(meles meles) population dynamics - Oxford Journals

Journal of Mammalogy, 90(6):1392–1403, 2009

AN ANALYSIS OF EURASIAN BADGER (MELES MELES) POPULATION DYNAMICS: IMPLICATIONS FOR REGULATORY MECHANISMS DAVID W. MACDONALD,* CHRISTOPHER NEWMAN, PIERRE M. NOUVELLET,

AND

CHRISTINA D. BUESCHING

Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, Tubney House, Abingdon Road, Tubney OX13 5QL, United Kingdom

Based on 15 years of observations of a badger (Meles meles) population at Wytham Woods in the central United Kingdom, we investigated which parameters governed demographic changes, using data recording the life histories of 868 individuals. We modeled the population in terms of a stage-classified matrix, giving an exponential population growth rate of r 5 0.063 (l 5 1.065). Population elasticity values, derived from this matrix, produced a relative order of importance of regulatory parameters governing this population growth rate, of: adult survival (Pa) . fertility (F) . juvenile survival (Pj) . age at 1st reproduction (a) . age at last reproduction (v). Thus, changes in Pa and F have the greatest potential to influence population growth rate. The population underwent a dramatic change in the last 5 years of the study, with a decline, then stabilization in population growth. However, this change was not related to any change in elasticity patterns between the 2 periods. Comparing the latter period to the preceding period of marked population growth revealed that fertility rate had little actual influence, whereas adult and juvenile survival rates were far more influential demographic variables. These findings prompted a 2nd, retrospective, analytical approach, a life-table response experiment (LTRE), revealing that the importance of Pj in the LTRE contrasted with its lesser prospective importance in the elasticity analysis. Change in fertility (DF) apparently had little environmental or genetic scope (according to the results of either technique) to influence regulation in this population. We also tested for delayed density dependence using the theta logistic model. Because territorial animals are expected to respond quickly to the effects of density dependence, corresponding to theta , 1, our rejection of this hypothesis indicated that the restrictions of territorial sociospatial regulation are relaxed in this badger population. These results are used to highlight population vulnerabilities. Key words: badger, carrying capacity, density dependence, elasticity, life-table response experiment (LTRE), matrix model, Meles meles, sensitivity

A century of research has explored constraints on animal populations (e.g., Andrewartha and Birch 1954; den Boer and Reddingius 1996; Lack 1954; Nicholson 1933; Oli and Dobson 2001; Tamarin 1978; Turchin 1990, 1995, 1999) with the emerging generalization that most populations are subject to complex regulatory mechanisms (Krebs 1994; Murdoch 1970, 1994; Royama 1992; Turchin 1995). Factors explaining mammalian demographic characteristics include adult body weight (,40% of the reported studies), and other ecological attributes, such as environmental predictability, habitat, or dietary specializations (45%); reproductive

* Correspondent: [email protected]

E 2009 American Society of Mammalogists www.mammalogy.org

strategy (iteroparity versus semelparity) accounts for most of the remaining 15% (Gaillard et al. 1989). These attributes are determined by variation in the primary population parameters: age at 1st reproduction, fertility, and longevity, which again tend to scale with adult body size (Promislow and Harvey 1990). Measuring such regulatory mechanisms has been achieved only infrequently for large mammals in the wild, for example, lions (Panthera leo—Packer et al. 1991), Himalayan thar (Hemitragus jemlahicus—Caughley 1970), African buffalo (Syncerus caffer—Sinclair 1977), red deer (Cervus elaphus— Clutton-Brock et al. 1982), Soay sheep (Ovis aries—CluttonBrock et al. 1996), grizzly bears (Ursus arctos middendorffi— Mace and Waller 1998), wolves (Canis lupus—Post et al. 1999), and moose (Alces alces—Post et al. 1999). This is not only because to do so is difficult in practical terms and requires longer-term data than are generally available, but also 1392

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MACDONALD ET AL.—BADGER POPULATION REGULATION

because demographic processes (births, deaths, immigration, and emigration) and resultant population structure (age and sex ratio) affect the ecology and behavior of each individual in a population (Dunbar 1988). Here, we examine the processes underlying the demographic traits of a population of Eurasian badgers (Meles meles) at Wytham Woods in the central United Kingdom, collected over a 15-year interval (1987–2001) and based upon 868 individual life histories (see also Macdonald and Newman 2002). Badger populations provide a revealing model with which to explore population mechanics, because although their populations are sensitive to immediate extrinsic constraints, their behavioral ecology also demonstrates significant interpopulation adaptability (intrinsic responses, sensu Wolff [1997]). The former include environmental conditions such as the fluctuating availability and dispersion of resources (e.g., Carr and Macdonald 1986; da Silva et al. 1993; Johnson et al. 2002; Kruuk 1978a; Macdonald 1983a, 1983b; Macdonald and Newman 2002) and the latter include the badger’s adaptable sociospatial behavior (Macdonald et al. 2004), which varies considerably with region, resources, and populations (Johnson et al. 2002). The badger’s intraspecific behavioral flexibility sets a framework within which density-dependent effects can be examined (Macdonald et al. 2002). Modeling regulatory mechanisms.—Exponential growth rate, l (where l 5 er, lnl 5 r; with r representing the intrinsic growth rate), is a derived function of 5 life-history parameters: a , age at 1st reproduction; Pj , juvenile survival; Pa , adult survival; F , fertility, and v , age at last reproduction. The phenomena producing changes in these demographic parameters, and metrics derived from these relationships, determine the sensitivity of l, which varies depending on life-history patterns (Roff 1992; Stearns 1992). A key problem for statistical methods intended to test regulatory mechanisms arises if they are too insensitive, and removed from biological reality, to cope with the complexities of population dynamics encountered in the field (Hanski et al. 1993; Turchin 1990; Zeng et al. 1998). One approach to the study of population dynamics, life-history evolution, and conservation biology that is used increasingly to circumvent these shortcomings is matrix population modeling, and this has offered useful guidance to the management of wild populations (Caswell 1989; de Kroon et al. 2000; Heppell et al. 2000; Oli and Zinner 2001; van Tienderen 2000). These models facilitate the analysis of large data sets using a comprehensive methodology. Parameterization of the Leslie matrix model (Leslie 1945, 1948) requires life-table data summarizing age-specific survival and reproduction. Sufficiently complete demographic data sets are difficult to collect, especially with longer-lived organisms, thus our badger population data afford a rare opportunity for the thorough examination of demographic processes in a population of medium-sized carnivores. Although population growth rate (l) is quantifiably sensitive to changes in life-history variables (P), the sensitivity of l to perturbations in one life-history variable effect (e.g., survival) may not be comparable to another life-history variable effect

