At the suburb level, the zero-order correlations between lead in air and assault rates peaked at a 21-year lag for most sites. The correlations at the 21-year lag were strong and significant for all sites (range r = .506 to r = .802, all p values ≤ .022) except Rydalmere (r = .386, p = .215), which had the shortest time series (see Figs. 1 and 2). Without adjusting for major socio-demographic correlates of crime, lead in air accounted for 26–64 % of the variance (ω²) in assault rates at each site 21 years later (15 % for Rydalmere). It is notable that in the four metropolitan suburbs, the data points are tightly clustered, with mean annual lead in air levels markedly lower than in the two smelting communities of Boolaroo and Port Kembla (Fig. 2). The maximum annual value was 5.9 μg/m³ (1987) in Boolaroo and 7.8 μg/m³ (1979) in Port Kembla. This can be compared to the current national air lead standard of 0.5 μg/m³ (expressed as an annual average) [32]. Lead in air concentrations in metropolitan suburbs also exceeded 0.5 μg/m³ until some years after the introduction of unleaded petrol in 1985 [18].

Major socio-demographic correlates of crime were subsequently added as covariates in the 21-year lag mixed model. Primary analyses included socio-demographic covariates for the years in which the assaults were committed. As suggested by Bellinger [14] we also examined models that controlled for socio-demographic variables at the time of lead exposure, but these variables did not reach significance in either model and consequently were excluded from the analyses to avoid multicollinearity between the two sets of socio-demographic variables.

As a test for discriminant validity, mixed models that examined the relationship between lead in air and fraud rates were also examined for the 15–24 age-crime curve. There were some small statistically significant relationships, but the largest effect of lead as a predictor of fraud rates (lagged 15 years) accounted for only 5.5 % of the variance. It is apparent that the explanatory power of lead in air is minimal in relation to fraud rates, which contrasts markedly with assault rates.

At the state level, strong positive correlations between petrol lead emissions and death by assault rates were found only for the states with the largest populations, highest population densities and greatest petrol lead emissions, namely, NSW and Victoria. In these states, correlations peaked at the 18-year lag, which reflects the age-crime curve described in the literature [28]. A simple linear regression model showed that lead emissions in NSW accounted for 34.6 % of the variance in death by assault rates 18 years later. Every 2000 additional tonnes of lead emitted was associated with one additional death. Moreover, there is a clear temporal pattern to the data. The death by assault rate increases over the period 1976 to 1992, corresponding to increases in petrol lead emissions 18 years prior. In the subsequent period from 1992 to 2012 the death by assault rate falls, reflecting the reduction in petrol lead emissions 18 years prior. This hysteresis effect is shown in Fig. 3. In Victoria, the most densely populated state, a simple linear regression model showed that lead emissions accounted for 32.6 % of the variance in death by assault rates 18 years later. Every 1667 additional tonnes of lead emissions was associated with one additional death. The hysteresis pattern observed in the NSW data was also evident in the Victorian data. In states and territories with low population densities and low absolute emission levels, the correlation was negative.

At a national level, the data also demonstrated a positive correlation between lead emissions and death by assault rates, but the association was weak. National lead emissions accounted for only 7 % of the variance in national death by assault rates 18 years later, as the health and behavioral effects of lead emissions are dissipated at larger geographic scales.

Our study tested the hypothesis that there is a significant correlation between air lead exposure and rates of aggressive crime in later life. The results demonstrate that after controlling for major socio-demographic correlates of crime there is a strong positive relationship between lead in air levels and subsequent crime rates. This has important implications for public health globally.

This is the first Australian study to test the hypothesis that lead exposure is associated with subsequent aggressive criminal behaviors at a range of spatial scales. Lead in air concentrations accounted for 29.8 % of the variance in assault rates 21 years later in the six localities measured, after adjusting for socio-demographic covariates. In the most populous Australian states of NSW and Victoria, total lead petrol emissions accounted for 34.6 and 32.6 %, respectively, of the variance in death by assault rates 18 years later. Given the variety of possible determinants of criminal behavior, these are remarkable findings. The R² values for the states are not atemporal, but reflect secular trends in the variables as indicated by the hysteresis loop in Fig. 3.

These results are robust because the study relies on statistics from official government and industry agencies that have collected relevant datasets independently of each other. We operationalized our hypotheses using two variables for lead exposure (lead in air concentrations and annual lead petrol emissions) and three variables for recorded crime (assault, death by assault and fraud) across different spatial and temporal scales. The suburbs varied in size, lead levels, crime rates, and socio-demographic characteristics, and a variety of statistical methods were utilized to analyze the data. Consequently, the consistency of the relationships across the models suggests the results are robust.

The association between lead in air and lagged assault rates at the suburb scale exists regardless of whether the source of lead is smelting or petrol. Five of the six sites have positive and significant correlations, with the sixth (Rydalmere) being affected by the small sample size (Fig. 1). This is important because the temporal pattern of lead emissions varies across sources and sites and yet the outputs remain compatible with our hypothesis. Notably, the strongest relationship was found in the smelting town of Boolaroo (R² = 0.64), and the third highest was in the smelting town of Port Kembla (R² = 0.36); these suburbs had the highest levels of lead pollution. Removal of a single outlier in the lead in air data set for Port Kembla (7.8 μg/m³, 1979) lifted R² to 0.59.

