form mathematical solution; the result of the model may be easily broadcast to a large sample, i.e. linear, exponential, and logistic growth are equations easily extrapolated.

simulation: open form mathematical solution: the model is so complex that a multitude of complex mathematical equations interact to obtain a result; complexity requires computers; may have different result every time, or may have same result – not necessarily stochastic – all dependant on the interaction of the equations.

dynamic: model represents phenomena that changes through time. simulation models are dynamic.

static: model represents phenomena that do not change through time – lacks a temporal dimension.

-mechanistic: ‘…a mechanistic model attempts to represent dynamics in a manner consistent w/ real world phenomena.’ how is that different from nearly every other model? mechanistic models try to represent real world conditions, as opposed to purely hypothetical situations that may attempt to reproduce results through completely unrealistic processes (situations that may never occur outside the lab).

-process-based: ‘…model components were specifically developed to represent specific ecological processes.’ example: to model how quickly a set # of runners reach the finishing line of a race, a process-based model may map out the amount of runners, their meals and metabolic rates, they rates of dehydration and muscle fatigue, the distance, the weather, and their running histories AS OPPOSED TO defining the amount of runners and a speed variable to determine the average time required to reach the finish line.

-empirical: ‘…a model with formulations based on simple, or correlative, relationships. This term also implies that model parameters may have been derived from date (the usual case…).’

-in reality, most models are a combination of the 3 prior terms, so it is difficult, if not useless, to try to categorize models using these terms.

spatial models are used when ‘the variables, inputs, or processes have explicit spatial locations.’ while not all landscape models require a spatial component, spatial models have become increasingly popular in recent years due to the rise of cheaper, more capable computers, and the fact that spatial locations do, in fact, bear useful information for most landscape questions. there are 3 general conditions for developing a spatial model:

1. ‘spatial pattern may be one of the independent variables in the analysis…how some ecological response variable changes as a funtion of the configuration of landscape elements.’ using a map may be enough for the inclusion of spatial patterning, although it does not necessarily include a temporal dimension.

2. ‘a spatial model is needed when predicting spatial variation of an attribute of interest and how it changes through time.’ an example then shows yearly maps of great britain overlayed w/ color coded density chart showing the change of a species population throughout the landscape. this is somewhat the opposite, or backward analysis of #1. whereas #1 may change the landscape to disover changes in how species interact, #2 observes how species interact w/ an existing landscape over a period of time.

3. ‘a spatial model is required when the question involves sets of processes or biotic interactions that generate pattern.’ the model starts off w/ a blank slate and lets a pattern develop based on the interaction of 2 or more species in response to a set of stimulus.

building a model:

1. define the problem: basically a mission statement; a model may or may not be necessary depending on the complexity of the problem; additionally, this statement helps determine how complex the model needs to be.

2. develop the conceptual model: essentially identify the size of the model, expected interactions and variables, driving variables (which are external to the model – they effect the model but are not themselves affected); also define expected outcomes, scale/grain/resolution – the same interactions may have different outcomes based on the scale/resolution of the model. how many interactions are necessary to define? few or many? some models start simple and add complexity, while others start complex and prune out the unnecessary. flow diagrams are the bomb at this stage!

3. select model type: this involves selecting from the whole mess of terms defined above. analytic should be used if the model is simple, as results are elegant and…simple! but my personal belief is that models should always be stochastic, dynamic, simulations – as that is as close to reality as these terms allow. this is equivalent to decreasing grain size and increasing resolution – reality is composed of as many complex interactions as you can muster, so may as well attempt to model them. PROBLEM – the increase in variables may royally screw the model as what is simulated may not resemble reality due to certain excluded or unrealized variables that do exist in nature.

4. model development: create the model structure through varieties of mathematical equations. it is unclear which equations may be the best, so constant revision may occur. among the model types available: graph theory, diffusion theory, game theory, percolation theory, fractal geometry, chaos theory, optimization theory, aspects of probability theory such as Markov chains or Bayesian models.

5. computer implementation: do existing programs suffice, or are new programs and languages required to create the model? accuracy is supremely important! any mess-up in the coding will screw the model. documentation is also supremely important, either through notation in the code or a manual, b/c what seems logical at the time of coding may not appear logical in the future.

6. parameter estimation: selection of value of model parameters, inputs, and initial values. not the same as calibration, which just tweaks the model. parameter estimation requires that initial values be inserted that are known to be historically accurate – this is the starting point. if the starting values are off-base, then the entire model will be skewed, and no amount of tweaking will help.

7. model evaluation: this step involves comparing the model to real-life examples. did it perform as expected? were the assumptions reasonable? was the input data acceptable? how sensitive is the model behavior to the assumptions? models may be compared, graphically, statistically, or in tabular form. comparisons should be based on model objectives. sensitivity analysis is the evaluation of the relative importance of particular parameters within the model’ – a slight change in one parameter may have a drastic effect on the outcome of the model, while a major change in a different parameter will have a barely perceptible effect.

8. experimentation and prediction: now’s the time to put all the hard preparation to work! if the model seems to work, go forth and conquer – make predictions and analyze landscapes. as models continue to evolve and are able to handle increasingly complex simulations, modeling will move from testing of hypotheses to actual planning, conservation, and design tools.

final notes on models:

1. know thy model

2. errors propogate

3. all models are simplifications of reality

4. there are never enough data

5. high-tech methods to not guarantee a good model

6. keep an open mind