Environ Biol Fish (2011) 90:111–120 DOI 10.1007/s10641-010-9723-9 Does a snapshot show the whole picture? Intrinsic limitations to growth inference of the short lived and fast growing Eric P M Grist & George D Jackson & Mark G Meekan Received: 23 November 2009 / Accepted: 26 September 2010 / Published online: 14 October 2010 # Springer Science+Business Media B.V 2010 Abstract Individual growth patterns in ecology are often determined from population field data through the use of regression and model selection inference analyses However, such approaches are typically unable to provide insight into dynamic processes when based upon collections of ‘snapshot’ data that consist of only a single observation for each individual We caution how model selection inference from size-at-age data may lead to growth models that are mis-specified in the case of species such as squid and fishes that display fast and variable growth and for which, field data of the early part of the lifespan are typically sparse and difficult to obtain E P M Grist (*) WCA Environment Ltd, Brunel House, Volunteer Way, Faringdon, Oxfordshire SN7 7YR, UK e-mail: ericgrist@googlemail.com G D Jackson Institute of Antarctic and Southern Oceanic Studies, University of Tasmania, Private Bag 77, Hobart, Tasminia 7001, Australia M G Meekan Australian Institute of Marine Science, University of Western Australia (MO96), 35 Stirling Highway, Crawley, WA 6009, Australia Keywords Longitudinal data Growth patterns Regression curve Introduction Regression methods are increasingly applied to infer individual growth patterns from size-at-age data, with the implicit assumption that a collection of snapshots of several individuals is equivalent to an observation of the complete growth record of the same individuals (e.g., Erickson et al 2004; Arkhipkin and Roa-Ureta 2005; Klaich et al 2008) However, several factors may combine to mask the most accurate description of growth from such snapshot data (Lipinski and Roeleveld 1990; Grist and des Clers 1999) Most obviously, these include missing data and sampling bias but also temporal or spatial pooling of field samples which can strongly influence the configuration of sizeat-age plots (Ricker 1979) In addition, the cumulative effects of individual variability may result in a greater scattering of size-at-age data points with increasing age, as typically observed in size-at-age plots of species that have short life spans and fast growth such as squid (Arkhipkin and Roa-Ureta 2005) and clupeid fishes (Meekan et al 2006) Such effects complicate regression-based inference and may imply that the ‘best fit’ curve is mis-specified where data are inadequate to support the relationship being fitted For example, a ‘best fit’ growth trajectory may exhibit an asymptotic tendency in the upper part of the size-at-age data set, 112 simply because that is where data of older individuals typically have the greatest variance ‘Asymptotic growth’ may then be an inevitable artefact of the statistical analysis, rather than a real biological process for some species For short-lived and fast growing species such as squid it is thus unsurprising that the form and processes that contribute to their growth continue to be debated but generally remain unresolved (Smith et al 2005; Challier et al 2006) In the case of squid, a broader understanding of growth has been gained from aquaculture (Hatfield et al 2001; Forsythe 1993) and size-at-age data derived from statoliths of individuals collected from the field (Jackson 1994; Perez and O’Dor 2000; Jackson and O’Dor 2001), as well as abundance fluctuations from general additive models (GAMS) applied to empirical environmental data (e.g., Bellido et al 2001) Predominantly, these have shown that the asymptotic growth at later life history stages associated with energy limitations, as occurs in fishes, appears to be absent in squid (O’Dor and Hoar 2000) so that their growth may be best described as non-asymptotic (Alford and Jackson 1993; Forsythe 1993) Arkhipkin and Roa-Ureta (2005) recently argued that squid growth can be best modelled by an S-shaped Schnute growth curve However, their argument relied wholly on regression analyses applied to size-atcapture-age field data collected for a variety of squid species with arbitrary conditions that samples should cover 2/3 of the lifespan and contain at least 150 individuals For the reasons outlined above, this raises a broader concern on how far such ‘best’ statistical models derived from field data may be applied in isolation to make valid inferences about dynamic ecological processes (Richards 2005) Here, we more generally show how the use of snapshots of size-at–age for regression analysis may result in the assignment of inappropriate growth models for fast growing, short-lived species These life history characteristics mean that the opportunity for repeated sampling of the same cohort is often very limited, so that snapshots are often the only data source available for growth analysis of such species When this is the case, we show that “best fit” growth models must be treated with caution as they may not provide an accurate representation of real patterns both at individual and population levels Environ Biol Fish (2011) 90:111–120 Materials, methods and results Field data set Records of individual growth were obtained for the fast growing tropical sprat Spratelloides gracilis by back calculation (biological intercept technique, Campana 1990) of standard lengths at daily intervals (thin lines, Fig 1a) from otolith radius data (Meekan et al 2006) These data were derived from a cohort (n=102) that hatched over a single summer season collected from the field using light traps (Meekan et al 2001) Back-calculation techniques assume that increments are laid down at daily intervals within otoliths and if used appropriately provide accurate and reliable information about growth histories of fishes (Vigliola and Meekan 2009; Wilson et al 2009) For the study species here, this assumption has been validated experimentally by Milton et al (1991) Size-at-capture data were also plotted (bold circles) with ages at capture ranging from 38 to 90 days The 52 day (=90-38) age range of the captured cohort thus spanned the greater portion (0.6=52/90) of the life history up to the point of capture Growth trajectories (thin lines) were obtained by conjoining straight lines between daily growth increments This fast growing species clearly displays an increasing individual variability in growth with increasing age Figure 1(b) shows the daily growth calculated from the otolith record (n=6,451, small dots) for each individual, together with respective ‘best fit’ curves determined by nonlinear mixed effects regression (Lindstrom and Bates 1990) of a logistic (solid), exponential (dashed) and simple two-phase (dash-dot) growth model (Appendix A) These candidate models were selected respectively as the most parsimonious sigmoid (‘S-shaped’), non-asymptotic, and piecewise descriptions of post hatch growth Regression modelling with retrospective back-calculated data sets requires a more sophisticated statistical treatment (than with snapshot data) which takes into account interdependences within the data from repeated measures of the same individuals Such data are also referred to as ‘longitudinal data’ and ‘mixed effects’ models are typically employed as here in their analysis (Zuur et al 2009) We then used model selection inference with the Akaike Information Criterion (AIC) in conjunction with associated Akaike weight (AW) to select the best Environ Biol Fish (2011) 90:111–120 113 Fig Field data for the fast growing tropical sprat Spratelloides gracilis (Meekan et al 2006): a size-at-capture-age (bold circles, n=102) with individual growth trajectories superimposed; b size-at-capture-age (bold circles, n=102) and backcalculated size-at-age from otoliths (small dots, n=6,451) with best fit curves determined by nonlinear mixed