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(e.g., age at last reproduction) because the units each variable type is measured in are not complementary (e.g., Pa and Pj are probabilities and can have values only between 0 and 1, whereas F is not under such a restriction). Elasticity analyses address this problem (Caswell 2001; Caswell et al. 1984; Coulson et al. 2003; de Kroon et al. 1986, 2000). Elasticity analyses provide proportional sensitivities, which quantify potential changes in l with respect to proportional changes in life-history variables (Caswell 1997, 2001; de Kroon et al. 1986, 2000) and can be compared over time within a population or between populations and species (de Kroon et al. 2000; Oli and Zinner 2001). Significantly for our analyses, sensitivity and elasticity reveal only the potential influence of changes in demographic variables; that is, they reflect the influence that would result from small absolute or proportional changes in demographic variables. However, some demographic variables may not change when populations in natural environments grow or decline, because the environment or life history of particular species may constrain the ‘‘scope’’ for change (sensu Dobson and Oli 2001). For example, age at 1st reproduction is often relatively inflexible in annual-breeding mammalian species in temperate environments (Oli et al. 2001). Life-table response experiment (LTRE) analyses distinguish actual from potential demographic influences on population growth (after Caswell 1989, 2001; Oli et al. 2001) by decomposing them into contributions attributable to changes in underlying demographic variables. However, age at 1st reproduction does not appear as an explicit variable in age-classified matrix models (and has some capacity for variation in badger populations under certain circumstances), thus the sensitivity of population growth rate to this variable requires partial demographic data models (Caswell 1989; Cole 1954; Oli and Zinner 2001), using ‘‘stage-based’’ life-cycle analyses (e.g., adult or juvenile). Partial models parameterize age at maturity and age at last reproduction, which can occur late into a badger’s life span (see Macdonald and Newman 2002), thus the population’s sensitivity to a suite of demographic variables can be estimated directly. Using both postbreeding census sensitivity and elasticity analyses compared to LTRE analyses (Caswell 2001; Oli et al. 2001; Tuljapurkar and Caswell 1997), we explore the parameters to which the population is most responsive. We also consider the implications of density dependent parameter responses influencing intrinsic growth rate, using a thetalogistic model, which in turn allows us to estimate population carrying capacity (K). Species displaying territoriality are expected to respond quickly to density-dependent effects, producing values of theta , 1. Mechanisms in context: biological interpretation.—Mammalian life histories tend to be related to environmental predictability (Calder 1984; Pianka 1970). Predictable environments favor efficiency, whereas unpredictable ones, or circumstances subject to anthropogenic perturbations, promote opportunistic productivity. Badgers tend to succeed best in predictable environments, and are thus vulnerable to environmental perturbations and limited in their capacity to respond (Macdonald et al. 2006; Tuyttens and Macdonald 2000).

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TABLE 1.—Life-history trait values, parameter values, and results of sensitivity and elasticity analyses. The population data are pooled either over the 15-year study interval, the first 10-year period, or last 5-year period. As in the text l1 and l2 growth rates are obtained from age-specific and stage-specific matrix models. a 5 age at 1st reproduction; Pj 5 juvenile survival; Pa 5 adult survival; F 5 fertility; v 5 age at last reproduction. l1 from age-classified model

l2 from stage-classified model

Life-history trait 15 years First 10 years Last 5 years Estimated parameters in the partial matrix model 15 years First 10 years Last 5 years

1.065 1.113 0.964

1.066 1.110 0.981

a

Pj

Pa

F

v

2 2 2

0.717 0.767 0.627

0.837 0.876 0.762

0.267 0.269 0.262

15 15 15

20.110 20.100 20.110

0.275 0.266 0.293

0.724 0.726 0.717

0.987 1.002 0.954

0.002 0.002 0.002

20.100 20.090 20.120

0.185 0.184 0.187

0.568 0.573 0.557

0.247 0.243 0.255

0.028 0.029 0.026

Sensitivity of l to change in parameter 15 years First 10 years Last 5 years Elasticity of l to change in parameter 15 years First 10 years Last 5 years

