The Ideal Free Pike: 50 Years of Fitness-Maximizing Dispersal In

Proc. R. Soc. B (2006) 273, 2917–2924 doi:10.1098/rspb.2006.3659 Published online 16 August 2006

The ideal free pike: 50 years of fitness-maximizing dispersal in Windermere Thrond O. Haugen1,2, Ian J. Winfield3, L. Asbjørn Vøllestad1, Janice M. Fletcher3, J. Ben James3 and Nils Chr. Stenseth1,* 1Centre for Ecological and Evolutionary Synthesis, Department of Biology (CEES), University of Oslo, PO Box 1066 Blindern, 0316 Oslo, Norway 2Norwegian Institute for Water Research, PO Box 173 Kjelsa˚s, 0411 Oslo, Norway 3Centre for Ecology & Hydrology, Lancaster Environment Centre, Library Avenue, Bailrigg, Lancaster, Lancashire LA1 4AP, UK The ideal free distribution (IFD) theory is one of the most influential theories in evolutionary ecology. It predicts how animals ought to distribute themselves within a heterogeneous habitat in order to maximize lifetime fitness. We test the population level consequence of the IFD theory using 40-year worth data on pike (Esox lucius) living in a natural lake divided into two basins. We do so by employing empirically derived density-dependent survival, dispersal and fecundity functions in the estimation of basin-specific density- dependent fitness surfaces. The intersection of the fitness surfaces for the two basins is used for deriving expected spatial distributions of pike. Comparing the derived expected spatial distributions with 50 years data of the actual spatial distribution demonstrated that pike is ideal free distributed within the lake. In general, there was a net migration from the less productive north basin to the more productive south basin. However, a pike density-manipulation experiment imposing shifting pike density gradients between the two basins managed to switch the net migration direction and hence clearly demonstrated that the Windermere pike choose their habitat in an ideal free manner. Demonstration of ideal free habitat selection on an operational field scale like this has never been undertaken before. Keywords: density dependence; predator–prey interaction; habitat use; dispersal; Esox lucius

1. INTRODUCTION distributions with observed distributions (Swain & Wade The ideal free distribution (IFD) theory, as proposed by 1993; Marshall & Frank 1995; Doncaster et al.1997). Fretwell and Lucas (Fretwell & Lucas 1970; Fretwell 1972), However, studies having compared observed with IFD- predicts that individuals within a habitat complex consisting predicted distributions all base their predictions on theory of areas differing in quality will, if costs are negligible, alone (e.g. Morris 1997; Morris & Davidson 2000). To our distribute themselves in a way that results in equalized mean knowledge, no large-scaled study utilizing data-based individual fitness among habitats as a result of individuals a priori knowledge of how fitness varies with density for a seeking to maximize their own fitness by making optimal given habitat complex has been reported. habitat choices (Holt & Barfield 2001). This process can be In this paper, we test the population level consequence of considered an evolutionary game and when the population theIFD theory using 40-year worth capture–mark–recapture settles down at equilibrium, fitness should be equal across (CMR) data on pike (Esox lucius) from Windermere in habitats. It has recently been demonstrated that the IFD is northwest England. This lake comprises two basins that an evolutionary stable strategy in single-species systems differ in productivity. We estimate empirically derived (Cressman et al.2004). Although such a large-scale density- and basin-specific fitness functions, incorporating survival- and dispersal probability as well as fecundity, to prediction was the original motivation of the IFD theory, produce predictions of expected spatial distributions of the most of its tests relate to small-scale habitat use of foraging Windermere pike. These model-based predictions are individuals over fairly short time periods (see, e.g. Tregenza compared with the observed historical spatial distributions. 1995; Sutherland 1996; Lampert et al. 2003). Recently, During the study period, a 6-year density-manipulation some large-scale population-level IFD-motivated studies experiment was performed. The result of this manipulation have been published (Bautista et al.1995; Brown et al. 1995; provides a basis for experimentally testing our statistically Marshall & Frank 1995; Swain & Wade 1993 reviewed in derived conclusion regarding the presence of an IFD- Diffendorfer 1998; Morris et al. 2004; Shepherd & Litvak motivated habitat selection in Windermere pike. 2004), predominantly covering only a short time span. Only a few studies have compared IFD-predicted 2. THE WINDERMERE PIKE AND THE IDEAL FREE * Author for correspondence ([email protected]). DISTRIBUTION MODEL SYSTEM (a) Long-term data series The electronic supplementary material is available at http://dx.doi. org/10.1098/rspb.2006.3659 or via http://www.journals.royalsoc.ac. Pike is the top predator in Windermere, primarily preying uk. upon perch, Perca fluviatilis (Le Cren 1987). The lake

Received 7 May 2006 2917 q 2006 The Royal Society Accepted 26 June 2006 2918 T. O. Haugen and others Natural scale distribution in pike

N north Scotland (a) basin

Windermere 106 north basin 105 Wales England 104 age 2–7 perch 3 age 3–9 pike 10 age 2 pike 106 south basin 105 population size 104 3 10 south 1940 1950 1960 1970 1980 1990 2000 basin