effects regression (Lindstrom and Bates 1990); c size-at-capture-age (bold circles, n=102) and d 38 day back-calculated sizeat-age (bold circles, n=102), with best fit curves determined by maximum likelihood regression Models are exponential (dashed), simple two-phase (dash dot) and logistic (solid) The corresponding AIC and Akaike weights are shown in Table out of the three ‘best fit’ candidate models (Appendix B) The Akaike weight is interpreted as the probability that a model is the best in the candidate set (Burnham and Anderson 2002) Results are displayed in Table The AIC and Akaike weights provide only a relative comparison between candidate models A handle on absolute goodness of model fit can be obtained by way of the r-squared (coefficient of determination) statistic also exhibited in Tables However, this statistic is not a robust measure for comparing nonlinear models so such a comparison should be treated as approximate Table Akaike information criterion (AIC) with corresponding Akaike weights and model rankings for each candidate model obtained from ‘best fit’ curves to the complete field capture and back snapshot data for Spratelloides gracilis of Fig ‘Best fit’ Parameters r2 p AIC Akaike weight Model rank Exponential A=13.34, m=0.02 0.7496 44,589 0.0000 Simple two-phase A=10.02, m=0.04, t*=11.59 0.8793 37,179 0.0000 Logistic A=5.95, m=0.09, K=40.29 0.9197 34,569 1.0000 S gracilis model Complete data (Fig 1b) Capture snapshot (Fig 1c) Exponential A=24.53, m=0.01 0.5191 603.74 0.4729 Simple two-phase A=20.62, m=0.01, t*=10.77 0.5229 604.93 0.2602 Logistic A=17.66, m=0.03, K=57.29 0.5231 604.88 0.2669 38 day-Back snapshot (Fig 1d) Exponential A=10.58, m=0.03 0.8571 587.22 0.0000 Simple two-phase A=7.10, m=0.05, t*=11.46 0.9297 520.61 0.0000 Logistic A=5.58, m=0.09, K=38.79 0.9394 498.76 1.0000 r2 coefficient of determination, p number of parameters 114 Consistent with the overall sigmoid shape of the otolith data set of Fig 1(b) to which the models were fitted, the logistic model curve ranked as the preferred model with the lowest AIC (= 34,569) and associated Akaike weight of 1.0000 (to decimal places) But typically in the field, only the size-at-capture-age data (solid circles) would be available to estimate the growth If only these snapshot data were available, what would be concluded from applying model selection inference? We performed a second regression analysis with the same three candidate models, using only size-at-captureage data Respective ‘best fit’ curves obtained with these fewer data (solid circles) using Maximum Likelihood Estimation (MLE) with the Gauss-Newton algorithm and Levenberg-Marquardt modifications for global convergence (Seber and Wild 1989), are shown in Fig 1(c) The exponential model (dashed) with AIC= 603.74 and associated Akaike weight of 0.4729 was ranked as the ‘best’ model but with little to visually distinguish it from the other two models (Table 1) This observation is consistent with the rule of thumb suggested by Burnham and Anderson (2002) that models within AIC units of the ‘best’ model are still considered to be supported by the data relative to the best model In summary, there was no compelling evidence that the logistic model was the ‘best’ description of growth from the candidate set of models because of (1) information deficiency on growth during the early part of the life history and (2) cumulative effects of individual variability at the time of capture The significance of these two limiting factors was investigated further by applying model selection inference using only the earliest possible snapshot of the complete data cohort (constrained by the youngest individual captured, which was 38 days old), obtained by back calculation to the respective size-at-age prevailing at 38 days before the capture date, as shown in Fig 1(d) With these snapshot data, model selection inference now strongly identified the logistic model as the best candidate model, with an Akaike weight of 1.0000 This clearly demonstrates the importance of incorporating information on growth in the early part of the life history Results and parameter estimates from this analysis were similar to those obtained with the full data record, with the logistic model again being selected as the best model and other candidate models being ranked in the same order as previously Environ Biol Fish (2011) 90:111–120 Figure shows the results of repeating the same exercise on each back-calculated snapshot from the otolith record from day 38 to day before the capture date From this more protracted analysis, it is evident that the cohort would have had to have been caught 17 days or more before the actual capture date for results to be in agreement with those previously obtained using the complete data record The information content in the size-at-age snapshot would only then have been sufficient for model selection inference to overcome the cumulative effects of individual variability and identify the logistic model as the best model, in agreement with the analysis performed on the complete otolith data record Field data set Culture studies in the laboratory have demonstrated that juvenile squid exhibit a two-phase growth pattern so that early post-hatch growth is exponential until a threshold point is reached, after which time growth shifts to a much slower rate (Forsythe and van Heukelem 1987; Forsythe 1993; Hatfield et al 2001; Andre et al 2009) Analyses of squid gladius field data suggest that later growth may typically be close to linear (Perez and O’Dor 2000) However, statolith ageing techniques have generally not been used for back calculating daily growth patterns, but rather for determining age at capture which hence produce only Fig Akaike weights for the exponential (x and dashed line), simple two-phase (+ and dash-dot line) and logistic (O and solid line) best fit candidate models for Spratelloides gracilis obtained from regressions performed at daily increments with backcalculated otolith size-at-age snapshots ranging from to 38 days before capture Unanimous support for the logistic model is not evident for at least 17 days before the capture date, when the lifespan coverage of the entire data set is 0.71 [=52/73=(90-38)/ (90-17)] Environ Biol Fish (2011) 90:111–120 one data point for each individual Squid aging is a very young field relative to the aging of fish from otoliths To date it has generally proven impractical to attempt back calculations of growth rate of individual squid from statolith microstructure because of uncertainties connected with growth increment width, nonplanar structure and other unresolved non-linear relationships Estimation of squid field growth must hence rely on such size-at-capture-age snapshots for different individuals, where age is obtained from the count of statolith increments Typical size-at-capture-age data (n=144) for open ocean squid are exhibited in Fig 3(a), obtained for the species Nototodorus gouldi (females) from trawl samples taken from four different regions in southern Australia that had hatched between January and April 2000 (see Jackson et al 2003) To minimize any sex specific variation in growth, only samples from the same sex (arbitrarily, females here) were chosen The sample covers the size range and maturity stages typically encountered in trawls for N gouldi, which is the most abundant ommastrephid squid in this region Respective ‘best fit’ curves were determined for, exponential, simple two-phase and logistic models by Fig Field size-at-captureage data (bold circles) for female Nototodorus gouldi squid (Jackson et al 2003), n=144, with a ‘best fit’ curves obtained by MLE regression for exponential [dashed, AW=0.0000], simple two-phase [dotted, AW= 0.0000] and logistic [solid, AW=1.0000] models; b simple two-phase model trajectories superimposed from a hatchling size A=0.1 g and exponential growth rate m=0.06 Simulated trajectories are shown c with size-at-captureage (stars) and