In well-established, persistent populations, such as the badger population studied here (see Macdonald and Newman 2002; Macdonald et al. 2002), key demographic characters, such as fertility and age at 1st reproduction, will be under evolutionary and physiological constraint. Thus, behavioral modification of the remaining, and limited, sociological and spatial controls on population dynamics appear to be the only proximate means by which the badgers can respond to the pressures of changing density (Macdonald et al. 2004). Considering that the number of badgers within our study area has doubled since formal capture–mark–recapture monitoring began in 1987 (Macdonald and Newman 2002), we hypothesize that a phase-dependent dynamic change (sensu Stenseth and Ims 1993) in population regulation occurred during this study interval. The result has been a ‘‘K-shifting’’ (Pianka 1970; Reznick et al. 2002) of key life-history variable rates as density increased, with an associated increase in competition for resources. Defined by this change in the trends of population growth rate (Table 1), we divided the study into 2 phases: a period of population growth, l . 1 (1987–1996), and a period of slight decline and stabilization l 1 (1997– 2001). Key to our interpretation of the demographic processes at work in this population, and to our broader understanding of the role regulatory processes play in population dynamics we consider: Which parameters govern the regulation of this population, which life-stages are most responsive to these regulatory mechanisms, and which parameters are under constraint, using elasticity and LTRE comparisons? What are the implications for our broader understanding of regulatory mechanisms in population dynamics? Are the observed regulatory mechanisms density dependent? How important are physiological and evolutionary constraints

versus adaptive behavioral tactics? What are the implications and applications for conservation?

MATERIALS AND METHODS Badger trapping.—Data were collected at Wytham Woods, 5 km northwest of Oxford, in central England, United Kingdom (global positioning system reference 51:46:26N; 1:19:19W—Macdonald and Newman 2002; Macdonald et al. 2004). Badgers have been studied continuously at this site since the 1970s (Kruuk 1978a, 1978b) and the population has been marked 4 times per annum since 1987 (for detailed methods see Macdonald and Newman [2002]). All trapping and handling procedures were in accord with the United Kingdom Animals (Scientific Procedures) Act, 1992, approved by an institutional ethical review committee, and met guidelines approved by the American Society of Mammalogists (Gannon et al. 2007). On 1st capture, each badger was given a unique identifying tattoo in the inguinal region. Morphometric measures of mass, body length (tip of snout to sacrum), and body condition (subcutaneous fat score), inter alia, were recorded upon each capture. Absolute numbers of individuals caught were subsequently modified by retrospective minimum number alive calculations following the methodology of Macdonald and Newman (2002), allowing 3 subsequent years to refine the minimum numbers alive given. Jolly–Seber (Jolly 1965) capture–mark– recapture models have been found to consistently overestimate badger numbers in high-density populations where trapping efficiency is high (Rogers et al. 1997) and minimum number alive estimates better allow comparison with previous major studies. The benefits of a reliable, irrefutable minimum exceeded the risk of a moderate negative bias on ultimate

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population size (Efford 1992; see also Pryde et al. 2005). Excluding 1987 (1st study year), trapping efficiency for this population remained relatively constant throughout with a mean of 83.69% (SE 5 1.32%) of the minimum number alive–estimated population being returned by the trapping effort from 1 year to the next: indices and numbers trapped both followed similar trends. We reinforced confidence in this use of minimum number alive by concurrent behavioral studies at our study site where focal groups of badgers were given clip marks in their fur for recognition and observed by video-surveillance (Stewart et al. 1997). There was no evidence of a substantial population of unmarked (i.e., never trapped) animals in these studies (Baker et al. 2005, 2007; Buesching et al. 2003; Hewitt et al. 2009). Also, genetic evidence indicates that parenthood is well accounted for in our trapped sample (Dugdale et al. 2007, 2008). Finally, capture– mark–recapture, most commonly used in the context of survival analysis, focuses on providing survival estimates, whereas the aim of the present study is to estimate the impact of a broader range of parameters on population dynamics (survival, fertility, and age at 1st and last reproduction). We chose to use a single framework, presented by Oli and Zinner (2001), to parameterize our model; comparison of our survival data to survival data obtained by the Cormack–Jolly–Seber capture–mark–recapture model did not differ significantly (see below), and thus validates our approach. More than 90% of individuals were of known age, but for the remainder, we estimated age from tooth wear, quantified on a 5-point scale (see Ahnlund 1976; da Silva and Macdonald 1989; Hancox 1988). These estimates correlated significantly with known age (linear regression of 1996 data: F 5 508.99, d.f. 5 1, 237, P 5 0.001, r2 5 0.7982). The regression equation, age 5 22.51 + 2.10 (tooth wear), was used to estimate the age of individuals not 1st encountered as cubs (,10%). Offspring could not be matched to mothers directly within social groups during this study interval (but see Dugdale et al. 2007). Females caught during the January gestation period were pregnancy-tested by ultrasound scanning with an external 5.0-MHz sector probe (Kontron, Bletchley, United Kingdom). Females not ultrasound scanned, but subsequently found to have teats characteristic of nursing mothers, also were included as breeders (see Dugdale et al. 2007; Macdonald and Newman 2002), a method we have since validated through the genetic assessment of maternity. Females, as the productive sex, were used exclusively to model all predictive growth models. Demographic variables for the female population were established using standard fertility table techniques (after Lotka 1945), although male and female population and sex-ratio dynamics vary little from one another in this population (Dugdale et al. 2003; Macdonald and Newman 2002). Survival.—High trapping efficiency relative to minimum number alive estimates along with minimal immigration and emigration in this population (Macdonald et al. 2008) facilitated the estimation of age-specific (i) survival for each