1 km

(b) (c) (d) 1.0 1.0 north north N→S 1.0 south 0.8 0.8 )

t 0.9 0.6 0.6 0.8 0.4 0.4 fecundity ( 0.7 survival probability

0.2 dispersal probability 0.2 S→N south mean relative individual 0 0 0.6 −2 −1 012 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 pike abundance pike abundance gradient pike abundance (t–1) Figure 1. The study lake, abundance time-series and density-dependence of demographic components. (a) The study lake and time-series of annual pike and perch abundance estimates. (b) Estimated survival response with corresponding 95% confidence boundaries (dashed lines) as a function of age 3–9 pike abundance for males in the two study basins. (c) Estimated dispersal probability with corresponding 95% confidence bounds (dashed lines) as function of age 3–9 pike abundance gradient between the north and south basins. (d ) The relationship between mean individual fecundity and pike abundance. The bubble sizes are proportional to the mean body weight of mature females during the spawning season. (b) and (c) have been estimated under a mean abundance of age 2 pike and mean abundance of perch. consists of two basins (figure 1a) differing in morphology the CMR data demonstrated that survival was much and productivity (Le Cren 1987). Both pike and perch more sensitive to variation in pike density in the south have been subjected to extensive investigations since 1940, basin compared with the north basin (figure 1b). On the and during this time period, data on the total catch in other hand, between-basin dispersal probability was standardized gears have been recorded (Kipling 1983, see much more sensitive to the between-basin pike abun- electronic supplementary material). Based on these catch dance gradient for the north-basin pike compared with data, the abundance of pike and perch have been the south-basin pike (figure 1c). Samples of more than estimated annually for each basin (des Clers et al. 1994). 20 years of individual fecundity data facilitated the The estimates of population abundance clearly demon- estimation of abundance-related fecundities (figure 1d ). strate that both species have experienced profound annual The mean relative (to maximum) fecundity was fluctuations over the 50-year period for which such data estimated as a decreasing exponential function of pike are available (figure 1a). density and varied slightly between basins (table 1). An extensive CMR sampling programme on pike Having these basin- and density-dependent fitness and covering most of the same 50-year period as described dispersal components at hand enabled us to generate (Kipling & Le Cren 1984) enabled us to derive estimates estimates of expected fitness under a variety of basin- of age- and size-specific survival and dispersal prob- specific pike density settings, and hence predict how the abilities, all as functions of perch- and pike abundances Windermere pike ought to distribute themselves accor- (Haugen et al. submitted). The resulting model fitted to ding to the IFD theory.

Proc. R. Soc. B (2006) Natural scale distribution in pike T. O. Haugen and others 2919

Table 1. Parameters used for ﬁtness estimation. (Survival and (a)5000 dispersal parameters are taken from Haugen et al. submitted) south and have been estimated on a logit scale, and all covariates north have been standardized to meanZ0 and s.d.Z1. The model explained 81 and 94% total and process variance in survival, respectively. For dispersal, the model explained 66 and 87%, respectively. The model structure for the fecundity models is: fecundity(t)Zbexp(bage 3–9 pike abundance(tK1)), 0 1 1000 where the pike abundance is on a standardized scale. The ﬁtted models explained 66 and 71% variation for the south and north basins, respectively.) 500 response term estimate s.e.m.

survival intercept 1.35 0.10 netting effort (30 yd net days) basin 0.14 0.24 experimental sex 0.25 0.10 period perch abundance K0.02 0.08 100 age 2 pike abundance 0.41 0.13 age 3–9 pike abundance K1.40 0.23 (b) 1.0 basin!age 3–9 pike abundance 1.00 0.27 age 2 pike abundance!perch K0.22 0.12 abundance 0.8 dispersal intercept K3.62 0.47 basin 0.07 0.49 sex 0.99 0.43 age 3–9 pike abundance K0.54 0.29 0.6 gradient basin!age 3–9 pike abundance 2.74 0.66 gradient 0.4 perch abundance gradient 0.35 0.32 basin!perch abundance K1.45 0.62 relative intrinsic fitness gradient 0.2 fecundity intercept (north basin) 0.814 0.015 age 3–9 pike abundance K0.136 0.027 (north basin) 0 intercept (south basin) 0.836 0.012 age 3–9 pike abundance K0.150 0.024 (c) (south basin) 0.4

(b) Density-manipulation experiments 0.3 As mentioned earlier, the Windermere system experienced profound density variations both in the prey and the predator species from 1943–1995, an important pre- 0.2 requisite for performing field-based tests of the IFD theory. In addition, the between-basin pike density structure has been manipulated over a period of 6 years. 0.1 From 1956–1962, the staff at the Freshwater Biological Association performed an experiment where they manipulated the pike densities in the two basins such that high 0 densities were created in the north basin during the 3 net north-to-south dispersal probability years, 1956–1958 (i.e. low fishing effort in the northern basin relative to the southern basin, figure 2a). During the −0.1 3 subsequent years, the densities in the two basins were 1950 1960 1970 1980 1990 manipulated in the opposite direction. The high-fishing year intensity treatment resulted in 15–28% removal of the pike population in the basin involved, whereas only 0.8–2.1% Figure 2. Basin-specific annual values offishing effort, dispersal were removed during the low-effort treatment. This and intrinsic fitness. (a) The total basin-wise fishing effort produced tremendous density gradients between the two during the winter fisheries in Windermere, 1950–1990. Pay basins. On average, the first treatment period resulted in attention to the 1956–1962 period when the pike density an abundance difference of 1800 individuals in favour of manipulation experiments were carried out. (b) Relative (to lake maximum)basin-wiseannualintrinsic fitness (w ).These values the north basin, whereas the second produced a gradient t illustrate what would be the expected fitness consequences if of 4100 individuals in favour of the south basin. For there were, on average, no net dispersals between the basins. comparison, the average population sizes in the two basins NS SN (c) Annual net north-to-south dispersal rates (jt Kjt ) were 5400 and 6300 individuals in the period 1944–1995 estimated from mark-recapture data.

