Use of high potency statins and rates of admission for acute kidney injury: multicenter, retrospective observational analysis of administrative databases

Department of Anesthesiology, Pharmacology and Therapeutics
University of British Columbia
V8W 1Y2VancouverVictoria, BCCanada

Department of Medicine
University of Calgary
CalgaryCanada

Institute for Clinical Evaluative Sciences
TorontoCanada

Health Quality Council
SaskatoonCanada

Manitoba Centre for Health Policy
University of Manitoba
WinnipegCanada

Department of Medicine
University of Montreal
MontrealCanada

Community Health and Epidemiology
Dalhousie University
HalifaxCanada

Division of Nephrology
University of Western Ontario
LondonCanada

Centre for Clinical Epidemiology
McGill University
Lady Davis Institute
Jewish General Hospital
MontrealCanada

Use of high potency statins and rates of admission for acute kidney injury: multicenter, retrospective observational analysis of administrative databases
10.1136/bmj.f880OPEN ACCESS Colin R Dormuth assistant professor 1 , Brenda R Hemmelgarn associate professor 2 , J Michael Paterson scientist 3 , Matthew T James assistant professor 2 , Gary F Teare director of quality management and analysis 4 , Colette B Raymond research scientist 5 , Jean-Philippe Lafrance assistant professor 6 , Adrian Levy head 7 , Amit X Garg professor of medicine 8 , Pierre Ernst professor of medicine 9 , Canadian Network for Observational Drug Effect Studies (CNODES)
Objective To quantify an association between acute kidney injury and use of high potency statins versus low potency statins.Design Retrospective observational analysis of administrative databases, using nine population based cohort studies and meta-analysis. We performed as treated analyses in each database with a nested case-control design. Rate ratios for different durations of current and past statin exposure to high potency or low potency statins were estimated using conditional logistic regression. Ratios were adjusted for confounding by high dimensional propensity scores. Meta-analytic methods estimated overall effects across participating sites.

Introduction

Evidence has indicated that statin use could lead to unintended adverse renal effects. 1-3 A large scale, randomized controlled trial-JUPITER (Justification for the Use of Statins in Prevention: an Intervention Trial Evaluating Rosuvastatin)-compared high dose (20 mg) rosuvastatin with placebo in almost 18 000 patients. 4 Data subsequently reported to the United States Food and Drug Administration (FDA) showed a non-significant increase of 19% in acute renal failure (risk ratio 1. 19, 95% confidence interval 0.61 to 2.31). 5 The non-significant risk increased further to 35% (1.35, 0.81 to 2.23) when the endpoint also included doubling of serum creatinine. A large, population based cohort study of over two million patients also reported that statin use was associated with a greater than 50% increase in risk of acute renal failure, with evidence of raised risk within the first year of statin use, and a dose-response effect. 3 In a Canadian product monograph for rosuvastatin, the most potent statin, the manufacturer also reported renal impairment in some patients who received 80 mg of the drug in investigational clinical trials. 6 It remains unclear whether statin therapy is specifically associated with greater adverse renal effects. In the light of data alluding to a possible dose response, we aimed to explore a possible association between statins and kidney injury by comparing patients who were prescribed high potency statins with those prescribed low potency statins. The main advantage of using exposure to lower potency statins as a reference group was an expectation that a substantial amount of unmeasured confounding by indication would thus be eliminated. A comparison of high versus low potency might also be informative for treatment where statin use is clearly supported by evidence of total mortality benefit (for example, in patients who have had myocardial infarction), but where evidence of incremental benefit for high potency statins versus low potency statins is questionable. 7 In the inaugural study of the Canadian Network for Observational Drug Effect Studies (CNODES), 8 we used the administrative healthcare records of two million people to assess the association between treatment with high versus low potency statins and hospitalization for acute kidney injury in patients with and without chronic kidney disease. CNODES is part of the new Canadian Drug Safety and Effectiveness Network, initiated by Health Canada and administered by the Canadian Institutes of Health Research. The principal aim of CNODES is to collaboratively analyze existing healthcare databases using observational research methods, to provide rapid answers to questions on drug safety and effectiveness.

Methods

Setting and source population

We used a common analytical protocol to conduct studies of statins in acute kidney injury in seven Canadian provinces (Alberta, British Columbia, Manitoba, Nova Scotia, Ontario, Quebec, and Saskatchewan; source population 33 million in 2011), as well as in two international databases in the United Kingdom (General Practice Research Database (GPRD), 11.6 million) and the US (Caremark-Medicare database, 1.2 million). The study populations were patients aged 40 years or older, newly treated with statins between 1 January 1997 and 30 April 2008. In three provinces, only patients aged 65 years and older were available, and four of the databases were established after 1997.

Data sources

All participating jurisdictions contributed data from their respective administrative healthcare databases. Prescription data included, at a minimum, patient level records specifying the drug dispensed, the quantity or days' supply of treatment, and the date of dispensation. The GPRD was an exception in that written prescriptions were recorded rather than actual drugs dispensed. Physician claims and hospitalizations databases included date of service encounter or hospital admission, up to 25 ICD-9 or ICD-10 (international classification of disease, 9th or 10th revisions) diagnosis codes, and procedure and billing codes. The Saskatchewan databases and GPRD included laboratory test data. The GPRD also included body mass index and smoking status. All databases have been used extensively in observational research.

Cohorts of patients according to statin use

Our analytical approach was to conduct as treated analyses using nested case-control methodology. This design is a good alternative to cohort analysis when studying time dependent exposures, and its computational efficiency is well suited to analyzing rare events in large databases. 9 In each jurisdiction, patients from the source population were included in cohorts of chronic or non-chronic kidney disease if they were newly dispensed a statin between 1 January 1997 (or one year after the beginning of data availability) and 30 April 2008.

We defined a dispensing event as new if no cholesterol lowering drug (World Health Organization Anatomical Therapeutic Class C10) or prescription for niacin was dispensed in the previous 365 days. The date of the new statin prescription was defined as the cohort entry date. Daily statin doses were categorized according to their potency in lowering serum concentrations of low density lipoprotein (LDL) cholesterol.