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study year (j), as the proportion of individuals surviving until the next year: P(i)(j) ~

N(i)(j) N(i{1)(j{1)

:

Mean Pis over the study period (as the arithmetic mean of the yearly estimate) were calculated in order to deduce the survivorship function (l(i)): i

l(i) ~ P Px : x~0

This method facilitated the use of all available data, including those from the early years of the study during which, inevitably, cohorts were incomplete. Fertility.—For each study year, age-specific fecundity was estimated as one-half times the average litter size, assuming a 50:50 primary sex ratio (after Dugdale et al. 2003), per reproductive female, derived from ultrasound and lactational data, and the proportion of reproductive females in each age class. Fertility was estimated using the postbreeding census formula (Caswell 2001). Because it was not possible to determine maternity definitively across the entire focal badger population during the study, a maternity function was derived as the mean of the number of offspring in each year j, N0j, and the number of reproductive females of age i at year j, Nijpregnant (i 5 1, adjusted for the number of males in the population, assuming a 50:50 sex ratio [Dugdale et al. 2003]). The mean number of offspring (adjusting also for cub sex ratio) per pregnant female was subsequently estimated by dividing the total number of cubs in the year j + 1 by the number of pregnant females in the year j: N(i~0) ( jz1) M(N pregnant )j ~ P pregnant : Nij i

This value was then modified by the proportion of reproductive females in each age class to obtain mi: mij ~

Nij pregnant M(N pregnant )j : Nij

Thus, overall, the maternity function was calculated as the mean of the yearly mis combined with survival for each-age i as: Fi ~Pi mi : Separate analysis for the first 10 and the last 5 years of the study period.—Age at 1st reproduction (i.e., primiparity) can have a large impact on population growth (Cole 1954); hence, it was necessary to derive a stage-classified matrix to infer sensitivity and elasticity. Using the methodology of Oli and Zinner (2001) for postbreeding census, a transition matrix was constructed including Pj , juvenile survival, Pa , adult survival, F , fertility, a , age at 1st reproduction, and v , age at last reproduction, from which l, the population growth

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rate, was calculated. Each year, before sexual maturity, Pj approximates juvenile survival; subsequently, for each sexually mature age class, Pa approximates survival and is associated with concomitant fertility F. As detailed by Oli and Zinner (2001), Pj, Pa, and F are chosen such that the dominant eigenvalue, l, and corresponding right eigenvector, e, of the age- and stage-classified matrixes are approximately equal. That is: v P

ei Fi

F& i~av P i~a

ei

a P

v{1 P

ei P i

, Pj & i~1a P i~1

, Pa & ei

ei Pi

i~az1 v{1 P

the expected number (or density) of individuals at + 1 in generation t + 1 as a function of the number of individuals in the previous generation. We performed a nonlinear regression using an iterative procedure and a least-squares criterion to apply the Ricker equation, that is, to estimate r and K, a simpler and more reliable method than to parameterize all density-dependent survival rates and to attempt to fit these into a matrix model (Matlab [MathWork 2007; MathWorks Ltd., Natick, Massachusetts], and its statistical toolbox, the function ‘‘nlinfit’’):

:

Nt

Ntz1 ~Nt ermax ð1{ K Þ ,

ei

i~az1

Survival (juvenile and adult) also can be estimated using the capture–mark–recapture approach. Thus, for comparative purposes and for completeness, we also estimated survival of juveniles and adults using the program MARK (White and Burnham 1999); these values were compared to the estimated values from the equation above. We base our further analyses on values estimated from the Oli–Zinner equation (Oli and Zinner 2001) in the interests of parsimony, that is, with both fertility and survival estimated in the same way, and because of minor differences in our Oli–Zinner–derived estimates and the results of Cormack–Jolly–Seber estimates (see ‘‘Results’’). Estimated population dynamic trajectories for both age- and stage-specific models were constructed and compared to the observed variation in numbers of badgers. As stated, defined by the changing character of l, we divided the study into 2 phases: a period of population growth, l . 1 (period 1: 1987–1996), and a period of slight decline and stabilization, l 1 (period 2: 1997–2001; Table 1). We constructed stage-specific matrices and performed subsequent sensitivity and elasticity analyses for each time period separately. Deterministic projections were performed using the population transition matrix from period 1 and period 2 independently. Subsequently, LTRE analyses (calculating parameters to create mean sensitivity values) were undertaken to contrast the relative contributions to the change in l attributable to key population parameters between the 2 periods; thus: X Ll Dai , Dl& Lai AT i that is, the change in l is equivalent to the sum of the changes in parameter values (Pj, Pa, and F) weighted by their average sensitivity during the full study period. This formulation facilitates a relative comparison of parameter influences on change in exponential growth rate. The predictions of these simulations were compared to the actual data, allowing the magnitude of change in parameter values, and their sensitivities and elasticities, to be estimated. Analysis of density dependence.—The Ricker model (Ricker 1954, 1958) is a classic discrete population model that gives

