Population responses of small mammals to food supply and predators: a global meta-analysis

Authors


Summary

  1. The relative importance of food supply and predation as determinants of animal population density is a topic of enduring debate among ecologists. To address it, many studies have tested the potential effects of food on population density by experimentally supplementing natural populations, with much focus on terrestrial vertebrates, especially small mammals.
  2. Here we perform a meta-analysis of such experiments, testing two complementary hypotheses: (i) small mammal populations are bottom-up limited and (ii) population increases in response to food supplementation are constrained by predation, a top-down limitation.
  3. In the 148 experiments recorded, food supplementation had an overall positive and significant effect, increasing population densities by 1·5-fold. Larger population increases occurred when predation was reduced and populations were open to immigration. Predation appeared to be unimportant when populations were closed to immigration. Immigration was the major mechanism underlying increases in abundance by increasing local population density and crowding. Contributions of increased reproductive rate could be detected, but were minor compared to immigration, and no effects were detected from survival.
  4. Our analyses support the view that animal population density is determined by both bottom-up and top-down forces. They also suggest the possibility that food supplementation experiments might unintentionally create ecological traps by aggregating both prey and predators in small areas of the landscape. We suggest an alternative experimental design to increase the contribution that food supplementation experiments can make in future.

Introduction

One of the central questions in ecology is what determines population density (Krebs 2002). Over the last century, a plethora of potential factors has been suggested, including those that are intrinsic to populations such as social, physiological and genetic factors, and others that are extrinsic including weather, the supply of food and other resources, predation and disease (Power 1992; Sinclair & Krebs 2002; Korpimäki et al. 2004). For animal populations, the relative importance of each factor, in particular, food and predation, has been a frequent and major focus of debate, forming the core of the classical bottom-up vs. top-down controversy (Hairston, Smith & Slobodkin 1960; Menge & Sutherland 1976; White 1993; reviews in Shurin, Gruner & Hillebrand 2006; White 2008). Many ecologists now agree that both factors play relevant and perhaps interactive roles and should be considered in any general explanatory framework of population density (Sinclair & Krebs 2002; Korpimäki et al. 2004; Munch et al. 2005). However, an overall consensus regarding the relative importance of bottom-up and top-down effects has not yet emerged (Hunter 2001; Krebs 2009; Salo et al. 2010), as illustrated by two recent reviews that provide contrasting evidence for the importance of predation in terrestrial systems (White 2008; Salo et al. 2010).

The difficulty in reaching a consensus can be attributed to a number of factors, including differences in the methodology used in population studies (Hunter 2001), the ecosystems studied (Shurin, Gruner & Hillebrand 2006), and in conceptual issues regarding the meaning of ‘regulation’ in populations (e.g. Murray 1999a; White 2001, 2008; Berryman 2004). It has been suggested that the most straightforward way to avoid these ongoing controversies and advance population ecology is to adopt a mechanistic approach based on experimental manipulations (Krebs 1988, 2002, 2009; Turkington 2009). A mechanistic approach allows the direct testing of causal mechanisms that affect population size while controlling for other confounding factors, which is rarely possible with approaches based solely on the observations or time-series modelling (Lambin et al. 2002; Benton, Plaistow & Coulson 2006; Krebs 2009). Experiments also have limitations (e.g. Moon, Stiling & Cattell 1999; Hunter 2001) as appropriate controls and replicates are frequently difficult to implement in field conditions; nonetheless, experiments provide the strongest tests of causality (Hunter 2001; Korpimäki et al. 2004).

Even before the explicit advocacy of the mechanistic approach, many manipulative experiments had been carried out to test the effects of predation on prey density. The experimental evidence for predation-impacts has been summarized recently, in both aquatic and terrestrial environments, in a number of quantitative meta-analyses (Shurin et al. 2002; Borer, Halpern & Seabloom 2006; Salo et al. 2007, 2010). A common conclusion in these reviews was that predator removal generally increases prey population numbers, thus providing strong evidence for top-down control. Equally interesting, the magnitude of predator impacts on prey density may be quite variable depending, for example, on the geographical origin of the predator (native vs. introduced to the study area; Salo et al. 2007), the efficiency of predator removal by experimenters (Salo et al. 2010), and the type of ecosystem and organism studied (Shurin et al. 2002; Poore et al. 2012).

