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Can a rudderless species survive?

Rinaldo B. Schinazi

TL;DR

A species which has to find its birth place to reproduce but has no navigation skills and relies on chance alone would survive if and only if the probability that a given individual find its birth place is strictly larger than 1/2.

Abstract

Some species of salmon and sea turtle are famously good at finding their birth place to reproduce after having travelled vast expanses of ocean. In contrast, imagine now a species (maybe ancestral to the salmon or turtle) which has to find its birth place to reproduce but has no navigation skills and relies on chance alone. Would such an imaginary species survive? According to our (very simple) model it would survive if and only if the probability that a given individual find its birth place is strictly larger than 1/2.

Can a rudderless species survive?

TL;DR

A species which has to find its birth place to reproduce but has no navigation skills and relies on chance alone would survive if and only if the probability that a given individual find its birth place is strictly larger than 1/2.

Abstract

Some species of salmon and sea turtle are famously good at finding their birth place to reproduce after having travelled vast expanses of ocean. In contrast, imagine now a species (maybe ancestral to the salmon or turtle) which has to find its birth place to reproduce but has no navigation skills and relies on chance alone. Would such an imaginary species survive? According to our (very simple) model it would survive if and only if the probability that a given individual find its birth place is strictly larger than 1/2.
Paper Structure (2 sections, 2 theorems, 6 equations)

This paper contains 2 sections, 2 theorems, 6 equations.

Table of Contents

  1. The model
  2. Proof of Theorem 1

Key Result

Theorem 1

If $\beta\leq 1/2$ the branching Markov chain Y dies out for all $\alpha$ in $(0,1)$. If $\beta>1/2$ there exists $\alpha_c\in (0,1)$ such that Y has a positive probability of surviving for $\alpha>\alpha_c$ but dies out for $\alpha\leq \alpha_c$.

Theorems & Definitions (2)

  • Theorem 1
  • Lemma 2