High potency statin treatment was defined as at least 10 mg rosuvastatin, at least 20 mg atorvastatin, and at least 40 mg simvastatin; all other statin treatments were defined as having low potency. Our categorization was derived from a systematic review and meta-analysis of randomized controlled trials that quantified the effects of statins on LDL cholesterol concentration. 10 The analysis showed that statins clustered around three levels of LDL reduction. One group (defined as low potency) produced a reduction of about 35%, another (defined as high potency) reduced concentrations by about 45%; 80 mg rosuvastatin lowered concentrations by 60%. This classification is similar to ones used elsewhere. [11][12][13] We grouped 80 mg rosuvastatin with the middle group, owing to relatively few of such prescriptions. Therefore, statins were categorized as high or low in our study, according to whether they would produce a theoretical reduction in LDL cholesterol concentration of less than 45%, or at least 45%. 12 Patients were excluded if they were younger than 40 years (<66 years in jurisdictions that only had drug data for senior citizens), had less than one year of enrolment in their medical system, or received any cholesterol lowering drug or underwent dialysis in the previous year. Finally, we assigned eligible patients to cohorts of chronic and non-chronic kidney disease according to whether they had at least one hospitalization or physician medical encounter for non-dialysis dependent, chronic kidney disease in the previous three years. The web appendix lists definitions of chronic kidney disease.

Acute kidney injury endpoint

The primary endpoint was hospitalization for acute kidney injury, defined using a validated algorithm (diagnosis code for acute kidney injury in any of the following listed diagnoses: ICD-9 584, 584.5, 584.6, 584.7, 584.8, or 584.9; ICD-10 N17, N17.0, N17.1, N17.2, N17.8, or N17.9). 14 15 High dimensional propensity scores High dimensional propensity scores (hdPS) were estimated for all patients in the cohorts. The hdPS algorithm is available as downloadable SAS software files from the Brigham and Women's Hospital. 16 As described in detail elsewhere, 17 hdPS is an empirically driven, multistep process to adjust for confounding bias in observational studies. The hdPS algorithm prioritizes thousands of variables at the drug, diagnostic, procedural, and demographic level according to their potential to cause multiplicative bias in the estimate of an exposure-outcome association (for example, rate ratio). Typically, the 500 variables most likely to cause bias are included in a propensity score model. We used logistic regression to estimate the predicted probability (as measured by the propensity score) of exposure to high potency statins versus low potency statins, conditional on all of the included covariates.

In addition to the 500 covariates empirically selected for the propensity score models, we also included the following prespecified covariates: year of cohort entry, hospitalization, order for a laboratory test, greater than four distinct drugs dispensed, greater than four physician visits, hypertensive disease, hypercholesterolemia, peripheral vascular disease, congestive heart failure, and injury or poisoning, all within the year prior to cohort entry (web appendix). Propensity score models were estimated using logistic regression.

As treated analysis

In each cohort described above, we defined a follow-up end date for each patient as the earliest occurrence of an acute kidney injury endpoint, date of death, date of emigration, 24 months after initiation on statin treatment, a dispensing for cerivastatin, or 31 March 2010. Cerivastatin was not among the statins included in the analysis. We identified all cases of the endpoint occurring within patients' follow-up windows and defined the date of admission for acute kidney injury as the index date. For each case, we randomly selected ten controls from a matched risk set comprising patients of the same sex and age within one year (if no controls were available, within five years), who also entered the cohort within 90 days before or after the case's cohort entry date.

We used conditional logistic regression to estimate matched odds ratios for three mutually exclusive durations of current exposure (≤120, 121-365, and 366-730 days) and past exposure (no exposure within 120 days of the index date). Patients who received both a high and low potency statin in the same current exposure category or as past exposures were categorized as receiving high potency statins in that particular category. Adjusted matched odds ratios were estimated by including the tenth of the propensity score (nine binary indicator variables); diagnosis of diabetes; and prior use of angiotensin II converting enzyme inhibitors or receptor blockers, non-steroidal anti-inflammatory drugs, thiazide diuretics, and loop diuretics. In addition, we assessed potential drug-drug interactions with statins by including main effect variables and interaction variables for three types of compounds: macrolide antibiotics, fibrates, and calcium channel blockers.

Fixed cohort analysis

We also conducted fixed cohort analyses on the cohorts in each jurisdiction, where the statin exposure category was defined by the initial prescription at cohort entry. We expected that fixed cohort estimates would be biased towards the null hypothesis, mostly because of dilution of risk due to treatment non-adherence and dose escalation. The hdPS model used in this analysis was the same as the model in the as treated analysis, but it estimated effects for 180 days of follow-up after cohort entry instead of two years. For patients with non-chronic or chronic kidney disease, we used logistic regression to estimate odds ratios for statin potency and acute kidney injury. Odds ratio estimates were reported as relative risks, and the logistic regressions included tenth of propensity score (nine binary indicator variables); category of age (in five year groups); diagnosis of diabetes; and prior use of angiotensin II converting enzyme inhibitors or receptor blockers, non-steroidal anti-inflammatory drugs, thiazide diuretics, and loop diuretics.

Meta-analysis

All analyses were undertaken independently at each site, which were kept blind to results from the other sites until the meta-analysis was conducted. For the meta-analysis, we pooled the studies from each site using either fixed effect or random effects models according to results of χ 2 tests for heterogeneity. 18 Matched odds ratios were reported as rate ratios. Inverse variance weighted odds ratios and 95% confidence intervals were calculated to estimate the total effect across all study populations.

Results

Study populations

Overall, 2 067 639 patients in participating databases were newly exposed to statins during the study period, of which 673 410 (33%) received high potency statins (table⇓); the sizes of the source populations varied broadly. We recorded 59 636 patients with chronic kidney injury using statins within three years before cohort entry. The table also shows baseline characteristics of the overall study population, matched and unmatched on propensity score, which demonstrates the comparability of patients using high potency and low potency statins on measured factors conditional on their propensity scores. The mean age of study participants was 68 years, although in jurisdictions with younger patients the mean age was between 61 and 65 years. Fifty percent of patients were women.

Rates of acute kidney injury

In the Canadian jurisdictions with patients younger than 65 years, the risk of hospitalization for acute kidney injury at six months in patients with non-chronic kidney disease receiving low dose statins (that is, the reference group) ranged from 1.2-1.4 per 1000 patients (in British Columbia, Manitoba, and Saskatchewan) to 3.5 per 1000 patients (in Quebec). The corresponding risk was 1.0 per 1000 patients in the GPRD. In the remaining jurisdictions with data for adults aged 65 years and older only, the corresponding risk was 3.1 per 1000 patients thousand in Ontario, Nova Scotia, and Alberta, and 4.0 per 1000 patients in the US Medicare Caremark database. Rates were substantially higher in patients with a history of chronic kidney disease: 23-45 per 1000 patients in first six months after statin initiation in Canada, 10 per 1000 patients in the GPRD, and 63 per 1000 patients in the US Medicare Caremark database.

