Refuge availability and within-species differences in cannibalism determine population variability and dynamics

Theoretical studies show that both cannibalism and intraspecific resource competition can have major effects on population dynamics. Cannibalistic intensity, offspring size, harvesting and refuge a ...


INTRODUCTION
Cannibalism is a common phenomenon in nature and may have strong impacts on population dynamics (Ricker 1954, Fox 1975a, Polis 1981, Hastings and Costantino 1991, Cushing 1992, Claessen et al. 2004. Theoretical studies have shown that density dependent cannibalism and a small time-delay is enough to generate population cycles and that intense cannibalism may lead to large amplitude cycles and even extinctions (Hastings andCostantino 1991, Claessen and. In spite of this, there are few clear empirical examples of cannibal driven cycles (but see Dennis et al. 1997, Elliott 2004, Wissinger et al. 2010. Still, recruitment regulation by cannibalism, which is the key element behind cannibal-driven cycles has been recorded in several species including fish (Polis 1981, Andersson et al. 2007, the flower beetle Tribolium (Hastings and Costantino 1991, Dennis et al. 1997, Benoit et al. 1998, salamanders (Wissinger et al. 2010), leeches (Elliott 2004), isopods (Leonardsson 1991) and backswimmers (Fox 1975b, Orr et al. 1990.
Cannibalistic interactions are typically sizedependent and in particular the smallest sized victim that a cannibal can possibly capture has been shown to be crucial for dynamics (Claessen et al. 2002). For example, the lower size limit to cannibalism differs between species and has been shown to determine the population dynamics of different fish species . Furthermore, the size of the offspring is also of importance for the dynamics. With large and intermediate hatchling sizes, cannibalism can be regulating and harvesting adults will in such populations have a destabilising effect (van Kooten et al. 2007(van Kooten et al. , 2010. Correspondingly, experimental studies in Tribolium systems have shown that harvesting of adults can result in both stabilisation as well as destabilisation depending on the intensity of the harvesting (Dennis et al. 1995(Dennis et al. , 1997.
The presence of refuges is generally considered to stabilise population dynamics. In predatorprey systems refuge availability for prey results in decreased predator efficiency, which dampens or even extinguishes predator-prey cycles (Rosenzweig and MacArthur 1963, Stenseth 1980, Krivan 1998. Refuge availability will also reduce cannibalism and in the case where cannibalism induces population cycles in the absence of refuges, addition of refuges can be hypothesised to stabilise dynamics. However, the situation is more complex since prey and predator belong to the same population and, may also compete for the same resources. Increasing competition for resources within a population may lead to cohort cycles . Thus refuge availability may have a destabilising effect when decreased cannibalism results in higher population densities and subsequent intensified competition (Cushing 1991, van den Bosch andGabriel 1997). Experimental studies on how cannibalistic population dynamics are affected by refuges are however few (but see Benoit et al. 1998Benoit et al. , 2000, and none have examined the population dynamical effects of increased competition among and within cohorts. Here we used two strains of the common guppy (Poecilia reticulata), that differ in both overall cannibalistic voracity and offspring size, to study the effects of cannibalism and resource competition on population dynamics. We manipulated the availability of structural refuges and harvesting intensity on large cannibals in long term population experiments and made the following predictions: (1) The scope for cannibalism to affect recruitment is large in both populations due to the large offspring size and the low per capita fecundity. In the absence of refuges we therefore expected the populations to display cannibal-driven cycles. We further expected that the population with higher cannibalistic propensity and smaller offspring should show more fluctuating dynamics. (2) We expected harvest of large females to have a destabilising effect as it could allow pulses of recruits to break through the cannibal regulation. (3) We expected the presence of refuges to reduce cannibalism and to potentially have a stabilising effect on population dynamics. Still, because refuge availability may lead to intensified resource competition as a result of increased survival of juveniles, fluctuations influenced by cohort competition could counteract the stabilising effect of reduced cannibalism. To study this we carried out cross correlation analyses of the timing of peaks in densities of different stages, as the timing of these differs between the fluctuations driven by cannibalism and those driven by cohort competition.

