Nature Vs Nurture Summary

[Natalie Omahony]

Thankyou for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Not only does the model provide statistically optimal fittings to the observed distributions, but it also reveals the evolutionary origin of complex networks in terms of the interplay between both nature and nurture factors. Compared with the classical complex network models8,13,28,30, the model still includes the preferential attachment mechanism, leading us to conclude that the scale-free property of complex networks should be understood as a mechanism, such as the preferential attachment mechanism, rather than a specific index, thus potentially resolving the long-standing debate about whether complex networks have scale-free properties.

Suppose there are two nodes of different node weights and degrees in the network. The red node has a larger weight but a smaller degree (with three incident links). The blue node has a smaller weight but a larger degree (with six incident links). As new links are added to the network, if the network evolution is nature-dominant, then new links prefer connecting to the red node; else, if the network evolution is nurture-dominant, then new links prefer connecting to the blue node.

At each time step, two nodes are randomly and independently chosen, and a link is established between them. The probability of choosing a node depends on the nature weight ω and the nurture degree k of the node, given by

We have gathered thirty-two real-world networks that span across social, informational, technological, biological and economic domains from the Colorado Index of Complex Networks (ICON). These networks vary in size, ranging from tens of thousands to hundreds of millions of nodes. Our data includes the most representative network platforms such as Facebook, Twitter, Wikipedia, Amazon, YouTube, Google, and Academia, among others. Descriptions for these networks can be found in Supplementary Table 1.

Figure 2 (and Supplementary Fig. 2) shows the optimal fitting results of the distributions of both degree k [Eq. (2)] and degree-ratio η [Eq. (3)] for thirty-two real-world networks. The parameters N and T in Eqs. (2) and (3) are fixed as the numbers of nodes and links of the fitted data, respectively. The optimal values of the fitting parameters \(\omega _\max \), α, and b are provided in Supplementary Table 2. We find that the nature-nurture model simultaneously reproduces both the degree and the degree ratio distributions of real-world networks fairly well. These results suggest that the coupling of both nature and nurture factors of nodes plays an essential role in the evolution of complex networks.

In conclusion, we propose a model of network evolution aiming to shed light on the evolutionary origin of complex networks. The optimal fitting results of the analytical solutions in the model reproduce the degree distributions and degree ratio distributions of both static and dynamic networks. These findings indicate that the coupling of both nature and nurture factors of nodes plays a crucial role in the evolution of complex networks, and our model can rather universally account for the evolution of complex networks. However, the strength of the nature and nurture components of the growth might vary, which furthermore gives a characterization of the network growth. In social networks, the nurture factor of nodes is dominant, implying that individuals can improve their social value through their acquired efforts instead of solely relying on their innate background. Conversely, in non-social networks, the nature factor of nodes plays a leading role, where the innate attributes and functions of agents provided by the system determine their acquired state and development in the system, suggesting that whether nodes are people determines the dominant factor influencing the evolution of complex networks.

In our work, we have not explicitly addressed the issue of network directionality. The primary goal of our study is to investigate the universal mechanisms that can be adaptable to the evolution of both undirected and directed networks. For directed networks, we treat the sum of node outdegrees and indegrees as the total degrees of a node, followed by calculating the degree distribution without explicitly delving into the directionality consideration. One way to modify our model to impose directionality is to specify edge directions between two nodes via some additional assumptions. For instance, in cases where two nodes are selected at each time step, the direction of the edge could be determined from the node with a lower weight or degree to the node with a higher weight or degree. In the future, it would be interesting to explore the effect of imposing network directionality on the network evolution (cf. ref. 28).

In spirit, our work conforms to the tradition of emphasizing the emergent scale-freeness of network evolution models. An interesting future direction would be to link this model to the other tradition of identifying scale-freeness by statistical tests14. One could potentially do this with a more direct statistical inference of the growth mechanisms (cf. ref. 44). Regardless, even in such a well-studied topic as general growth models for fat-tailed networks, there are open questions with unexplored solutions.

B.Z. was supported by the Startup Foundation for Introducing Talent of NUIST and the Qinglan Project of Jiangsu Universities. P.H. was supported by JSPS KAKENHI Grant Number JP 21H04595. Z.G. is supported by the National Natural Science Foundation of China with Grant Number 72371137. X.L. was supported by the National Nature Science Foundation of China with Grant Numbers 72025405, 72088101 and 72001211, and the Hunan Science and Technology Plan Project with Grant Number 2020TP1013.

All authors contributed to the research. B.Z. and X.M. conceived the research, performed the experiments, and analyzed the data. Z.G., C.Z., and Y.H. cleaned the data. B.Z. and X.M. wrote the first draft of the manuscript. P.H. and X.L. reviewed and edited the manuscript.

Gloria Steinem is a journalist and social activist in the feminist, peace and civil rights movements. A fellowship to India in the late 1950s inspired her to fight for the rights of women and the poor. Steinem founded Ms. Magazine in 1972, and is the author of four books.

I didn't go to school until I was 12 or so. My parents thought that traveling in a house trailer was as enlightening as sitting in a classroom, so I escaped being taught some of the typical lessons of my generation: for instance, that this country was "discovered" when the first white man set foot on it, that boys and girls were practically different species, that Europe deserved more textbook space than Africa and Asia combined.

Instead, I grew up seeing with my own eyes, following my curiosity, falling in love with books, and growing up mostly around grown-ups -- which, except for the books, was the way kids were raised for most of human history.

Needless to say, school hit me like a ton of bricks. I wasn't prepared for gender obsessions, race and class complexities, or the new-to-me idea that war and male leadership were part of human nature. Soon, I gave in and became an adolescent hoping for approval and trying to conform. It was a stage that lasted through college.

I owe the beginnings of re-birth to living in India for a couple of years where I fell in with a group of Gandhians, and then I came to the Kennedys, the civil rights movement and protests against the war in Vietnam.

But most women, me included, stayed in our traditional places until we began to gather, listen to each other's stories and learn from shared experience. Soon, a national and international feminist movement was challenging the idea that what happened to men was political, but what happened to women was cultural -- that the first could be changed but the second could not.

I had the feeling of coming home, of awakening from an inauthentic life. It wasn't as if I thought my self-authority was more important than external authority, but it wasn't less important either. We are both communal and uniquely ourselves, not either-or.

Since then, I've spent decades listening to kids before and after social roles hit. Faced with some inequality, the younger ones say, "It's not fair!" It's as if there were some primordial expectation of empathy and cooperation that helps the species survive. But by the time kids are teenagers, social pressures have either nourished or starved this expectation. I suspect that their natural cry for fairness -- or any whisper of it that survives -- is the root from which social justice movements grow.

So I no longer believe the conservative message that children are naturally selfish and destructive creatures who need civilizing by hierarchies or painful controls. On the contrary, I believe that hierarchy and painful controls create destructive people. And I no longer believe the liberal message that children are blank slates on which society can write anything. On the contrary, I believe that a unique core self is born into every human being -- the result of millennia of environment and heredity combined in an unpredictable way that could never happen before or again.

The truth is, we've been seduced into asking the wrong question by those who hope that the social order they want is inborn, or those who hope they can write the one they want on our uniquely long human childhoods.

But the real answer is a balance between nature and nurture. What would happen if we listened to children as much as we talked to them? Or what would happen if even one generation were raised with respect and without violence?

3a8082e126