The harvest of wildlife and fisheries populations has been the subject of considerable debate for almost a century (Baranov 1918; Beverton and Holt 1957). Difficulty with monitoring fish stocks and unexpected changes in harvest encouraged the use of modeling (e.g., Getz and Haight 1989) and the development of theory to guide harvest management, which was then applied to a number of North American waterfowl populations (Anderson and Burnham 1976). More recently, the issue of harvest was examined as a conservation problem (Reynolds et al. 2001), and symmetrically incidental exploitation (e.g., diffuse mortality induced by human activities in an otherwise protected species) was considered as an exploitation problem (Lebreton 2005). Whatever the context, a central question in harvest dynamics is that of compensation; does harvest, as a specific cause of mortality, add its effects totally independently of natural mortality or is the effect partially or totally compensated?
Harvest management of most waterfowl, particularly in North America, is currently guided by the assumption that harvest mortality is at least partially additive (Johnson et al. 1993; Conn and Kendall 2004), and if compensation occurs, it is primarily through density dependence in survival probability and reproduction (Anderson and Burnham 1976; Nichols et al. 1995). Harvest mortality may be compensated through density-dependent increases in survival or reproduction postharvest, such that harvest mortality may have no effect on overall survival or growth rate of the population. The evidence for additive or compensatory harvest mortality is mixed (Nichols et al. 1984; Rexstad 1992; Smith and Reynolds 1992; Gauthier et al. 2001; Williams et al. 2002; Sedinger et al. 2007; Sedinger and Herzog 2012) and is least compensated in populations with higher inherent survival probability. Evidence for density-dependent regulation of survival and reproduction in waterfowl is inconsistent (Johnson et al. 1992; Anderson et al. 1997; Sedinger et al. 1998; Viljugrein et al. 2005) and may be too weak for compensation to occur (Lebreton 2005). Moreover, detecting density dependence (Lebreton 2009) or a negative correlation between natural mortality and harvest (Schaub and Lebreton 2004) is the subject of notable statistical difficulties (Otis and White 2004). As a consequence, some retrospective analyses may overestimate the prevalence of density dependence (Shenk et al. 1998; Lebreton 2005). Furthermore, distinguishing between the effects of harvest and density on abundance is difficult because harvest regulations are typically liberal when abundance is high and conservative when abundance is low (Smith and Reynolds 1992; Sedinger and Rexstad 1994; Sedinger and Herzog 2012).
Because of the continuing debate about the role of density dependence in compensation, alternative functional forms of the relationship between harvest and population change may be required to fully represent these dynamics (Runge and Johnson 2002; Conn and Kendall 2004). We examined how heterogeneity or individual variation in survival and recruitment of Pacific black brant (Branta bernicla nigricans; hereafter brant) may provide an alternate explanation for the relationship between harvest and population dynamics. Others (Johnson et al. 1984, 1988; Lebreton 2005) previously demonstrated through statistical and population models that individual heterogeneity in survival and reproduction can lead to compensation even in the absence of density dependence, and we further these findings using data on a specific population and new modeling tools.
The consequences of harvest are linked to the expected contributions of the harvested individuals to future population growth, which are measured by reproductive value (MacArthur 1960; Kokko 2001). Harvest of an individual with high reproductive value has more effect on population dynamics than harvest of an individual of low reproductive value (Brooks and Lebreton 2001; Kokko 2001; Hauser et al. 2006). Disproportionate harvest risk of individuals in poor physiological condition (Greenwood et al. 1986; Dufour et al. 1993) is consistent with the hypothesis that heterogeneity in reproductive value provides some compensation for harvest mortality. Heterogeneity in reproductive value of individuals has been clearly linked to a number of characteristics (e.g., age, gender); however, unexplained sources of heterogeneity may have additional effects on reproductive value and harvest dynamics, and these sources of heterogeneity have created modeling challenges (Vaupel and Yashin 1985; Link et al. 2002).
In human health studies, individual heterogeneity is considered as a random variable with a continuous distribution in so-called “frailty” survival models (Vaupel 1990), and these models have also been successfully used in studies of free-ranging vertebrate (e.g., Cam et al. 2002). An alternative is to consider that demographic parameters are distributed according to a discrete distribution; the population is a mixture of several types of individuals differing in parameters such as survival probability. Pledger and Schwarz (2002) reviewed capture–recapture survival models with heterogeneity either continuous or based on finite mixtures, and they concluded that two-level mixtures (i.e., considering the population is composed of two types of individuals) often provided an adequate representation of individual heterogeneity (but see Dorazio and Royle 2003). We explored a novel application of finite mixture models to multiply demographic parameters.
Rich, longitudinal data sets are still needed to model individual heterogeneity. The long-term study of brant in western Alaska (e.g., Sedinger et al. 2008; Nicolai et al. 2012) presented an excellent opportunity for us to examine new methods for simultaneously modeling heterogeneity in capture, recruitment, and survival probability and explore how this variation may change through time. We use estimated levels of heterogeneity to explore implications of this heterogeneity for understanding effects of historical harvest rates for brant on population dynamics. Our main objectives were (1) to quantify levels of heterogeneity and examine factors affecting heterogeneity and (2) model the effects of individual heterogeneity on harvest dynamics through matrix models. We predicted that individual heterogeneity in survival and recruitment would exist in the brant population, and that heterogeneity would compensate for some harvest.