d with ‘best fit’ curves obtained by MLE regression for exponential [dashed, AW=0.0000], simple two-phase [dotted, AW=0.0000] and logistic [solid, AW=1.0000] models The ‘best fit’ model with associated Akaike weight (AW) is given in square brackets throughout 115 MLE regression to these data and are also shown in Fig 3(a) The AIC values were 1,818, 1,820 and 1,784 with associated Akaike weights (to decimal places) of 0.0000, 0.0000 and 1.0000 respectively Hence the logistic model, with the lowest AIC, would be selected as the best model by model selection inference However, we note the sample contains few data for young fast growing individuals and so conveys little information on the early portion of an individual growth trajectory Forsythe (2004) has suggested this typical absence of information as a main reason why two-phase growth is rarely evident in field-based data of squid In terms of information content, the N gouldi data are thus analogous to a snapshot, such as that exhibited previously for the fast growing Spratelloides gracilis in Fig 1(c) Application of model selection inference to deduce the underlying growth pattern is therefore subject to similar intrinsic limitations To investigate the importance of information deficiency on juvenile growth, we conducted a simulation experiment in which a simple two-phase mechanistic growth model (Appendix A) was parameterised from the N gouldi size-at-capture-age data Figure 3(b) shows a set of simple two phase model 116 Environ Biol Fish (2011) 90:111–120 trajectories consistent with these snapshot data The trajectories were obtained by solving for t* and then finding the duration of the linear growth phase from the tangent linking the exponential growth phase to the final size (Appendix C) This enabled the level of individual growth variability in each phase of growth to also be estimated and represented empirically for import into stochastic simulations of growth (Appendix C) A typical realisation of the growth trajectories generated by the mechanistic model is shown in Fig 3(c) for a cohort of individuals hatching on the same date, together with the corresponding size-atcapture-age snapshot (stars) The inherent level of individual variability was sufficient to scatter trajectories so as to induce an apparent asymptotic tendency into the snapshot data In Fig 3(d) we show respective ‘best fit’ curves fitted to these data by MLE regression for the usual candidates of exponential (dashed), simple two-phase (dash dot) and logistic (solid) models In Table 2, the results and parameter values obtained with model selection inference applied to these simulated data are compared with those obtained previously with the field data of Fig 3(a) Not only are the respective best fit logistic model (AIC=1.0000) parameter values similar to those in Fig 3(a), but there was no support for either the simple two-phase or exponential models (AIC = 0.0000 in each case) from the data However, each individual in our simulation actually ‘grew’ along a simple two-phase model growth trajectory that was neither asymptotic nor S-shaped (quintessential properties of the logistic model) Further investigations were carried out by comparing distributions associated with (a) Akaike weight and (b) the r-squared statistic obtained for each of the three candidate models when fitted to 1,000 random snapshots generated by the simple two phase mechanistic model A relative comparison by Akaike weight is shown in Fig 4(a) and demonstrates that the logistic model (solid) strongly outperformed the other two candidate models, consistently achieving an Akaike weight above 0.95 In contrast, the exponential (dashed) and simple two phase (dot dash) candidate models rarely achieved an Akaike weight beyond 0.05 The corresponding distributions associated with ‘absolute’ goodness of fit as measured by the r-squared (coefficient of determination) statistic are shown in Fig 4(b) These are consistent with the rankings of Fig 4(a) but also indicate there was little to separate the ‘best fit’ curves for each model in absolute terms In conclusion, model selection inference was unable to identify the underlying dynamic that had generated the simulated data, even when that model of individual growth (the simple two-phase model) was included as a candidate model Without information on the mechanistic processes by which these data are generated, the potential for misidentifying the underlying growth process is hence readily apparent Table Akaike information criterion (AIC) with corresponding Akaike weights and model rankings for each candidate model obtained from the ‘best fit’ curves in Fig 3(a) with Nototodorus gouldi field capture snapshot data and in Fig 3(d) from a single realisation generated by the simple two stage model Discussion For many species, growth information is available only from size-at-capture-age data This is particularly ‘Best fit’ Parameters r2 p AIC Akaike weight Model rank Exponential A=4.76, m=0.02 0.6378 1,818 0.0000 Simple two-phase A=1.90, m=0.03, t* =195.23 0.5939 1,820 0.0000 Logistic A=0.01, m=0.05,K=1027.81 0.7153 1,784 1.0000 N gouldi model Field data (Fig 3a) Realisation (Fig 3d) Exponential A=2.95, m=0.02 0.5653 1,840 0.0000 Simple two-phase A=0.22, m=0.04, t*=192.44 0.5656 1,852 0.0000 Logistic A=0.0019, m=0.06, K=930.70 0.6558 1,827 1.0000 r2 coefficient of determination, p number of parameters Environ Biol Fish (2011) 90:111–120 Fig Regression model performance of the exponential (dashed) simple two phase (dash dot) and logistic (solid) models over 1,000 realisations of snapshot data generated from the simple two phase mechanistic model: a relative comparison by distribution of Akaike weight; b by distribution of r-squared coefficient (coefficient of determination) true for species that are fast growing and short lived, where repeated sampling of a growing cohort can be difficult to achieve, simply due to practical constraints Traditionally, these data have been used to infer a growth curve to describe individual growth in the field However, it is essential to recognise the inherent limitations of such field data sets that provide only a snapshot of each individual’s progress over the course of a brief lifetime Additionally, ecological processes may be better modelled by piecewise functions that often cannot be readily determined by maximum likelihood estimation methods (Grist 2000; Toms and Lesperance 2003) We showed that regression analysis with model selection inference can consistently fail to identify the most accurate model of growth due to a lack of fundamental information in snapshot datasets In our study, the reasons for this were identified as an absence of growth information 117 on younger individuals in tandem with the cumulative effects of individual variability increasing with age Observations with captive individuals may not necessarily extrapolate to the field, but it is still, nevertheless, possible to incorporate them into analyses for evaluation In the case of squid, since repeated observations of growth in time are available for individuals held in the laboratory and these clearly demonstrate two-phase growth, it seems reasonable to assume as a default hypothesis that the same process also occurs in the field The reasons for asymptotic growth prevailing in fish and several other organisms have been long established on the basis of physiology and extended life duration (von Bertalanffy 1957) Contrastingly, there are biologically sound reasons why squid growth should not be asymptotic and life duration relatively short (see review by Jackson and O’Dor 2001) In brief, they include: (1) a rapid and efficient digestive system with a protein-based metabolism that converts energy into growth rather than storage; (2) continual recruitment of new muscle fibres (hyperplasia) throughout growth in contrast to asymptotic fish growth in which hyperplasia ceases; (3) efficient use of oxygen and (4) low levels