CHAPTER 2 – EVALUATING POPULATION RECONSTRUCTION TECHNIQUES WITH SIMULATED DATA
I developed a quantitative population model in Microsoft Visual Basic 6.0 to evaluate 3 reconstruction techniques with simulated data. I evaluated Downing reconstruction (Downing 1980), virtual reconstruction (Roseberry and Woolf 1991) and Reverse Order reconstruction (specifically designed for this study). I generated a known population forward in time via Leslie Matrix equations, applied a specific harvest event and used the resulting harvest matrix to estimate population size via each of the 3 reconstruction techniques.
I evaluated the effect of incorporating stochasticity into population generation on reconstructed population estimates, by including different levels of process error to simulate environmental stochasticity. I also evaluated the effect of different levels of measurement error, collapsing age classes, variations in harvest rate mortalities, and biases in aging on population estimates by incorporating these errors in the simulation model.
I found that Downing and virtual reconstruction consistently underestimated the actual population size in all scenarios examined. The percent underestimate was related to the natural mortality rates chosen in the population generation. Because these reconstruction techniques do not include a natural mortality term, it is assumed that the lack of inclusion of natural mortality rates in these techniques results in the underestimate. Downing and virtual reconstruction estimate the population size similarly to one another, generally within 5% of each other. Reverse Order reconstruction more closely estimated the actual population size, but was more data intensive and included a natural mortality rate. I also found that measurement error resulted in more uncertainty with population estimates than process error for all 3 reconstruction techniques evaluated. This is likely to due to the fact that measurement error acts independent of the actual population size; i.e. changes in the population size are not reflected in the harvest.
Population reconstruction is a technique that estimates a minimum population size based on age-specific harvest data (Downing 1980, Roseberry and Woolf 1991). Population reconstruction techniques share the following characteristics: 1) utilization of catch-at-age data, and 2) backward addition of cohorts to estimate a minimum population size. Minimum input data include total number of animals in the harvest and age-specific harvest numbers (Williams et al. 2002). These data are readily available for most exploited species (Gove et al. 2002). Despite current use of these methods, the robustness of population reconstruction techniques to violations of assumptions has not been evaluated. I used simulation models to examine the robustness of population reconstruction to violations of assumptions and to evaluate the impact of biases and errors on reconstructed population estimates.
White-tailed deer (Odocoileus virginianus) and black bear (Ursus americanus) are two of the most important large game species in the eastern United States (Baker 1984, Bunnell and Tait 1981). Wildlife biologists require an index of population size and/or trends in order to set appropriate harvest regulations to achieve desired management goals (control, stability, or conservation) and set appropriate levels of harvest for these species. Some wildlife managers currently use population reconstruction techniques to produce population estimates from harvest data (see Chapter 3). From these estimates, estimates from other techniques, and/or independent indices, harvest limits can be set and regulations can be determined. If being used for wildlife management and policy, it is essential that estimates, or trends, produced from population reconstruction accurately represent the dynamics of the harvested population.
Population reconstruction techniques have received little critical evaluation of their effectiveness and accuracy in estimating wildlife population sizes. Roseberry and Woolf (1991) outlined several techniques used to analyze harvest data and applied each to a tightly managed white-tailed deer herd at Crab Orchard National Wildlife Refuge, Illinois. The authors cautioned that their analyses and evaluations were meant to be an overview and may not be applicable to all datasets or species (Roseberry and Woolf 1991). Roseberry and Woolf found that Downing reconstruction is a “powerful tool” for populations where most annual mortality can be accounted for (Roseberry and Woolf 1991). There are no other published evaluations of this technique, though sophisticated statistical models using auxiliary information and cost optimization equations for population reconstruction techniques have been developed recently (Bender and Spencer 1999, Gove et al. 2002, Skalski and Millspaugh 2002). However, none of these papers addressed the robustness of population reconstruction techniques to violations of assumptions or recommend situations for which population reconstruction techniques are appropriate.
