In Tokyo, a Woman’s Lineage Returns in 10 Generations. In Akita, It Takes 500.

In Tokyo, a woman’s descendants return to her birth prefecture in just 10 generations. In Akita, it takes 500. This isn’t a forecast. It’s not about individual families. It’s a new demographic measure—mean recurrence generation—that reveals how deeply migration reshapes the long-term reproductive structure of populations, even when fertility is at replacement level nationwide. According to a 2026 study by Oizumi, Kinjo, and Chino (Oizumi et al., 2026), the average number of generations it takes for a lineage to produce a descendant in its region of origin varies dramatically across Japan’s 47 prefectures, exposing hidden imbalances in population replacement. Tokyo’s tight reproductive loop—where people leave, have children elsewhere, and those children or grandchildren return—contrasts sharply with Akita’s open-ended pathways, where once a lineage departs, it rarely circles back. These differences persist despite similar fertility rates, challenging the assumption that replacement-level fertility ensures regional stability. The finding reframes how we understand population decline, urbanization, and demographic resilience—not just in Japan, but in any country with internal migration.

The Science

The study builds on multiregional stable population theory, a framework that models how fertility, survival, and migration interact across space and time. At its core is the multiregional Leslie matrix—a mathematical tool that projects population change by tracking age- and region-specific transitions. From this matrix, demographers derive key quantities: the intrinsic growth rate, the stable age distribution, and reproductive value. These summarize long-term population dynamics, but they compress complex intergenerational pathways into single numbers.

Oizumi and colleagues go deeper. They introduce migration genealogies—sequences that trace how a woman’s birth region connects, through survival and movement, to the birth regions of her daughters, granddaughters, and beyond. The innovation lies in decomposing these genealogies into first-return paths: lineages that leave a reference region, reproduce elsewhere for one or more generations, and then produce a descendant back in the original region. The moment of first return is critical. It marks the closure of a reproductive loop.

The authors define a first-return distribution, which assigns a probability to each generation at which a lineage first returns. When discounted at the intrinsic growth rate, this distribution satisfies an Euler–Lotka-type normalization—a hallmark of stable population theory. From this, they derive the mean recurrence generation: the expected number of generations until a lineage first returns to its region of origin.

This measure is not a prediction. It does not assume that current migration patterns will persist for centuries. Rather, it is a structural property of the demographic system defined by period fertility, survival, and migration rates. Like life expectancy or generation time, it summarizes the implications of current conditions for long-term population structure.

The analysis applies this framework to Japan, using census data, vital statistics, and life tables from 2010, 2015, and 2020. The model includes all 47 prefectures, with age structured in five-year intervals up to 85+. To isolate the effects of migration and regional fertility differences, the authors scale fertility rates so that the national net reproduction rate is exactly one—replacement level—while preserving relative differences across prefectures. This allows them to compare reproductive pathways under a common national condition.

What They Found

The most striking result is the vast disparity in mean recurrence generation across prefectures. Based on 2020 data:

• Tokyo: approximately 10 generations
• Akita: approximately 500 generations
• Fukushima: varies significantly across observation years

These numbers are not guesses. They are derived from real demographic rates—fertility, mortality, and migration flows—observed in Japan. The mean recurrence generation is calculated as the normalized product of stable births and reproductive value, and at replacement level, it equals the reciprocal of the sensitivity of net reproduction to within-region fertility (Oizumi et al., 2026).

Mean Recurrence Generation by Japanese Prefecture (2020)

Label	Value
Tokyo	10
Kyoto	15
Osaka	25
Fukushima	80
Akita	500

Source: Oizumi et al. (2026), based on 2020 Japanese census and vital statistics.

The contrast between Tokyo and Akita is particularly revealing. Both have low fertility, and both contribute similarly to their own births in the immediate generation—what the authors call "one-generation birth contributions." Yet their long-term reproductive structures are worlds apart. In Tokyo, migration creates a dynamic equilibrium: people leave, but their descendants frequently return. In Akita, outmigration dominates, and return pathways are weak. Once a lineage departs, it is unlikely to come back.