Proc. R. Soc. B (2006) 2920 T. O. Haugen and others Natural scale distribution in pike for the north and south basins, respectively. These When modelling the second Fretwellian step (equation experiments produced anomalous density gradients (3.2)), we estimated the expected realized fitness (l) as: compared with the rest of the 1943–1995 period, and N N; N ; S; S Z N N NN N; S N N enabled the density-dependent habitat selection of the lt x t x tK1 x t x tK1 St x t jt x t x t Ft x tK1 Windermere pike to be explored in more detail. N N SN N S N S CSt x t jt x t ;x t Ft x tK1 S N N S S S S SS N S S S lt x t ;x tK1;x t ;x tK1 Z St x t jt x t ;x t Ft x tK1 3. MATERIAL AND METHODS C S N NS N; S S N ; ð : Þ (a) The structure of the argument St x t jt x t x t Ft x tK1 3 2 The estimates of density-dependent survival and movement where j is the annual dispersal probability and superscripts of probabilities provide the components for deriving the apriori SN and NS indicate dispersal from south to north basin and density dependence in fitness in the two basins of the lake. from north to south basin, respectively. In order to explore Finding the densities for which the fitness in the two basins of the unique contribution from pike abundance on survival, the lake are equal, defines the density combinations (x N and dispersal and fecundity variation, we fixed perch and age 2 x S) in the different parts of the lake corresponding to the IFD. pike abundance at their mean values (i.e. meanZ0). The age Since the observed densities were used as independent 2 pike constitute both potential prey and competitors for the covariates in the estimates of the fitness components while in age 3–9 pike. This did not produce a perch abundance the two basins of the lake, we can compare the predicted IFD gradient between the two basins, a factor known to affect densities (x N and x S) with the observed (x N and x S). Windermere pike dispersal (table 1; Haugen et al. submitted). It might be said that the l function is a highly simplistic (b) From intrinsic to realized fitness fitness function for an age-structured species living in a According to the IFD theory, observed habitat choices may temporary variable environment like the pike in Windermere. result from individuals distributing themselves within the Choosing the appropriate fitness measure is not an easy task, habitat complex in order to maximize their individual fitness. especially with varying population size. However, a modelling This will result in equalized mean individual fitness among study performed by Benton & Grant (2000) demonstrated habitats when the population is at equilibrium. Hence, in that measures of reproductive performance, like the l used in order to test the IFD theory, a priori habitat-specific fitness our study, produce reliable results when compared with more estimates are essential prerequisites (Tyler & Hargrove 1997; advanced, but less tractable methods (methods like Shepherd & Litvak 2004). However, the Fretwellian idea is ‘evolutionarily unbeatable strategies’). Furthermore, as based on a two-step procedure where individuals first choose stated by Holt & Barfield (2001), even crude fitness measures whether to move to another habitat or not, according to can quite reasonably capture the IFD outcome. Having said habitat fitness gradients (or ‘suitability gradients’ in Fretwell’s this, we are well aware that the l fitness function used in this terms—here we refer to the initial basin-specific fitness as study relies on the strong assumption that survival from egg to intrinsic fitness). Then, as a second step, if the individuals age 3 does not depend on female quality. It is well known in choose habitats optimally, the fitness gradients will diminish fishes that large females produce larger eggs than small and consequently, fitness is equalized across habitats females (also the case in pike; Kipling & Frost 1969) resulting (corresponding to the realized fitness). In the present study, in larger offspring (not necessarily the case in pike; Wright & the two basins of Windermere are treated as two habitats as Shoesmith 1988) with better prospects of survival. We tested they are known to differ in quality (Le Cren 1987), and the the sensitivity of the predicted isodar to variation in effective aim is to predict the annual between-basin distribution of fecundity, where effective fecundity was estimated as the pike. We do so by adopting the two-step IFD process predicted fecundity (see §3d) multiplied with a survival described earlier. coefficient bsurv that affected the slope of the density- For the first Fretwellian step (equation (3.1)), the intrinsic dependent fecundity function. The sensitivity of the pre- fitness (w) was estimated as the product of mean probability of dicted isodar to bsurv was tested first, under similar bsurv survival (S ) and mean number of eggs (F ) for a given basin and between basins and second, under conditions with basin- year, both being functions of age 3–9 pike abundances (table 1) specific bsurv values. The first analyses covered up to a doubling of the fecundity slopes resulting in predicted isodars ) varying between 0.85 and 0.91 (elasticities varied between N N; N Z N N N N wt x t x tK1 St x t Ft x tK1 0.10 and 0.14). The second analyses covered up to a twofold ; ð3:1Þ S S; S Z S S S S difference between basins in fecundity slopes producing wt x t x tK1 St x t Ft x tK1 isodars varying between 0.84 and 0.87 (elasticities varied between 0.02 and 0.07). We therefore find the predicted where x is standardized estimated annual abundance (estimated isodar results to be very robust regarding the assumption of for May) of age 3–9 pike, S is the annual survival rate and egg-to-age 3 survival among females without variation. superscripts of N and S indicate the basin. With these estimates of the fitness components, we could By differentiating these basin-specific density-dependent explore the fitness consequences of the deduced density- fitness functions, we were able to predict the expected net dependent dispersal probabilities. The resulting l values N S dispersal direction and probability. The predictions of could be presented as surfaces in the x t versus x t space. between-basin dispersal rates were compared with annual In accordance with the IFD theory prediction of equal observed migration rates assessed from the CMR data. In fitness across habitats, we wanted to estimate the between- particular, we explored the between-basin dispersal pattern basin pike distributions over which mean fitness is equal observed during a pike density manipulation experiment between basins. The intersection between the two fitness N N S S N S (see §2b). surfaces ðlt ðx t ; x t ÞZlt ðx t ; x t ÞÞ, also called the isodar

Proc. R. Soc. B (2006) Natural scale distribution in pike T. O. Haugen and others 2921