As treated analysis

Patients who started high potency statins were 34% more likely to be hospitalized for acute kidney injury than those who started low potency statins in the first 120 days of treatment (fixed effect rate ratio 1.34, 95% confidence interval 1.25 to 1.43; fig  1⇓). The elevated effect was attenuated with longer durations  2⇓).

The χ 2 tests for heterogeneity were not significant for all meta-analyses except for past use in patients with chronic kidney disease. In that analysis, a random effects estimate of the total effect was reported. We checked for effect modification of statin potency by macrolide antibiotics, calcium channel blockers, and fibrates, but did not find any significant interactions. The fixed cohort analysis also showed a significantly increased risk for acute kidney injury within six months of treatment initiation in both groups of patients with non-chronic and chronic kidney disease (web fig).

Discussion

In this study of over two million patients newly treated with a statin, we found a significant relative increase of 34% in the rate of hospitalization for acute kidney injury within 120 days of initiation for patients receiving high potency statins versus low potency statins. Our as treated analysis was based on an expectation that less than perfect treatment persistence and a high tendency for subsequent switching to higher doses might cause a fixed cohort analysis to underestimate the risk while actually on treatment. Loss of some patients to follow-up and competing risks also could have contributed to an underestimation of the effect. The as treated analysis, which allowed quantification of risk from different durations of current exposure, indicated that risk remained elevated for at least two years.

Although we used multiplicative models to answer our study questions, it is the subsequent translation of relative risks into numbers needed to treat to harm that provides the most useful metric for prescribers, regulators, and decision makers. In this regard, we estimate that 1700 patients with non-chronic kidney disease need to be treated with a high potency statin instead of a low potency statin for 120 days to cause one additional hospitalization for acute kidney injury. A number of 1700 patients is sufficiently large for there not to be enough patients enrolled in randomized trials to find an association between acute kidney injury and statin use with high precision. However, our definition of acute kidney injury was chosen to be highly specific and thus probably excluded a number of patients with real but milder cases, which could have underestimated the absolute risk.

Further studies are necessary to determine the biological mechanism linking statins to kidney injury. The elevated risk in patients using high potency statins could be related to an increased risk of rhabdomyolysis. Another mechanism could be the statin induced suppression of coenzyme Q10, a fat soluble enzyme with antioxidant properties. Statins have been shown to block the production of coenzyme Q10, 19 20 and placebo controlled trials of coenzyme Q10 treatment in humans and animals with kidney disease have shown improvements in renal function within 28 days of use. 20 21 Other studies have shown an association between statin treatment and proteinuria. 5 22 Pleiotrophic statin effects should also be contemplated.

Comparison with existing evidence

According to data from the JUPITER trial, as published by the FDA, 5 the maximum likelihood estimate of the relative risk was 1.11 for any renal event over a median follow-up duration of 1.9 years, and 1.19 for acute renal failure. Our rate ratio estimate was 1.15 for acute kidney injury for patients treated for one to two years. Over all treatment durations in our analysis, the average rate ratio was 1.17, or 1.20 if past treatment was excluded. The compatibility of these results with our hypothesis, their agreement with the maximum likelihood estimate observed in the large JUPITER trial, and the high degree of precision obtained from our study population, together lend meaningful support for this increased risk.

Similarity between our results and other epidemiologic studies is mixed. One multicenter study of statin use and acute kidney injury in patients with community acquired pneumonia (CAP) reported an odds ratio of 1.32 for acute kidney injury in patients with CAP who received statins compared with statin naive patients. 23 By contrast, a meta-analysis of four observational studies of rosuvastatin, designed to study multiple outcomes but which included renal failure, reported no difference between rosuvatstain and other statins. 24 This meta-analysis is impossible to interpret from a statin potency perspective, because the control patients received other statins of all different potencies.

It is also important to note that most statin treatment in randomized trials was of low potency. The JUPITER trial showed that about 450 patients needed to be treated with 20 mg rosuvastatin per day instead of placebo for two years to prevent one death from myocardial infarction, stroke, or cardiovascular disease (combined endpoint). 4 It remains to be shown whether the number needed to treat to benefit with high potency statins instead of low potency statins (versus placebo) would outweigh the combined risk of acute kidney injury, rhabdomyolysis, and diabetes.

Implications

In a meta-analysis of clinical trials of statins, the Cholesterol Treatment Trialists (CTT) reported that more intensive statin treatment in secondary prevention was associated with a 0.3% reduction in absolute risk in major coronary events per year of treatment, compared with less intensive statin treatment over a mean of five years. 25 Some have argued that an absolute risk reduction of 0.3% per year overstates what could be expected in typical clinical practice. 7 Importantly, the trials comparing more intensive treatment with less intensive treatment included in the CTT meta-analysis were mostly comparisons of a low dose of a particular statin versus the highest possible dose of that same statin. In reality, clinicians would not choose between, for example, 10 mg of atorvastatin and 80 mg of atorvastatin. Given what is likely to be a small magnitude of incremental cardiovascular benefit of high potency statins over low potency statins in reality, a pressing question is how to identify patients for whom the risk-benefit balance for high potency statin treatment is unfavourable.

Methodological considerations

Chronic kidney disease status could have been misclassified at cohort entry using ICD codes from administrative data. However, in view of the specificity of these definitions (99%), 26 we do not believe that any potential misclassification (that is, in relation to the small number of participants with chronic kidney disease being misclassified as having non-chronic kidney disease) would be substantial enough to have influenced the estimate of effect in the patients with non-chronic kidney disease.

Our outcome of acute kidney injury was defined using a validated algorithm with high specificity but low sensitivity. Thus, the absolute rates of acute kidney injury identified in hospitalization records would underestimate the true incidence based on changes in serum creatinine. However, we do not expect that our definition of acute kidney injury would have resulted in differential misclassification of patients during the study period. Acute kidney injury would have been an unexpected outcome of treatment, and patients with true injuries misclassified as non-injuries would have been those not hospitalized for the disease, and were probably less clinically relevant than those captured by our specified definition.

Although our results are much more compatible with the maximum likelihood estimates of renal harm in the JUPITER trial than with a null hypothesis, confounding by indication remains a possible threat to the validity of our results. To minimize this bias, the reference group consisted of patients who also received statin treatment. We adjusted for a broad spectrum of possible confounders using hdPS scores. There was probably a non-significant trend over time towards increasing use of high potency statins, which necessitated the inclusion of calendar year of cohort entry as a covariate in the models.

