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Avoiding Mistakes in Population Modeling:
Impact Assessment

List of common mistakes in population modeling

Failing to incorporate cumulative impacts

When different impacts affecting a population or metapopulation are assessed singly, their effects may be underestimated. For example, if a fish population is affected by both fishing and pollution, the population may be assessed to be viable under each of these threats, but it may be threatened when both factors are assessed together in one model. Although singly assessing threats is a valid method of analyzing their effects, if such analyses are not made in the context of other existing threats, they may give a biased picture of the status of the population.

One of the advantages of population modeling is the ease with which effects of multiple factors can be incorporated to assess their population-level consequences. This is possible (although more complicated) even when there is interaction among the factors or threats such that the presence of one factor changes how much the population is affected by another factor. For example, lower survival rates, carrying capacity or Rmax caused by a toxic substance may make the population more susceptible to overharvest. In such a situation, if data are available to adequately model the population dynamics under different levels of pollution (esp. when there is density dependence), then the interaction of this factor with harvest will emerge as one of the results of the model.

Selecting the wrong spatial scale (or a single scale)

When a threat factor impacts a certain area, the identification of the assessment population has important consequences for the relevance and significance of the results of impact assessment. For example, suppose that an oil spill affects a small area that is only part of a population of an affected species. The assessment can focus (1) only on the part of the population affected by the spill, (2) on the whole (biological) population, part of which is affected, or (3) on the regional metapopulation (one population of which is partly affected).

The first option will result in the largest magnitude of predicted impact (e.g., in terms of proportional reduction in the population), but the relevance of the results will depend on the context. For example, whether the species is a sensitive species used as an indicator of threats to the ecosystem, or whether it is a threatened or an an economically important species, may determine how the results at different spatial scales are interpreted. If the species is a common and widespread species, used as an indicator for human health purposes, then any effect would be relevant, even if the biological population is not affected. For example, deformations or tumors in common but sensitive aquatic species in a small area may signal a relevant impact even if there are no population-level effects. If, on the other hand, the impact is specific to the species under study, and the species is of interest by itself (not necessarily an indicator species), then larger scales may also be relevant, although the spatial scale may also be a political or sociological question (for "charismatic" species, such considerations may imply local assessments). Larger scales may be relevant especially if recovery actions (in addition to impacts) are being considered: successful recovery of an impacted population may depend on its interaction with other populations.

In many cases, it may be best to make assessments at multiple spatial scales, with at least one scale for providing the larger regional context, and a smaller scale for assessing the more local implications.

Reference population includes impact effects

Impact assessment often involves predicting population-level effects at various levels of a threatening factor. In its simplest formulation, this means comparing two scenarios: baseline (or, reference) and impact. If the model parameters for the baseline scenario are estimated from data that includes some level of the threatening factor, the impact may be overestimated.

Uncertainty masking impact

When a model includes large parameter or structural uncertainties, the resulting uncertainty in model outcome may, if not properly handled, mask the impact. For a very simple example, suppose that the risk of a 50% decline in a population is predicted as ranging from 0.1 to 0.4 under the baseline (no impact) scenario and 0.2 to 0.5 under the impact scenario. The large overlap in these risk estimates may be mistakenly interpreted to mean that significant impact cannot be demonstrated. However, this interpretation may be wrong, depending on the source of uncertainty. Suppose that uncertainty in two factors (say, average adult survival, S, and temporal variation in fecundity, VF) contribute most to the uncertainty in results, such that when these factors are held constant, there is very little uncertainty in the results. Suppose that for each extreme value of these factors, the results look as follows:

Risk of a 50% population decline in 50 years:
    Baseline              Impact    
       Low S High S   Low S High S
High VF  0.4 0.3   0.5 0.4
Low VF  0.2 0.1   0.3 0.2

Thus, even though the results are highly uncertain, and there is a large overlap between the risks under the baseline and impact scenarios, it is clear that this particular impact is causing an additional risk of 0.1, under all combinations of the uncertain parameters. Thus, it is possible to be rather certain of the magnitude of the impact, even when it is not possible to be certain of the risk under either scenario (for a full example, see Akçakaya & Raphael 1998)

