Research Article Population Momentum: Implications for Wildlife Management DAVID N. KOONS,1 Alabama Cooperative Fish and Wildlife Research Unit, School of Forestry and Wildlife Sciences, Auburn University, AL 36849, USA ROBERT F. ROCKWELL, Department of Ornithology, American Museum of Natural History, New York, NY 10024, USA JAMES B. GRAND, USGS Alabama Cooperative Fish and Wildlife Research Unit, School of Forestry and Wildlife Sciences, Auburn University, AL 36849, USA Abstract Maintenance of sustainable wildlife populations is one of the primary purposes of wildlife management. Thus, it is important to monitor and manage population growth over time. Sensitivity analysis of the long-term (i.e., asymptotic) population growth rate to changes in the vital rates is commonly used in management to identify the vital rates that contribute most to population growth. Yet, dynamics associated with the long- term population growth rate only pertain to the special case when there is a stable age (or stage) distribution of individuals in the population. Frequently, this assumption is necessary because age structure is rarely estimated. However, management actions can greatly affect the age distribution of a population. For initially growing and declining populations, we instituted hypothetical management targeted at halting the growth or decline of the population, and measured the effects of a changing age structure on the population dynamics. When we changed vital rates, the age structure became unstable and population momentum caused populations to grow differently than that predicted by the long- term population growth rate. Interestingly, changes in fertility actually reversed the direction of short-term population growth, leading to long- term population sizes that were actually smaller or larger than that when fertility was changed. Population momentum can significantly affect population dynamics and will be an important factor in the use of population models for management. (JOURNAL OF WILDLIFE MANAGEMENT 70(1):19–26; 2006) Key words demography, elasticity, population growth rate, population momentum, population size, sensitivity, transient dynamics. In wildlife management, agency and stakeholder goals are often stable age distribution but often do because age distributions are centered on the population, its size, and the change in size over rarely known. When changing a vital rate in a sensitivity analysis, time. To meet these goals, managers often focus on the population we assume that the change would not perturb the population out growth rate because it can be manipulated to increase population of a stable age distribution (Mills and Lindberg 2002). It is size in the case of conservation (e.g., Fujiwara and Caswell 2001) unknown how robust this assumption is in wildlife populations or decrease size in the case of control (e.g., Rockwell et al. 1997, (Citta and Mills 1999, Mills and Lindberg 2002). Merrill et al. 2003). Management actions can affect vital rates enough to disrupt the Sensitivity analysis of the population growth rate to changes in age structure. Before the age distribution begins its approach to the underlying vital rates (e.g., fecundity, survival, growth, the stable age distribution after a perturbation, the population size maturation, recruitment, movement) has become a popular tool can change rapidly (Neubert et al. 2002). These dynamical in wildlife and conservation studies to prioritize management responses to an unstable age structure are known as transient actions aimed at producing change in population growth rate (e.g., dynamics (see Fig. 1), which occur in nature. The cessation of red Brault and Caswell 1993, Crowder et al. 1994, Doak et al. 1994, deer (Cervus elaphus) culling on the Isle of Rum, Scotland, has Heppell 1998). Sensitivity analysis can help answer important life changed the red deer age structure, causing transient population history and ecology questions as well (e.g., papers within Heppell dynamics to persist since culling stopped (Clutton-Brock and et al. 2000b, Dobson and Oli 2001, Oli and Dobson 2003). Coulson 2002, Coulson et al. 2004). In addition, when examining Nonetheless, predictions made from analytical sensitivity the potential benefit of turtle-excluder devices on shrimp trawls to analyses can be unreliable when vital rates change simultaneously loggerhead sea turtle (Caretta caretta) populations, Crowder et al. by different amounts, as they do in the real world (Citta and Mills (1994) found that sudden improvements in survival rates caused 1999, Mills et al. 1999, 2001). Furthermore, analytical sensitivity instability in the age structure. The ensuing transient dynamics analyses inherently assume existence of a stable age distribution, resulted in a population size very different than that predicted by which means that calculations depend on the long-term (i.e., asymptotic projections, which essentially is the phenomenon asymptotic) population dynamics (de Kroon et al. 2000, Caswell better known as population momentum (Keyfitz 1971; see Fig. 1). 