There was also a small imbalance after propensity score matching between patients using high potency and low potency statins in the proportion that had congestive heart failure (table), which is a known independent risk factor for acute kidney injury.

In view of the difference between and the relative numbers of patients exposed to high potency statins versus low potency statins, we estimate that at least a 25-fold independent relative increase in the risk of acute kidney injury associated with congestive heart failure would be needed to spuriously produce our risk estimate of 1.34 in our population (that is, association between acute kidney injury with statin potency). A 2.0 risk of acute kidney injury associated with congestive heart failure would produce a spurious association between statin potency and acute kidney injury of about 1.01. Diagnosis of congestive heart failure was included in the propensity score models, and outcome models were adjusted for use of loop diuretics in the year before cohort entry. Ethical approval: Ethics approval for each study was obtained from the respective academic institutions in each province.

Data sharing: CNODES is not permitted to release individual level data or aggregated data with small cell sizes. The analytical protocol for this analysis is available on request.

What is already known on this topic

Various data sources have pointed to a possible harmful effect of statins on the kidney, although previous analyses have not specifically looked at acute kidney injury

What this study adds

Prescription of high potency statins (≥10 mg rosuvastatin, ≥20 mg atorvastatin, ≥40 mg simvastatin) is associated with an increased rate of hospital admission for acute kidney injury, compared with lower potency statins Increased risk of admission occurs early after starting statin treatment and remains elevated for at least two years Prescribers should consider this potential risk when contemplating use of high potency statins in clinical practice, particularly when treatment with a low potency statin is an option *One to one matching was used. Within the same sex and age within one year, each patient using high potency statins was matched to a patient using low potency statin with the nearest propensity score. If multiple controls had the same propensity score, one was chosen at random.

No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribeof current exposure. The rate of hospitalization for acute kidney
injury did not increase significantly in patients with chronic
kidney disease (1.10, 0.99 to 1.23; fig

in certain jurisdictions). Except where prevented by insufficient data or small cell size limitations, all prespecified outcomes in the protocol are reported. A copy of the study protocol is available on request. All coauthors contributed to roundtable discussions on protocol development and all provided critical revisions to the manuscript. BRH, MTJ, J-PL, and AXG were instrumental in defining the acute kidney injury outcome and identifying patients with chronic kidney disease. CBR assisted with exposure definitions. JMP, GFT, AL, and PE contributed to numerous study design issues and critical revision of the manuscript. CRD was responsible for drafting the manuscript and incorporating suggestions of coauthors and he is the guarantor of the manuscript. The final manuscript was approved by the publications subcommittee of CNODES.Funding: CNODES is funded by a grant from Health Canada, the Drug Safety and Effectiveness Network, and the Canadian Institutes for Health Research that oversaw the peer review and funding process.Competing interests: All authors have completed the ICMJE uniform disclosure form at www.icmje.org/coi_disclosure.pdf and declare: support from Health Canada, the Drug Safety and Effectiveness Network, and the Canadian Institutes for Health Research for the submitted work; PE receives consultancy and speaker's fees from Astra Zeneca, Boehringer Ingelheim, Merck, and Nycomed, and a research grant from Boehringer Ingelheim; AL receives consultancy fees from Oxford Outcomes (now Icon), a company that carries out contracted work for pharmaceutical companies; no other relationships or activities that could appear to have influenced the submitted work.This study was made possible through data sharing agreements between
CNODES member research centres and the respective provincial
governments of Alberta, British Columbia, Manitoba, Nova Scotia,
Ontario, Quebec and Saskatchewan. We thank Sebastian Schneeweiss
and Jun Liu of the Division of Pharmacoepidemiology and
Pharmacoeconomics at Brigham and Women's Hospital for their
expertise and assistance in analyzing the US Medicare data and use
of the high-dimensional propensity score method; and James M Wright
for sharing expert knowledge of pharmacology and clinical trial evidence
for statins.

CNODES investigators: Samy Suissa (principal investigator, McGill
University); David Henry and Michael Paterson (Ontario); Colin Dormuth
(British Columbia); Brenda Hemmelgarn (Alberta); Gary Teare
(Saskatchewan); Patricia Martens and Patricia Caetano (Manitoba);
Pierre Ernst, Jacques LeLorier, and Robert Platt (Québec); and Adrian
Levy (Nova Scotia).

Contributors: CRD was responsible for overseeing the development of
the study protocol and the creation of a data analysis plan that was
adapted for use in each jurisdiction and each data set. All variables and
all outcomes were specified in that protocol and any deviations from
this were for technical reasons only (for example, variable coding of
administrative data

Table Table 1|
TableBaseline characteristics of patients receiving high potency and low potency statins (1997-2008) Patients with chronic kidney disease Patients without chronic kidney disease Patients with chronic kidney disease Patients without chronic kidney diseaseFull cohort

Subset with matched
propensity score*
Full cohort

Subset with matched
propensity score*

Low potency
statins (n=37
295)

High
potency
statins (n=22
341)

Low potency
statins (n=20
511)

High potency
statins (n=20
511)

Low potency
statins (n=1
356 934)

High potency
statins
(n=651 069)

Low potency
statins (n=633
054)

High potency
statins (n=633
054)
(continued)

Full cohort

Subset with matched
propensity score*
Full cohort

Subset with matched
propensity score*

Low potency
statins (n=37
295)

High
potency
statins (n=22
341)

Low potency
statins (n=20
511)

High potency
statins (n=20
511)

Low potency
statins (n=1
356 934)

High potency
statins
(n=651 069)

Low potency
statins (n=633
054)

High potency
statins (n=633
054)

No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe Figures Fig 1 As treated analysis of hospitalization for acute kidney injury up to two years after cohort entry in patients without chronic kidney disease. *Crude rate ratios were obtained from conditional logistic regression, conditioned on the matching variables age, sex, and cohort entry date No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe Fig 2 As treated analysis of hospitalization for acute kidney injury up to two years after cohort entry in patients with chronic kidney disease. *Crude rate ratios were obtained from conditional logistic regression, conditioned on the matching variables age, sex, and cohort entry date No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe
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A Quantitative Test of Hamilton's Rule for the Evolution of Altruism
Published May 3, 2011