In parallel, many studies have tested the potential effects of food on population density by experimentally supplementing natural populations, with much focus on terrestrial vertebrates, especially small mammals (Boutin 1990). Experiments with terrestrial invertebrates and aquatic animals usually have a community approach; moreover, food supplementation in aquatic systems generally has been achieved indirectly through nutrient enrichment (Borer, Halpern & Seabloom 2006), which may increase not only the food supply but also vegetation cover, thus potentially reducing predation pressure and making it difficult to assess the separate impact of food on animals. Experiments on food supplementation with terrestrial vertebrates were last summarized 22 years ago in a detailed review by Boutin (1990). He concluded that food supplementation leads to an overall 2-fold increase in population density, but also that added food was unable to prevent major declines in fluctuating populations. The observed increases in population density were mediated by increases in survival, reproduction and immigration of individuals to supplemented plots (Boutin 1990). Boutin (1990) also noted that different populations varied considerably in their responses to added food, but the scarcity of studies at the time hampered any general explanation of such variability. Since Boutin's (1990) review, many additional food supplementation experiments have been conducted using varied methods and under different ecological conditions, allowing now, for the first time, a comprehensive test of whether and how food affects density in animal populations.

Here we perform a meta-analysis of food supplementation experiments, testing two complementary hypotheses: (i) small mammal populations are bottom-up limited and (ii) population increases in response to food supplementation are constrained by predation, a top-down limitation. Our predictions for these hypotheses are that food supplementation increases the population density of the target populations (hypothesis 1) and also that such increases will be less accentuated in areas subjected to higher predation pressure (hypothesis 2). To understand the mechanisms driving observed changes in population density, we also investigate how food supplementation affects survival, reproduction and immigration. We also attempt to explain the variability in the responses of populations to food supplementation, by analysing the mediating roles of factors such as species' feeding habits, body mass, ecosystem productivity, the size of the experimental area and the duration of the experiment. We focus our analyses on small non-flying mammals (<2 kg) because they have been the primary targets of food supplementation experiments (Boutin 1990).

Materials and methods

We included in the review only experiments carried out under field conditions, including experiments using outdoor enclosures. The detailed search strategy and the criteria for combining experiments for analysis are presented in Appendix S1.

Response variables

Five response variables were extracted from each experiment: population size, immigration, reproduction, survival and body mass. In quantifying these response variables, we considered only data obtained during the experimental period, defined as the period during which effects of food supplementation were expected to occur, as inferred from the methods, results and discussion of each publication. In some studies, the experimental period was coincident with the period of food supplementation, but in others, the experimental period started after the beginning of food provision and ended after the end of the food provision. For each response variable, we calculated a single average value for each treatment that summarized the entire experimental period of each experiment. Whenever possible, we also recorded variability measures (standard error, standard deviation or variance) or calculated them from raw data.

Population abundance was inferred in most papers as the minimum number of animals known to be alive; some studies used probabilistic estimators, whereas others reported the numbers of captured individuals or catch-per-unit-effort indexes of capture success. Preliminary comparisons indicated that the abundance index or estimator used had little effect on the reported responses of populations to food supplementation, thus we combined studies in a single data set. To analyse the effects of food supplementation on reproduction, survival, body mass and immigration, we restricted our analyses to the set of studies that also evaluated population sizes, because our focus was to understand the underlying processes that mediate variation in population size in response to food supplementation. To obtain consistent effect sizes for reproduction, survival and immigration, we restricted our analyses to publications that used the most common estimation method for each response variable, as detailed in Appendix S1.

Explanatory variables

We first classified each species in each experiment as a ‘target’ or a ‘non-target’ of food supplementation to exclude species that were not expected to respond to the added food in the original studies. In the experiments of Brown & Munger (1985), for example, neither the herbivorous Neotoma albigula or insectivorous Onychomys spp. were expected to respond to added seeds; the authors used these species as non-responsive ‘controls’ to gauge the effects of seed addition only on granivorous rodents. We classified the diet of each species as omnivore, granivore, herbivore or insectivore based on the original papers and Nowak (1999). Omnivore species were considered as ‘targets’ in all studies. The classification of the remaining species as ‘targets’ or ‘non-targets’ was based on the information presented in the original studies and by the match between the diet of each species and the type of supplemented food.

We then evaluated whether the amount of food that was provided to the target animals in each study was, in fact, sufficient to allow increases in their population numbers. To do this, we quantified, for each experiment, the amount of energy provided to populations by experimenters and the amount of energy needed to support one individual of the focal species, as detailed in Appendix S2. We focused our analyses on the energetic content of the added food only, assuming that other properties, such as protein content, were not limiting (but see, for example, McAdam & Millar 1999). Also, we focused on maximum potential increases in numbers because unknown quantities of the added food were frequently consumed by organisms other than the focal species.

