full story - main, expanded and hidden

1. prior to the game
uncle Fred, as a scientist and explorer goes on many adventures discovering new stuff, goes missing without a word one day
his nephew Nathan, who spends a lot of time with him, sometimes joining in on adventures, goes to look for him in his house one day

2. during the game
he finds his house deserted, finds a special suit for him and a portal in a hidden room to a magical secret world, where he goes after Fred
in this world he soon finds a small society of sentient grown frog-people, secluded in a cave, spawned from what Fred sent through the portal - frog eggs and rubbish turned to houses
among them is a young frog-girl named Maddie, a protégé and another admirer of Fred, who gives info on Fred and his way
together they set out of the cave and reach Sky Haven, dwelling of so called "Strays", frogs that left the cave to find new place to live
Maddie finds these people kind, accepting and above all, open-minded towards discovery and decides to stay with them for a while
nephew departs to Ice Cave, where he eventually finds Fred, telling him about Maddie
uncle Fred reveals a one use portal, lets nephew use it and rather than chasing academic fame decides to stay with those he created and had impact on, mainly Madelyn

3. second half of the game
after many years, nephew visits uncle's house one more time and gives account how he decided not to chase treasure in adventures but in his daughter

there isn't much to add, this talks about the story we don't see (or play through), mainly about Nathan's choice of fatherhood

Nate's route mirrors Fred's, as both had a girl waiting for them
Fred's change of heart by the end inspired Nate to leave behind the idea of expeditions and direct his focus on his daughter
let's break it up:

1. Nate's desire to walk in his uncles shoes
Nate's love of adventure doesn't need proof as the whole game is filled with references to it, but what his family thought about it matters here
we don't know exactly if they saw Fred's adventures as foolish, but we do know that they didn't want Nathan to follow suit
we discover this from 2 memories ingame

1. camping trip prolonged to 3 days because of blizzard, which scared Nathan's mother a lot
2. Nate reminiscing how he loved to come around uncle's house and help with projects, but mother disliked it, how he wanted to join in on expeditions, but his mother wouldn't allow willingly
   in one dialogue, it is revealed, that Nate is fatherless, and we can therefore assume he sees Fred as his father figure - a thing which he shares with Maddie

2. Fred's relationship with Maddie
Fred is childless, but he doesn't feel any effects as, supposedly, he is too caught up in his work
in Fred's journal, we can read that he named Maddie after his former "journey companion" and that she "lives up to her expectations" in her "eagerness to learn"
this and many accounts of Fred from Madeline show us that they cared about each other deeply, almost on a parent-child basis
in the end, Fred presents his love for discovery and also how he wants to get praise from his colleagues and the scientific community as a whole, but upon learning how much danger Maddie risked to be with him and realizing, how much he means to her, he decides to spend his life with her and the people he created and helped grow

3. Nate's choice
seeing Fred ultimately choosing a child had an effect on him and pushed him to seek family life as well
we could assume, that Nate, being fatherless and seeing Fred as a father figure, being in the same situation as Maddie, could make him realize that the parent he needed in Fred and that Fred chose to be for Madeline, he would wat to be for someone else

4. themes of frog-people
we could also compare life journey of Madeline and Fred to events in game, mainly frog-people
at start, there are frog-people hidden in their cave, afraid of the world and power of crystals
then, there is city of strays who overcame their fear and are now discovering secrets of the world and using crystals to their benefits
afterward, there is ice cave, a deep cold world of remainders of lost world, civilisation that came before

Maddie was with the people scared of the world, but her curiosity, care for Fred and opportunity coming from Nate made her break out to a next stage of life, but she didn't wish to go to lengths that Fred was going
Fred went further, left people behind in his own pursuit of discovery, until he learned how much he means to Maddie and how much she means to him
Nate got through the whole journey because of Fred, but seeing his decision in the end inspired him to change his path

so, at the start of the game, we are told that Fred has gone missing without a word
after our adventure, Nate says that he didn't tell of it to his mother, that she might not believe it and that he himself isn't sure if he believes it
we are also shown and told how his family considered Fred dead (also the shrine in his house)

now, "it was all a dream" is a classic story trope, but it fits to the whole story and mainly with meaning of secret texts
throughout the game, there are many texts written in frog-alphabet, but some of these are hidden, these are, in order in which you find them throughout the game:
DENIAL - ISOLATION - ANGER - BARGAINING - DEPRESSION - ACCEPTANCE

for those uninitiated, these are, in their most known form, 5 stages of grief
they are the stages of how a human processes a loss of a loved one

other translatable texts are found on the big flying blocks in ice cave
2 of them are letters to a loved but dead person
the other is a motto "on the winds we sail for the sun's eternity"
coupled with ice cave being physically the grave of past civilisation, we can give it the theme of afterlife

with this info, we can change the themes of the game progression to these stages:
birth, growing up being scared of the world, breaking free and discovering, reaching afterlife

for the main character, Nate, it would have different meaning if we couple it with aforementioned grief:

• denial - clinging to hope of him being alive - trying to find him
  
• isolation - hiding from everyone/the world/truth - hiding in a dark cave
  
• awakening - coming back to the world - reaching Sky haven with open minded people
  
• acceptance - accepting passing of a loved one - finding Fred in "afterlife"/cemetery that is Ice cave

so, then the "real" events would most probably look like this:
Fred doesn't show up for a long time
Nate goes looking for him, finds him dead working on one of his experiments
Nate goes through stages of grief, represents them as a journey we experience in the game
Nate accepts death of his father figure and decides, instead of pursuing his uncle's career to be a father to someone else

all in all, what was trying to be represented in this game is told in chapter above, what lies ahead is just some match work of possibilities

considering Fred's death being only hinted at, there is much speculation left to be, which branches from these two options:
Fred died in his house, either by suicide or accident
Fred died elsewhere, Nate either doesn't find him or finds him dead/dying

1. Fred committed suicide
if we consider Ice cave to be a representation of afterlife/death, we could assume that both Fred's and Nate's path were the same paraphrased through the themes of this game, only difference being that through this "dream", Nate saw Fred chose to come back to his pseudo-kid (Maddie representing Nate) instead of suicide, and therefore Nate, being inspired choses to not commit suicide out of grief

2. Madeline is the daughter narrator Nate speaks to
considering the journal entry of frog Madeline being named after a similar girl Fred met on his journey, and that dialogue where Nate is repulsed when his daughter asks him if he was attracted to Madeline (which could just have the original meaning of her being frog in that story or maybe Nate was racist and she was from a tribe?), we could assume two possibilities:
2.1 Fred dies at home, Nate finds his journal, seeks out Madeline and takes her as his own
2.2 Fred dies in cave, story of game is real but with indigenous people, Nate find's him dying/dead, Fred conveys through last breath / journal that he should've stayed with Maddie

we could also consider that Fred never explicitly decides to return to Maddie, only shows how much she means to him in journal and Nate creates that "ending" or puts his own choice in there