2001; Ehrle´n et al. 2001, Mills and Lindberg 2002). Methods Population momentum could occur in wildlife populations when used to examine contributions of stochastically fluctuating vital management or large environmental perturbations (e.g., hurri- rates to population growth rate typically focus on asymptotic canes, floods, fires, epidemics) cause any vital rate to change by an dynamics also (e.g., life-table response experiments [Horvitz et al. amount large enough to alter the age structure, but it has not been 1997], and life-stage simulation analysis [Wisdom et al. 2000]). explicitly examined. Simulation-based sensitivity analyses do not need to assume a If wildlife populations experience population momentum, estimating the effects of this momentum on population size 1 E-mail: [email protected] should be considered when developing conservation and manage- Koons et al. Population Momentum 19 ment plans. Here, we use computer simulation to examine the and 1.05) or declining (k1 ¼ 0.65 and 0.95) by greater and lesser control and conservation of hypothetical wildlife populations. To amounts in supplemental experiments using a similar application simulate management practices focused on population growth of constants. rate, we halted population growth or decline by changing survival or fertility rates, which often have different elasticity values Virtual Management Experiments (Heppell et al. 2000a, Sæther and Bakke 2000). It is often Here, we consider populations growing so fast that they could suggested that management focus efforts on the vital rate with the cause environmental damage and populations declining so fast highest elasticity to get the best return in population growth for that they could face extinction (i.e., the growing and declining their effort (Caswell 2000). Yet, we show that short-term populations defined above). For the a ¼ 3 life history, we also population growth and eventual size following some virtual consider populations growing and declining at rates within the management experiments are so different from the expectations of common bounds of long-term environmental variation (i.e., k1 ¼ asymptotic analysis that our findings could influence the way we 1.05 and 0.95). manage populations for control and conservation. Depending on the bird or mammal life history, either survival or fertility may functionally contribute the most to the asymptotic Methods population growth rate and the other the least (Heppell et al. Data Simulation 2000a, Sæther and Bakke 2000). Thus, we focused our experi- To examine population momentum following management ments on changing adult survival or fertility. In the first set of actions, we created 3 life histories with stationary asymptotic experiments for each life history, we started with the growing growth rates (k1 ¼ 1) that mature at 1, 2, and 3 year(s) of age. We population as the initial condition and then decremented survival designed life histories in which survival rates to age i (Pi ) increase rate of adult age classes by the necessary amount to attain with the age of maturity (a) and fecundity (m, the average number stationary asymptotic growth (i.e., the amount required to change of daughters born to a reproductively mature female) decreases, k1 from 1.2 to 1). We performed a similar experiment by which is the pattern observed across birds and mammals (Sæther decrementing fertility. In the second set of experiments for each 1988, Gaillard et al. 1989, Promislow and Harvey 1990). life history, we started with the declining population as the initial In our population model, we calculated fertility (F) assuming a condition and then augmented survival rate of adult age classes by prebreeding census (F ¼ P1*m), with birth occurring at one time of the necessary amount to achieve stationary asymptotic growth, and the year. Fertility and the age-specific survival rates for each life then performed similar experiments by augmenting fertility. history were parameterized into a population projection matrix (A). To elucidate the effects of managing the asymptotic population 2 3 FF F growth rate, we assumed that populations initially had a stable age 4 5 distribution and projected the actual dynamics caused by an A ¼ P2 00 ð1Þ unstable age structure following perturbations to a vital rate. We 0P3þ P3þ then measured the resulting population momentum (M) accord- This model assumes conditions under geographic closure and ing to Keyfitz (1971): density independence. Although density