Study organism
Our study organism, the common guppy Poecilia reticulata, is a small poecilid fish that lives in freshwater ponds and streams. Litters arrive at approximately 25 days interval under laboratory conditions (Reznick and Yang 1993) and the generation time is 10 weeks or longer in laboratory depending on food availability (Reznick and Bryga 1987; see also the Appendix). Many studies on life-history characteristics have been performed with guppies in Trinidad where they coexist with different predators and have evolved different life-history characteristics in response to the predation environment (Magurran 1998). Guppies from high predation environments have a smaller size and lower age at maturity, a larger reproductive allocation and smaller sized offspring (Magurran 1998, Reznick et al. 2001. One of the populations in this study originated from a high predation site in the v www.esajournals.org Turure River in the Oropuche drainage situated on the southern slopes of the Northern Range in Trinidad. The other population originated from a low predation site in the Quare River also on the southern slopes of the Northern Range. It is known that the per capita fecundity of Turure guppies from high predation environments is higher than that of Quare guppies from low predation environments (S. Auer, unpublished data) and that the propensity for cannibalism and cannibalistic voracity is higher for the Turure high predation population in laboratory conditions when no refuges are present (Nilsson et al. 2011). It is also known that cannibal efficiency is affected by the presence of refuges and that juveniles increase refuge use in response to cannibal presence (Nilsson et al. 2011).

Experimental setup, treatments and sampling
The experiment was performed at the Department of Ecology and Environmental Science, Umeå University, Sweden, from May 2007 to August 2009. Forty aquaria were used in the experiment, each with a volume of 132 L receiving 20 L of water per hour from a circulation system. Feeding took place 8 times per day when two portions of fish food (2 3 9 mg sera micrograin) were dropped on the water surface in each aquarium. The treatments were set up as a full factorial design with refuges and harvesting for each population (Turure and Quare). There were 5 replicates of each treatment including controls, harvesting treatments, refuge treatments and refuge and harvesting treatments. In the refuge treatments, 4 refuges made of green plastic filter material were placed in each aquarium (weight 55 grams each) spread over a volume of 5 L (see the Appendix for a photograph). Two of the four refuges were positioned close to the bottom with the help of a small piece of metal. The harvesting targeted females larger than 25 mm in standard length, a size at which guppies have become efficient cannibals (Nilsson et al. 2011). The harvesting rate was 0.02 per day and the total number of individuals to be removed was calculated after each sampling and subsequent removal of females took place once a week. Each aquarium was stocked with populations with identical size-structure, consisting of 82 individuals ranging between 6.5 and 28 mm in size (standard length). When populations went extinct, aquaria were restocked with the same size structure.
Sampling took place every fifth week and the experiment lasted for 116 weeks resulting in 22 sampling occasions in total. During sampling, all individuals in each aquaria were removed with the help of a large net and sorted into males, juveniles and females (males were identified by inspection of the gonopodium, juveniles and females were separated in a casual manner based on size). Each group was photographed and afterwards returned to the aquaria. The photographs were analysed using an image analysing program where all individual were counted and measured.
The populations were divided into 6 classes: vulnerable juveniles (6 , L 10 mm), nonvulnerable juveniles (10 , L 12 mm), intermediate sized individuals (12 , L 17 mm), if not classified as males) small females (17 , L 20 mm), cannibals (L . 20 mm) and males. Guppy juveniles are most susceptible to cannibalism when they are newborn, and as they grow in size their risk of being cannibalised decreases. The upper size limit for the vulnerable size class (10 mm) was determined by the size threshold where juveniles were no longer susceptible to cannibalism, obtained from previous experiments estimating attack rates with both Turure and Quare populations (Nilsson et al. 2011).

Statistics
Analyses of variances were performed for overall treatment effects on the coefficient of variation (CV ¼ standard deviation/mean, log transformed before the analysis) for total population density. Population that went extinct and restocked populations were included in this analysis. The significance level was generally set to P , 0.05 although the major part of the main analyses resulted in significant levels that were substantially lower. We therefore did not carry out any formal corrections for multiple testing (Abdi 2010) but rather discuss cases with limited significance when relevant. To detect cycles and estimate periodicity, autocorrelations were estimated for total population density, density of vulnerable juveniles and cannibal density. Cross-correlations were estimated for cannibal vs. vulnerable juvenile density and vulnerable juvenile density vs. the density of intermediate sized individuals as well as vulnerable juvenile density vs. non-vulnerable juvenile density (the two latter presented in the Appendix). We used cross-correlations to assess the timing of peaks in densities of different stages since this is a good indicator of what kind of cycles are present.

Coefficient of variation
The Turure populations showed a higher variation (coefficient of variation, CV) in total population density compared to the Quare populations ( Fig. 1, Table 1). The presence of refuges decreased population variability, whereas harvest increased population variability in both populations (Fig. 1, Table 1, Appendix). Population and refuges had very strong effects on variation in density whereas the effect of harvest was weaker and would turn non significant if any correction for multiple tests were made.