(Morris 1988), represents the combination of densities in the fitted basin-specific mean-scaled fecundity (FtZfecundityt / two basins corresponding to ideal free basin distribution of pike max(fecundity)) at year t to standardized pike abundance at in Windermere. Werefer to this realized-fitness-surface-derived time tK1(figure 1d; Craig & Kipling 1983). In total, 20 years of isodar as the predicted isodar. The confidence bounds of the fecundity data were available based on 1847 individuals. The predicted isodar were estimated by a parametric bootstrapping mean-scaled fecundity was predicted from a decreasing method (Schweder in press). First, a total of 3000 sets of exponential function and varied slightly between basins parameter values were re-sampled from the variance– (table 1). A total of 71 and 66% of the variance was covariance matrix of the survival, dispersal and fecundity explained by the fitted models for the north and the south parameter estimates, assuming that all parameters were basins, respectively. normally distributed on their estimation scales (logit scale for survival and dispersal and linear scale for fecundity). Second, 4. RESULTS isodars were estimated for all 3000 of the re-sampled sets of Comparisons between annual basin-specific intrinsic parameters. Finally, percentile statistics were assessed at every fitness demonstrate that between-basin gradients in 0.05 unit of x N (i.e. standardized abundance of north basin intrinsic fitness have existed throughout the study period pike). The confidence bounds were then fitted by a spline and the south basin, on average, has the highest intrinsic function (d.f.Z3) to the assessed 97.5 and 2.5 percentile fitness (figure 2b). From 1949–1990, the annual dispersal data, respectively. was in favour of north-to-south migration for all but 7 By applying the dispersal probabilities to a matrix of all years (figure 2c). In particular, during 1956–1958, possible basin-specific pike abundances, we could predict the migration in the north-to-south direction had the highest expected distribution of pike under which dispersal will estimated probabilities over the entire data series. During equalize fitness across the two basins. In order to evaluate the the next 3 years, the highest habitat-specific dispersal rate predictive power of the predicted basin distributions of pike, was, for the only period in the entire data series, in favour we compared them with the 50 years of historical abundance of the south-to-north direction. estimates available from Windermere. The predicted density-dependent realized fitness surfaces differ between the two basins (figure 3a,b), the (c) Estimation of survival and dispersal probabilities main difference being that the north-basin fitness is more Survival- and dispersal probabilitieswere estimated as functions sensitive to variation in the north-basin pike abundance of annual pike- and perch abundances in May, incorporating sex than the south-basin pike fitness. As can be seen, north- and basin effects, by fitting 37 years of CMR data (Haugen et al. basin pike, on an average, have lower expected realized submitted). Using the software MARK (White & Burnham fitness than the south-basin pike when north-basin 1999), we fitted the CMR data to a multistate model structure abundance is high. However, the expected realized fitness (Brownie et al.1993; Nichols & Kendall 1995), which is highest for north-basin pike when both south-basin and provided estimates of basin-specific survival and dispersal north-basin pike abundances are low. probabilities under the influence of both density-dependent The predicted isodar (figure 3c, solid black line) and -independent factors (table 1, Haugen et al.submitted). explains 69.7% inter-annual variations in the historical Because suitable pike area is similar between the two basins, abundance estimates and 74% abundance estimates were standardized (i.e. (ln(abundance)Kmean(ln(abundance))/ confined by its 95% confidence envelope. The fitted linear std(ln(abundance)) abundance estimates were used as density isodar (figure 3c, solid red line) explains 70.1% inter- in all models. The optimal model structure was chosen using annual variations in the historical abundance estimates. quasi-corrected Akaike’s information criterion (Burnham & Anderson 1998) that corrected for a slight over-dispersion (c^Z1:2). There was no indication of lack of fit to the chosen 5. DISCUSSION 2 Z : conditional Arnason–Schwarz model structure (c39 49 3, The results found in this study support predictions derived pZ0.13, see electronic supplementary material for a brief from the IFD theory and clearly indicate that: (i) pike in introduction to the CAS parameterization). The best model Windermere choose habitat according to intrinsic fitness explained 81 and 94% of the total and process (adjusted for gradients and consequently (ii) distribute themselves in a sampling error) variance in survival, respectively. For dispersal, way that equalizes fitness across habitats. the best model explained 66 and 87%, respectively. All Under conditions with intrinsic habitat fitness gradients, estimates provided in this paper relate to individuals that are the IFD theory predicts that dispersal ought to occur to larger than 55 cm (‘large pike’ in Haugen et al.submitted), and equalize fitness between the two basins. On application of survival and dispersal probabilities have been estimated at a this theory to the estimated basin-specific intrinsic fitness half-year scale (however, note that in the fitness estimation, we values, the IFD theory predicts habitat-specific dispersal use annual values). Since all pike caught in the gill-net sampling probability to be highest for the north-to-south direction as of the scientific sampling programme were retained and intrinsic fitness, in general, is higher in the latter. This reported, and as this gill netting is the only removal sampling prediction is clearly supported by the between-basin occurring in Windermere for this species, the survival estimates dispersal estimates revealed in this study (figure 2c). The could be interpreted as natural survival estimates. In addition, pike density-manipulation experiments provide further owing to the closed nature of the Windermere system, survival support for an IFD-driven habitat choice in Windermere and dispersal were estimated under no influence of immigration pike: (i) during the first period (1956–1958), migration in from or emigration to external systems. the north-to-south direction increased to ‘historical’ levels (the highest estimated for the entire data series) and (ii) (d) Estimation of density-dependence in fecundity when the fishing effort regime was changed so as to lead to Gonad investments in pike are constrained by conditions high densities in the south basin and low in the north basin, prevailing 1 year prior to spawning (Billard 1996). Wetherefore the net dispersal probability was, for the only period in the

Proc. R. Soc. B (2006) 2922 T. O. Haugen and others Natural scale distribution in pike

(a) (b)

1.0 1.0 0.8 0.8 0.6 0.6

0.4 0.4 lambda

lambda 0.2 0.2 0 0 2 2 pike abundance, south pike abundance, south 1 1 2 2 0 1 0 1 − 0 − 0 1 1 −1 −1 − − 2 −2 2 −2 pike abundance, north pike abundance, north