Markus Waibel firstname.lastname@example.com
School of Engineering
Laboratory of Intelligent Systems
Ecole Polytechnique Fédérale de Lausanne
LausanneSwitzerland

Dario Floreano
School of Engineering
Laboratory of Intelligent Systems
Ecole Polytechnique Fédérale de Lausanne
LausanneSwitzerland

Laurent Keller email@example.com
Department of Ecology and Evolution, Biophore
University of Lausanne
LausanneSwitzerland

University of Edinburgh
United Kingdom

Nick H Barton
A Quantitative Test of Hamilton's Rule for the Evolution of Altruism
Published May 3, 2011Received September 13, 2010; Accepted March 21, 2011;Academic Editor: Funding: This research was funded by the Swiss National Science Foundation, the European Commission ECAgents and Swarmanoids projects, and the European Research Council. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. *
The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb 2 c.0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory. Citation: Waibel M, Floreano D, Keller L (2011) A Quantitative Test of Hamilton's Rule for the Evolution of Altruism. PLoS Biol 9(5): e1000615.

Introduction

One of the enduring puzzles in biology and the social sciences is the origin and persistence of altruism, whereby a behavior benefiting another individual incurs a direct cost for the individual performing the altruistic action. A solution to this apparent paradox was first provided by Hamilton [1], who showed that a behavior increases in frequency when rb 2 c.0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While this rule has provided an important framework in which to conceptualize social evolution [2][3][4][5][6][7][8][9][10][11][12], it is based on several assumptions, including weak selection, additivity of costs and benefits of fitness components, and a special definition of relatedness that uses statistical correlations among individuals rather than genealogy to describe similarity. Several studies investigated how violations to these assumptions may lead to failures of Hamilton's original 1964 rule [13][14][15][16][17][18][19][20][21], but it is yet unclear how the combined effects of these factors may affect the evolution of altruism in organisms with a complex mapping between genotype and phenotype. It also remains to be investigated to what extent Hamilton's original 1964 rule is influenced by factors such as drift and interactions between loci within genomes [22,23].

To investigate how a complex mapping between genotype and phenotype can affect the course of social evolution, we conducted artificial evolution with groups of robots in simulations by modifying a system recently developed to investigate the evolution of cooperative transport [24]. Eight small (26264 cm) Alice robots [25] and eight food items were placed in a foraging arena with one white wall and three black walls. The performance of robots was proportional to the number of food items successfully transported to the white wall and the robots were given the option to allocate the fitness rewards of successfully transported items to themselves (selfish behavior) or share them with other group members (altruistic behavior-in this case the fitness reward of the food item was shared equally between the seven other robots in the group). By choosing appropriate fitness values for shared and nonshared food items (see Materials and Methods), it was possible to precisely manipulate the benefits and cost of helping behavior (i.e., the c and b values of Hamilton's rule, see Materials and Methods).

The robots were equipped with two motorized wheels and three infrared distance sensors that could detect food items up to 3 cm away, a fourth infrared distance sensor with 6 cm range allowing to distinguish food items from robots, and two vision sensors mounted on top of the robot to perceive the color of the arena walls ( Figure 1A). These six sensors were connected to a neural network comprising six input neurons, three hidden neurons, and three output neurons ( Figure 1B). Two output neurons determined the speeds of the wheels, while the third neuron determined whether the food items successfully collected were shared or not. The genome of the robots (33 genes) encoded the 33 connection weights of the neural network (see Materials and Methods) and thus determined how sensory information was processed and how robots behaved. Our analyses reveal that this system resulted in both pleotropic and epistastatic effects as well as a high proportion of mutations having strong effects on behavioral traits (i.e., leading to deviations from the assumption of weak selection).

Results

We conducted 500 generations of selection in a population consisting of 200 groups. The probability of robots to transmit their genomes from one generation to the next was proportional to their individual fitness (see Materials and Methods). The selected genomes were randomly assorted and subjected to crossovers and mutations to create the 1,600 new genomes (200 groups of 8 robots) forming the next generation [24].

This experimental setup allowed us to independently manipulate the relatedness between robots within a group and the cost-tobenefit ratios of helping. To quantitatively test Hamilton's rule for the evolution of altruism, we investigated how the level of altruism (defined as the proportion of food items shared with other group members) changed over generations in populations with five different c/b ratios and five relatedness values (see Materials and Methods). For each of these 25 treatments, the selection experiments were conducted in 20 independently evolving populations. Because of the impossibility to conduct hundreds of generations of selection with real robots, we used physics-based simulations that precisely model the dynamical and physical properties of the robots. We previously showed that evolved genomes can be successfully implemented in real robots [26] that display similar behavior to that observed in the simulations.

Because the 33 genes were initially set to random values, the robots' behaviors were completely arbitrary in the first generation. However, the robots' performance rapidly increased over the 500 generations of selection ( Figure 2). The level of altruism also rapidly changed over generations with the final stable level of altruism varying greatly depending on the within-group relatedness and c/b ratio ( Figure 3). When the c/b value was very small (0.01), the level of altruism was very high in the populations where within-group relatedness was positive (i.e., 0.25, 0.5, 0.75, and 1.00) and close to zero when robots were unrelated ( Figure 4). In the treatments with other c/b values, the level of altruism was also very low when the relatedness was close to 0 and the level of altruism also rapidly increased when the relatedness became higher than a given value. In all cases, the transition occurred when r became greater than c/b, as predicted by Hamilton's rule.

When the relatedness was equal to c/b, there was an intermediate level of altruism with the frequency of altruistic acts not differing significantly from the initial value, which was 0.5 (four one-sample Wilcoxon tests, df = 19, all p.0.368). This is the expected pattern because the inclusive fitness of robots, comprising both their own fitness points and those gained from altruists, is independent of whether or not they behave altruistically when r = c/b. Under such conditions, the level of altruism should vary only as a result of drift over generations, thus leading to important between-population variation in the level of altruism. Consistent

Author Summary

One of the enduring puzzles in biology and the social sciences is the origin and persistence of altruism, whereby a behavior benefiting another individual incurs a direct cost for the individual performing the altruistic action. This apparent paradox was resolved by Hamilton's theory, known as kin selection, which states that individuals can transmit copies of their own genes not only directly through their own reproduction but also indirectly by favoring the reproduction of kin, such as siblings or cousins. While many studies have provided qualitative support for kin selection theory, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. In this study, we conduct simulations with the help of a simulated system of foraging robots to manipulate the costs and benefits of altruism and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different costs and benefits of altruistic behavior, we show that kin selection theory always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects, as well as mutations with strong effects on behavior and fitness. In addition to providing a quantitative test of kin selection theory in a system with a complex mapping between genotype and phenotype, this study reveals that a fundamental principle of natural selection also applies to synthetic organisms when these have heritable properties.

with this prediction, the standardized variance (F = Var(p)/pq) in altruism when r was equal to c/b (F = 0.204) was significantly higher than when r was greater than c/b (F = 0.018; Mann-Whitney, df = 13, p = 0.002) and when r was smaller than c/b (F = 0.015; Mann-Whitney, df = 13, p,0.003).