We classified populations in each experiment as either ‘open’ or ‘closed’ to immigration. ‘Closed’ populations included those where immigration was reduced or completely inhibited by the experimental design, such as populations in fenced areas, on small islands, or in areas surrounded by low quality habitats. Levels of predation in experimental sites were categorized as either ‘reduced’ or ‘not-reduced’, based on the information presented in each paper. ‘Reduced’ predation levels refer to situations where predation was deliberately reduced as part of the study, and also where it was reduced in the system for biogeographic or anthropogenic reasons, as in the case of some islands. We did not consider the experimental increase of vegetation cover as a reduction in predation. ‘Not-reduced’ refers to situations where predators were present in the study area and were not manipulated.

Boutin (1990) suggested that populations are more likely to respond to food supplementation when environmental conditions are severe, such as in winter, than at other times. To test this, we classified the environmental conditions prevailing during each experiment as ‘poor’ vs. ‘fair to good’, as in Boutin (1990), basing this on information presented in the original papers. Because such conditions are likely to prevail only for limited periods before changing, we confined our analyses to short-term experiments that were conducted over a single season. Similarly, populations in relatively low-density situations could be expected to respond differently to food supplementation from those at high density (Murray 1999b). However, we were unable to properly test this density effect because relatively few studies reported the population density context under which the experiment was carried out. We also expected that the populations living in sites with higher climatic variability (e.g. deserts) would be more likely to respond strongly to food supplementation, on the assumption that they have high behavioural and social plasticity to respond to resource pulses (e.g. Dickman et al. 2010; Letnic et al. 2011). To test this hypothesis, we obtained estimates of seasonality of rainfall for each study site, using the coefficient of variation in precipitation from the WorldClim database (Hijmans et al. 2005). We also obtained estimates of net primary productivity (NPP) for each site from Imhoff et al. (2004), to test the hypothesis that food supplementation would facilitate greater increases in population size in sites with low primary productivity (Oksanen et al. 1999; Korpimäki et al. 2004). The NPP and the coefficient of variation in precipitation were not correlated for the set of studied sites (r = −0·10, P = 0·42, n = 61).

We determined the average adult body mass of each species from Smith et al. (2003). We also recorded whether supplemented food was available to animals outside the traps during the sampling period or not, considering that the supplemented food could reduce animal trappability, potentially leading to underestimation of population sizes and recapture rates (e.g. Boutin 1984). Finally, we recorded the mean size (in ha) of the study area receiving food and the duration (in months) of the supplementation period. The social and mating systems of species could also affect their responses to food supplementation, but information on spacing behaviour and territoriality is scarce for many small mammals (Ostfeld 1990; Stockley & Bro-Jørgensen 2011). Hence, this effect could not be considered formally in our analyses, although we consider it later when discussing the results.

Statistical analyses

We quantified the effects of food supplementation on population density using the response ratio (Hedges, Gurevitch & Curtis 1999), that is, the ratio of population size in supplemented compared to that in non-supplemented areas. The response ratio provides a direct and intuitive measure of manipulation effects and has good statistical properties for meta-analyses (Hedges, Gurevitch & Curtis 1999). In the analyses presented in the main text, we followed recent meta-analyses (e.g. Salo et al. 2010; Poore et al. 2012) and did not weight each effect size by the inverse of its variance, because variability measures were reported in only 62% of the experiments reviewed. However, for comparative purposes, we followed Hoeksema et al. (2010) and weighted effect sizes by the inverse of study sample size, estimated as the summed number of replicates or years in control and supplemented areas. This approach assumes that studies with higher sample sizes provide more precise estimates of effect sizes (Hoeksema et al. 2010). Finally, for the studies that reported variability measures, we also calculated the standardized mean difference, Hedges' d, for comparison, because of its widespread use in meta-analyses (Borenstein et al. 2009; see Appendix S3). We show in the main text and figures only the results for the unweighted response ratio, briefly commenting on whether the results for weighted response ratios and Hedges' d were similar (detailed results are presented in Appendix S3). For immigration, survival, body mass and reproduction, we quantified effect sizes using only the unweighted response ratio, because the vast majority of studies did not report variability measures for these variables.

