Did the laws of Yovel accommodate and adjust for the possible different population growth rates of the different tribes? Or was the land allocation to the tribes fixed regardless of changes in population sizes of the different tribes?

The land allocation to the tribes was fixed and did not adjust for population changes — each tribe's portion was permanently assigned and returned to that fixed tribal inheritance every Yovel, regardless of whether the tribe had grown or shrunk in population. However, the Torah's system did contain a built-in accommodation for population differences at the time of the original allocation, using the lottery (goral) system combined with tribe size.

Key Takeaways

The original land distribution did account for tribal population size — larger tribes received larger portions [Numbers 33:54].
Once allocated, each family's ancestral portion (achuzah) was permanently fixed and returned to the original owner every 50 years via Yovel [Leviticus 25:10-13].
The Yovel system was designed to preserve the original allocation, not to continuously recalibrate based on demographic change.
Subsequent population shifts within or between tribes were not accommodated by any automatic reallocation mechanism.
The deeper theological logic is that the land belongs ultimately to God, and human demographic changes do not override the Divine apportionment.

The Original Allocation: Population-Sensitive

The Lottery Combined with Tribe Size

The Torah explicitly states in [Numbers 33:54]:

וְהִתְנַחַלְתֶּם אֶת־הָאָרֶץ בְּגוֹרָל לְמִשְׁפְּחֹתֵיכֶם לָרַב תַּרְבּוּ אֶת־נַחֲלָתוֹ וְלַמְעַט תַּמְעִיט אֶת־נַחֲלָתוֹ "You shall apportion the land by lot among your clans — to the larger you shall give a larger portion, and to the smaller you shall give a smaller portion."

This verse establishes a two-part mechanism:

The goral (lottery) determined which region went to which tribe.
The size of the portion was scaled proportionally to the tribe's population as counted in the census of Numbers 26.

Rashi [Numbers 26:54] explains that the census taken just before entering the land was directly connected to the land division — the count was needed precisely to calculate proportional allocations.

The Census as the Basis

The second census in Numbers 26 was taken immediately before the allocation [Numbers 26:2-4], strongly implying its purpose was to calibrate the land distribution. Ramban (Nachmanides) [Numbers 26:1] notes that this census served multiple purposes, including ensuring equitable distribution of the land proportional to each tribe's fighting strength and population.

Yovel: A System That Froze the Original Allocation

The Core Mechanism

Once the original allocation was made, the Yovel (Jubilee) system operated to permanently preserve it [Leviticus 25:10, 13]:

וְשַׁבְתֶּם אִישׁ אֶל־אֲחֻזָּתוֹ "Each person shall return to his ancestral holding."

אִישׁ אֶל־אֲחֻזָּתוֹ תָּשֻׁבוּ "You shall return, each to his ancestral holding."

The word achuzah (אֲחֻזָּה) — ancestral holding — is critical. It refers to the original, divinely-apportioned inheritance, not a dynamically recalculated share.

Sales Were Temporary, Not Permanent

The genius of the Yovel system was that land sales were really long-term leases [Leviticus 25:15-16]. The price of land was calculated based on the number of years remaining until the next Yovel — meaning the land would always revert. This locked in the original tribal and family allocations permanently.

The Sefer HaChinuch [Mitzvah 330] explains that one of the core purposes of Yovel is to prevent permanent economic stratification — but crucially, the reference point for restoration is always the original ancestral portion, not a newly calculated share based on current population.

Why Population Changes Were NOT Accommodated

Theological Rationale

The Torah states [Leviticus 25:23]:

כִּי־לִי הָאָרֶץ כִּי גֵרִים וְתוֹשָׁבִים אַתֶּם עִמָּדִי "For the land is Mine — you are but strangers and sojourners with Me."

Ramban [Leviticus 25:23] explains that because the land belongs to God, its allocation is a Divine decree that humans cannot permanently alter. Population fluctuations are a human variable; the Divine apportionment is eternal.

Practical Mechanisms Within the Fixed Framework

While the tribal allocation was fixed, there were internal mechanisms that individuals could use to adapt:

Land sales (temporary leases until Yovel) allowed families to adjust economic circumstances.
Inheritance laws (yerushah) distributed a father's portion among his sons, naturally subdividing plots as families grew.
The daughters of Zelophehad case [Numbers 27, 36] shows that even inheritance adjustments were carefully managed to prevent land from crossing tribal boundaries — reinforcing the permanence of tribal allocations.

The Talmudic View

The Talmud [Bava Batra 117a] discusses how the land was divided both by the number of those who left Egypt and by those who entered the land, with complex opinions about the exact methodology. Rashi and Tosafot there debate the precise formula, but all agree the allocation was a one-time, fixed event — not a rolling recalculation.

A Tension Worth Noting

There is an inherent tension in the system: a tribe that grew dramatically (e.g., Judah) would find its fixed portion increasingly insufficient per capita, while a tribe that shrank would have more land per person. The Torah does not provide a legal mechanism to correct this over time.

Some commentators suggest this was intentional — the Netziv (Ha'amek Davar) [Numbers 33:54] implies that population shifts were understood as part of Divine providence, and the land boundaries themselves were meant to shape and influence the destiny of each tribe, not merely reflect their demographics.

The bottom line: Yovel was a preservation mechanism, not a recalibration mechanism. It restored the original Divine allocation every 50 years, treating that original apportionment as eternally normative regardless of how tribal populations evolved over time.

For personal guidance on any practical halachic matters related to these topics, consult your local rabbi or posek.