The fact that the level of altruism remained slightly greater than 0 when r was smaller than c/b and slightly lower than 1 when r was greater than c/b can be explained by mutations maintaining some behavioral variability in the population. In line with this view of the level of altruism being at mutation-selection equilibrium, the level of altruism became significantly closer to zero (Pearson's r = 0.643; Mann-Whitney, df = 13, p,0.001) as the strength of selection increased (i.e., when the value r 2 c/b became more negative, only negative values of r 2 c/b considered for the correlation). Similarly, the level of altruism became significantly closer to 1 (Pearson's r = 0.805; Mann-Whitney, df = 13, p,0.004) as the strength of selection for higher levels of altruism increased (i.e., when the value r 2 c/b increased, only positive values of r 2 c/b considered in the correlation).

To determine whether mutations in our neural network had pleiotropic and epistatic effects and whether there were departures from weak mutations effects, we conducted additional experiments at the last generation in two treatments with intermediate r and c/b values (treatment 1: r = 0.25, c/b = 0.75; treatment 2: r = 0.75, c/ b = 0.25). First, for each treatment, we subjected 4,000 individuals (one in each group) to a single mutation of moderate effect (see Materials and Methods). In the first experiment, performance was significantly affected by a much higher proportion of the mutations than the level of altruism (Table 1). Importantly, 1.36% of the mutations affecting the level of altruism also translated into a significant change in performance, indicating widespread pleiotropic effects. Similar results were obtained in the second experiment with 4.91% of the mutations affecting the level of altruism also significantly affecting performance. Second, we tested for epistatic effects by comparing the effect of a single mutation in 4,000 individuals with two allelic variants at another locus (see Materials and Methods). The genetic background significantly influenced the effect of the mutation in 2,371 (59.3%) of the cases in the first treatment and 2,336 (58.4%) of the cases in the second treatment. These results demonstrate that epistatic interactions are also widespread. Finally, our experiments showed frequent departures from weak effects on behavior and fitness. Performance changed by more than 25% for 1,616 (40.4%) of the mutations in the first treatment and 1,776 (44.4%) of the mutations in the second treatment, and the level of altruism changed by more than 25% for 552 (13.8%) and 1,808 (45.2%) of the mutations in the first and second treatment, respectively.

Discussion

Although Hamilton's original 1964 rule provides a general framework of how natural selection works [17,27], its theoretical and empirical applications usually involve the limiting assumptions of weak selection and additivity of costs and benefits of fitness components as well as the absence of pleiotropic and epistatic gene interactions [15,16,28] (but see [13] for relaxations of some of these assumptions in concrete applications), leading to the conclusion that the rb 2 c.0 rule should be used with caution when there are pleiotropic, epistatic, and non-additive effects [29,30]. Interestingly, the genetic architecture of the robots in our system also led to departure from all these assumptions with the exception of nonadditivity of costs and benefits of fitness components. However, the occurrence of non-additive (epistatic) effects of mutations at several loci in the genome leads to a situation that is conceptually similar to non-additivity of costs and benefits of fitness components [22]. In both cases, the fitness depends non-additively on gene action, with the interaction involving alleles at two loci on the same genome in the case of non-additive (epistatic) gene effects, and alleles at two homologous loci on two different genomes in the case of nonadditivity of costs and benefits of fitness components.

Despite the fact that the assumptions mentioned above were not fulfilled, Hamilton's original 1964 rule always accurately predicted the conditions under which altruism evolved in our system. Whatever the c/b value used, altruism always evolved in populations where r was greater than c/b. This finding is important given that the assumption of weak selection, additivity of costs and benefits of fitness components and absence of pleiotropic and epistatic gene interactions are also likely to be violated in real  organisms that also have a complex mapping between genomes and phenotypes.

Another important issue relates to the measure of relatedness. There has been considerable confusion in the literature since relatedness coefficients actually measure more than pedigree coefficients and because different derivations of Hamilton's rule take as their focal trait a variety of different quantities [16,17,30]. In the original derivation of Hamilton's rule [1] and many that followed (e.g., [12,31]), the trait of interest was the genetic value at a single gene position and the regression coefficient of relatedness corresponded to an identity in state relative to the population average [31]. The interest in social evolution where social partners tend to be genealogical kin [1] has led to the use of Wright's F statistics as a measure of relatedness (e.g. [12,22,32]). Alternatively, Hamilton's rule has been derived to express the change in the social behavior phenotype (e.g., [16,22,33,34]), often considered as a quantitative trait with many underlying gene positions contributing. In this case the coefficient of relatedness represents a regression of some measure of the individual's genetic value for that trait such as a breeding value [17], p score [16], gene frequency [1,12], or partner phenotype on its own phenotype value [34].

Interestingly, the simple genetic structure of our groups leads to all these measures of relatedness being identical. In all our  experiments groups were started by individuals randomly chosen from the previous generations. The relatedness between these founding individuals is therefore zero as they are not more genetically or phenotypically similar within groups than between groups. Positive within-group relatedness was created by cloning the founding individuals. Thus, positive relatedness was only due to one-generation coancestry and the probability that benefits of altruism being provided to a clone compared to an unrelated individual. Such a breeding system is conceptually very similar to that Hamilton had in mind when trying to explain the evolution of reproductive altruism in social insects where the sterile (altruistic) workers are the offspring of their mother queen (the individual benefitting from the altruistic worker behavior). The relatedness in such a system can also be described in terms of identity by descent [35], which provides an approximation of identity in state for rare genetic variants (see [31] for a recent review). Of interest would be to test in future studies how the evolution of altruism is influenced by more complex population structures where the effect of strong selection may lead to variation in within-genome differences in the covariance between genes in different individuals. Because the rewards provided by the food items were either assigned to the focal individual who successfully transported it (selfish behavior) or shared equally between all the other group members (altruistic behavior), the fitness effects were additive and there were no synergetic effects. Thus, the cost incurred by an individual sharing altruistically a food item and the benefits to the other group members was not dependent on the recipients' genotypes and the proportion of them being altruistic. The lack of such synergetic effects results in the costs and benefits associated with an altruistic act being independent of the genotypic composition of the groups and the overall level of altruism in the population (i.e., there are no frequency-dependent effects). In natural systems there are frequently synergetic effects and this is one of the main reasons why it is not possible to reliably quantify the cost and benefits associated with altruistic actions (e.g., [15,16,36,37]).