We ln-transformed the response ratio for all analyses, resulting in normally distributed values as inferred from visual assessment of histograms and normal quantile plots. When analysing unweighted response ratios, we applied one-sample Student's t tests to evaluate overall effects of food supplementation on population density, body mass, reproduction, survival and immigration. To determine the relative importance of predation, population closure to immigration, NPP, seasonality in precipitation and body mass as determinants of the magnitude of density increases, we used an information-theoretic approach, comparing alternative explanatory linear models comprising additive and interactive effects of those explanatory variables. The only interaction with a clear a priori hypothesis was between predation and population ‘closure’. A null model was also considered for comparison, comprising only the intercept and residual errors as parameters, thus resulting in a total of 40 candidate models. All explanatory variables were treated as fixed factors, and the parameters of each model were estimated by restricted maximum likelihood. Model performance was compared by quantifying the corrected Akaike Information Criterion (AICc) of each model, the Δi (=AICci − minimum AICc) and the wi, the weight of evidence that model i is the best model in the set (Burnham & Anderson 2002).

We also applied two-sample t tests to compare unweighted response ratios between replicated and unreplicated experiments, between periods of ‘poor’ vs. ‘fair to good’ environmental conditions, and between studies where food was or was not available during the sampling period. Correlations between effect sizes and area and time length of the experiment were tested using Pearson correlations. The correlation between actual (observed) and maximum potential density increases (as allowed by the extra energy provided by experimenters) was tested using Spearman's correlation, because of non-normality of the maximum potential increase values. For the same reason, we calculated confidence intervals by bootstrapping (using 1000 bootstrap replicates) when comparing the median of actual increases and the median of maximum potential increases. Finally, we also tested for potential publication bias in our data set of studies (Appendix S4). All calculations were carried out in the R environment, version 2.13.0 (R Development Core Team 2011).

Results

In total, 148 experiments were retained to evaluate the effects of food supplementation on small mammal population densities (Appendix S3), an increase of ca. 145% in the number of experiments since Boutin′s (1990) review (= 60). These experiments were carried out using 70 species from 38 genera of small mammals, with 131 experiments involving rodents. Six experiments reported information on non-target species, for which food supplementation had no detectable effect on population sizes [mean unweighted response ratio (RR) = 1·01, 95% confidence limits (CL) = 0·69–1·48; Student's t = 0·06, P = 0·95]. These six experiments were dropped in all subsequent analyses. The remaining 142 experiments revealed an overall positive and significant effect of food addition on population density (RR = 1·53, 95% CL = 1·41–1·65; t = 10·74, P < 0·0001). Similar results were obtained when analysing data using weighted response ratios or Hedges' d (see Appendix S3).

For 62 experiments (38 species), we were able to estimate the maximum potential increase in population size that could have been allowed by the extra energy supplied by the experimenters. The median of the maximum potential increases in population size was 25·08 (95% CL = 14·76–38·04), whereas the median of the observed increases in the same set of experiments was only 1·39 (95% CL = 1·15–1·61). Therefore, maximum potential increases allowed by energy addition were more than 18 times the observed increases, indicating that population increases were not constrained by the addition of insufficient amounts of food. There was no correlation between observed and possible population increases (Spearman's r = 0·03, P = 0·83, n = 62). Similar results were obtained when the analyses were restricted only to animals positively affected by food addition (response ratios >1; maximum potential increases: median = 27·29, 95% CL = 15·17–43·10; observed increases: median = 1·55, 95% CL = 1·21–1·85; correlation: r = 0·01, P = 0·93, n = 52).

Populations of insectivorous mammals did not increase significantly with food supplementation (RR = 1·01, 95% CL = 0·44–2·32; t = 0·04, P = 0·97, n = 6), whereas omnivores, granivores and herbivores showed a clearly positive and similar response to food addition (combined RR = 1·55, 95% CL = 1·44–1·68; t = 11·53, P < 0·0001, n = 136; Fig. 1). Similar results were found when analysing weighted response ratios or Hedges' d (see Appendix S3). Therefore, we dropped the six experiments with insectivores and combined the other diet classes for further analyses.

Figure 1.

Effects of diet category on variation in population density in response to food supplementation. Means and 95% confidence intervals for effect sizes (unweighted response ratios) are shown, with the number of experiments in parentheses. The horizontal dashed line indicates no response to food supplementation.

