Density Dependence and Advanced article Independence Article Contents . Introduction: Concepts and Importance in Ecology Mark A Hixon, Oregon State University, Corvallis, Oregon, USA . Mechanisms of Density Dependence . Old Debates Resolved Darren W Johnson, Oregon State University, Corvallis, Oregon, USA . Detecting Density Dependence . Future Directions Online posting date: 15th December 2009 Density dependence occurs when the population growth parameter of interest involves population dynamics, rate, or constituent gain rates (e.g. birth and immi- including the population growth rate and the four primary gration) or loss rates (death and emigration), vary caus- demographic (or vital) rates – birth, death, immigration ally with population size or density (N). When these and emigration – although related parameters, such as growth and fecundity, are also investigated. See also: parameters do not vary with N, they are density-inde- Population Dynamics: Introduction pendent. Direct density dependence, where the popu- Use of the words ‘density dependence’ alone normally lation growth rate or gain rates vary as a negative means ‘direct density dependence’ (or compensation): the function of N, or the loss rates vary as a positive function of per capita (proportional) gain rate (population or indi- N, is necessary but not always sufficient for population vidual growth, fecundity, birth or immigration) decreases regulation. The opposite patterns, inverse density as N increases (Figure 1a) or the loss rate (death and/or dependence or the Allee effect, may push endangered emigration) increases as N increases (Figure 1b). The populations towards extinction. Direct density depend- opposite patterns are called inverse density dependence (or ence is caused by competition, and at times, predation. It depensation). When the parameter of interest does not vary is detected observationally by analysis of abundance time- as a function of N, then that parameter is said to be density- series; however, experimental field manipulations pro- independent. Note that a demographic rate may have both a density-dependent component, the strength of which is vide the most rigorous analytical methods for both defined by its slope, and a density-independent component, detecting and understanding underlying mechanisms. defined by its y-intercept (Figure 1c). Future directions include expanded and more detailed mechanistic field data integrated with more sophisti- cated population models. DD DD DI DI IDD Loss rate Gain rate Introduction: Concepts and Import- IDD ance in Ecology (a) NN(b) DD In simplest terms, density dependence occurs when an ecological or behavioural parameter varies as a causative dd function of density (number or cover of organisms per unit area) or abundance (number or cover within a particular habitat), signified as N (Royama, 1977). Most often, the Loss rate di (c) N ELS subject area: Ecology Figure 1 Possible effects of population density on per capita demographic rates. Panels A and B illustrate density-dependent (DD), density- How to cite: independent (DI) and inversely density-dependent (IDD) gain rates (e.g. Hixon, Mark A; and Johnson, Darren W (December 2009) Density population or individual growth, fecundity, birth or immigration) and loss Dependence and Independence. In: Encyclopedia of Life Sciences (ELS). rates (e.g. death or emigration), respectively. Panel C illustrates both John Wiley & Sons, Ltd: Chichester. density-dependent (dd) and density-independent (di) components of a DOI: 10.1002/9780470015902.a0021219 density-dependent loss rate. The dd component is estimated by the slope of the curve, whereas the di component is estimated by the y-intercept. ENCYCLOPEDIA OF LIFE SCIENCES & 2009, John Wiley & Sons, Ltd. www.els.net 1 Density Dependence and Independence conservation biology for preventing endangered species from going extinct. 0 r Mechanisms of Density Dependence a The proximal causes of demographic density dependence are competition, and in special circumstances, predation (including parasitism and disease). Competition is directly b density-dependent by definition, being a function of the 0 N ratio between population size and resource availability. Thus, competition for living space, for spatial refuges from Figure 2 Density dependence does not necessarily result in population harsh conditions, for prey refuges, for nutrients and food regulation. Curves a and b both illustrate direct density dependence, and for reproductive opportunities all can cause density- because the instantaneous population growth rate (r) decreases with population density (N). However, only the population represented by curve dependent responses in demographic rates (Keddy, 1989). a is regulated, because growth is positive at low densities