Understanding the impact of human harvest is fundamental to the effective management of many wildlife populations. Such understanding has been elusive because harvest mortality may compensate for other sources of mortality when the mortality process is density dependent. This problem is exacerbated by the ubiquitous positive correlation between harvest regulations and population size: more harvest is allowed when populations are larger. Connelly et al. (2003) studied the impact of harvest regulations on sage-grouse Centrocercus uropha-sianus using three sets of regulations: closed season, 1-bird bag and seven-day season, 2-bird bag and 23-day season. Connelly et al. (2003) reported a generally negative correlation between harvest regulations and increase in number of males on leks for harvest regulations that ranged from a hunting closure to a 23-day season with a 2-bird bag. Because lek sizes were smaller where hunting was closed there was confounding between harvest and population density, making it difficult to distinguish harvest effects from those of population density. Based on a simple simulation the apparent effects of harvest on change in population size observed by Connelly et al. (2003) could be produced entirely by density-dependent phenomena. Additionally, λ (finite rate of population increase) was greater in areas with more restrictive harvest regulations. λ is a ratio of Nt 1 to Nt, however, and there is a negative sampling covariance between λ and Nt; we expect λ to be larger when Nt is smaller based purely on this statistical fact. The study by Connelly et al. (2003) is an important attempt to study effects of harvest on population dynamics of sage-grouse. We do not argue that either additive mechanisms in survival or compensatory mechanisms in survival or reproduction influence the relationship between harvest and population dynamics of sage-grouse, but that correlation between population size and harvest regulations, combined with statistical issues make it impossible to distinguish between these two hypotheses in Connelly et al. (2003).
Human harvest of wildlife has been a central issue in management of their populations for decades. For managers to effectively manage harvest, it is essential that they understand the impact of harvest on average survival rate at the population level. Errington & Hamerstrom (1935) proposed the idea of a harvestable surplus, in which habitat held numbers of a population that survived the most limiting season (typically winter in temperate North America) to below some threshold. Harvest of individuals above this threshold would have no effect on survival rate for the population as a whole because a number greater than that harvested would have died anyway. Anderson & Burnham (1976) formalized the concepts of additive and compensatory mortality for waterfowl harvest. Compensatory harvest mortality requires that harvest mortality reduces the mortality rate of the unharvested segment of the population such that there is no relationship between magnitude of the harvest and average survival rate in the population. Often, harvest is thought to be compensatory only below some threshold harvest rate that can be no greater than the mortality rate that exists in the absence of hunting (see Nichols 1991 for details). Additive harvest mortality, in contrast, adds to mortality in the population from sources other than hunting, resulting in reduced average survival at the population level in the face of hunting. A corollary of compensatory harvest mortality is that there must be some density dependence in the ‘natural’ mortality process.
Clearly, understanding the effect of harvest on annual survival in wild populations has important implications for managing these populations. In North America it has been difficult to understand the relationship between harvest and survival rates in harvested populations because managers typically reduce harvest rates when populations are low and increase harvest rates when populations are high (e.g. Sedinger & Rexstad 1994). Although managers view this approach as sound management, it completely confounds the effects of population density and harvest on annual survival. If survival rates decline at high harvest rates, is it because of the harvest rates themselves or because of the density-related effects of the corresponding high population level (Nichols et al. 1984, Nichols & Johnson 1989, Nichols 1991)?
Connelly et al. (2003) examined the effects of harvest of sage-grouse Centrocercus urophasianus in Idaho, USA, on changes in the sizes of leks in the studied populations. Understanding effects of harvest is an especially important issue for sage-grouse because their range has contracted significantly over the past several decades, and some local populations have declined (Connelly & Braun 1997, Schroeder et al. 1999, Connelly et al. 2000). Currently, all possible impacts on sage-grouse populations are being considered by managers.
Connelly et al. (2003) used three measures of population change to assess the effect of harvest regulations in two regions of Idaho on dynamics of sage-grouse populations. Data collection by Connelly et al. (2003:335) was conducted in the years immediately, “following a drought and widespread population declines”. First, they examined response to hunting regulations of population rate of change for samples of individual leks. Specifically, they calculated rate of change in lek size before more restrictive hunting regulations were implemented and subtracted this rate of change from those calculated after regulations were implemented. Leks were assigned to one of three regulation packages: 1) closed season; 2) 7-day season with a 1-bird bag; and 3) 23-day season with a 2-bird bag. Second, Connelly et al. (2003) compared the maximum level of male attendance on leks during the first two years of implementation of more restrictive regulations versus the last two years of the study (four to five years after implementation of harvest treatments), calculated the increase and expressed it as λ, the finite rate of increase over the study. They then analyzed variation in λ in relation to region and hunting regulations using a two-factor Analysis of Variance (ANOVA). Third, they regressed the natural logarithm of lek attendance for each lek-survey route against year, calculated the slope (as a measure of population change over the study), and used ANOVA to assess variation in population change among regions and harvest treatments.
Connelly et al. (2003) found that leks in the area where harvest was closed grew more rapidly than did those experiencing harvest, although they found little difference between growth of leks experiencing 7-day seasons with a 1-bird bag and those experiencing 23-day seasons with a 2-bird daily bag. They concluded that hunting may slow the growth of sage-grouse populations and that hunting restrictions combined with habitat conservation may be the most successful approach to recovering sage-grouse populations.
We believe there are two fundamental underlying problems with using the results of Connelly et al. (2003) to conclude that harvest affects sage-grouse populations. The first issue regards covariance between harvest regulations and population size, which has been ubiquitous in regulation of wildlife harvest in North America (Nichols et al. 1984, Nichols & Johnson 1989, Nichols 1991, Sedinger & Rexstad 1994) and made it difficult, if not impossible, to discern the role of harvest in regulation of wildlife populations. The second issue is statistical; use of ratios or percentage changes to assess relative rates of population change can introduce statistical artifacts into population analysis (Eberhardt 1970, Raubenheimer 1995). Specifically, in this case λ has a negative covariance with Nt+1 even in the absence of any biological relationship between the two parameters. These two issues introduce the same biases into assessments of population regulation, albeit for different reasons; they cause managers to overestimate the