The model selection results indicated that predation, immigration and their interaction were the main determinants of variation in population density in response to food supplementation (Table 1). Despite some model uncertainty, these variables were consistently present in the top 8 models, and they were the only ones present in the most plausible model. The null model was relatively much less plausible (Δi = 9·02, wi < 0·01). In open populations, increases were higher for populations that were subject to reduced predation pressure (2·8-fold on average), compared to populations where predation pressure was not reduced (1·5-fold; Fig. 2). This difference was clear even after controlling for differences in sample size between treatments (n = 8 and 100, for reduced and not-reduced predation levels, respectively). The average increase obtained in 1000 random subsamples (each of size 8) taken from populations where predation pressure was not reduced was 1·5 (95% CL = 1·15–2·03), clearly smaller than the 2·8-fold increase observed for populations that were subject to reduced predation pressure. In closed populations, predation reduction had no clear effect on population responses to food supplementation (Fig. 2). Similar results were obtained when analysing weighted response ratios (see Appendix S3). When only replicated studies were analysed using Hedges' d, no variable explained substantial variation in the data, because this analysis included only 2 studies with open populations in which predation was reduced (see Appendix S3).

Table 1. Performance of models predicting variation in population density in response to food supplementation
Model rankVariablesLog-likelihood K AICcΔi w i
  1. K, number of parameters in the model; AICc, corrected Akaike Information Criterion; Δi, AICci − minimum AICc; wi, Akaike weight; *, interactions between variables. Pred, predation; Immi, immigration; Prec, coefficient of variation in precipitation; Mass, body mass; NPP, net primary productivity.

  2. The model without variables represents the null model, including parameters only for the intercept and residual error.

  3. Only models within a 95% confidence interval of summed wi values and the null model are shown.

1Pred + Immi + Pred*Immi−75·555161·560·000·14
2Pred + Immi + Pred*Immi + Mass−74·656161·950·390·12
3Pred + Immi + Pred*Immi + Prec−74·786162·220·650·10
4Pred + Immi + Pred*Immi + Mass + Prec−73·747162·350·790·10
5Pred + Immi + Pred*Immi + NPP−75·086162·801·240·08
6Pred + Immi + Pred*Immi + Mass + NPP−74·087163·041·470·07
7Pred + Immi + Pred*Immi + Prec + NPP−74·507163·872·300·05
8Pred + Immi + Pred*Immi + Prec + NPP + Mass−73·398163·912·350·04
9Pred + Immi−77·844163·992·430·04
10Pred + Immi + Prec−76·825164·102·540·04
11Pred + Immi + Prec + Mass−75·886164·412·850·03
12Pred + Immi + Mass−77·075164·603·030·03
13Pred + Immi + NPP−77·385165·233·660·02
14Pred + Immi + NPP + Mass−76·526165·704·130·02
15Pred + Immi + NPP + Prec−76·576165·794·220·02
16Pred + Immi + NPP + Prec + Mass−75·587166·034·470·02
17Pred + Prec + Mass−78·135166·735·160·01
18Pred−80·293166·775·200·01
19Pred + Prec−79·264166·835·260·01
20Pred + Mass−79·344166·995·430·01
31none−83·252170·589·02<0·01
Figure 2.

Interactive effects of predation and immigration on variation in population density in response to food supplementation. Means and 95% confidence intervals for effect sizes (unweighted response ratios) are presented, with sample sizes in parentheses. The horizontal dotted line indicates no response to food supplementation.

There were no evident differences in effect size between replicated and unreplicated experiments (t = 1·34, d.f. = 134, P = 0·19), between periods of poor vs. fair to good environmental conditions (t = 0·04, d.f. = 41, P = 0·97), or between studies where food was or was not available during the sampling period (t = 0·59, d.f. = 134, P = 0·56). Also, effect sizes showed no apparent correlation with the time length of the experiment (Pearson's correlation, r = −0·01, P = 0·93, n = 136). There was a positive correlation between effect size and the area of the experiment (= 0·22, P = 0·01, n = 136; Fig. 3). However, points were very scattered and the correlation became non-significant after removing from the analysis the six experiments that used very large areas (36 ha; r = 0·09, P = 0·30, n = 130). When the analyses were restricted to experiments with open populations where predation was not reduced (n = 100), no significant effects of replication, environmental conditions, food availability, length of time or size of area on effect sizes were detected (for all tests - t tests: t < 0·87, P > 0·39; correlations: r < 0·19; P > 0·06). Similar results were obtained when analysing weighted response ratios (Appendix S3).

Figure 3.

Correlation between density increases (unweighted response ratios) and the area (ha) receiving food in each experiment.