Harvesting yield
Harvesting had a dramatic effect in the Turure populations without refuges and all replicates of the Turure harvest treatment went extinct. Three of these populations were restocked of which one went extinct again. One replicate of the Turure control treatment also went extinct. The total number of harvested individuals was lower in the refuge treatments (F 1,16 , p ¼ 0.011). On average, 13 individuals in the Turure harvest treatment, 7.8 individuals in the Turure harvest and refuge treatment, 10.8 individuals in the Quare harvest treatment and 6 individuals in the Quare harvest and refuge treatment were harvested during one year of the experiment. Two replicates from the Turure harvest treatment without refuges present were excluded from the analysis as they went extinct at an early stage and hence had a very low yield.

Autocorrelations
The effects of population origin and refuges on  v www.esajournals.org population variability were much stronger than the effect of harvesting. This result was partly a result of the extinctions in several of the harvested populations and partly a result of that the harvesting yield was low when refuges were present. We will therefore focus the more detailed analyses of population variability using autocorrelation and cross-correlation analyses on the effects of population origin and refuges. The total density autocorrelations for the Quare control treatment showed a clear negative correlation around lag 7 (significant at the p ¼ 0.05 level in 4 out of 5 replicates) and a positive correlation around lag 15 (significant in all 5 replicates) corresponding to a cycle period of 75 weeks ( Fig. 2A). The total density autocorrelations for the Turure control treatment showed a negative correlation around lag 10 (significant in 4 out of 4 replicates, one replicate went extinct before the 10th sampling) and a tendency for a positive correlation around lag 18 (present in 4 replicates, significant in one replicate). These results suggest that the periodicity of the Turure populations (90 weeks) was longer than that of the Quare populations ( Fig. 2A). In contrast to control populations, no clear patterns were seen in the total density autocorrelations for the Quare refuge treatment or the Turure refuge treatment (Fig. 2B). More detailed analyses of total density autocorrelations that support the results presented above are given in the Appendix.
The Quare population showed substantial peaks in juvenile densities in all treatments, although the relative magnitudes of peaks were higher in the control treatments due to overall lower densities (Fig. 3). The peaks in vulnerable juveniles in the Turure populations were generally higher in the refuge treatment, but, the relative magnitude of these peaks was higher in the control treatment when taking the low densities in controls into account. Vulnerable juvenile density autocorrelations did not show any strong patterns for the Quare control treatment, which was also the case for the Turure control treatment (Fig. 4A). In contrast, vulnerable juvenile density autocorrelations for the Quare refuge treatment showed negative correlations at lag 5 and also around lag 15 (significant in 3 out of 5 replicates) and positive correlations around lag 10 (present in 4 replicates but not significant) corresponding to a cycle period of 50 weeks (Fig. 4B). The vulnerable juvenile density autocorrelations for the Turure refuge treatment showed similar patterns to the Quare refuge treatment described above but were less clear (Fig. 4B). In summary, cycles with a periodicity of approximately one and a half years (75 weeks) were present in total density for the Quare control treatment, while the periodicity in Turure control was somewhat longer (90 weeks). Cycles with the periodicity of one year (50 weeks) appeared in the density of vulnerable juvenile density for the Quare refuge treatment and a v www.esajournals.org tendency for a similar pattern was also present in the Turure refuge treatment.

Cross-correlations between cannibal and vulnerable juvenile density
Large females are both efficient cannibals and have a high reproductive output. We performed cross-correlation analyses with the densities of vulnerable juveniles and cannibals to evaluate if high juvenile densities co-occurred with high cannibal density. A lag of þ1 in the cannibalvulnerable cross-correlation means that a peak in cannibal density is followed by a peak in juveniles on the following sampling occasion. This is a pattern expected for dynamics driven by cohort competition but not for cannibal-driven cycles (Claessen et al. 2000).
The Quare control treatment showed considerable variation between replicates in the cannibal-vulnerable density cross-correlation. The significant correlations were in general negative and occurred at various lags (À1, À2, þ3, þ7; Fig.  5A). The Turure control treatment showed positive correlations around lag À5, although the correlations would span over several lags and were not significant. Negative correlations were observed at lag þ4 and þ5 (also spanning over several lags, significant in 2 replicates; Fig. 5A). Importantly, there were no significant positive correlations at lag 0 or þ1 for any of the control v www.esajournals.org populations, which suggest that a high cannibal density did not result in high recruitment, furthermore suggesting the lack of fluctuations driven by cohort competition.
In contrast to control populations, cross-correlations between cannibal and vulnerable juvenile densities for the Quare refuge treatment showed positive correlations around lag 0 (significant in 4 out of 5 replicates). Negative correlations were not as distinct, but occurred at a lag around À3 (significant in 2 out of 5 replicates; Fig. 5B). The Turure refuge treatment showed the same pattern as the Quare refuge treatment with positive correlations at a lag around þ1 (significant in 3 out of 5 replicates) and negative correlations at a lag around À3 (significant in 3 out of 5 replicates; Fig. 5B). More detailed analysis of the cannibalvulnerable juvenile density cross-correlations can be found in the Appendix.
In summary, the vulnerable juvenile densities and the cannibal densities were overall synchronised in the refuge treatments, but not in control treatments.