where Nt is population size at time t, rmax is intrinsic growth rate or maximum per capita growth rate, and K is carrying capacity. This equation facilitated the estimation of intrinsic growth rate (rmax) values for the population and for carrying capacity (K). The outputs of this model were contrasted with other density-dependent models (e.g., logistic or Beverton– Holt—Beverton and Holt 1956, 1981) to establish consistency. We then tested the null hypothesis that density was constant over time (using an F-test). Finally we tested whether a density independent model could interpret the observed densities (comparing each density dependent model against Nt+1 5 aNt). To compare such a heterogeneous set of models we used the Akaike information criterion (corrected for small sample size [AICc]—Burnham and Anderson 2002; Johnson and Omland 2004) given by: P 2K ðKz1Þ SSR2 : AICc ~{2 log z2Kz n{K{1 n Observed per capita growth rate per annum, r 5 ln(Nt+1/Nt), also was calculated from these census data and plotted against density. An obvious requirement for density dependence to be in operation is that ‘‘r’’ must be a decreasing function of population size. The analysis of r reveals the effects of environmental changes and management actions and gives the direction and intensity of density-dependent natural selection on life-history traits (Caswell and Takada 2004). However, the way in which r decreases may vary according to the type of density dependence in operation, thus we investigated the shape of the plotted curve within our range of data using the theta-logistic equation (Bellows 1981): N h t Ntz1 ~Nt ermax 1{ð K Þ , thus h Ntz1 Nt ln : ~r~rmax {rmax Nt K We infer the functional form of the curve as linear (h 5 1), convex (h . 1), or concave (h , 1). This method, similar to the one used by Sibly et al. (2005), was constructed independently using Matlab. Finally, we explored models incorporating time lags into the relationship between per capita growth rate and density. Previous analyses of this population by Macdonald et al. (2002) have indicated trends in

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FIG. 1.—Population dynamics as observed and modeled over the 15 years of study, modeling females, as the convention, as the productive sex. ‘‘Age-classified’’ expected data come from the full matrix model, ‘‘stage-classified’’ expected data come from the partial matrix model as defined by Oli and Zinner (2001). Our analysis is based on stable but not standing age distribution; we also plot observed density as a way of comparison. We observe a relatively accurate estimation of population dynamic trends. Both age- and stage-classified models yield results similar to the expected dynamics, thus, the stage-classified model (simpler in its formulation) is sufficiently accurate to simulate the dynamics of this population and analyze the sensitivity of parameters.

density dependence for survival of juveniles and adults, and fertility.

RESULTS Between 1987 and 2001, 868 individual badgers were marked (tattooed). Of these, 772 (88.9%) were 1st tattooed as cubs (including during the 1st year of the study). A total of 5,459 captures was made, 2,554 excluding recaptures within calendar years. The Wytham badger population more than doubled in size between 1987 and 1996 (period 1), decreased in the late 1990s (period 2), and has subsequently shown another upward trend since 2000 (Fig. 1; plot of the female population minimum number alive). Biannual bait-marking (Macdonald and Newman 2002) reveals that the area exploited by the population has been stable at approximately 6 km2. Consequently, population size and density are completely confounded. Density peaked at 49.5 badgers/km2 in 1996 and averaged 36.37 badgers/km2 (SE 5 2.55 badgers/km2) over the 15-year study period. Trapping efficiency averaged 83.69% (SE 5 1.32%); minimum number alive abundance indices and numbers trapped both followed similar trends. Partial models revealed that age at 1st reproduction, a, remained consistently (and inflexibly) at 2 years of age throughout the study interval, and subdivided periods (badgers exhibit delayed implantation, or embryonic diapause, dissociating 1st mating from potential reproduction—Thom et al. 2004; Yamaguchi et al. 2006). With a fertility of 0.267 this gives an F/a ratio of 0.134, confirming the predicted ‘‘slow-

FIG. 2.—a) Survivorship and b) maternity functions of Eurasian badgers (Meles meles) obtained from 15 years of study at Wytham Woods, United Kingdom. Solid curve shows the pooled functions of the overall 15-year data interval. Maternity function is defined as the fecundity function of age. The semilog scale of the ‘‘survivor function’’ plot shows a straight line when proportional survivals are constant.

type’’ life-history dynamics (Heppell et al. 2000; Oli and Dobson 2003; Promislow and Harvey 1990). Age-structured and partial life-cycle model.—From the ageclassified matrix, mean generation time equaled 5.8 years and mean individual lifetime reproductive output was 1.4 offspring. These values produce an exponential population growth rate of l 5 1.065 (Table 1). Age-specific survivorship and fecundity for the population are presented in Figs. 2a and 2b. The stageclassified matrix led to a very similar value, l 5 1.066 (Table 1), and similar projected dynamics of the population (Fig. 1). We were thus confident that the vital rates derived from the stageclassified matrix could be used as the basis for further analyses. By way of comparison, adult and juvenile survival also was estimated from the Cormack–Jolly–Seber model, using the program MARK. Juvenile survival was estimated at 0.67 (SE 5 0.03), whereas adult survival was estimated at 0.83 (SE 5

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TABLE 2.—Life-table response experiment: analysis illustrating the contribution to change in l of key population parameters (excluding for age at maturity and reproductive life span where change 5 0). We X Ll Dai &0:13) can verify that the sum of all contributions ( La T i A

i

equals the overall change in l between the 2 periods of interest (Dl < 0.13). It is thus clear that observed change in population growth rate between the 2 periods is attributable mainly to the influence of adult survival, followed by juvenile survival and finally fertility.