We recorded 64 experiments evaluating the effects of added food on survival (for 36 species), 58 on body mass (32 species), 46 on reproduction (28 species) and 28 on immigration (19 species; Appendix S1). To provide a comparative overview of how these variables were affected by food supplementation, we first restricted analyses to open populations, considering that immigration was not measured for closed populations. For open populations, food supplementation had a strong positive effect on immigration (t = 6·05, P < 0·0001, n = 28), a small but significant effect on reproduction (t = 3·15, P = 0·003, n = 38), and body mass (t = 3·06, P = 0·004, n = 44), and no evident effects on survival (t = −0·09, P = 0·93, n = 47; Fig. 4). Effect sizes for immigration were positively correlated with effect sizes for population size (Pearson's correlation, r = 0·69, P < 0·001, n = 28; Fig. 5). Effect sizes for reproduction, body mass and survival were not significantly correlated with effect sizes for population size (all analyses: r ≤ 0·18, P ≥ 0·27). If ‘closed’ studies are included, there are no significant changes in results for survival, body mass and reproduction.

Figure 4.

Means and 95% confidence intervals for effect sizes of immigration, reproduction, body mass and survival. Only experiments with populations ‘open’ to immigration are considered. The horizontal dotted line indicates no response to food supplementation.

Figure 5.

Correlation between the response ratio for immigration and the response ratio for population density in each experiment. Values represent ln-transformed unweighted response ratios.

Discussion

Food supplementation had an overall positive effect on the population density of small mammals, increasing densities by 1·5-fold on average and providing support for our first hypothesis and its associated prediction. Such increases are of similar magnitude to the effects of predator removal on small mammal populations (1·57-fold; Salo et al. 2010). However, food supplementation had no impact (response ratio ≤ 1) in 23 of 142 experiments (16%), despite relatively massive amounts of food being provided by experimenters. A lack of response indicates that either the quality of the food provided was inadequate or that other factors are more important than food. Food quality probably contributed to a lack of response in three of 20 experiments that fed insectivores with non-animal supplements (Leung 1994; Banks & Dickman 2000; Williams 2007). For the remaining experiments, other factors such as spacing behaviour (e.g. Orland & Kelt 2007), predation pressure (which was ‘not reduced’ in all cases) or competition may have constrained the magnitude of population increases. For example, interference competition with the black rat Rattus rattus prevented population increases in the Galápagos native rodent Nesoryzomys swarthi, despite the provision of large amounts of supplementary food (Harris & Macdonald 2007). The analyses also supported our second hypothesis that predation reduces the magnitude of population increases, but only in open populations. Predation appeared to be unimportant when populations were closed to immigration. Immigration was the major mechanism underlying increases in local abundance by increasing local population density and crowding.

Despite being ecologically meaningful, the overall 1·5-fold increase in population numbers caused by food supplementation is modest when compared to natural outbreaks observed in some small mammal populations associated with resource pulses, when population size may increase hundreds of times (Korpimäki et al. 2004; Holmgren et al. 2006). Also, the massive energetic input provided by experimenters could have produced much larger increases than were actually observed. Maximum potential increases are certainly overestimated in some cases, due to the consumption of added food by non-focal animals; however, most studies reported evidence that a large fraction of the added food reached the focal species, so that the supplemented food certainly could have allowed density increases greater than those observed in most studies. The critical question, as first raised by Gilbert & Krebs (1981), is thus why does food supplementation allow only such modest population increases? A first hypothesis is that added food was of low quality, lacking essential constituents such as protein that are needed for animal growth and reproduction (e.g. White 1978; McAdam & Millar 1999). This is probably the case for insectivorous species, but it is unlikely to provide a general explanation for all species in the remaining 136 experiments, considering that many authors explicitly reported evidence from the literature confirming the nutritional adequacy of the supplemental food. An alternative hypothesis is that the food was used by only a few individuals that then dominated the food sources (Boutin 1990). We consider this unlikely because most studies provided food evenly across experimental areas, and the few experiments testing the effect of spatial dispersion of food found little differences or even greater increases in density when food was patchily distributed (Predavec 2000; Harris & Macdonald 2007). The modest increases in density could also have resulted from food being provided for too short a period of time (Boutin 1990), but this too is contradicted by the absence of correlation between effect sizes and length of study in both open and closed populations, a meaningful result considering that some experiments provided food to animals for periods as long as 8 or 10 years (see Appendix S1).