0.2 1

0 pike abundance, south −1 0.0

− − − −2 0.2 0.4 0.6

−1012 pike abundance, north Figure 3. Estimated realized fitness surfaces and the predicted and linear isodars. The estimated realized fitness (l in: (a) the south basin and (b) the north basin as functions of basin-specific pike abundances. (c) The predicted isodar (i.e. the intersection line between the two fitness surfaces, thick black line) and the corresponding 95% confidence boundary lines (dotted lines). Numbers attached to grey lines represent isocline values for the difference lnorth basinKlsouth basin, where the zero isocline constitutes the predicted isodar. The red open dots constitute the historical pike abundance estimates and the red line is the S N estimated linear isodar for these abundances (sensu Morris 1988). This linear isodar (x t Z0:04C0:86x t ) explained 70.1% variation and the intercept is not significantly different from 0 ( pZ0.17), whereas the slope is significantly different from both 0 ( p!0.0001) and 1 ( pZ0.013). entire data series, in favour of the south-to-north direction. so as to be able to choose optimally between the two basins That is, when intrinsic fitness gradients were manipulated to within the course of a year. Indeed, estimates from the increase, the pike responded directly by increasing their CMR data clearly demonstrate that individual dispersal dispersal rate accordingly. probability is asymmetrically density-dependent between The IFD theory assumes that the cost of movement the two basins in favour of net north-to-south dispersal between habitats should be negligible and that all (figure 2c), and that habitat choice hence seems likely to individuals are able to assess the required habitat quality occur (figure 1c). information to make optimal habitat choices (Fretwell The IFD-expected spatial distribution of pike in 1972; Fretwell & Lucas 1970). Pike may move consider- Windermere (i.e. the predicted isodar) corresponded able distances (more than 2 km; Lucas 1992) during a day closely to the observed basin-specific distribution of pike and are known to be able to respond to density (Grimm & and explained almost as much of the inter-annual Klinge 1996). Windemere is not very large (7 km between variation in abundance estimates as did the fitted linear basin midpoints) compared to the daily dispersal distances isodar (figure 3c). This strongly suggests that pike in observed, and pike can be expected to have no difficulty in Windermere distribute themselves according to the IFD obtaining sufficient information with relatively few costs, theory. In fact, the slope of the linear isodar could be

Proc. R. Soc. B (2006) Natural scale distribution in pike T. O. Haugen and others 2923 qualitatively predicted to be less than 1 from the density- Billard, R. 1996 Reproduction of pike: gametogenesis, related fecundity and survival functions (figure 1b,d ). As gamete biology and early development. In Pike: biology survival in the southern basin drops off precipitously at and exploitation (ed. J. F. Craig), pp. 13–44. London, UK: high pike abundance, whereas relative fecundities are Chapman & Hall. almost similar between basins, these relationships imply Brown, J. H., Mehlman, D. W. & Stevens, G. C. 1995 Spatial strongly converging fitness functions that yield an isodar variation in abundance. Ecology 76, 2028–2043. (doi:10. with slope less than 1. This prediction is in accordance 2307/1941678) Brownie, C., Hines, J. E., Nichols, J. D., Pollock, K. H. & with the fitted slope (equals 0.86, figure 3c). Jonzeń et al. Hestbeck, J. B. 1993 Capture-recapture studies for (2004) demonstrate that the isodar method is sensitive to multiple strata including non-Markovian transitions. assumptions about temporal variation in habitat quality. Biometrics 49, 1173–1187. (doi:10.2307/2532259) In fact, the predicted isodar estimated in this study is Burnham, K. P. & Anderson, D. R. 1998 Model selection and based on fixed prey abundances (i.e. mean abundance of inferences. New York, NY: Springer. age 2–7 perch and age 2 pike). Obviously, the prey Craig, J. F. & Kipling, C. 1983 Reproduction effort versus the abundances fluctuate with time (figure 1a)inboth environment—case-histories of Windermere perch, Perca Windermere basins. When fitting a generalized additive fluviatilis L, and pike, Esox lucius L. J. Fish Biol. 22, model (GAM) with perch abundance as a predictor of the 713–727. (doi:10.1111/j.1095-8649.1983.tb04231.x) residuals from the predicted isocline model, a significant Cressman, R., Krivan, V. & Garay, J. 2004 Ideal free effect with estimated d.f.Z2.8 (decided by generalized distributions, evolutionary games, and population cross-validation) was found for north basin perch dynamics in multiple-species environments. Am. Nat. abundance and this variable explained 20.1% of the 164, 473–489. (doi:10.1086/423827) residual variation. This GAM showed that perch abun- des Clers S., Fletcher J. M., Winfield I. J., Kirkwood G. P., Cubby P. R. & Beddington J. R. 1994 Long-term changes dance had a significant contribution to the residual in Windermere perch and pike populations at the basin variation for large residual values, usually found when level. Institute of Freshwater Ecology, IFE Report densities of pike were low in both basins (figure 3c). Even WI/T11050d5/4. though perch abundance variation can explain some of the Diffendorfer, J. E. 1998 Testing models of source–sink deviation from the predicted IFD, a lack-of-fit test dynamics and balanced dispersal. Oikos 81, 417–433. (F1,48Z0.023, pZ0.88) indicated no systematic deviation Doncaster, C. P., Clobert, J., Doligez, B., Gustafsson, L. & from the predicted central tendency. This result was Danchin, E. 1997 Balanced dispersal between spatially further supported by fitting a GAM between historical varying local populations: an alternative to the source–sink north and south pike abundances, allowing the optimal model. Am. Nat. 150, 425–445. (doi:10.1086/286074) number of knots in the spine function to be decided by a Fretwell, S. D. 1972 Populations in a seasonal environment. generalized cross-validation procedure. The outcome of Princeton, NJ: Princeton University Press. this analysis showed that this relationship was best Fretwell, S. D. & Lucas, H. J. 1970 On territorial behavior explained by a straight line. In conclusion, the isodar and other factors influencing habitat distributions will not change, on inclusion of the perch abundance in birds. Acta Biotheoretica 19, 16–36. (doi:10.1007/ BF01601953) during estimation of the between-basin distribution of Grimm, M. P. & Klinge, M. 1996 Pike and some aspects of its pike, but will be predicted with a higher precision. Hence, dependence on vegetation. In Pike: biology and exploitation both the predicted and the fitted linear isodars relevantly (ed. J. F. Craig), pp. 125–156. London, UK: Chapman & describe the ultimate result of this study, the Windermere Hall. pike distribute themselves according to the IFD theory. Haugen T. O., Winfield I. J., Vøllestad L. A., Fletcher J. M., This study received support from the Research Council of James J. B. & Stenseth N. C. Submitted. Fifty years of Norway (141170/720 and 141170/S30) and benefited from capture–mark–recapture data reveals complex density- general support to the Centre for Ecological and Evolutionary dependent and density-independent interaction effects on Synthesis (CEES) of the University of Oslo. Support from the survival and dispersal in pike (Esox lucius). Ecology. Natural Environment Research Council to the Centre for Holt, R. D. & Barfield, M. 2001 On the relationship Ecology & Hydrology is also acknowledged. We are indebted between the ideal free distribution and the evolution of to Sophie des Clers and John Beddington for their kind dispersal (ed. J. Clobert, E. Danchin, A. A. Dhondt & J. D. provision of unpublished model parameter estimates used for Nichols), pp. 83–95. New York, NY: Oxford University estimating population sizes of Windermere pike and perch. Press. Jean Clobert, Jim Nichols and three anonymous reviewers are Jonzeń, N., Wilcox, C. & Possingham, H. P. 2004 Habitat thanked for commenting upon earlier versions of the paper, selection and population regulation in temporally fluctu- and Tore Schweder for inputs on the parametric boot- ating environments. Am. Nat. 164, E103–E114. strapping of isodar confidence bounds. We are also grateful to Kipling, C. 1983 Changes in the population of pike (Esox the Freshwater Biological Association for their joint steward- lucius) in Windermere from 1944 to 1981. J. Anim. Ecol. ship of these invaluable data. 52, 989–999. (doi:10.2307/4469) Kipling, C. & Frost, W. E. 1969 Variations in fecundity of pike Esox lucius L in Windermere. J. Fish Biol. 1, 221–237. REFERENCES (doi:10.1111/j.1095-8649.1969.tb03855.x) Bautista, L. M., Alonso, J. C. & Alonso, J. A. 1995 A field-test Kipling, C. & Le Cren, E. D. 1984 Mark-recapture experiments of ideal free distribution in flock-feeding common cranes. on fish in Windermere, 1943–1982. J. Fish Biol. 24, J. Anim. Ecol. 64, 747–757. (doi:10.2307/5853) 395–414. (doi:10.1111/j.1095-8649.1984.tb04811.x) Benton, T. G. & Grant, A. 2000 Evolutionary fitness in Lampert, W., McCauley, E. & Manly, B. F. J. 2003 Trade-offs ecology: comparing measures of fitness in stochastic, in the vertical distribution of zooplankton: ideal free density-dependent environments. Evol. Ecol. Res. 2, distribution with costs? Proc. R. Soc. B 270, 765–773. 769–789. (doi:10.1098/rspb.2002.2291)