The case of Fukushima is more complex. Its mean recurrence generation fluctuates across years, likely reflecting the ongoing demographic effects of the 2011 earthquake, tsunami, and nuclear disaster. This sensitivity to external shocks underscores how mean recurrence can serve as an indicator of demographic fragility.

The study also examines fertility sensitivity—the extent to which changes in local fertility affect national population growth. Tokyo shows high sensitivity, meaning that boosting fertility in the capital would have a disproportionate impact on national reproduction. Akita, by contrast, has low sensitivity, reflecting its weak closed reproductive pathways.

Change in Mean Recurrence for Fukushima Prefecture (2010–2020)

Label	Value
2010	60
2015	100
2020	80

Source: Oizumi et al. (2026). Fluctuations reflect changing migration patterns after the 2011 disaster.

Why This Changes Things

For decades, demographers have treated replacement-level fertility as a proxy for population stability. If the total fertility rate is 2.1, the population will eventually stabilize—so the thinking goes. But this assumes a closed system. In reality, internal migration decouples national and regional dynamics. A country can be at replacement level while some regions grow and others collapse.

The concept of mean recurrence generation makes this visible. It shows that population replacement is not just a matter of how many children are born, but where those children are born and where their descendants end up. Two regions with identical fertility can have vastly different long-term prospects depending on their migration genealogies.

This has profound implications for policy. In Japan, rural depopulation is often framed as a fertility problem. The solution, then, is to subsidize childbearing. But Oizumi et al. show that even if rural fertility were to rise, the impact on long-term population stability would be limited if return pathways remain weak. A child born in Akita today may move to Tokyo, have children there, and those children may never return. The reproductive loop stays open.

Conversely, Tokyo’s short mean recurrence suggests that the capital is not just a sink for migrants, but a hub of reproductive circulation. People leave, but their descendants come back. This closed loop reinforces Tokyo’s demographic resilience, even as its fertility rate remains low.

The findings also challenge how we model population scenarios. Most projections assume that migration patterns will continue as they are, or that they will stabilize. But mean recurrence reveals the structural inertia of demographic systems. A region like Akita is not just shrinking—it is becoming demographically isolated. Its population is not just smaller; it is different in kind, with fewer ties to future reproduction in the region.

Globally, this matters. Countries from South Korea to Italy to Romania face similar patterns of urbanization and rural decline. The standard response—boost fertility—may be insufficient if migration genealogies are not addressed. Policies that encourage return migration, support diaspora connections, or create regional reproductive hubs could be more effective than blanket child subsidies.

What's Next

The study opens several avenues for future research. First, the framework could be applied beyond Japan. Urban-rural divides, regional inequality, and internal migration are global phenomena. Does Paris have a shorter mean recurrence than rural Auvergne? Does Seoul close its reproductive loops faster than Jeju? Comparing recurrence across countries could reveal universal patterns or cultural specificities in demographic structure.

Second, the model could be extended to include male lineages or broader family networks. The current analysis focuses on female genealogies, following standard demographic practice. But incorporating patrilineal or bilateral descent might yield different insights, especially in societies with strong patrilocal residence norms.

Third, mean recurrence could be integrated into population forecasting. While it is a period measure, not a forecast, it could serve as an early warning system for demographic fragility. A rising mean recurrence might signal that a region is losing its reproductive connectivity, even before population decline becomes visible.

Finally, there are limitations. The model assumes constant rates, which is unrealistic over hundreds of generations. It also treats migration as probabilistic, not driven by individual decisions or structural forces like housing markets or education systems. And it does not account for international migration, which could alter regional dynamics in countries with high immigration.

But these are not flaws—they are invitations. The power of mean recurrence lies in its simplicity. It reduces a complex web of life courses and family histories to a single, interpretable number. That number tells us not just how many people are being born, but how deeply rooted they are in the places they come from.

In a world of increasing mobility, that rootedness matters. We are not just counting bodies. We are tracing lineages. And in doing so, we see that population stability is not just about fertility—it’s about return.