From an empirical perspective, our study is therefore valuable because there have been many tests of Hamilton's rule, but these studies are usually not quantitative due to the impossibility of assessing the costs and benefits of altruistic acts, even in the most simple social systems such as those documented in some bacteria [10,38], social amoebae [39], or even synthetic microbial systems [36]. Our study also demonstrates that contrary to some misunderstandings [3], kin selection does not require specific genes devoted to encode altruism or sophisticated cognitive abilities, as the neuronal network of our robots comprised only 33 neurons. More generally, this study reveals that a fundamental principle of natural selection also applies to synthetic organisms when these have heritable properties [40].

Materials and Methods

Experimental Setup, Robots, and Neural Architecture

Groups of eight Alice micro-robots and eight food items were placed into a 50650 cm foraging arena. We chose a collective foraging task to investigate the evolution of altruism, because foraging efficiency is a key factor for many biological social groups such as ant or bee colonies [41]. Foraging required robots to locate a food item, to position themselves in front of the item, and to push it into a 4-cm-wide target zone along the white wall of the arena (the three other walls were black).

Robots were controlled by a feed-forward neural network consisting of six sensory input neurons, one bias input neuron, and six neurons with sigmoid activation. The robots had four infrared distance sensors, three of them sensing objects within a 3 cm range and the fourth, which was placed higher, having a 6 cm range. These sensors allowed robots to locate the food items and distinguish them from robots. Robots were also equipped with two vision sensors to see the white wall [24].

These six sensory inputs were scaled to a range of [21; 1]. In addition to the sensory inputs the neural network also comprised a bias input set to a constant value of 21, which was used to encode the neuron firing threshold. These seven inputs were connected to three neurons in a hidden layer, which in turn connected to three output neurons. The strength of these 33 connections was determined by 33 genes, whose values ranged from 0 to 255 (i.e., 8 bit resolution per gene). The activation of each of the six hidden and three output neurons was calculated by multiplying each of its input values by its associated connection weight, summing over all inputs, and passing the sum through the continuous tanh(x) function to obtain the neuron's activation value in the range of [21; 1]. The activation value of the first output neuron controlled the left motor speed, the second the right motor speed, and the third whether or not the successfully pushed food items were shared with other group members.

Relatedness, c/b Ratio, and Artificial Evolution

We used five different levels of relatedness in the experiments. To create groups of unrelated individuals (r = 0), we randomly distributed the 1,600 individuals in the 200 groups. To obtain groups with a relatedness of r = 1, we cloned one individual 7 times and formed groups with 8 genetically identical individuals. To create groups with a relatedness of approximately r = 0.75, we used two individuals (A and B) and cloned one seven times (clone proportion A:B = 1:7). The resulting relatedness in these groups was thus r,0.7492. To create groups with a relatedness close to r = 0.5, we similarly composed each group of three types of clones but in proportions 6:1:1, which led to r,0.5357. To create groups with a relatedness close to r = 0.25, we again composed each group of three types of clones, but this time using proportions 3:3:2, which resulted in a relatedness of r,0.2468. The genetic composition of groups thus differed from that of most animal groups in that some individuals were clones (r = 1) rather than belonging to kin classes such as full siblings (r = 0.5) or cousins (r = 0.125). However, in the absence of preferential interactions between kin, social evolution should be influenced by the average group relatedness. This is because genetic relatedness depends on interaction probabilities of genes [4], which in our model is equivalent to interaction probabilities between clonal individuals. Our experimental setup prevented preferential interactions between individuals by randomizing starting positions, having all robots being identical, and using a neural network that did not allow individuals to memorize past interactions.

To manipulate the c and b value of Hamilton's rule we modified the fitness values for shared and non-shared food items that were successfully transported. When non-shared, a food item provided a reward c to the selfish individual. When shared, the food item provided no direct benefit to the focal individual but a benefit b equally shared by the seven other robots in the group. The c/b ratios used were calculated using Queller's approach [42]. We used a value of 0.01 for the smallest c/b ratio because with a value of c/b = 0, there is no selection for foraging efficiency when r = 0, hence resulting in many populations going extinct (because no items were successfully foraged).

The foraging efficiency of each group was evaluated 10 times for 60 seconds and the inclusive fitness of each individual was estimated according to the number of food items collected and not shared + the number of food items that other group members collected and shared (these values being multiplied by c and b/7, respectively). The probability of the genome of a given robot to contribute to the next generation was directly proportional to the robot's inclusive fitness (roulette wheel selection with replacement [43]). Selected genomes were paired to conduct a crossing over with a probability of 0.005. The resulting genomes were subjected to mutation (probability of 0.005 per bit; i.e., 0.04 per gene). This process of selection, recombination, and mutation was repeated until there were enough genomes for the 1,600 individuals (200 groups) of the next generation. The level of altruism was calculated for each group as the proportion of collected food items that was shared within a group: A = n(a)/(n(a) + n(s)), where n(a) was the number of collected food items individuals shared and n(s) the number of items individuals did not share.

All 25 selection experiments were repeated 20 times (20 independent replicates). Evolution lasted for 500 generations for each experimental condition. For statistic analyses, the fitness and the level of altruism of all 200 groups in each of the 20 replicates were averaged over the last 10 generations. Means were compared with Mann-Whitney tests as Shapiro-Wilk tests showed that in many treatments the data did not follow a normal distribution.

Calculating Relatedness, Costs, and Benefits

In each of the individually evolving populations, altruistic interactions always occurred within groups, while the reproductive competition occurred at the level of the population. To manipulate the relatedness, we cloned genomes for each group and formed groups of different proportions of clones. Each group was composed of k different types of clones with respective frequencies
x i , i = 1 … k, P i x i~1 .
The genetic relatedness r quantifies the greater (or smaller) genetic similarity between individuals compared to the population average. Using the regression definition of relatedness [16,42],
r~P j (q l { p p) P j (q j { p p)~ q q{ p p 1{ p p ,
where j indexes the individuals in the population and l indexes the social partner of j.