Proc. R. Soc. B (2006) 2924 T. O. Haugen and others Natural scale distribution in pike

Le Cren, E. D. 1987 Perch (Perca fluviatilis) and pike (Esox Schweder T. In press. Confidence nets for curves. In lucius) in Windermere from 1940 to 1985—studies in Advances in statistical modeling and inference: essays in population dynamics. Can. J. Fish. Aquat. Sci. 44, 216–228. honor of Kjell A. Doksum (ed. V. Nair). Riveredge, NJ: Lucas, M. C. 1992 Spawning activity of male and female World Scientific. pike, Esox lucius L., determined by acoustic tracking. Can. Shepherd, T. D. & Litvak, M. K. 2004 Density-dependent J. Zool. 70, 191–196. habitat selection and the ideal free distribution in Marshall, C. T. & Frank, K. T. 1995 Density-dependent marine fish spatial dynamics: considerations and cautions. habitat selection by juvenile haddock (Melanogrammus Fish Fisheries 5, 141–152. (doi:10.1111/j.1467-2979. aeglefinus) on the southwestern Scotian Shelf. Can. J. Fish. 2004.00143.x) Aquat. Sci. 52, 1007–1017. Sutherland, W. J. 1996 From individual behaviour to population Morris, D. W.1988 Habitat-dependent population regulation ecology. Oxford, UK: Oxford University Press. and community structure. Evol. Ecol. 2, 253–269. (doi:10. Swain, D. P.& Wade, E. J. 1993 Density-dependent geographic 1007/BF02214286) distribution of Atlantic cod (Gadus morhua) in the southern Morris, D. W. 1997 Optimally foraging deer mice in prairie Gulf of St-Lawrence. Can. J. Fish. Aquat. Sci. 50, 725–733. mosaics: a test of habitat theory and absence of landscape Tregenza, T. 1995 Building on the ideal free distribution. effects. Oikos 80, 31–42. Adv. Ecol. Res. 26, 253–307. Morris, D. W. & Davidson, D. L. 2000 Optimally foraging Tyler, J. A. & Hargrove, W. W. 1997 Predicting spatial mice match patch use with habitat differences in fitness. distribution of foragers over large resource landscapes: a Ecology 81, 2061–2066. (doi:10.2307/177095) modeling analysis of the ideal free distribution. Oikos 79, Morris, D. W., Diffendorfer, J. E. & Lundberg, P. 2004 376–386. Dispersal among habitats varying in fitness: reciprocating White, G. C. & Burnham, K. P. 1999 Program MARK: migration through ideal habitat selection. Oikos 107, survival estimation from populations of marked animals. 559–575. (doi:10.1111/j.0030-1299.2004.12894.x) Bird Study 46, 120–139. Nichols, J. D. & Kendall, W. L. 1995 The use of multi-state Wright, R. M. & Shoesmith, E. A. 1988 The reproductive capture–recapture models to address questions in success of pike, Esox lucius—aspects of fecundity, egg evolutionary ecology. J. Appl. Stat. 22, 835–846. (doi:10. density and survival. J. Fish Biol. 33, 623–636. (doi:10. 1080/02664769524658) 1111/j.1095-8649.1988.tb05505.x)