of antioxidative defence Additionally, O’Dor and Hoar (2000) have argued that the physical geometry of squid implies an absence of energy constraining factors such as oxygen limitation and declining growth rates usually associated with fish Hence it follows that whenever information is available on metabolic and physiological parameters, it is vital to incorporate them into models of individual growth (Grist and Jackson 2004; O’Dor et al 2005) Snapshots will often be the only type of size-at-age data available for many species, particularly when life history phases occupy habitats that are difficult to sample such as deepwater or oceanic environments For such species, back-calculation of growth histories from hard parts such as otoliths, statoliths or scales can provide an alternative means of generating longitudinal records to describe patterns of growth and maturation (Vigliola and Meekan 2009) When back-calculation is unavailable, so that analysis of snapshot data cannot be avoided, a better understanding of individual growth can be made by incorporating physiological, metabolic and growth information collected from both laboratory and field-based studies, so that models not rely wholly on statistical inference from snapshots Additionally, analyses of aged individuals that are grouped 118 Environ Biol Fish (2011) 90:111–120 according to hatch season or (preferably) hatch month that thus would be expected to have experienced more similar conditions, will reduce the chance of introducing artefacts into the analysis through pooling individuals that grew in different environments We have demonstrated by way of simple counter examples in this paper that to assert the validity or invalidity of a specific growth model purely on regressions to snapshot data may often prove inadequate With the proliferation of inference-based model selection methodology in applied ecology, there is a concomitant requirement for increasing awareness of its limitations to be recognised Researchers employing these techniques to field data collected for fast growing and short lived species should especially consider these when attempting to determine ecologically dynamic processes Appendix A Exponential growth The exponential growth model is the continuous function in which individual size s(t) at post hatch t is given by sðtÞ ¼ Aemt ðA1Þ where A is the initial hatchling size and m is the exponential growth rate coefficient hatch age t is given by the piecewise continuous function  sðtÞ ¼ Aemt at b 0< t t» < t t» ðA3Þ where A is the initial post hatch size, m is the exponential growth rate coefficient, t* is a threshold age, a and b are constants The most parsimonious description, specified by only parameters (A, m, and t*) which we refer to as the simple two-phase model, is where the growth trajectory continues after t* into the second phase at a tangent to the first phase exponential curve (Grist and Jackson 2007) This is consistent with the biological interpretation that physiological development achieved after exponential growth is completed would be sufficient to maintain that growth rate until the end of the lifespan (not unreasonable for squid) The size s(t) of an individual at age t by the simple two-phase growth model is hence given by  mt Ae 0< t t» sðtÞ ¼ ðA4Þ Ct þ D t » < t where C and D are constants, which at t* simulta» neously satisfy ds=dt ¼ mAemt ¼ C and sðt »Þ ¼ » » Aemt ¼ Ct » þ D ðso D ¼ Aemt ð1 À mt »ÞÞ Appendix B Logistic growth The Akaike Information Criterion (AICk) of a model k is defined as The logistic growth model is the asymptotic continuous function in which individual size s(t) at post hatch t is given by AICk ¼ À2 ln Lðb qj Þ þ 2p sðtÞ ¼ K þ ½ðK=A À 1ÞeÀm t Š ðA2Þ (for example, Richards 1959), where A is the initial hatchling size, m is the growth coefficient and K is the asymptotic value to which individual size must tend with increasing age ðA5Þ where Lðb qj Þ is the maximum likelihood estimate of the model parameters when outcome j (the data) is observed, and p is the number of model parameters in model k (for example, see page 66 of Pawitan 2001) Denoting AICmin as the minimum AIC of all the candidate models considered and defining the quantity Δk=AICk – AICmin, the Akaike weight wM of a particular model M is defined as Two-phase growth eÀð ΔM Þ=2 wM ¼ P Àð ΔkÞ=2 e Forsythe (1993) proposed a two-phase growth model for squid in which individual size s(t) at post where the summation in the denominator is taken over all the candidate models The Akaike weight wM of ðA6Þ k Environ Biol Fish (2011) 90:111–120 the model M can be interpreted as the probability that model M is the best model in the candidate set (Burnham and Anderson 2002) Appendix C Our objective is to obtain a handle on individual variability present in the data in order to investigate how it may affect snapshots of size and age There is no direct information available on the separate variations in the underlying growth parameters for hatch mass A, exponential growth rate m or transition time t* for this squid species In these circumstances, application of Occam’s razor implies that total variation is most effectively encapsulated by a single parameter distribution Such a distribution was determined heuristically by solving t* for each individual across all the data, with hatch mass A and exponential 119 growth rate m held at values typically estimated for juvenile open ocean squid of A=0.1 g and m=0.06 (e.g Grist and Jackson 2007) The t* distribution obtained gives a handle on individual variability during the first phase of growth and simultaneously gives rise to an associated dependent distribution for the duration of the linear second growth phase Whereas both these distributions must have a dependence on hatch mass and exponential growth rate, the nature of that dependence cannot be ascertained from the available information Simulations of expected snapshot data were generated by independently drawing from each of these two empirical distributions (which closely followed normal distributions) with the above typical values for hatch mass and exponential growth rate The distributions are shown in Fig and were used to generate the realisation data shown in Fig 3(c and d) References Fig Empirical frequency distributions (with superimposed normal distributions]) n=3144, of durations of a exponential growth phase (= transition age t*) and b second (linear) growth phase associated with Fig 3(b), that were used to generate the snapshot realisation of Fig 3(c and d) and Fig Alford RA, Jackson GD (1993) Do cephalopods and larvae of other taxa grow asymptotically? Am Nat 141:717–728 Andre J, Grist EPM, Semmens JM, Pecl G, Segawa S (2009) Effects of temperature on energetics and the growth pattern of benthic octopuses Mar Ecol Prog Ser 374:167–179 Arkhipkin AI, Roa-Ureta R (2005) Identification of ontogenetic growth models for squid Mar Freshwater Res 56:371–386 Bellido JM, Pierce GJ, Wang J (2001) Modelling intra annual variation in abundance of squid Loligo forbesi in Scottish waters using general additive models Fish Res 52:23–29 Burnham KP, Anderson DR (2002) Model selection and multimodel inference, a practical information-theoretic approach Springer Verlag, New York Campana SE (1990) How reliable are growth back-calculations based on otoliths? Can J Fish Aquat Sci 47:2219–2227 Challier L, Orr P, Robin J (2006) Introducing inter-individual growth variability in the assessment of a cephalopod population: application to the English Channel squid Loligo forbesi Oecologia 150:17–28 Erickson GM, Makovicky PJ, Currie PJ et al (2004) Gigantism and comparative life-history parameters of tyrannosaurid dinosaurs Nature 430(7001):772–775 Forsythe JW (1993) A working hypothesis of how seasonal temperature change may impact the field growth of young cephalopods In Okutani T, O’Dor RK, Kubodera T (eds) Recent advances in cephalopod fisheries biology Tokai University Press, pp.133–143 Forsythe JW (2004) Accounting for the effect of temperature on squid growth in nature: from hypothesis to practice Mar Freshwater Res 55:331–339 Forsythe JW, van Heukelem WF (1987) Growth In: Boyle PR (ed) Cephalopod life cycles vol II, comparative reviews Academic, London, pp 135–156 190 Environ Biol Fish (2011) 90:183–195 separate river fragments Although sturgeon population numbers are known to vary among river segments within the river (Haxton 2002, 2006), this was not evident from the genetic data Population structure due to isolation or differentiation was not detected between any of our sampling locations within the Ottawa River, with broad congruence among analytical approaches Levels of genetic diversity within and among lake sturgeon sites in the Ottawa River (observed heterozygosity and allelic richness) were comparable to data obtained from other lake sturgeon populations in the Great Lakes basin (McQuown et al 2003; Welsh et al 2003; Welsh and McClain 2004; Welsh et al 2008), as well as for other sturgeon species (Smith et al 2002; Wirgin et al 2002; Dugo et al 2004; Zhao et al 2005) The lack of variation in genetic diversity among river segments underscored the historical Fig Scatter plot of pairwise FST values against a geographic distance and b number of barriers between nine sampling sites within the Ottawa and the St Lawrence Rivers, showing correlation coefficients from partial Mantel tests groups specified (data not shown) Multiple runs with different parameters (assuming no admixture, increasing burn-in and resampling iterations, using varied subsets of loci) did not alter these results (data not shown) When Structure was run using population information, the results showed that the most reasonable number of populations was three, representing the St Lawrence River, Lac Dollard Des Ormeaux as a distinct second group, and a third comprised of all other Ottawa River sites, with Holden Lake and Chenaux appearing to be a mix of both the Ottawa River groups (Fig 4c) Discussion Despite extensive fragmentation of the Ottawa River by hydroelectric dams, there was little evidence of genetic erosion or isolation among lake sturgeon demes in the Fig Scatterplot of pairwise FST values versus number of barriers for sampling groups based on putative natural barriers (also the two oldest dam sites) for a within the Ottawa and the St Lawrence Rivers and b within the Ottawa River only, showing correlation coefficients from partial Mantel tests Environ Biol Fish (2011) 90:183–195 191 Fig Structure results for individual-based analysis of genetic structure within and among sampled segments of the Ottawa River, as well as outgroup populations, grouped by sampling location a population number (K) of for the Ottawa, St Lawrence and Mattagami Rivers; b K=2 for the Ottawa and St Lawrence Rivers; and c K=3 for the Ottawa and St Lawrence Rivers assuming no admixture and using a priori population information to identify putative genetic groups connectivity of the river, as there was no association between allelic richness or heterozygosity with size or flow order (upstream to downstream) of river segments The results of our study indicate that lake sturgeon formerly comprised a single panmictic population in the Ottawa River and that upstream movement by sturgeon was not prevented prior to development for hydroelectric purposes The slight but non-significant differentiation between the Ottawa River and the St Lawrence River concurred with earlier work by Guénette et al (1993) who reported weak differences between the Ottawa and St Lawrence Rivers based on mitochondrial DNA Evidence of low differentiation among lake sturgeon populations has been observed throughout most of the Great Lakes basin (McQuown et al 2003; Welsh et al 2008), despite very large distances between tributaries Welsh et al (2008) observed similarly low levels of population differentiation between the St Lawrence and Des Prairies River, which flows into the St Lawrence near Montreal, Quebec, and has also been impacted by dams, logging and pollution Other genetic surveys have similarly suggested that the St Lawrence River and its tributaries form part of a regional gene pool that also includes the lower Great Lakes (Ferguson and Duckworth 1997; McQuown et al 2003; Welsh et al 2008) The lack of genetic evidence for fragmentation in this system likely reflects the long generation time of lake sturgeon, and should not be interpreted as habitat connectivity Published studies indicate that genetic differentiation in fragmented habitats may only be detectable in species with short generation times (Carlsson et al 1999; Koskinen et al 2002; Heggenes and Roed 2006) For example, populations of European grayling (Thymallus thymallus) which have been isolated from one another since the 1930s (approximately 12 generations) exhibit genetic differentiation 192 that is positively correlated with the number of separating weirs (Koskinen et al 2002) By contrast, long generation times may buffer the genetic effects of habitat fragmentation and destruction (Gibbs 2001; O’Grady et al 2008) Similar results have been observed in other studies of animals with long generation times, including other fish (Lippé et al 2006; Reid et al 2007) and mammals (Goossens et al 2005) Given the long generation time of lake sturgeon (22–36 years; Haxton 2008), fragmentation has probably occurred too recently for neutral genetic markers to detect significant changes in genetic structure despite hydroelectric dams presenting absolute barriers to upstream movement In at least one section of the river, sampled adult sturgeon were older than the year of dam construction (Haxton 2006) It is therefore unlikely that we would be able to detect significant genetic consequences of barrier construction on lake sturgeon, as genetic effects would be reflected in biological time (generations) rather than sidereal time (years) (O’Grady et al 2008) Fragmentation effects on other sturgeon populations and species are therefore expected to be similarly difficult to detect based on genetic data (Guénette et al 1993; Ferguson and Duckworth 1997; Welsh and McLeod 2010), and are most likely to be detected using abundance and demographic data (Lenhardt et al 2006; Haxton and Findlay 2008) Although larval drift over dams could maintain some degree of connectivity among river segments via unidirectional (downstream) gene flow, assuming that at least some larvae survive to maturity and reproduce, the lack of differentiation among river reaches prevented testing our predictions of asymmetric gene flow Based on studies of larval drift, however, it seems more likely that the remaining diversity reflects longevity rather than larval dispersal and recruitment In a multi-year study of larval drift in an unimpounded portion of the Sturgeon River, Michigan, most sturgeon larvae and juveniles travelled downstream 45 km or less within 25 to 40 days after spawning (Auer and Baker 2002) In the Des Prairies River, Quebec, D’Amours et al (2001) observed a 30-fold reduction in larval catch success between sampling transects and 19 km downstream from a known spawning site These movement distances are substantially smaller than those separating the dams on the Ottawa River, suggesting that substantial downstream larval drift or dispersal is unlikely (Haxton 2002, 2006) Environ Biol Fish (2011) 90:183–195 The persistence of historical levels of genetic variability by lake sturgeon throughout the Ottawa River despite the presence of dams is encouraging, as retention of genetic diversity and adaptive resources is essential for enabling adaptive responses to environmental changes and selective pressures (Willi et al 2006) Based on published levels of diversity for other sturgeon populations and species (Smith et al 2002; Dugo et al 2004; Welsh et al 2008), other extant populations may have retained comparable adaptive potential Retention of genetic diversity despite fragmentation was