I developed quantitative population models to evaluate the robustness of 2 specific reconstruction techniques as described by Roseberry and Woolf (1991): Downing reconstruction (Downing 1980, Roseberry and Woolf 1991) and virtual reconstruction (Roseberry and Woolf 1991). We also developed a more data-intensive reconstruction technique called Reverse Order reconstruction, specifically for this study, because we were concerned about the lack of incorporation of a natural mortality term in the other reconstruction techniques. These reconstruction techniques are discussed in more detail below
Population Models in Wildlife Management
Models are simplified representations of mechanisms in natural systems, accompanied by a set of underlying assumptions (Bunnell and Tait 1980). Population models are representations of the real population and can be quite structurally complex, with the potential to include almost limitless biological and mathematical detail. Models are especially useful as evaluation tools, because they allow for complete control over variable manipulation and quantitative analysis of how changes in parameters affect model output (Williams et al. 2002).
In wildlife management, models are especially useful to create and explore the effects of varying management strategies (Hilborn and Mangel 1997, Williams et al. 2002). For population reconstruction techniques, models are useful tools to evaluate the effects of violations of assumptions, biases, changes in management strategies, and sampling errors on estimates. Population models that use harvest data are useful to evaluate demographic data nested within harvest data and to determine optimal management strategies (Hayne 1984).
Importance of Errors
Harvest data have inherent limitations for use in population estimation due to differential sex and age vulnerability to harvest, hunter selectivity, changes in hunter effort, and harvest regulations (e.g. size or age limits). Harvest data are affected by other sources of error, particularly process and measurement errors. These errors are often difficult to quantify, but can have substantial impacts on the actual population, the observed population, and the estimated population (Hilborn and Mangel 1997).
Process error is the error associated with uncertainties in vital rates or population growth rates (Hilborn and Mangel 1997). In this model, process error can affect fecundities, natural survival or harvest survival rates. Process error is difficult to quantify as it represents the stochasticity associated with natural growth of populations (Hilborn and Mangel 1997). Measurement error, or observation error, is independent error that does not act on the growth of the population or parameters affecting population growth. Rather, measurement error is the result of sampling errors or observation errors (Hilborn and Mangel 1997) and is present in the data, but not in the actual population. In summary, process error is stochasticity incorporated into the parameters that affects population growth rates. Measurement error is the result of independent error that affects the population as seen by the observer. Both types of error can result in high variances associated with point estimates, thereby making trend detection difficult or inaccurate
Types of Model Simulations
The first simulation conducted was a “base run;” this simulation had no incorporated error. The base run was used to evaluate how each reconstruction technique performed given an ideal population and harvest matrix. After the base run, I conducted simulations that were divided into 3 categories: harvest characteristics, sampling characteristics, and environmental variability.
Simulations evaluating harvest characteristics determine the effect of variations in harvest rates on the reconstructed population estimates. Quality Deer Management (QDM), for example, is a management strategy that aims to minimize the harvest mortality rates on young deer, allowing for a higher harvest of the older, trophy animals (Harper 2002). However, many exploited deer populations have a high harvest rate on all animals because there are no size or age regulations. I also varied harvest rates to violate the Downing Reconstruction assumptions that the mortality rates for the last 2 age classes are equal and that the proportion of harvest mortalities are constant over time.
Simulations evaluating sampling characteristics determine the effect of variations or errors in sampling on reconstruction population estimates. Observer, or measurement, error is an important consideration when evaluating harvest data. Poor reporting rates, incorrect recording, inaccurate aging, and collapsing age classes are factors that can affect harvest data used in reconstruction techniques
CHAPTER 1 – REVIEW OF RECONSTRUCTION TECHNIQUES AND METHODS IN FISHERIES AND WILDLIFE LITERATURE
INTRODUCTION AND JUSTIFICATION
WHITE-TAILED DEER NATURAL HISTORY
WHITE-TAILED DEER MANAGEMENT.
BLACK BEAR NATURAL HISTORY.
BLACK BEAR MANAGEMENT
POPULATION DYNAMICS AND ANALYSIS.
POPULATION RECONSTRUCTION TECHNIQUES
ALTERNATIVE POPULATION ANALYSES
CHAPTER 2 – EVALUATING POPULATION RECONSTRUCTION TECHNIQUES WITH SIMULATED DATA
CHAPTER 3 –APPLICATION OF POPULATION RECONSTRUCTION TECHNIQUES TO STATE HARVEST DATASETS AND DEVELOPMENT OF A STOCHASTIC POPULATION SIMULATION MODEL
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