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a high-oxygen atmosphere to revert back to a But this would still leave some unexplained Geosciences, Pennsylvania State University, low-oxygen state. This wonderful result might observations. For example, the Witwatersrand University Park, Pennsylvania 16802, USA. explain why oxygen levels stabilized perma- gold deposits in South Africa contain detrital e-mail: [email protected] nently following the GOE. minerals that were washed down streams But there are other unresolved issues in this between 2.8 billion and 3.0 billion years ago14. 1. Cloud, P. E. Am. J. Sci. 272, 537–548 (1972). 11–13 2. Holland, H. D. The Chemical Evolution of the Atmosphere and saga. There is evidence of low sulphur MIF In the presence of oxygen, these minerals Oceans (Princeton Univ. Press, 1984). values in rock formations of between 2.76 bil- should have become oxidized and dissolved. 3. Ohmoto, H. Geology 24, 1135–1138 (1996). lion and 2.92 billion years old, suggestive of So, either the oxygen levels were never high 4. Farquhar, J. et al. Science 289, 756–758 (2000). 5. Goldblatt, C., Lenton, T. M. & Watson, A. J. Nature 443, high atmospheric-oxygen levels preceding the enough for that, or they repeatedly went up and 683–686 (2006). accepted time of the GOE. So far, no high MIF came back down very quickly. Or perhaps oxy- 6. Brocks, J. J. et al. Science 285, 1033–1036 (1999). values have been reported in that time interval. gen concentrations did not increase at all, and 7. Hayes, J. M. & Waldbauer, J. R. Phil. Trans. R. Soc. Lond. B 361, 931–950 (2006). How can this be rationalized? the low-MIF anomaly seen in post-GOE rocks 8. Kump, L. R., Kasting, J. F. & Barley, M. E. Geochem. Geophys. One possible explanation — the so-called was produced by some entirely anoxic mecha- Geosyst. 2, 2000GC000114 (2001). ‘yo-yo’ atmosphere theory — was proposed nism, such as the shielding of solar ultraviolet 9. Catling, D. C. et al. Science 293, 839–843 (2001). earlier this year11. This theory suggests that rays by an organic haze13,15. 10. Holland, H. D. Geochim. Cosmochim. Acta 66, 3811–3826 (2002). oxygen levels first increased about 3.0 billion The jury is still out, but all these contradic- 11. Ohmoto, H. et al. Nature 442, 908–911 (2006). years ago, decreasing again about 0.2 billion tory observations are stimulating a lot of crea- 12. Ono, S. et al. S. Afr. J. Geol. (in the press). years later, before their final climb to high con- tive thinking. Let us hope that this will lead to 13. Peters, M. et al. Eos Trans. AGU 86, 52, Fall Meet. Suppl., Abstr. V21F-06 (2005). centrations 2.4 billion years ago (the GOE). a more unified understanding of a fascinating 14. Minter, W. E. L. in Evolution of Early Earth’s Atmosphere, Goldblatt and colleagues’ model5 explicitly era in Earth’s history. The ancient atmosphere Hydrosphere, and Biosphere — Constraints from Ore Deposits predicts that the atmosphere was bistable for may have had a more complex evolution than (Geol. Soc. Am. Mem. Vol. 198) (eds Kesler, S. E. & Ohmoto, H.) 105–109 (2006). ■ some time before the GOE, so maybe the yo-yo we imagined. 15. Goldman, S. & Kasting, J. F. Eos Trans. AGU 86, 52, Fall theory is correct. James F. Kasting is in the Department of Meet. Suppl., Abstr. PP41D-07 (2005).

ECOLOGY the fastest. But everyone with a boarding pass is trying to do the same. So the number of people in each queue is in dynamic equilibrium Moving to the ideal free home because, if one line moves more slowly than Douglas W. Morris others, passengers will swap queues. Thus, at any given time, the average wait before passing Pike move between two basins of a British lake to maximize their through the checkpoint is similar for everyone evolutionary fitness. This adaptive behaviour suggests that habitat at the end of the lines. Now apply the same principle to animals selection is more significant in population dynamics than was thought. choosing their habitat. At equilibrium, the distribution of individuals among habitats is evo- How should animals choose which habitat to spatial distribution of populations may often lutionarily stable3: no individual can improve its live in? An evolutionary biologist is likely to represent a dynamic equilibrium caused by fitness by moving to another habitat. But habi- answer that they should maximize their evo- habitat selection. tats and population sizes change, disturbing that lutionary fitness — the likelihood that their To understand the principle of the ideal free balance. Individuals will track those changes by genes will be passed on to future generations distribution, think of queues at airport security. moving from one habitat to another until their — and live in the habitat that will produce the As a passenger, you want to pass through as distribution regains its evolutionary stabil- most descendants. But there is a catch. If all quickly as possible. If there are several queues, ity. The density in every habitat thus depends individuals make the same choice, the habitat you choose the one that you think will move on the density in others, just as the length will become crowded, the probabilities of survival and reproduction will suffer, and fitness a will decline. Other habitats with fewer indi- b viduals might be a better option. So animals maximizing fitness through habitat selection will disperse among habitats until no individual can improve its fitness by moving. This ‘ideal free distribution’1 assumes that

an individual can estimate accurately the fit- Fitness ness that can be attained in different habitats,

and is free to move and occupy the ideal place Habitat 1 in habitat 2 Density that maximizes fitness. Many ecologists have questioned whether the theory is hamstrung by Habitat 2 these preconditions. Can such a model really apply to natural populations? Writing in Pro- Density Density in habitat 1 ceedings of the Royal Society, Thrond Haugen Figure 1 | Testing for an ideal free distribution. a and colleagues2 provide convincing evidence , Evolutionary fitness declines more quickly with increasing population density in habitat 2 than it does in habitat 1. Symbols at the intersections with that it can. They show that, every year, pike in horizontal lines represent densities where fitness is equal in both habitats (an ideal free distribution). a northern English lake move from a habitat b, The equilibrium densities can be plotted against each other to yield the expected distribution of with low fitness (a higher mortality rate) to individuals in the two habitats (the habitat isodar7). Haugen et al.2 do this for the northern and southern one with higher fitness, thus eliminating the basins of Lake Windermere, and compare these with actual data for pike populations collected since the initial difference. The research tells us that the 1940s. The agreement between the model calculations and the data is astoundingly good.