Dynamics in the control treatments: cannibal-driven cycles
Recruitment regulation has been shown in several fish populations and may be caused by both intra-and interspecific predation (Polis 1981, Andersson et al. 2007). Cannibalism is a classic example of density-dependence in delayed feedback cycles already described by Ricker (1954). Typically, the cycle length of this dynamics has the periodicity of 2-4 generations. Empirical examples of such cannibalistic cycles with a periodicity substantially exceeding the generation time includes the salamander populations studied by Wissinger et al. (2010) and the leech populations studied by Elliott (2004). Resource competition between cannibals and victims was virtually absent, at least in the salamander study by Wissinger et al. (2010). The dynamics may become more complex when cannibals and victims share resources, as was the case in our guppy populations. The most studied example in this context is the Eurasian perch that may display a mixture of cannibal cycles and cohort competition . In other studied species, cannibalism is the main regulating process despite that cannibals and victims share resources (Persson et al. 2006).
The results from our guppy populations suggest that the dynamics in the control treatment represents cannibal driven cycles. This interpretation can first be related to the relatively few and large offspring in guppies, which means that they are cannibalised directly from birth and that there is a high potential for cannibals to control victims. Second, the fact that high juvenile densities did not co-occur with high cannibal densities suggests that cannibalism had a strong negative effect on recruitment in control treatments. Third, the clear periodicity in total density in both populations suggests that cycles were present in controls. Fourth, the cycle period in control treatments was 75-90 weeks which is in the order of 2 times the generation time (estimated from growth experiments, see the Appendix for details).
The dynamics in the control treatments in the two populations were overall similar although the cycle period was somewhat shorter in the Quare control than in the Turure control populations. Furthermore, peaks in vulnerable juvenile density in the Quare control were much higher and were followed by higher and clearer peaks in the density of non-vulnerable juvenile individuals. We suggest that this difference in cycle period between the two populations is related to the overall lower cannibalism in the v www.esajournals.org Quare control populations. This conclusion is supported by individual level experiments that showed that Quare females had lower cannibalistic voracity than Turure females when no refuges were present (Nilsson et al. 2011). In addition, Quare juveniles are larger at birth and will hence spend a shorter time in the predation window, which may contribute to a lower level of cannibalism.

The effect of harvesting: extinctions and irregular dynamics
The effects of harvesting were overall substantially weaker than that of population origin and refuges. Still, harvesting tended to induce a higher variability in total population density when no refuges were present. A destabilising as well as a stabilising effect of harvesting adults has been shown in both models and experiments for the cannibalistic Tribolium system (Dennis et al. 1995(Dennis et al. , 1997. Models that include both cannibalism and resource competition have shown that harvest of large individuals in cannibalistic populations may lead to a destabilisation of population dynamics (van Kooten et al. 2007(van Kooten et al. , 2010. In stable cannibalistic populations, harvesting may result in more cohort-driven dynamics due to a decrease in cannibalistic pressure from harvesting adults. In populations with small offspring (and thereby a high number of offspring), harvesting may decrease the degree of cannibalism to such an extent that small juveniles successfully recruit into the population and are able to depress the shared resource before they become large enough to be efficiently cannibalised whereby cohort cycles may arise (van Kooten et al. 2010). Empirical support for that harvest of adults may lead to increased recruitment in cannibalistic systems has been found in populations of several fish species such as pike and perch (Alm 1951, Sharma andBorgstrøm 2008). In cannibalistic populations with large offspring size (and hence few offspring) such as guppy populations, this scenario is, however, less likely.
In our experiment harvesting generally led to increased population variability. In the Turure populations without refuges present, harvesting also resulted in extinctions in several populations. This can simply be explained by the low population densities due to cannibalism in combination with the stochastic component induced by harvesting. Another aspect is that harvesting likely decreased the reproductive potential in the populations, since large females (which were subjected to harvest) have a high reproductive output.
The presence of cannibals that were large enough to be harvested in the treatments without refuges was likely due to the relatively low resource competition and possibly some energetic gain from cannibalism. In contrast, few large cannibals were harvested in the refuge and harvest treatments. This result can be related to that increased resource competition due to higher total densities made it difficult for cannibals to grow as large as the harvesting limit. As a consequence, harvest in the refuge treatments had hardly any effects.