We believe that the small size of the experimental feeding areas and the corresponding high levels of immigration are the main causes of the modest increases in density observed in the experiments, as also suggested before (e.g. Boutin 1990; Predavec 2000; Meserve, Milstead & Gutiérrez 2001). Ninety percentage of the experiments we reviewed were conducted in areas smaller than 10 ha, and the six experiments conducted in very large areas (all 36 ha) resulted in relatively large increases in density (see Fig. 3). Small areas have a high perimeter to area ratio, meaning that the estimated size of the local population is affected greatly by the movement of animals from and to the surroundings (West 1982; Bowers et al. 1996). Indeed, our analyses confirmed that immigration was the main contributor to the observed increases in density in response to food supplementation, as previously recognized in many individual studies (e.g. Mares et al. 1982; Boutin 1984; Banks & Dickman 2000). Immigration increased 92% in response to food supplementation, and there was a clear correlation between increases in density and increases in immigration in response to food supplementation. The modest 1·5-fold increases in density observed in the experiments could thus simply reflect an upper limit set by the available pool of immigrants (Boutin 1990). The strong effects of food supplementation on immigration, but weak effects on survival and reproduction, could also explain why food supplementation is generally unable to change the overall pattern of population dynamics and, in particular, is unable to prevent major population declines in fluctuating populations as documented by Boutin (1990). In contrast, the much larger density increases observed during natural population outbreaks in some small mammals are caused by resource pulses that occur over very large, even continent-wide areas (Ostfeld & Keesing 2000; Korpimäki et al. 2004). Such pulses frequently increase both survival and reproduction (Ostfeld & Keesing 2000; Korpimäki et al. 2004), whereas immigration is certainly less important, because food is available both within and in the surroundings of sampling areas.

The relatively small or even undetectable contribution of reproduction and survival to changes in density caused by food addition should not be considered conclusive, because both parameters were probably underestimated in many of the individual studies. The two measures of survival used in most studies, recapture rates and residency times, may be difficult to interpret because they are affected not only by true survival but also by capture probability (e.g. Lebreton et al. 1992), and because they generally do not separate emigration from true death in open populations (but see Gilroy et al. 2012). Furthermore, such methods to estimate survival do not provide information on the very young, non-trappable individuals, which have been suggested to be ‘the Achilles heel of all populations’ (White 1978, 2008). Body mass, frequently used as a surrogate of survival in the literature, also can be calculated only for trappable individuals. Similarly, reproduction was measured in most studies only as the percentage of animals in breeding condition, whereas other more direct estimates such as litter size could indicate stronger effects of food supplementation (e.g. Karels et al. 2000).

Increases in survival and/or reproduction certainly occurred in closed populations, which increased in density even in the absence of significant immigration. Such increases would be expected because individuals in closed populations are in more favourable conditions to respond to food than individuals in open populations, for at least two reasons. Firstly, interspecific competition was generally negligible in closed populations: 17 of the 28 experiments with closed populations used enclosures where only the focal species was present, and at least two of the remaining experiments mentioned the absence or rarity of other species in the studied areas (Adler 1998; Díaz & Alonso 2003). Secondly, the use of fences to preclude dispersal in experiments with closed populations probably benefited individuals by reducing terrestrial predation. Such differences between open and closed populations should be reflected in correspondent differences in survival or reproduction. However, no such differences were detected in our data set, again suggesting limitations in the approaches used to estimate survival and reproduction in the individual studies.

Predation clearly constrained the magnitude of population increases in open populations, but it had only weak effects on closed populations. The increases in density caused by food supplementation probably attracted predators to the supplemented areas, the so-called pantry effect (Cole & Batzli 1978; Ford & Pitelka 1984; Huitu et al. 2003). This effect likely occurred on both open and closed populations, but it was probably stronger in the former because of the high levels of immigration, which aggregated individuals at single points in the landscape. In this sense, it is possible that food supplementation is artificially creating ecological traps, areas of apparently high-quality habitat but where survival and reproduction are actually reduced (Gates & Gysel 1978; Gilroy & Sutherland 2007). If this hypothesis is true, we would expect lower per capita reproduction and survival rates in food-supplemented compared to control populations. However, reliable data on such parameters, especially on a per capita basis, are scarce as discussed previously, hence this hypothesis cannot be tested at present. In addition, the weaker effects of predation in closed populations may be due to the use of fences, which are intended to preclude dispersal but may also unintentionally reduce the access of terrestrial predators (Desy & Batzli 1989). Thus, in many experiments with enclosures, the two predation treatments (reduced or not-reduced) may have differed mostly in aerial predation, with the two predation treatments experiencing similar levels of (reduced) terrestrial predation. This contrasts with experiments on open populations, where the predation treatments (reduced or not-reduced) differ frequently in both terrestrial and aerial predation pressure (e.g. Karels et al. 2000; Morris et al. 2011). Differences in the efficiency of predator exclusion may indeed be important, considering that the contrast in predator numbers between treatments – that is, the efficiency of predator removal – affects the magnitude of the increase in prey density (Salo et al. 2010).

