British naturalist Charles Darwin is a young father who lives a quiet life in an idyllic village. He is a brilliant and deeply emotional man, devoted to his wife and children. Darwin is especially fond of his eldest daughter Annie, a precocious and inquisitive ten-year-old. He teaches her much about nature and science, including his theory of evolution, and tells her stories of his travels. Her favourite story, despite the sad ending, is about the young orangutan Jenny, who is brought from Borneo to the London Zoo, where she finally died of pneumonia in the arms of her keeper. Darwin is furious when he learns that the family clergyman has made Annie kneel on rock salt as punishment for contradicting him about dinosaurs, as their existence and extinction contradicts the church's position that life is unchanging and that the Earth is very young.
Having returned from his expedition in the Galapagos Islands 15 years earlier, Darwin is still trying to finish a manuscript about his findings, which will substantiate his theory of evolution. The delay is caused by anxiety about his relationship with his devoutly religious wife, Emma, who fundamentally opposes his ideas and understands the threat to their religion that his work poses. Emma worries that she may go to heaven and he may not, separating them for eternity.
The film shows Annie in flashbacks and hallucinations, a vibrant apparition who goads her father to address his fears and finish his big work. It is apparent that Annie has died, and that her death is a taboo subject between Darwin and Emma, as both feel intense blame for her death. As a result of the strained relations between Charles and Emma, they stop making love entirely. Anguished, Darwin begins to suffer from a mysterious, fatiguing illness.
It is revealed that after Annie becomes ill in 1851, Darwin takes her to the Worcestershire town of Malvern for James Manby Gully's water cure therapy, against Emma's will. Annie's condition worsens, and she ultimately dies after her father, at her request, tells her Jenny's story once more. Darwin is devastated, and her death sharpens his conviction that natural laws have nothing to do with divine intervention. To his contemporaries, this is an idea so dangerous it seems to threaten the existence of God. In a box in Darwin's study, we discover the notes and observations that will become On the Origin of Species.
Having read his 230-page synopsis, Darwin's friends in the scientific community, Joseph Dalton Hooker and Thomas Henry Huxley, also encourage him. Huxley admiringly tells Darwin that with his theory he has "killed God", which fills Darwin with dread. In his hallucinations, he also feels that Annie disapproves of his procrastination.
Darwin receives a letter from Alfred Russel Wallace in 1858, which details the same findings as Darwin in 20 pages. He has mixed feelings about this; all his work may have been in vain, but on the other hand, as he will not have to write his book, the discord with Emma will heal. However, Darwin's friends urge him to continue, as his book is much more comprehensive.
After receiving treatment at Malvern himself, Darwin makes a pilgrimage to the hotel where Annie died. The journey marks a change in him; upon his return home, he is able to reconnect with his wife, and they speak to each other for the first time of their fears and grief over Annie's death. They specifically speak about the possibility that Annie died because she was genetically weak, as Darwin and Emma are closely related cousins. Their renewed devotion restores Darwin's health, and he is able to resume his work, as it also restores Emma's faith in their marriage, and she regains her strength to support his controversial work. Darwin decides that Emma must make the decision about publishing his work. After reading the manuscript, she quietly returns it to him, having addressed the package to John Murray publishers in London. Emma accepts that she is an "accomplice" now, but hopes that God will forgive them both.
Darwin walks down the lane, holding the package. When the postman arrives, Darwin falters, almost letting him go empty-handed. The postman rides away, unaware of the powerful idea about to be released onto the world. As Darwin walks home, the little figure of Annie walks alongside him.

Question: What does Darwin and Emma fear the most about Annie's death?
Answer: Darwin and Emma are scared that Annie died because they were cousins.
Alternative answer: That Emma died because she was genetically weak.