“Spiritism and Science complement each other: Science, without Spiritism, finds it impossible to explain certain phenomena just by the laws of matter; Spiritism, without Science, would lack support and proof.” (Allan Kardec, in “Genesis”, chapter I, item 16, pg. 21, 35th Ed., FEB, DF / Brasilia.)

Science
Charles Darwin (1809-1882), a famous English naturalist, created the rule of “biological gradualism” (evolutionism) and, throughout his great masterpiece, the book "The Origin of Species" (1859) he cited the Latin expression seven times Natura non facit saltum(1) (Nature does not leap). Darwin defended phyletic gradualism, i.e., that evolution occurs through small transformations over the course of several generations of living beings, thus configuring a slow and continuous evolutionary process.
The fact is that, since then, there has been scientific discussion among philosophers, who, based on quantum physics, consider the sentence "nature does not leap" as evidently incorrect, while there are scientists who, on the contrary, like Darwin, are gradualists (gradual evolution).
The gradualism
The biological gradualism, proposed by Darwin, in his mentioned book, argues that evolution proceeds by small successive changes, and not through big leaps.
Such an assertion contradicted the religious view of then, because it removed from the creationist tradition the presence of an all-powerful, omniscient creator - God!
The saltationism
In biology, saltationism represents a sudden change in a given organism, from one generation to another.
Before Darwin, most defenders of evolution were saltationists. Some argued, for example, that birds originated from dinosaurs, due to saltation; others mentioned the 6th finger of panda bears, only theirs, not the other bears; others, biologists, proposed the sudden appearance of several species, with long periods without changes in fossil organisms. Proof of this thesis is difficult, in some cases, due to the lack of fossil records.

Note: I reflect that the contradictors of Darwinian thinkers might praise themselves in the examples of civilization, which, yes, is evolving without leaps, always progressing, gradually. For example: from caves to current penthouses; from wagons and ox carts to luxury vehicles of the “Ferrari” or Lamborghini brands; from the 14-bis plane to the very modern Airbus A350 XWB; from the rustic canoe to the immense ocean liner; from the arrow to the hydrogen bomb; from electronic clutter to modern PCs, smartphones or smartTVs; from plasters and “pajelanças” * to nuclear medicine.
The list is endless...