and negative at See also: Competition; Predation (Including Parasites and high densities (i.e. the density-dependent curve crosses the dashed zero- Disease) and Herbivory growth line). Despite density-dependent growth of population b,this Predators can cause density-dependent mortality of their population never exhibits a positive growth rate and will eventually go prey by a variety of mechanisms (Taylor, 1984). First, a extinct. numerical response (population growth manifesting total density) of predators may be sufficiently responsive to prey availability to result in more predators when prey are abundant and vice versa. Second, an aggregative response Demographic density dependence is a concept of funda- (distributional shift manifesting local density) of predators mental importance in ecology (Kingsland, 1995), fisheries may congregate predators at high-density patches of prey, biology (Rose et al., 2001), wildlife management (Fowler, and vice versa. Third, a developmental response (indi- 1987), pest control (Walde and Murdoch, 1988) and con- vidual growth manifesting consumption rate) of predators servation biology (Ginzburg et al., 1990) because it is may increase predator consumption rates to match necessary for population regulation: the persistence of a increases in prey availability. Fourth, a type III functional population via bounded fluctuations and return tendency response, which is a sigmoid individual predator con- that preclude extinction (Murdoch, 1994; Turchin, 1999). sumption rate as a function of prey density, causes density- Thus, density dependence that results in the population dependent prey mortality at lower (but not higher) prey growth rate being positive at low values of N and negative at densities (Holling, 1959). high values of N causes a population to increase before declining to extinction and decrease before overshooting any carrying capacity (Figure 2, curve a). The concept of density dependence in the context of population regulation was first Old Debates Resolved modelled as the logistic equation of Verhulst (1838), with many subsequent elaborations. In fisheries and other har- An old debate in ecology was whether population dynamics vesting models, density dependence is incorporated into are regulated by density-dependent processes or driven by various stock-recruitment functions that are the basis of density-independent processes (Kingsland, 1995). Given that predicting sustainable yields (Beverton and Holt, 1957), each demographic rate is affected by both kinds of processes albeit with questionable accuracy (Holt, 2009). See also: (Figure 1c), such debates were misguided, yet they nonetheless Sustainable use of Populations and Overexploitation waxed and waned through the years. The last manifestation It is important to note that density dependence is was the recruitment limitation hypothesis (Doherty, 1981), necessary but not always sufficient for population regu- formulated for demographically open populations whose lation because density dependence can be under- or over- replenishment relies on external input following settlement compensating (Turchin, 1995). Therefore, the detection of of dispersal stages (recruitment), as occurs in many marine density dependence is not necessarily tantamount to dem- species as well as some plants and terrestrial arthropods. This onstrating population regulation (Figure 2). hypothesis asserted that post-settlement mortality was Inverse density dependence can manifest as the Allee density-independent, so that variations in the external effect, in which a population declines past a lower threshold recruitment rate alone drove local population dynamics where extinction becomes inevitable (Courchamp et al., (Doherty, 1998). The hypothesis was originally proposed for 1999). This effect often occurs when declining population seafloor-associated marine fishes, a group for which most density causes the birth rate to decline due to decreasing subsequent field experiments have detected density depend- frequency of contact between potential mates. Under- ence (Hixon and Jones, 2005). The current consensus is that standing the circumstances under which inverse density both density-independent and density-dependent processes dependence occurs is therefore a primary focus of operate in natural populations, with the latter necessary at 2 ENCYCLOPEDIA OF LIFE SCIENCES & 2009, John Wiley & Sons, Ltd. www.els.net Density Dependence and Independence some time and place for populations to persist (Hassell, 1986; long-term average, they exhibit a return tendency toward Turchin, 1995; Hixon et al., 2002). the average trajectory – a necessary but not sufficient condition for population regulation. One should exercise caution when using differences in Detecting Density