NEWS & VIEWS NATURE|Vol 443|12 October 2006

system will move away from its former equilibrium. So with each passing year — if pike are ideal and free — their net annual dispersal should be biased towards the southern basin. And it was, most of the time. There was a three-year anomaly when pike reversed their dispersal and headed north. This coincided WWW.BRITAINONVIEW.COM with a remarkable, serendipitous experiment. Fisheries officials, during only those three years, had reduced the population of pike in the northern basin by approximately 20%. Most previous tests of ideal free theory have been at a small scale where foragers choose between patches differing in food supply6. Pike in Lake Windermere provide compelling evidence that the ideal free distribution occurs Figure 2 | Divided lake. Lake Windermere is separated by a shallow sill into two habitats for pike. at much larger scales where populations are regulated. Dispersal between basins equalizes of one security queue depends on the others. will demand more proof. Do pike disperse to fitness and homogenizes population growth. There are two ways to test the theory. First, the basin where higher fitness was assured? Although we need additional tests and experi- you can do an experiment: you measure the And, when placed in an experimental envi- ments at these large scales, the message seems fitness, density and dispersal of a model spe- ronment, do pike adjust their habitat choice clear: if you study populations, then you must cies living in adjacent habitats. Then you vary to equalize fitness? include the potential for habitat selection. ■ the population size; the densities and fitness of Haugen et al.2 answer both questions. The Douglas W. Morris is in the Department of individuals in the two habitats should also vary. population density in both basins increases Biology, Lakehead University, Thunder Bay, If, despite changes in density, the mean fitness during spawning. Although the southern Ontario P7B 5E1, Canada. actually remains equal in each habitat, the ani- basin is more productive, pike survival in the e-mail: [email protected] mals are following an ideal free distribution. south decreases more quickly with popula- But what if you can’t do the experiment? tion density than it does in the north. Thus, 1. Fretwell, S. D. & Lucas, H. L. Acta Biotheor. 19, 16–36 (1969). 2. Haugen, T. O. et al. Proc. R. Soc. Lond. B doi:10.1098/ Then you can stand the theory on its head. the fitness curves in the two basins diverge rspb.2006.3659 (2006). Instead of testing whether fitness is equal, you (Fig. 1). At an ideal free equilibrium, every 3. Cressman, R., Kr˘ivan, V. & Garay, J. Am. Nat. 164, 473–489 measure fitness at different population sizes fish in each basin will, on average, produce the (2004). in different habitats. You assume that fitness is same number of descendants. But even if the 4. White, G. C. & Burnham, K. P. Bird Study 46, 120–139 (1999). 5. Burnham, K. P. & Anderson, D. R. Model Selection and equalized, and then calculate how many ani- system is in equilibrium after spawning, the Inference (Springer, New York, 1998). mals should live in each habitat (Fig. 1). different survival rates in each basin cause fit- 6. Tregenza, T. Adv. Ecol. Res. 26, 253–307 (1995). Haugen et al.2 use an incredible data set to ness to rebound more rapidly in the south. The 7. Morris, D. W. Evol. Ecol. 2, 253–269 (1988). perform this second type of test. For more than 40 years, biologists captured, measured, marked and recaptured pike (Esox lucius) in Lake Windermere in northwest England. This CELL BIOLOGY lake has two basins (Fig. 2), which are separate pike habitats. Pike reproduce only once each year, so it is appropriate to census their densi- Mitochondria shape up ties and assess habitat selection annually. Barbara Conradt The authors use capture histories of indi- vidually marked pike to estimate survival and 4 Mitochondria are central to the process of programmed cell death that dispersal of the fish. The probability of observ- kills damaged or superfluous cells. Surprisingly, components of the death ing a given fish depends on the probability of it staying alive between census periods, the machinery turn out to be essential for keeping these organelles in shape. probability of it being captured when alive, and the probability of it moving between the Proteins of the Bcl-2 family are evolutionar- of mitochondrial morphogenesis, but also of two basins. Each of these probabilities depends ily conserved regulators of programmed cell the apoptotic functions of Bcl-2 proteins. on such things as the size and sex of the fish, death (apoptosis). However, their mecha- Bax and Bak are prototypical ‘killer’ pro- and the basin in which it currently lives. Hau- nisms of action are still not fully resolved1,2. teins: their pro-apoptotic activities are low in gen et al. searched for the most likely models5 On page 658 of this issue, Youle and col- healthy cells but high in cells instructed to die; describing the pattern of pike captures in each leagues3 report that the mammalian Bcl-2 their overexpression in cultured mammalian basin. They merged these models with data on family members Bax and Bak have additional cells accelerates apoptosis; and, in mice lacking egg production to calculate density-depend- functions to their apoptotic ones: they control both Bax and Bak (Bax/Bak DKO mice), most ent population growth rates in the two habi- the morphology of mitochondria, the cellular apoptosis is blocked1,2. The ability of Bax and tats. By assuming that these growth rates were organelles responsible for energy generation. Bak to kill cells is intimately associated with the equalized through habitat selection, they could Other components of the apoptotic machinery mitochondria. Whereas these two proteins are back-calculate the number of pike expected in also perform tasks outside apoptosis4,5. These found singly in healthy cells, in cells earmarked each basin each year. There was a nearly perfect tasks are unrelated to the proteins’ apoptotic for apoptosis they tend to group together into fit between predicted and actual densities. roles, however, whereas the non-apoptotic oligomers in the outer mitochondrial mem- Thus, pike choosing between the two basins and apoptotic functions of Bax and Bak are brane (OMM). This oligomerization and of Lake Windermere behaved as though linked. This latest study therefore improves association with mitochondria has two con- capable of ideal free habitat selection. Critics our understanding not only of the regulation sequences: it causes the organelles to change