Some naturalists, even though respecting Darwin, continued saltationists, but proposing a combination with Darwin’s gradualism.
This position, it seems to me, has pacified the discussion…
So much so that, nowadays, there is an acceptance that, when it comes to "leaps" – a leap here meaning evolution - in Nature there are two aspects: gradualism (gradual philogenetic evolution) and saltationism (after certain natural events there are significant alterations - geological disasters, for example).
Although I am a layman, I position myself in this third alternative, that is, acceptance of both occurrences in Nature: gradualism and saltationism...
With an absolute inability to even technically risk arguments for or against biological leaps in Nature, I leave to the specialists their different opinions, certainly accredited.
Closing these reflections, supported by my research in the spiritist literature and some in Google (instant encyclopedic knowledge), it was established that:
Some authors suggest that the evolutionary scenarios of gradualism and saltationism, biological, are not mutually exclusive. On the other hand, both must be evaluated and taken into account to explain the complexity and enormous diversity of organic beings.
Spiritism
If the sciences deal with the material part of biological evolutionism, the Doctrine of Spirits, in a transcendent way, conceives evolutionary morality, not only biological, but also and mainly the spiritual evolution - of man and animals. Everything, everything, subordinated to the Divine Laws.
Human evolution
I am a simple researcher.
Therefore, I appeal to Kardec, who was concerned with the themes: material progress (of civilization, of peoples) and spiritual progress, receiving from the Spirits who supported him in the Codification of Spiritism multiple information, such as: Divine Justice, reincarnation (successive lives), mediumship, and so on. (In addition to listening to Kardec, I also consulted spiritist works on Evolution).
In "The Book of Spirits", by Allan Kardec, in the third part, in eleven chapters you will find the understanding of "Of moral laws - Of the divine or natural law". I emphasize that just such a section of this stupendous literary work already exposes, in detail, what the Doctrine of Spirits teaches about earthly existence, the radiance of everything that God created, maximally how Humanity should evolve: man, through reincarnation (successive lives).
Kardec, in possession of the information of the protecting Spirits about these Laws, pedagogically elaborated ten "Divine Laws", among them, the "Law of destruction" (transformation) and the "Law of Progress".
For me, it is crystal clear the understanding that, periodically, by the aforementioned Laws “shocks of Divine management” occur for the progress of Humanity, that is, reducing the terms: Nature “leaps”, yes.
Here are three examples:
1st - The Decalogue, with Moses; 2nd - The coming of Jesus (!), embodied, bringing us the first fruits of the Kingdom of Heaven (Love / Charity / Forgiveness); 3rd - The Codification of Spiritism, with Allan Kardec, on 04/18/1857, with the release of The Book of Spirits (O Livro dos Espíritos – “the LE”).
These blessed events, for me, represented three impressive “leaps” in the spiritual evolution of Humanity.
I record below three other examples of “leaps” in Nature, these, recorded in The Book of Spirits (the LE”) - (see the expression “from time to time”, repeated):
● Question 737 (of the Law of Destruction): Through destructive scourges God makes Humanity progress faster. (...) These subversions, however, are often necessary so that the advent of a better order of things can happen more quickly and so that it takes place in a few years, what would have taken many centuries to happen;
● Question 783 (from the Law of Progress): There is regular and slow progress, which results from the strength of things. When, however, a people does not progress as fast as it should, God subjects them, "from time to time", to a physical or moral shock that transforms them;
● Question 789: (from the Law of Progress) - (...) “From time to time” men of genius appear within Humanity and give it a boost; then come, as God's instruments, those who have authority and, in some years, make it advance by many centuries.
In the book “Evolution in two worlds”, by the spiritual author Andre Luiz, a rigorous and credible psychographics of the late Chico Xavier, shared with Waldo Vieira, 1st part, ch. VI, Evolution and Sex, item “Genealogy of the Spirit”, pg. 52-53, 11th Ed., 1989, Ed. FEB, Brasilia / DF, on human evolution, since the creation of the “Intelligent Principle”, it is stated that:
(...) With the Celestial Supervision, the intelligent principle spent, since the viruses and bacteria of the first hours of the protoplasm on Earth, more or less fifteen million centuries, so that it could, as a thinking person, although in phase embryonic of reason, launch its first issues of continuous thought to Cosmic Spaces. (!)
Evolution of animals
In this article I will not go into depth about the evolution of animals and the mysterious relationships that exist between them and man. The theme is too complex and “the starting point of the Spirit is one of those questions that are related to the origin of things and that God keeps the secret. It is not given to man to know them absolutely” (“The LE”, q.613).
It is that among the spiritists there are countless and serious personal opinions of scholars, for and against the thought that animals are interns in the mineral, vegetable and animal kingdoms, before their promotion to the rational.
I repeat: with personal opinions...
I copy, in passing, in-depth information contained in the aforementioned book “Evolution in two worlds”, by the Spirit Andre Luiz, 1st Part, ch. IX, “Evolution and brain”, pg. 67-68:
Girencephaly (characteristic of brains with circumvolutions and greater area of the cortex; example: primate brain) and lissencephaly (condition of brain without circumvolutions, which results in a small cortical area), obey the typifications traced by the Major Advisors, in the extensive domain of the vertebrates, preparing the human brain with the stratification of slow and multiple experiments on the vast class of living beings. Like young children, admitted to a kindergarten for rudimentary learning, disembodied noble animals, standing out from the nuclei of physiopsychic evolution in which they are grouped by symbiosis, they receive the intervention of celestial instructors, in special regions, exercising the nervous centers.
And in ch. XVIII - “Evolution and destiny”, from the same book, on p. 212:
(...) We will name the dog and the monkey, the cat and the elephant, the mule and the horse, as elements of your usual experience, more widely endowed with mental wealth, as an introduction to continuous thinking.
Still on the promotion of the irrational to rationality (from animal to man) I refer the reader to the book “A Caminho da Luz”, by Emmanuel / F.C. Xavier, ch. II, item The great transition, p.31, 13th Ed., 1985, Ed. FEB, Brasilia / DF, where, in summary, appears:
(...) The discoveries of Paleontology, as for the fossil man, are a testament to the biological experiments that the representatives of Jesus undertook, until they fixed the approximate characteristics of the future man in the “primate”. (...) "The hosts of the invisible made a definite transition in the pre-existing perispiritual body, of primitive men, in the sidereal regions and at certain intervals of their reincarnations...". My emphasis.
I see here, except for better judgment, a clue to the understanding of the so-called “missing link” of biologists and naturalists, never found on Earth: it is not processed on Earth, but in the spiritual world, by celestial geneticists...
Now, coupling the information from Kardec, Emmanuel and Andre Luiz, there is no doubt among Spiritists that man comes from animals.
Conclusion
The expression Nature does not leap, for me it must be understood as the personal opinion of philosophers, biologists and other Nature scholars, referring to the material progress, slow, although permanent. Within this focus, all human, scientific progress, particularly in the 20th century, from the Stone Age to the 21st century, fits. If the look of History is only focused on biology, or civilization, it still does not apply at all.
This is because the moral progress, of the whole Humanity, will only be reached by the sum of the spiritual progress of each human being, fully respected all the Divine Laws, inserted by God in the conscience of the Spirits, one by one.
To this end, Divine Providence grants each human being the blessing of free will, conscience and continuous intelligence, in addition to the means necessary to make their spiritual progress.
The decanted and sublime planetary regeneration will occur, therefore, depending on how time will be managed and experienced in the Good, Spirit by Spirit, that is, by us...

* Translator’s note: rituals of the shaman to heal.

(1) Natura non facit saltum (“Nature does not leap”), Latin phrase attributed to Gottfried Wilhelm Leibniz (1646-1716), German philosopher and mathematician, or to the Swedish naturalist and physician Carl von Lineu (1707-1778).