similarly attributed to species longevity in copper redhorse (Moxostoma hubbsi) (Lippé et al 2006) and black redhorse (M duquesnei) (Reid et al 2007) This is encouraging from a conservation perspective, and suggests that lake sturgeon and other long-lived species have some protection against significant erosion of genetic resources despite documented historical population collapses and a troubled history of anthropogenic impacts (Harkness and Dymond 1961; Haxton and Chubbuck 2002) Simulations of habitat fragmentation in white sturgeon have indicated that local extinction risks are highly dependent on migration rates, with upstream populations at higher risk of extinction (Jager et al 2001) Presently, lake sturgeon among segments of the Ottawa River are connected only by potential downstream larval drift, and the prevention of upstream migration by dams is thought to be inhibiting population recovery in impounded reaches (Haxton 2006; Haxton and Findlay 2008) Upstream populations may be at risk of extinction before evidence of population differentiation is observed (Gibbs 2001; Jager et al 2001; O’Grady et al 2008) To prevent this, facilitating upstream movement of adult fish over dams would mimic natural migration of fish and may help mitigate the effects of habitat fragmentation on future generations The rate at which fragmentation will impact a species is also related to the habitat volume and quality in each fragment Demographic studies of lake sturgeon in the Ottawa River have shown population declines up to 80% and potential localized extirpation (Haxton 2006) In sites such as Allumette Lake with large patches of connected habitat, sturgeon exhibit high abundances and demographic diversity (Haxton and Findlay 2008, 2009) In more limited and disconnected habitats such as Lac des Chats, however, Environ Biol Fish (2011) 90:183–195 lake sturgeon are scarce and have size distributions skewed toward larger adults suggesting little or no recruitment in these sites (Haxton and Findlay 2008, 2009) Similar results have been observed for redhorse suckers (Moxostoma sp.) in fragmented rivers, where isolated populations show differing and habitat-linked demographic structure despite apparent genetic continuity (Reid 2008) In simulations of habitat fragmentation in white sturgeon, localized populations were more likely to become extinct when habitat degradation was also occurring (Jager et al 2001) In general, fragmentation simulations have shown that effective conservation should be based on both habitat and population management (Gibbs 2001) Removal or mitigation of barriers and/or facilitated movement of fish around dams have the potential to counteract the effects of fragmentation, but will only be successful if critical habitat patches are available and connected (Jager et al 2001) Conclusions Our study shows that lake sturgeon in the Ottawa River represent a single genetic population that reflects its formerly continuous (historical) habitat, rather than contemporary habitat patches As it is unlikely that the existing dams will be removed in the foreseeable future, some alternate means of connectivity between habitat patches should be established to maintain the genetic cohesion of lake sturgeon in the Ottawa River These findings have significant implications for the sustainable management and rehabilitation of other sturgeon populations and species (Ferguson and Duckworth 1997, Lenhardt et al 2006) Altering existing barriers to allow fish passage, translocation of wild adult or juvenile sturgeon, or stocking hatchery-reared sturgeon from local sources are all potential options and each have their own associated pros, cons and caveats (Jager 2006a, b) In addition to maintaining genetic diversity, an emphasis should also be placed on maintaining high quality habitat throughout the river and fostering linkages among critical habitats for all life stages By restoring some degree of connectivity among habitat patches, these actions will significantly mitigate existing fragmentation effects and help ensure the long-term persistence of this unique species 193 Acknowledgments We would like to thank the field crews from the Ontario Ministry of Natural Resources Aquatic Science Unit, Pembroke and Kemptville Districts and the Quebec Ministry of Natural 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MR, Taylor CM, Pigg J (1991) Upstream extirpation of four minnow species due to damming of a prairie stream Trans Am Fish Soc 120:98–105 Wirgin I, Waldman J, Stabil J, Lubinski B, King T (2002) Comparison of mitochondrial DNA control region sequences and microsatellite DNA analyses in estimating population structure and gene flow rates in Atlantic sturgeon Acipenser oxyrinchus J Appl Ichthyol 18:313–319 Zhao N, Ai W, Shao Z, Zhu B, Brosse S, Chang J (2005) Microsatellites assessment of Chinese sturgeon (Acipenser sinensis Gray) genetic variability J Appl Ichthyol 21:7–13 Environ Biol Fish (2011) 90:197–205 DOI 10.1007/s10641-010-9732-8 Feeding efficiency and food competition in coexisting sexual and asexual livebearing fishes of the genus Poecilia Kristin Scharnweber & Martin Plath & Michael Tobler Received: 15 January 2010 / Accepted: 12 October 2010 / Published online: November 2010 # Springer Science+Business Media B.V 2010 Abstract Considering its immediate costs of producing dispensable males, the maintenance of sexual reproduction is a major paradox in evolutionary biology Asexual lineages that not face such costs theoretically should replace sexuals over time Nonetheless, several systems are known in which closely related sexual and asexual lineages stably coexist In the present study, we studied a sexual/asexual mating complex of a sperm-dependent parthenogenetic fish K Scharnweber (*) Department of Biology and Ecology of Fishes, Leibniz Institute of Freshwater Ecology & Inland Fisheries, Müggelseedamm 310, 12587 Berlin, Germany e-mail: scharnweber@igb-berlin.de M Plath Department of Ecology and Evolution, Institute of Ecology, Evolution and Diversity, J.W Goethe University Frankfurt, Siesmayerstrasse 70-72, Frankfurt am Main 60054, Germany M Tobler Department of Wildlife and Fisheries Sciences, Texas A&M University, 2258 TAMU, College Station, TX 77843, USA Present Address: M Tobler Department of Zoology, Oklahoma State University, 501 Life Sciences West, Stillwater, OK 74078, USA (amazon molly, Poecilia formosa) and its sexual congeners, the sailfin molly P latipinna and the Atlantic molly P mexicana We asked whether differences in feeding behavior could contribute to their stable coexistence We conducted a laboratory experiment to compare feeding efficiencies and also measured the competitive abilities between the two reproductive forms Additionally, we measured gut fullness of fishes caught in natural habitats Contrary to our predictions, we could not find P formosa to be less efficient in feeding We argue that food competition in mollies plays a minor role in mediating coexistence between closely related asexual and sexual mollies Keywords Aggressive interactions Competition Evolution of sex Foraging Gynogenesis Introduction Sexual reproduction prevails in nature, and especially in vertebrates only very few asexual forms have been described (about 50 species in 22 genera: Vrijenhoek et al 1989) The few systems in which asexual and closely related sexual lineages coexist offer a unique opportunity to examine the costs and benefits associated with both reproductive strategies (Moore and McKay 1971; Vrijenhoek 1979; Case and Taper 1986; Jokela et al 2009) The system investigated here includes the amazon molly, Poeci- 198 lia formosa, which is a unisexual, livebearing fish (family Poeciliidae) with a reproductive mode called gynogenesis (Kallman 1962; Hubbs 1964; Balsano et al 1972) In this special form of parthenogenesis, sperm of a host species is used to trigger the onset of embryonic development (Schlupp 2005), but fusion of the gametes does not occur (Hubbs 1964; Balsano et al 1985) Consequently, paternal genetic material is not usually incorporated during zygote formation, and offspring are simple clones of the mother (Rasch et al 1982; Turner 1982) The amazon molly arose as a hybrid between the Atlantic molly (P mexicana) and the sailfin molly (P latipinna), which also serve as sperm donors in the natural habitats (Hubbs and Hubbs 1932; Schlupp et al 1998) The spermdependency of the amazon molly has important ecological consequences, forcing it to coexist with closely related sexual species in the same habitat (Niemeitz et al 2002), where they actually form mixed-species shoals (Schlupp and Ryan 1996) In the coastal areas of Texas and the Mexican state of Tamaulipas, P formosa occurs sympatrically with P latipinna, while it is sympatric with P mexicana in rivers and streams in northeastern Mexico (Darnell and Abramoff 1968; Miller 1983; Schlupp et al 2002) The apparently stable coexistence of the two different reproductive modes is not easily explained considering the costs of sexual reproduction: asexuals, being allfemale, have a much faster population growth rate, because they not produce dispensable males contributing nothing but sperm to reproduction (Maynard Smith 1978) Sexuals also pay the cost of meiosis; due to recombination only half of their genes are passed to the next generation, and successful genotypes can be destroyed in every reproductive cycle (Williams 1975) Consequently, asexual reproduction should be a more successful strategy at least in the short term, and everything else being equal, asexuals should outcompete sexuals over time (Maynard Smith 1978; Bell 1982; Lively and Lloyd 1990; Ladle 1992; Barton and Charlesworth 1998) In mixed sexual/ gynogenetic systems like the amazon molly system, local extinction of the sexual forms should inevitably be followed by the local extinction of the asexuals due to the lack of sperm donors (Schlupp 2005; Kokko et al 2008) While metapopulation dynamics theoretically can explain the coexistence of the different reproductive Environ Biol Fish (2011) 90:197–205 modes (Kokko et al 2008), most models of coexistence assume some disadvantages for asexuals that balance the costs of sex (West et al 1999; Agrawal 2001) In addition, (slight) ecological differentiation or specialization between reproductive forms may also mediate coexistence (see the Frozen Niche Variation Model; Vrijenhoek 1979; Wetherington et al 1989; Vrijenhoek and Pfeiler 1997; Vrijenhoek 1998) For example, in a similar system of asexual and sexual fish (Poeciliopsis monacha-lucida) that mainly consume algae and detritus, the reproductive modes exhibited a reduced dietary overlap (Gray and Weeks 2001) and differed in the efficiency of handling different prey items (Weeks et al 1992) In studies of food consumption, P formosa were found to have a higher feeding rate when exposed to winter conditions than P latipinna (Fischer and Schlupp 2010) Furthermore, neonates of P formosa were shown to be more sensitive towards food stress (Tobler and Schlupp 2010) These differences in feeding ecology may contribute to the stable coexistence of both reproductive modes in the Poeciliasystem The present study was initiated to test further factors that may differ between the two reproductive modes For example, costs of sexual reproduction could be balanced if asexuals were inferior in acquiring resources Hence, we tested whether asexuals and sexuals differ in their feeding efficiency and competitive abilities In previous studies, P formosa was found to spend less time feeding than their sexual congeners (Heubel and Plath 2008; Padur et al 2009) However, the focus of those studies was on feeding time reduction by male harassment, and the experimental design did not allow for an assessment of competition between different females To examine whether asexuals have reduced competitive abilities as compared to sexuals, we designed a similar experiment allowing individual females (sexual or asexual) to feed in company of either a conspecific or heterospecific female, and we scored the time spent foraging as well as aggressive interactions If asexuals have a disadvantage in foraging, this could also be reflected in lower gut fullness in the field With a second approach, we therefore augment our data set by measuring gut fullness of asexual (P formosa), and sexual (P latipinna and P mexicana) females collected from various natural populations Environ Biol Fish (2011) 90:197–205 199 Material and methods Laboratory experiments For the experiment on feeding efficiency and competition, P formosa and P latipinna were caught from the Guadalupe River in central Texas (Table 1) and transferred to the laboratory at Texas A&M University in College Station To avoid any effects caused by sexual harassment (Plath et al 2003; Heubel and Plath 2008), only females were used in the feeding experiment Fish of both species, including males, were maintained in 120×30×40 cm aerated holding tanks at 24°C and an illumination cycle of 12 L:12D Fish were fed twice a day with “Hikari tropical algae wafers” food tablets Test subjects could acclimatize to the laboratory for at least weeks before the feeding experiments and thus had enough time to familiarize with the food source All fish involved in a trial were starved for 24 h prior to the start of the experiment, making sure that they were motivated to feed throughout the feeding tests We measured all fish for standard length (SL) to the nearest mm after experiments were ended To test the feeding efficiency and competitive ability of the two species, focal fish were successively allowed to feed with a conspecific and a heterospecific competitor The order of the two treatments was balanced and alternated between trials The experimental tank (49×27×24 cm) was equipped with two clear Plexiglas cylinders (diameter 9.5 cm), one on each side A food tablet was placed on the bottom in the front portion of the tank The focal fish was introduced in one cylinder and the competitor in the Table Study sites of coexisting asexual (P formosa) and sexual mollies (P latipinna, P mexicana) Study site River basin Latitude Longitude Sites with P latipinna Central Texas Guadalupe river 29.857 −97.868 Lincoln Park Rio Grande (Bravo) 25.900 −97.479 Weslaco Rio Grande (Bravo) 26.121 −97.962 Sites with P mexicana Mante Río Guayalejo 22.705 −99.001 Barretal Río Soto La Marina 24.079 −99.123 Rio Juanillo Río San Fernando 24.608 −98.299 other cylinder After of acclimatization, the cylinders were gently removed We then recorded the time passed until the focal female started to feed on the food tablet (latency time) Trials in which individual fish did not start to feed were terminated after 20 and fish were given a ceiling value of 1,200 s If the focal fish started to feed, a 5-min observation period began, during which we recorded the time the focal female spent feeding on the food tablet Furthermore, aggressive behaviors, including biting, chasing, and tail-beating (see Parzefall 1969; Parzefall 2001), were quantified, and we distinguished between aggressive behaviors directed from the focal female toward the competitor and vice versa In total, we tested 62 individuals (33 P formosa and 29 P latipinna) Gut fullness in natural populations Data on gut fullness were reanalyzed from a previous study investigating patterns of trophic niche segregation by analyzing gut contents (Scharnweber et al., in prep.) We investigated three mixed populations of P formosa and P latipinna in Texas, USA, including an introduced population in the Guadalupe River (Hubbs et al 1953), and three populations of P formosa coexisting with P mexicana in Tamaulipas and Nuevo León, Mexico (Table for collection sites) To eliminate potential confounding effects of sex differences, only females were included in the analyses In total, we investigated 394 individuals (227 P formosa, 100 P latipinna, and 67 P mexicana) Collections took place