The stabilising effect of refuges
Refuge availability is in contemporary ecological theory generally considered to decrease population variability in predator-prey systems (Stenseth 1980, Krivan 1998. This was also the case in our study, although the mechanisms are different from predator-prey systems in that cannibals and victims are coupled over the lifecycle. It is easy to envision that refuge addition leading to a decrease in cannibalism may stabilize cannibal-driven cycles. However, the situation is more complex as cannibals and victims also compete for a shared resource. In our experiments, refuge availability clearly had a stabilising effect on total population variability, but there were also indications of the presence of population fluctuations with a shorter period length (50 weeks) in juvenile and Quare cannibal densities when refuges were present. The density of female adults was also somewhat pulsed, reflected in variability in adult densities as high as or higher than in control treatments. Furthermore, densities of vulnerable juveniles and cannibals in the refuge treatment were highly synchronised. The co-occurrence of this synchronized juvenile-cannibal periodicity and of overall high densities of in particular intermediate sized individuals in refuge treatments points towards a cyclicity induced by higher resource competition and lower per capita food availability (observe that the inflow of food was constant; see the Appendix for details).
v www.esajournals.org In the absence of cannibalism, size-structured consumer-resource systems have generally been shown to exhibit high amplitude generation cycles driven by cohort competition (Persson et al. 1998, de Roos and. Although cannibalism and refuge use have not been theoretically analysed in combination, our results suggest that cannibal thinning of recruits in combination with the relatively low per capita fecundity of guppies may prevent juvenile cohorts from depressing the shared resource level to such an extent that proper (high amplitude) generation cycles emerge. This result is agreement with theoretical studies that show that cannibalism may be stabilising in systems that incorporate other density dependent processes like competition (Cushing 1991).
In conclusion, both cannibalism and cohort competition may generate cycles in size-structured populations . Our results provide clear evidence for cannibalistic cycles in both guppy populations in controls where the fluctuations were higher in the more cannibalistic population (Turure). The presence of refuges increased population densities and led to population fluctuations with a shorter period and lower amplitude than the cannibalistic cycles and these fluctuations could be related to cohort competition. The cyclicity of these fluctuations was also more clear in the less cannibalistic population (Quare) having a higher total density. We argue that the circumstance that cannibalism was also present in refuge treatments prevented the populations from exhibiting high amplitude generation cycles. Finally, we suggest that the smaller offspring and the higher cannibalistic voracity in the Turure than in the Quare population were the main factors behind the population differences in dynamics. The significance of this difference is reinforced by that the difference in population variability (CV) between the guppy populations was higher than that previously observed between different species of fish (van Kooten et al. 2010) SUPPLEMENTAL MATERIAL

Detailed analysis of total density autocorrelations
To compare the lags in total density autocorrelations, and hence the periodicity in different treatments, the highest (positive) correlation value and the lowest (negative) correlation value was selected for each replicate and included in an Analysis of Variances. The first positive correlations at very short lags were ignored. Several replicates lacked positive correlations. For example, only one out of five replicates in the Turure refuge treatment had any positive correlation except for the initial ones (this can be seen by the lack of data points in Fig. 4). We selected the strongest correlation. There was no weighting depending on the actual value of the correlation.

Positive correlations
The Turure population had longer lag at the highest positive autocorrelation than did the Quare population (Table A1). This pattern was largely driven by the control treatments. No effects of refuges were found (Table A1), this is likely partly due to that the refuge treatments had few positive correlations. These findings support the statements in main text about cycle length in the different populations.

Negative correlations
There were no significant treatment effects on the differences in lags at the most pronounced negative correlation for total population density (Table A2). However, when comparing the periodicity of the Turure control and the Quare control treatment, excluding the extinct replicate (one Turure with negative correlation at short lag in this case) resulted in significantly longer lag for the Turure control ( p ¼ 0.0084). This supports that Quare control has a shorter cycle length than Turure control, which was found when looking at the positive correlations.