Several variables tested had no detectable effects on population increases, including NPP, precipitation seasonality, body mass and time length of the experiment. Environmental conditions were also unimportant, contrary to the conclusion of Boutin (1990), who suggested that populations were more food-limited in periods of ‘poor’ environmental conditions. This discrepancy may reflect differences in the data set or in the methods used (‘vote counting’ vs. meta-analysis). The absence of detectable effects of all these variables on population increases cannot be attributed to low power of the tests or inadequacy of the analyses, considering our large sample sizes and the use of different approaches to estimate effect sizes. We attribute the results instead to the large mediating effect of immigration on population increases, because the variables tested are more likely to affect survival and reproduction than immigration. In this sense, the remaining variation in effect sizes could perhaps be accounted for by variables related to immigration, such as the ratio between home range size and the area of sampling (Bowers et al. 1996). Unfortunately, it is not possible to test this properly with the data at hand, because there are no estimates of home ranges in the studied sites for most species. It is also possible that the absence of effect of NPP on density increases reflects the inadequacy of NPP as an indicator of food availability for animal populations (Huston & Wolverton 2009).

Conclusions

Our analyses support the view that animal population density is determined by both bottom-up and top-down forces (Sinclair & Krebs 2002; Korpimäki et al. 2004; Munch et al. 2005; Krebs 2009; Letnic et al. 2011). Food supplementation as usually has been performed in field experiments generally produces a crowding effect, increasing density in the treatment area by immigration of nearby individuals. The magnitude of increase is constrained at least in part by predation. Future experiments should be designed to address the hypothesis that food supplementation creates ecological traps, for example, by monitoring predators within and in the surroundings of supplemented and control plots. Close monitoring of the predators, for example, using GPS collars (Moseby et al. 2012), would allow researchers to pinpoint the activity and movements of predators in and around food-supplemented sites, and remote cameras (Lazenby & Dickman in press) could be used to monitor interactions of predators with prey in the vicinity of feeding sites. Wildlife managers would be particularly interested in the potentially negative effect of the use of food supplementation to recover populations of endangered species (e.g. Armstrong & Seddon 2008).

In addition, the limitations of most designs of food supplementation experiments so far must be identified. There is a clear trade-off between the two experimental approaches most used in the literature, namely the provision of food to open populations and the fencing of populations within enclosures. Experiments with open populations have the advantage of using a natural ecological situation, but they are susceptible to the potentially confounding effects of immigration. Experiments with enclosed populations avoid the potential problems of immigration, but they are usually carried out under artificial conditions that restrict both dispersal and some ecological interactions. These two approaches certainly allow strong tests of particular hypotheses, but their drawbacks hamper the evaluation of more general ecological questions, such as whether food is the main driver of population cycles (e.g. Korpimäki et al. 2004).

We suggest that such general questions may be addressed using an alternative experimental design, and more appropriate estimates of reproduction and survival. The alternative experimental design is rarely explored in the literature: the provision of food over large areas of habitat, encompassing both sampling areas and a large boundary strip (as in Karels et al. 2000). With this design, the population of each sampling area would not be artificially crowded with immigrants, while experiencing all the ecological interactions that are present in the natural system, and reproduction and survival would be less likely to be underestimated because the probability of recapturing mobile animals would be increased. The provision of food over large areas may be more costly and time-consuming, but also may require fewer resources than those needed to install and maintain population enclosures. Considering that food is usually provided in great excess to local populations, as indicated by our analyses of energy availability, it might not be necessary to increase the total amount of food, only to increase its dispersion over the landscape. Food supplementation experiments have allowed enormous advances in population ecology and will certainly continue to do so, especially if innovative experimental designs are combined with different sampling methods to obtain even more reliable parameter estimates.

Acknowledgements

We are grateful to André F. Mendonça, Camila S. Barros, Maja Kajin, Marcelo M. Weber, Matheus F. Dalloz, Natalia O. Leiner, Priscilla L. Zangrandi, Stan Boutin, Vinicius F. Farjalla and an anonymous reviewer for comments on earlier versions of this paper. Support was provided by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro e Conselho Nacional de Desenvolvimento Científico e Tecnológico.

Data accessibility

Raw data used in analyses: uploaded as online supporting information (Appendix S1 and S2).

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