In our system p p corresponds to the average probability of a focal individual being genetically identical to another member of the population and q q to the average probability of a focal individual being a genetically identical clone of another member of its group. Assuming that populations contain m groups with n individuals each,
p p~X i x i nx i {1 mn{1 q q~X i x i nx i {1 n{1
In all experiments the independently evolving populations consisted of m = 200 groups, each composed of n = 8 individuals.

Given that the evolution of social behavior is influenced by the relative rather than the absolute values of costs and benefits, we arbitrarily set czb~1 and calculated the costs c and benefits b for the expected transition from selfish to altruistic behavior as b~1 rz1

Pleiotropic Effects

To test for pleiotropic effects, we studied the outcome of a single mutation on two behavioral measures, performance and altruism. Performance was determined as the number of food items collected by an individual, and the level of altruism as the percentage of these food items shared with other group members. One mutation was performed on one individual in each of the 200 groups for each of the 20 replicates at the last generation for each of two treatments with intermediate values of relatedness and c/b ratio (treatment 1: r = 0.25, c/b = 0.75; treatment 2: r = 0.75, c/b = 0.25). All 8,000 individuals were subjected to a mutation of medium effect. This was achieved by flipping, for each individual, the third of the eight bits of a randomly chosen gene, hence always resulting in a mutation size 632. We chose this value because it was the median value of the mutations (range 6128) the robots were subjected to in the 500 generations of selection. The performance and level of altruism of each mutated individual was then evaluated in 100 independent trials in its group and compared to its performance and level of altruism before the mutation (Wilcoxon rank sum tests using a 5% significance level).

For the first treatment (r = 0.25, c/b = 0.75), rank sum tests could be conducted for 3,961 out of the 4,000 individuals as 39 individuals did not collect any food item either before or after the mutation, hence preventing determination of the level of altruism. For the second treatment (r = 0.75, c/b = 0.25), rank sum tests could be conducted for 3,848 out of the 4,000 individuals, as 152 individuals did not collect any food item either before or after the mutation.

Epistatic Effects

To test for epistatic effects, we used the same individuals as used in the experiment on pleiotropic effects and assessed the performances of individuals without a mutation F(0) and with a mutation F(A). We then subjected each of these 16,000 individuals (8,000 without and 8,000 with a mutation) to a new mutation B (also of median effect) and assessed their fitnesses F(B) and F(AB). We then compared whether this new mutation had a similar effect on the fitness of individuals with and without the first mutation by evaluating each of the resulting 32,000 individuals in 100 independent trials and calculating z scores based on the standard deviation (SD) and mean fitness F z~F (AB){F (A){F (B)zF(0) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (SD(AB) 2 zSD(A) 2 zSD(B) 2 zSD(0) 2 )=100 q Z scores could be calculated for 3.998 and 3,978 out of the 4,000 individuals for the first and second treatment, respectively (2 and 22 individuals, respectively, did not collect any food items). Statistics used a 5% (z = 2) significance level.

Weak Selection

Models of social evolution, as most models in evolutionary biology, usually resort to weak selection, where different individuals have very similar fitness. To test whether the mutations frequently had large effects (i.e., whether there was departure from weak selection), we determined how frequently a mutation of median effect resulted in a greater than 25% change in performance and the level of altruism (4,000 individuals per treatment). Note that the value of 25% was arbitrarily chosen as there is no convention of what change in fitness can be assumed to be a departure of weak selection. Again Wilcoxon rank sum tests were performed on the 100 trials per individual with a 5% significance level.

Figure 1 .
1Physical robots and neural network controller. (A) The Alice robots used in the experiments were equipped with infrared distance sensors (IR) and vision sensors (camera). (B) The input neurons (small circles) of the artificial neural network were connected to internal and output neurons (large circles) by 33 connection weights (lines connecting circles). doi:10.1371/journal.pbio.1000615.g001

Figure 2 .
2Mean group foraging efficiency during the 500 generations of selection. Lines represent the mean number of items transported successfully for each of the 25 treatments (five relatedness values 6five c/b ratios, 20 replicates per treatment), with yellow dashed lines representing treatments where r = c/b, red lines treatments where r , c/b, and blue dotted lines treatments where r . c/b. doi:10.1371/journal.pbio.1000615.g002

Figure 3 .
3Mean level of altruism during the 500 generations of selection. Lines represent the mean level of altruism, defined as the proportion of food items shared with other group members, for each of the 25 treatments (five relatedness values 6five c/b ratios, 20 replicates per treatment), with yellow dashed lines representing treatments where r = c/b, red lines treatments where r , c/b, and blue dotted lines treatments where r . c/b. doi:10.1371/journal.pbio.1000615.g003

Figure 4 .
4Mean level of altruism at the end of the 500 generations of selection. The mean (6SD) level of altruism as a function of the c/b ratio and level of relatedness (20 replicates per treatment) for r = c/b (yellow lines), r , c/b (red lines), and r . c/b (blue lines). Dashed lines are fits based on a model by McNamara et al. [44-46]. doi:10.1371/journal.pbio.1000615.g004

Table 1 .
1Effects of a single mutation on performance, altruism, and both.Treatment
Performance
Altruism
Both

r = 0.25, c/b = 0.75
2,524
86
54

r = 0.75, c/b = 0.25
376
243
189

Number of individuals for whom a single mutation of moderate effect
significantly altered only performance, only the level of altruism, and both
performance and the level of altruism (i.e., pleiotropic effects). Experiments
were performed on 4,000 individuals in the two treatments with intermediate r
and c/b values (see Materials and Methods).
doi:10.1371/journal.pbio.1000615.t001

PLoS Biology | www.plosbiology.org
May 2011 | Volume 9 | Issue 5 | e1000615
AcknowledgmentsWe thank M. Chapuisat, P. Dürr, A. Gardner, J. Goudet, A. Grafen, L. Lehmann, S. Mitri, D. Queller, F. Rousset, the ETH Zurich's Seminar of Statistics, the academic editor, and two anonymous reviewers for discussions and comments on the manuscript. L.K. thanks Stanislas Leibler, who hosted him during his sabbatical at Rockefeller.Author ContributionsThe author(s) have made the following declarations about their contributions: Conceived and designed the experiments: MW DF LK. Performed the experiments: MW. Analyzed the data: MW DF LK. Wrote the paper: MW LK.
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