Detailed analysis of cannibal-vulnerable juvenile cross-correlations
To compare the correlations at zero lag for the cannibal and vulnerable juvenile densities we selected the correlation value at lag 0 and performed an analysis of variance (Table A3).
There was a strong correlation between cannibals and vulnerable densities when refuges were present, whereas when no refuges were present this was not the case (Table A3).
Post hoc tests for the ANOVA on total population variability Post hoc tests for the analysis of variances on treatment effects on coefficient of variation for total population density (corresponding to Table  1) can be found in Table A4.

Growth rate estimates
To check if our division into size-classes was accurate and to obtain an estimate of the growth rate from the vulnerable to the invulnerable stage we used cross-correlation analyses between the densities of vulnerable and non-vulnerable juveniles. In general the cross-correlations showed significant positive correlations around lag þ 1 which means that a peak in vulnerable juveniles was followed by a peak in non-vulnerable juveniles after 5 weeks. This fits well with the assumption that vulnerable juveniles grow into the non-vulnerable stage in 5 weeks (one sampling interval, results not shown).
To obtain an estimate of the growth of vulnerable juveniles we performed cross-correlations with the density of intermediate sized individuals and vulnerable juveniles. The Quare control treatment showed clear positive correlations at lags À1 and À2 (significant in 3 out of 5 replicates), which means that a peak in vulnerable juvenile density was followed by a peak in intermediate sized individuals in the subsequent sampling or after two or three sampling occa-  Fig. A1A). The Turure control treatment also showed positive correlations at lags À1 and À2 (significant in 3 out of 5 replicates; Fig. A1B). Both harvest treatments were similar to the controls. In the Quare refuge treatment 4 replicates showed significant positive correlations at lag þ 2 or þ 4 (Fig. A1). This result suggests that a peak in intermediate sized individuals is followed by a peak in juveniles after 2-4 sampling occasions (10-20 weeks). To summarise, in the control treatments a peak in vulnerable juvenile density was followed by a peak in the density of intermediate sized individuals after approximately 2 sampling occasions (10 weeks) for both populations. In the refuge treatments, a peak in Fig. A2. Female growth at different food levels. The thin black line represents growth at ad libitum food levels (from S. Auer), the fat black line represent growth at intermediate food levels, the dark grey line represents growth at low food levels and the light grey line represents growth at very low food levels (modified from Barlow 1992). The grey dotted lines represent the average size at first reproduction at ad libitum food levels (27 mm) and size at maturation obtained from literature (17 mm). The large black crosses mark the transition from the vulnerable and the invulnerable juvenile stage in our experiment, verified by cross-correlations. The small grey cross represents the intermediate size-class, based on the relationship between vulnerable juveniles and intermediate sized individuals in cross-correlations (when no refuges were present). v www.esajournals.org intermediate sized individuals seemed to be followed by a peak in vulnerable juvenile density after 3 sampling occasions (15 weeks).
These results suggest that juveniles grew into the intermediate stage in 10 weeks in control treatments. However, they were still likely to be affected by resource competition as they did not grow as fast as under ad libitum conditions (Fig.  A2). With a size at first reproduction of 27 mm, this results in a generation time of approximately 40 weeks (or lower) as the size at reproduction can be expected to be lower when not feeding ad libitum (Fig. A2). The observed cycle period in the control treatment (75-90 weeks) is thus 2 times the generation times or more.
In the refuge treatments the periodicity was 50 weeks and hence only slightly longer than the generation time which is expected for cohort cycles. Moreover, the high population density in refuges treatments is expected to have led to a lower per capita food availability in refuge treatments compared to controls, hence the guppies are expected to have grown slower in the refuge treatments making the time to reach maturity to be longer than 40 weeks. Additional support for a cohort cycle in the refuge treatments comes from the fact that it was difficult to detect a clear transition from vulnerable to intermediate sizes in the these treatments, which is in line with theoretical predations on formation of a stunted cohort. Instead the transition from intermediate sized individuals to large adults, that can reproduce and give rise to a new cohort of juveniles, was more evident.

Photograph of an aquarium
We have provided a photograph of an aquarium containing refuges (Fig. A3). The feeder can be seen to the left above the water surface. The inlet of water is the hose in the middle and the outlet is close to the surface at the right. The aquarium is covered with black plastic on 3 sides. v www.esajournals.org