Change in parameter value Dai Ll Sensitivity over all periods Lai AT Contribution to observed change in l

Juvenile survival

Adult survival

Fertility

0.140

0.114

0.007

0.275

0.724

0.987

0.0385

0.0825

0.0069

0.01). The 95% confidence interval derived for these estimates includes our Oli–Zinner equation estimate (Table 1); thus, there were no significant differences between the values we examine here and those derived from a capture–mark– recapture framework. Sensitivity analyses of parameter values revealed that fertility had the greatest influence on l, followed closely by adult survival, juvenile survival, and age at 1st reproduction (which has a negative value because an increase in age at 1st reproduction necessarily decreases population growth rate). Age at last reproduction was the least influential parameter (Table 1). In elasticity analyses, adult survival was the most influential factor, followed by fertility (about one-half as influential), juvenile survival, and the age at 1st reproduction. Again, age at last reproduction was found to have the least impact on population growth rate (Table 1). The separate analyses of period 1 (growth) and period 2 (decline) showed no significant differences in the factors influencing the population’s dynamics despite demonstrable changes in demography. Potentially, minor differences in survival (for example variation between estimates derived from the Cormack–Jolly– Seber model rather than minimum number alive and the Oli– Zinner equation) could have considerable impacts on sensitivity and elasticity. Combining our estimate of fertility and age at 1st and last reproduction with Cormack–Jolly–Seber estimates of survival, we derived comparative elasticity values, for comparison to our Oli–Zinner model values (presented in Table 1): age at 1st reproduction 5 20.11; age at last reproduction 5 0.02; juvenile survival 5 0.18; adult survival 5 0.58; and fertility 5 0.242. Demonstrably there were no qualitative, and only minor quantitative, differences, adding support to our parsimonious approach to parameter estimation (i.e., Oli–Zinner equation estimating fertility and survivals). Life-table response experiment analyses.—Life-table response experiment analyses retrospectively indicated that adult survival accounted for the greatest component of the total change in l (64%), with juvenile survival following (30%); fertility had the least influence (about 5%), excluding age at maturity and reproductive life span, where change was found to equal 0 (Table 2).

FIG. 3.—Minimum number alive retrospective index; 1987 and 2002 with a fitted Ricker’s model (solid curve—Ricker 1954, 1958) extrapolating into the future. The model significantly accounts for most of the variation in our data (r2 5 0.86, P , 0.001).

Analysis of density dependence.—Carrying capacity (K) and maximum growth rate (rmax) were estimated from nonlinear regression using the Ricker equation (see ‘‘Materials and Methods’’; Fig. 3): K 5 147 individuals (females; 95% confidence interval: 124–170) and rmax5 0.26 (95% confidence interval: 0.12–0.42). By way of comparison and validation, application of the logistic equation (Verhulst 1838), and the Beverton–Holt model (Beverton and Holt 1981) both gave similar results to the Ricker model (K 5 148, rmax 5 0.28, and K 5 148, rmax 5 0.28, respectively). The Beverton–Holt model (Beverton and Holt 1956) is characterized by recruitment that approaches an asymptote as the parental population size increases. The Ricker model (Ricker 1958) describes populations in which recruitment declines as population size tends toward infinity. Testing the hypothesis that the regression trajectory follows a Ricker equation trend versus the hypothesis that there is no specific trend in density, using an F-test, supported the latter position (r2 5 0.86, F 5 35.65, d.f. 5 1, 13, P , 0.001). The Ricker model, as well as the logistic and Beverton–Holt models, produced a significantly better fit than did a simple linear model (Nt+1 5 aNt, density independent model) for population density with time. The quality of fit of the theta-logistic model was best when h 5 6 3 1023; however, assuming h to be different from 1 (or 0) increased the value of the parameter estimate; thus, for our population data, AICc favored a model with linear density dependence (i.e., h fixed at 1). The incorporation of time lags into the models did not improve the fit of the data significantly (Coulson et al. 2004).

DISCUSSION Over the course of this study we observed a population more than double in size and then restabilize at a new, higher, equilibrium point. Stage-classified matrix models produced an

