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Currently we have many species which are "good enough" for current environment, some species emerge, another die. So let's say that they could be close to some local optima. Does the evolution head to some optimum that in future we will have only one species which will be superior to all other extinct form of life?

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    $\begingroup$ The environment is highly variable thus it is unlikely (I'm going to say impossible) that a single species would be the best in all possible environments. Species do often exist close to a "local optima" - see fisher's geometric model of adaptation - there's a recent paper showing that it seems to be a good model for real world adaptation $\endgroup$ – rg255 Apr 21 '16 at 18:07
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    $\begingroup$ The question is unclear in many ways. First, you seem to be assuming that all species are evolving in the same fitness landscape, when all species (and populations) exist in their own fitness landscape. Second (assuming that a global optima really exists), why would this imply that all species but one should go extinct? Third, other species (the entire foodweb) constitutes "the environment" for a particular species, which means that the environment is never stable (since all species evolve). $\endgroup$ – fileunderwater Apr 22 '16 at 7:45
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An issue in the question that I will ignore

You say

Does the evolution head to some optimum that in future we will have only one species which will be superior to all other extinct form of life?

Firstly, it is a little bit weirdly phrased. By "superior" I suppose you would refer to a species that could outcompete all the other. This sounds very impossible to me firstly for simple ecological reasons. However, it would be a long answer to fully address this point and I don't feel like addressing (I might not be very much able to) in addition to the other questions.

Evolution vs Natural Selection

Just for a start. Evolution is way more than just Natural selection. There are plenty of other absolutely essential processes such as mutation and drift that are important to understand.

What is Natural Selection?

Natural selection is the process by which most fit individuals end up being at higher frequency in the population as a result of reproducing more and surviving better. Natural selection does not necessarily diminish the probability of a species to get extinct. It will not necessarily increase the ability of a species to compete another. It will not necessarily increase the rate of increase in the number of individuals in the species.

local vs global optima

Reading you post you seem to understand the concept of local vs global optimum (from algorithmic maybe). If selection alone was acting in the population and if mutations were feeding genetic variation to this population at a low enough rate, then population will ultimately reach a local optimum and will get stuck there forever. They would never reach a potential higher local optimum somewhere else. Drift may allow for such switch though, it is refer to "shifting balance theory".

Envrionmental change

The environment changes much faster at a local scale that you seem to think. When talking about environmental change for a lineage, we are not only talking about important ice age or current days global warming but we are talking about more subtle and more frequent changes. Imagine a species of unicellular living in a 50 cubic centimeter puddle. For them environmental change are drastic and frequent. So do population really have time to achieve any equilibrium. It is here a general question that comes in many field of evolutionary biology and also outside biology. Are the system that we study expected to be at equilibrium (in regards at some variables at least) in nature or are they never given the time to reach any equilibrium?

Mutations and drift

Mutation and drift are stochastic processes in evolutionary biology (among others). Mutations is the ultimate production of genetic variation. Most mutations are deleterious but not all are. The exact mutation (and mutational effects) and number of mutations that will occur in a population in a given amount of time is a stochastic process. Genetic drift refers to the random sampling of individuals that are chosen to survive. Drift is inversely proportional to the population size and you may want to have a look at this post to get some intuition for why this is the case.

How much fitness is lost du to ever occurring mutations?

As mutations are always occuring we might wonder how far is a population from its optimum due to these deleterious mutations.

Let's consider a very simple model.

Let $p$ be the frequency of the wild-type (not mutant) allele, $s$ be the deleterious effect of the mutation in the homozygote mutant and $h\cdot s$ be the deleterious effect in the heterozygote. The mean relative fitness in the population is

$$\bar w = 1 - 2 p (1-p) h s - (1-p)^2s$$

Let's define the mutation load $L$ as $1-\bar w$. As a consequence

$$L = 2 p (1-p) h s - (1-p)^2s$$

At selection-drift equilibrium the expected frequency of $p$ is $p=\frac{\mu}{hs}$, where $\mu$ is the mutation rate. As a consequence the

$$L = 2\mu$$ and $$\bar w = 1- 2\mu$$

Let's assume that fitness effect at different loci are multiplicative (no epistasis). As a consequence an individual carrying $n$ deleterious mutations has a fitness of

$$\prod_{i=1}^n 1-s_i $$.

Let's further assume that all mutations have the same deleterious effect on fitness, that is $s_1=s_2=...=s_n=s$. Let $l$ be the number of nucleotides on which deleterious mutations can occur. Coming back to $w=1-2\mu$, we can say that over all loci in the genome the fitness is

$$\bar w = \prod (1-2\mu) ≈ e^{-\sum_{i=0}^l 2 \mu} = e^{-2\mu l} = e^{-U}$$

, where $U=2\mu l$ is the genome-wide deleterious mutation rate. According to best estimates, in humans $U≈2.2$ and therefore our load is $L = 1-e^{-2.2} ≈ 0.9$.

From this simple model, we would expect that 90% of the mean fitness of a population is lost due to ever recurring deleterious mutations. This sounds pretty big and suggest that we'll always be pretty far way from an actual optimum.

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The short answer is NO.

Here, very briefly (since it would take to much to properly analyze all the aspects of this topic), is why:

First of all, the environment is constantly changing so there will be no such thing like 'the end of evolution'. Even if you try to stabilize the environment artificially (a lab setup) the organisms will continue to interact each other, mutations will occur, new stuff will evolve anyway. (here one example https://en.wikipedia.org/wiki/E._coli_long-term_evolution_experiment)

Moreover, each environment is made up by sub-environments (niches) that can be colonized by different organisms each of them will tend over time to adapt to their niche while competing with all the other organisms in the nearby environments but no organism will ever be the fittest for all those niches.

Zooming into molecular evolution, there are some enzymes that have reached "perfection" in the sense that they can catalyze a certain reaction at the maximum speed possible (https://en.wikipedia.org/wiki/Diffusion_limited_enzyme). However, even in these cases, such enzymes are well fit to their local environment (the specific cell type) and they will not work as well (or at all) in different conditions. So, even if they may perform a reaction perfectly, they may always evolve. For example, they may change substrate specificity of temperature stability or they can evolve different reaction mechanism.

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