The study suggests that features of the physical environment, in this case atmospheric pollution, may be more important than previously considered in explaining early adult criminality. After adjusting for major socio-demographic variables (population age distribution, education, income), lead in air remained the largest determinant of variance in assault rates. It accounted for 5.5 times as much of the variance as the single most important socio-demographic factor and 2.8 times as much as the combined socio-demographic covariates (Table 3).

The study outcomes are consistent with the neuro-psychological literature, which suggests that the principal behavioral traits affected by childhood lead exposure are reduced impulse control and related impacts on aggressive behaviors [11, 12, 33–36]. Childhood blood lead exposure is also associated with reduced adult brain volume in the prefrontal and anterior cingulate cortex areas that are responsible for executive functioning, mood regulation and decision-making [37].

Our study reveals the importance of lead in air as a determinant of rates of aggressive crime. This is consistent with Marcus et al.’s [10] meta-analysis of >8000 children and adolescents, which showed a significant association between lead exposure and conduct problems in later life. By contrast, fraud, which is a non-impulsive, non-aggressive crime, was only associated weakly with prior exposure to lead in air (ω² ≤ 5.5 %).

This study has data limitations that are typical of other ecological studies, like herd immunity. The measured correlations between lead in air and subsequent rates of aggressive crime may be underestimated due to lack of congruence between the populations exposed to lead and the populations measured for later criminal behaviors [38]. This is a consequence of the deaths and out-migration of some lead-exposed individuals, the births over the period subsequent to the measurement of exposure to lead, and the in-migration of other individuals who have been exposed to lead at unknown concentrations and localities. Quantifying the impact of these processes is difficult due to limited data availability at the suburb level. Over the period 2001–2014, which is only part of the study time period, there was population growth in all six suburbs: Earlwood 3.2 %, Port Kembla 3.9 %, Boolaroo 4.4 %, Lane Cove 10.9 %, Rydalmere 16.6 % and Rozelle 30.7 %. All but the last suburb were below the national average growth of 21.9 % for that period [39]. There was also substantial turnover in the membership of the populations of all six suburbs due to migration. The percentages of people aged over 5 years who lived in a different local area 5 years before the 2011 census were substantial: Earlwood 22.0 %, Port Kembla 23.3 %, Boolaroo 26.9 %, Rydalmere 28.0 %, Lane Cove 36.8 % and Rozelle 49.4 %. Whilst more of the in-movers to the high turnover suburbs of Lane Cove and Rozelle came from other parts of Australia, there were also significant numbers who moved from overseas. Of the population aged 5 and over in 2011, 11.9 % of Rozelle’s population and 9.9 % of Lane Cove’s population were living outside Australia 5 years earlier [39].

With respect to lead in air, it would be desirable to have broader and more detailed spatial and temporal coverage. However, we have used the best available data for which there are also corresponding crime data. For the suburb level analysis, lead in air concentrations were sourced from a single air monitoring station to characterize exposure across the selected geographic area. For the state and national analyses, lead petrol emissions were estimated from petrol sales and are a proxy for population lead exposure. With respect to crime rates, data on assaults are those reported to police, which may be under-inclusive due to unreported crime or over-inclusive due to unsubstantiated allegations. Assault data is based on the suburb where the assault took place, not the offender’s residence, which might be more closely linked with lead exposure. Similarly, death by assault data are based on the state or territory in which the death was registered, not the residence of the person who caused the death. Nonetheless, we have found noteworthy results in the face of limitations that might have been expected to obscure the relevant relationships.

Finally, the study suggests productive areas for future research with respect to lead and other neurotoxic metals [40]. This study is one of association not causation. More specificity could be obtained by examining the blood lead concentrations of individuals and undertaking a prospective longitudinal study of their behavioral responses. While a few studies have achieved this benchmark [10, 12, 34], more research is required across different populations and contaminants. Better data will help formulate evidence-based policies to improve health and social outcomes.

Taken together, the results of the present study highlight that atmospheric lead standards require systematic review by national and international agencies. At present, standards vary widely. For example, the lead in air standard is 0.5 μg/m³ (annual) (1 μg/m³, seasonal) in China, 0.5 μg/m³ in Australia and 0.15 μg/m³ in the USA. The method for calculating acceptable levels also varies. In Australia the standard is based on an annual average, with no upper limit on short-term spikes; in the USA it is based on a 3-month rolling average, which is more restrictive on polluters. Future revisions of lead in air standards need to be tied to demonstrable health outcomes, cognizant of their impact on anti-social behaviors.

Measures need to be taken to reduce or eliminate extant sources of atmospheric lead pollution wherever practicable. Exposures from these sources have the potential to increase anti-social behaviors and impose unnecessary societal costs. These sources include existing mining and smelting operations in Australia and elsewhere, and lead petrol consumption in countries where it is still sold: Algeria, Iraq, and Yemen [41]. In these countries, some 103 million people remain at risk from the use of lead petrol [42]. There are also policy implications for communities that have been historically affected by the deposition of atmospheric lead in populated places such as homes, gardens, playgrounds and schools. These depositions present an ongoing risk because the half-life of environmental lead exceeds 700 years [43].

This study found a robust relationship between lead in air and subsequent rates of aggressive crime at suburb, state and national population levels using multiple analytic methods and data sources. These results add to the existing body of literature that highlights the sequelae of lead exposure. Fortunately, exposure to lead is preventable and remedial intervention is cost effective [8]. Given the overwhelming evidence that there is no safe lower threshold for lead toxicity, remediation programs are essential to mitigate these effects and should be a clear priority for immediate policy change.