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exponential growth rate of r 5 0.063 (l 5 1.065). Sensitivity analyses revealed a relative order of importance of demographic parameters: Pa . F . Pj . a . v (where Pa is adult survival, F is fertility, Pj is juvenile survival, a is age at 1st reproduction, and v is age at last reproduction). Through elasticity analyses and comparison with LTRE results, however, we identified that adult and juvenile survival rates were the demographic processes that were actually most influential in producing changes in population size. Which parameters govern the regulation of this population, which life stages are most responsive to these regulatory mechanisms, and which parameters are under constraint, based on elasticity and LTRE comparisons?— Although the population underwent a dramatic change in size in the final 5 years of the study, with a decline, then stabilization, this change in dynamics was not related to any change in elasticity values. Comparing this latter period to the preceding period of marked population growth revealed that Pj and Pa were consistently 2–3 times more influential in the LTRE analyses than in the elasticity predictions. The importance of Pj, as revealed by the LTRE, contrasted with its lesser prospective importance in the elasticity analysis. Change in fertility (DF) apparently has little environmental or genetic scope to influence badger population regulation: F was predicted to be about one-half as important as Pa in the elasticity analysis, but actually had a tiny influence according to the retrospective LTRE. Adult survival and fertility were the parameters showing greatest elasticity. Among the Carnivora, mustelids vary between species in terms of life-history variables (Johnson et al. 2000; King 1983). According to the ratio of population fertility (F) compared to age at 1st reproduction (a—Oli and Dobson 2003), our results indicate that Eurasian badgers have life histories that demonstrate an ‘‘intermediate–slow’’ lifehistory strategy, most akin to those of ‘‘large mammal’’ (Heppell et al. 2000; Promislow and Harvey 1990). This is characterized by delayed maturity and low reproductive rates (for comparative data sets, see Oli and Dobson [2003]; see also Tuyttens and Macdonald [2000]), in terms of a trade-off between somatic and reproductive effort (Oli and Dobson 2003). Thus, species with a 5 1 and F . 1 will have a greater elasticity for a and F, whereas species with a . 1 and F , 1 will have a greater elasticity for Pa and Pj (Coulson et al. 2003). The badger is an intermediate case and, as Oli and Dobson (2003) predicted, the greatest influence in the elasticity analysis was attributable to Pa and F. Small and mid-sized mustelids that lack embryonic diapause (Lindenfors et al. 2003; Thom et al. 2004) tend to demonstrate F/a ratios . 1 and are characterized as having ‘‘fast’’ life-history strategies (for example stoats [Mustela erminea]—King 1983). Species of Martes that exhibit diapause are intermediate (0.15 , F/a , 1). Here we demonstrate the Eurasian badger to be a relatively ‘‘slow’’ life-history strategist, typical for a larger mustelid, and most sensitive to perturbations affecting survival while least influenced by effects on fertility under conditions of environmental stability (see Oli and Dobson 2003).

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What are the implications for our broader understanding of regulatory mechanisms in population dynamics?— Aside from practical implications for the detailed understanding of population dynamics for species management and conservation (Caswell 1989; de Kroon et al. 2000; Heppell et al. 2000; Oli and Zinner 2001; van Tienderen 2000), at the theoretical level our study illustrates clearly that elasticity analysis and LTRE experiments address different facets of population modeling. The former predicts how population growth rate could respond to a proportionate change in a primary population parameter (e.g., adult survival), whereas the latter describes what proportion of observed change is attributable to each parameter. Elasticities are not realistic insofar as they do not take environmental and genetic constraints on life histories into account, which is why prospective and retrospective analyses (Caswell 2001) can sometimes fail to correspond precisely (Dobson and Oli 2001). Our analyses identified v, the age of last reproduction, as the life-history variable with the lowest relative influence on l for this badger population, a finding that resonates with the conclusions of Oli and Dobson (2003) for other mammalian species. The proposition by Cole (1954) and Lewontin (1965) that age at 1st reproduction, a, would have the largest relative influence on l was not supported; this failure of Cole’s (1954) prediction may have arisen because he used values of reproductive rates larger than those commonly observed for mammals (Oli and Dobson 2003). Are the observed regulatory mechanisms density dependent?— Because elasticity analyses did not show major differences between the period of population growth (period 1) and subsequent stabilization (period 2), we postulate that intrinsic factors, such as density dependence, might have a stabilizing influence on population dynamics. Carrying capacity, derived from the logistic model, was in overall equilibrium at 147 (female) individuals with a maximum growth rate of 0.26. When tested against the null hypothesis that there was no increase in population density, or exponential increase (corresponding to a constant growth rate), this model fitted well. In order to evaluate the nature of the competition underlying the observed changes in population density during the study interval we considered several permutations of the densitydependence model. First, incorporating time lags into the density-dependent demographic models did not improve the fit of these data (Coulson et al. 2003). Second, we explored variations in estimated per capita growth rate (r) with density using a theta-logistic equation (Caswell and Takada 2004). This approach has been the subject of some debate, especially using negative values for theta (Doncaster 2006; Getz and Lloyd-Smith 2006; Peacock and Garshelis 2006; Ross 2006). Territorial animals are expected to respond quickly to the effects of density dependence, corresponding to theta , 1. The best fit of our data was associated with h 5 6 3 1023, indicative of a strong regulatory effect of density long before carrying capacity is approached. Our rejection of this hypothesis indicated that the restrictions of territorial socio-