Underestimating impacts of toxicity, habitat loss, habitat fragmentation, and harvest

Several of the mistakes discussed in this page may result in underestimating impacts in general. For example, impacts may be underestimated if simulation time horizon is too long or too short, if uncertainty is not properly incorporated, if impacts are estimated from short-term experiments, if cumulative effects are ignored, or if impacts are assessed at the wrong spatial scale. In addition, there are several other issues discussed elsewhere that may lead to an underestimation of the specific impacts of toxicity, habitat loss, habitat fragmentation, and harvest.

Incorrectly modeling impact under density dependence
Modeling mortality due to toxicity as harvest
Overestimating Rmax ; Bias in Rmax
Ignoring spatial structure

Habitat Fragmentation
Ignoring spatial correlation
Ignoring spatial structure
Not using demographic stochasticity

Habitat Loss
Not using density dependence
Not incorporating delayed effects of catastrophes

Using (the wrong type of) density dependence
Overestimating Rmax ; Bias in Rmax
Ignoring spatial structure

Difference between experimental and model time steps

When impacts on particular parameters (such as effect of pollution on survival rate) are estimated from short-term experiments, these data cannot be directly used in a population model with longer time steps and time horizon. This type of data comes, for example, from dose-response experiments. The experiments are usually run for short periods of time (e.g., 2 weeks), compared to a time step of the model (e.g., 1 year). Using the "response" from an experiment to model population-level impacts requires extrapolating, which depends not only on the difference between the two time scales, but also on the expected trends in the concentration of the pollutant during the longer time step (e.g., the expected mortality under the "average" concentration during a year, if the model’s time step is 1 year, or the cumulative mortality as a result of 1 year of exposure to a changing concentration of the pollutant).

Wrong time horizon or threshold

Impacts may be underestimated if simulation time horizon is too long or too short. In a very short time horizon, both baseline (non-impact; reference) and impact scenarios may yield very low risks, concealing the difference between the scenarios. For example, the risk of extinction of the spotted owl in the next 2-4 years may be very low, even under the most severe impacts. This is because the generation time of this species is about 7 years, and annual adult survival rate is relatively high (70% to 90%), so that even if mortality rate increases substantially and there is no reproduction at all, the population is unlikely to go extinct in such a short time. If the risk of extinction is low under both baseline and impact scenarios, the difference between them will also be small.

In a very long time horizon, both baseline and impact scenarios may yield very high risks (both close to 1) or very uncertain risks, making the difference between the two scenarios very small or very uncertain. In most situations, there will be a time horizon at which the difference between the scenarios is maximized, a time horizon at which the model results are most sensitive to impact. To find this time horizon, run both baseline and impact scenarios for a very long time (say, 500 years), and compare the "Time to extinction" results. For example, in the figure on the right, the difference between the scenarios is small at short and long time horizons, and maximum at about 200 time steps.

If the difference between the scenarios is too small at short time horizons and too uncertain at long time horizons, one solution is to focus on risk of decline (rather than extinction) at shorter time horizons. Risk of decline is the probability that a population will decline by a given percentage (or, to a given threshold). As in the case of selecting time horizons, too low or too high thresholds may be undesirable. The risk will be very small (and uncertain) for very low thresholds (for example, a threshold of zero, or extinction), so the difference between the scenarios may be very small.

This risk will be very high (close to 1 for both scenarios) for very high thresholds, again making the difference between the scenarios small. The reason is that even without an impact, the population is likely to hit a very high threshold (or decline by a small percentage) just due to natural fluctuations.

As in the case of selecting a time horizon, selecting an intermediate threshold will often maximize the difference. For example, in the figure on the right, the difference between the scenarios is small at both small and large thresholds, and maximum at about 30 individuals.

(See also Duration (simulation time horizon) too long or too short).

List of common mistakes in population modeling

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