between March and August 2009 Fishes from the sites Barretal, Central Texas, Weslaco, and Brownsville were collected twice, with at least months in between (i.e., during spring and summer) All specimens were caught using a seine (length m; mesh-width mm) Immediately upon capture, fish were euthanized using MS222 (Tricaine Methanesulfonate) and fixed in a 10% formaldehyde solution for subsequent analyses in the laboratory Whenever available, 15 individuals of each species and from each site were measured for gut fullness To so, fish were dissected, and the volume of the tubular intestine (including its content) was determined by introducing it into a measuring cylinder filled with tap water and measuring the volume of water replacement Then gut contents were carefully removed and the volume of the empty intestine was measured again as described above The difference between the two 200 volumes was used a measure of gut fullness We assumed that individuals that were more efficient foragers would have more food in their intestines Statistical analyses To analyze differences in feeding efficiency, General Linear Models (GLM) with repeated measures design were performed with latency time or total feeding time of the focal fish as dependent variable (with either a conspecific or heterospecific fish present as the repeated measures) and species identity of the focal fish as independent variable Likewise, for the analysis of aggressive behavior, numbers of aggressive behaviors (sum for all three behavior categories) directed against or received from the competitor were subjected to similar rmGLM To assess differences in gut fullness, fish collected from the same site but different sampling periods were pooled for data analysis The volume of gut contents was square root-transformed and subjected to analysis of covariance (ANCOVA), in which gut content volume was used as the dependent variable, and reproductive mode, host species (P latipinna or P mexicana), and study site (nested within host species) were treated as independent variables Standard length was used as a covariate For further analysis of temporal variation of gut fullness, we included only sites that had been sampled twice We ran a second ANCOVA, using the square root-transformed volume of gut contents as dependent variable and reproductive mode, host species (P latipinna or P mexicana), and study site (nested within host species) as well as time (spring/summer) as independent variables Standard length was used as a covariate In both analyses effect sizes were approximated using partial eta squared (η2p) Environ Biol Fish (2011) 90:197–205 Table Results of repeated measures General Linear Models (rmGLM) using (a) latency and (b) feeding times of individual focal females interacting with a conspecific and heterospecific partner female as dependent variables (repeated measures, rm) In (c) numbers of aggressive behaviors directed toward the partner female and in (d) numbers of aggressive behaviors received from the partner female when competing for food were the dependent variables Effect df F P η2p (a) Latency time until feeding commenced Within-subjects effects Rm 2.763 0.102 0.044 Rm×focal fish species 5.777 0.019 0.088 0.077 0.782 0.001 Error 60 Between-subjects effects Focal fish species Error 60 (b) Feeding time Within-subjects effects Rm 0.172 0.679 0.003 Rm×focal fish species 0.107 0.744 0.002 0.964 0.330 0.016 Error 60 Between-subjects effects Focal fish species Error 60 (c) Aggressive behavior directed against competitor Within-subjects effects Rm Rm×focal fish species Error 2.843 0.097 0.045 4.186 0.045 0.065 1.236 0.271 0.020 60 Between-subjects effects Focal fish species Error 60 (d) Aggressive behavior received from competitor Within-subjects effects Rm 0.879 0.352 0.014 Rm×focal fish species 0.001 0.971 [...]... effect of PS on G3, a positive direct effect of G3 on FL, and, consequently, a negative indirect effect of PS on FL The path model explained about 50% of the variance in G3 and about 56% of the variance in FL The effects of relevant environmental variables (i.e., SSTB and ZP) on G3 and FL were not significant Therefore, we used multiple regression to determine the effects of ZP, SSTO, and PS on growth of. .. mass) of parental fish was significantly lower than that of non-parental males (DuFresne et al 1990) This suggests that some aspect of parental care is costly, in terms of energy, for the parental fish However, it is not known which aspect of care this cost can be attributed to, although it is often hypothesised that it is likely to be fanning Higher fanning rates result in greater oxygenation of the... climate? Effects of warming, nutrient addition and fish on phytoplankton in shallow lake microcosms J Appl Ecol 40:782–7 92, http://dx.doi.org/10.1046/j.13652664.2003.00839.x Ostlund-Nilsson S, Mayer I, Huntingford FA (2007) The biology of the three-spined stickleback: Marine Biology Series 8, CRC Press 129 Pepin P (1991) Effect of temperature and size on development, mortality, and survival rates of the pelagic... experiments Freshwater Biol 47:2216–22 32, http://dx.doi.org/10.1046/j.1365-2427.2002.00963.x Wootton RJ (1976) The biology of the sticklebacks Academic Press, New York, p 387 Wootton RJ (1985) Effects of food and density on the reproductive biology of the three-spine stickleback with a hypothesis on population limitation in sticklebacks Behaviour 93:101–111 Environ Biol Fish (2011) 90:131–142 DOI 10.1007/s10641-010-9725-7... direct effect of POD on ICE, and, consequently, a negative indirect effect of ALPI on ICE, which was countered by a positive direct effect of ALPI on ICE of nearly the same strength These also resulted in a significant indirect effect of SAT on PDO In addition, we observed a significant direct effects of ALPI on SI, PDO on SI, and SI on ICE (Fig 5 and Table 4) We next analyzed the path model of the relationships... history of O keta (i.e., G1, SR, PS) between 1961 and 2002 (χ2 =4. 12, p=0.25, N= 40) The results indicated that SSTO directly affected G1 (Fig 6 and Table 5) In addition, the model revealed a significant direct effect of G1 on SR, and, consequently, an indirect effect of SSTO on SR The direct effect of G1 on SR was much stronger than the indirect effect of SST on SR, as indicated by the value of standardized... during the later period of life history in the Bering Sea A path model of the variables ZP, SSTB, PS, G3, and FL (Fig 7 and Table 6) was analyzed between 138 Environ Biol Fish (2011) 90:131–142 Table 4 Summary of the path model in Fig 5 The direction of the effect tested is indicated by the arrow (e.g., the effect of SAT on AO: SAT→AO) Paths fixed at zero are indicated as “0” Direction of effect Standardized... extensions of the box walls to the surface; Fig 1a) Overall, the fish spent 55% of their time away from their nests, and 45% of their time at their nests, with the rank order of time spent in behaviour being: hovering, fanning, prodding, glueing, cleaning, and building (Fig 1a) We did not detect statistically significant differences in time spent on fanning, number of events of fanning, or duration of fanning... behaviour and success of the male threespined stickleback We defined reproductive success as the ability of the male to maintain nests, to oxygenate fertilised eggs, and to hatch embryos that live for more than 10 days post-hatch Environ Biol Fish (2011) 90:121–129 Materials and methods The experiments were conducted at the University of Liverpool, UK, under authorisation of the UK Home Office, in an isolated... d.f. =2, p=0.01) Similarly to Experiment 1 there was a lower success of incubation with increased temperature Of the fish that completed nest building approximately 19% died whilst trying to incubate fertilised eggs The nine fish which successfully incubated eggs produced a total of 81 live larvae (i.e 9±2.5 larvae per successfully incubating fish), again with a similar number of larvae regardless of