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spatial regulation are relaxed in this badger population. That is, badgers should demonstrate the capacity for much higher per capita growth rate at densities below environmental capacity, such as experienced by founder populations in a new range or after a population perturbation (Coulson et al. 2004). Notably, with regard to phases of greater r- or K- selection (Pianka 1970), badger populations have been seen to recover to precull densities within 3–6 years of the United Kingdom government’s Department of Fisheries and Rural Affairs culling interventions (Macdonald et al. 2006; Tuyttens and Macdonald 2000). This finding would suggest that badger populations are subject to contest or territorial-type competition for density-limited resources (Nicholson 1954). How important are physiological and evolutionary constraints versus adaptive behavioral tactics?— The sociology of badger groups remains remarkably difficult to understand despite assiduous study. The numbers of litters each female can produce per year is physiologically and phylogenetically inflexible in these seasonal breeders, although there is potential scope for limited variability in litter size. The most obvious mechanism for a badger population to expand, therefore, would be through an increase in the number of females per group that breed successfully, that is, fecundity (Cresswell et al. 1992; Macdonald and Newman 2002; Woodroffe and Macdonald 1995). In this context, Macdonald et al. (2004) reported changes in spatial organization within territories for the Wytham badger population, such that some group members spread out among subsidiary setts (subterranean tunnel and den systems dug by badgers). They proposed that this distribution may circumvent sociological feedback mechanisms that otherwise affect individual fitness by restricting group sizes and production of cubs. The result is that the population can attain a higher population density than that that prevailed when fewer, more centralized, sett sites were used. This subtle flexibility of the badger’s established territorial behavior may facilitate the optimization of population size with regard to environmental carrying capacity (Cresswell et al. 1992). Such a scenario is again reminiscent of the suboptimal situations seen when badgers are culled (Macdonald et al. 2006), where survivors might exploit socially unconstrained breeding opportunities to increase population growth rate quickly (Coulson et al. 2004). Additionally, polygynandry, extragroup paternity, and multiple-paternity litters have been observed from this same focal study population (Dugdale et al. 2007), suggesting that functionally apparent group territories might not circumscribe discrete breeding units. This reveals an additional tier of social complexity and behavioral flexibility underscoring the adaptable nature of the badger’s social system. Adult survival (Pa) varies considerably within and between badger populations (Macdonald and Newman 2002), and is proximately influenced by environmental conditions, which dictate availability of earthworms (Lumbricus terrestris), a major component of the badger’s diet in lowland England (Fragoso and Lavelle 1992; Gerard 1967; Kruuk 1978a; Kruuk and Parish 1981; Macdonald 1980). Badger densities tend to

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be highest in areas where mild, damp conditions increase the availability of earthworms (Kruuk 1978b; Kruuk and Parish 1982). Earthworms are sensitive to microclimatic conditions (Fragoso and Lavelle 1992; Gerard 1967; Macdonald 1980). Consequently their distribution and abundance are heavily dependent on weather patterns, with the result that microclimate provides a good surrogate for badger food availability in parts of their range such as lowland England (Kruuk 1978a, 1978b). Insofar as weather conditions may considerably determine the badgers’ food supply, it is noteworthy that we observed the survival of both adult and juvenile age classes to have the most profound capacity to regulate population growth rate. Newman et al. (2001) highlight that for this same population juvenile survival is strongly regulated by coccidial parasitoses, which in combination with dry summer conditions can strongly reduce cohort survival. Similarly blood-borne parasitemias infect all badger age classes (Macdonald et al. 1999). What are the implications and applications for conservation?— Life-history analysis is a powerful, informative tool for guiding effective carnivore conservation efforts (Ferguson and Lariviere 2002) but requires a thorough understanding of the complex phenomena governing population regulation (Reynolds and Freckleton 2005; Sibley et al. 2006). Our study provides evidence that, although intrinsic behaviors can be modified to resist the influence of extrinsic forces, to facilitate optimal population growth, or ‘‘output,’’ it is environmental carrying capacity (in this instance, potentially dictated by the incidence of parasitic disease and abundance of earthworms) that regulated numbers through the process of mortality. Thus, factors that can potentially disrupt environmental carrying capacity for badger populations, such as agrienvironmental change (e.g., da Silva et al. 1993; Macdonald and Newman 2002), or modification of resource productivity and distribution (sensu Macdonald 1983a, 1983b; Macdonald and Carr 1989), for example, due to climatic change (Macdonald and Newman 2002), can disrupt the regulation of the population. Similarly, culling (e.g., Macdonald et al. 2006; Tuyttens and Macdonald 2000) also may disrupt the equilibrium of resource-based competition (Nicholson 1954). Other studies modeling elasticity matrices also highlight how disruption of a population parameter can negatively impact species viability. For example, hunting has been observed to negatively impact sexually segregated grizzly bear (Ursus arctos) population success (Wielgus et al. 2001) and interannual variation in survival of calves drives population regulation in elk (Cervus elaphus—Raithel et al. 2007). Experimental dissection of empirical systems is providing important insights into the details of the drivers of demographic responses and therefore dynamics (Benton et al. 2006). In the context of behavioral plasticity and evolution, the maximization of individual fitness also may lead to behavior patterns that result in the maximization of population growth rate (Rice 2004), as observed in our study (Macdonald et al. 2004), adding to the complexities of informed wildlife management (Koons et al. 2006).

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ACKNOWLEDGMENTS The considerable long-term efforts of the Badger Project team, past and present, are gratefully acknowledged, as are the comments of P. Johnson and H. Dugdale on emerging drafts of this manuscript. This manuscript also benefited from meticulous and expert comments by S. Dobson, T. Coulson, and M. Bonsall. Much of this core study was generously supported by the Peoples Trust for Endangered Species, with additional support from the Earthwatch Institute. Work was carried out under English Nature Licenses, currently 20061970 and Home Office License PPL 30/2318.

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Submitted 19 November 2008. Accepted 18 March 2009. Associate Editor was Harald Beck.