diff --git a/00019_Sustainable_fishing/en_article_proofreading.md b/00019_Sustainable_fishing/en_article_proofreading.md
index 944b1d2..2f0ecaa 100644
--- a/00019_Sustainable_fishing/en_article_proofreading.md
+++ b/00019_Sustainable_fishing/en_article_proofreading.md
@@ -3,66 +3,65 @@ keywords: quadratic function, function, quadratic equation
is_finished: False
---
-# Collapse of the cod fishery
+# Collapse of Cod Fisheries
+<!-- V nadpisech by měla být první písmena velká (kromě pedložek, spojek a členů), členy se většinou vynechávají. -->
-Coastal states have a huge wealth of fish in the oceans within their
+Coastal states have a vast wealth of fish in the oceans within their
grasp. This wealth is seemingly endless and stable. However, people
-have learned some bitter lessons that this is not the case. One of
-them dates back to 1992. The Gulf off Newfoundland has always been
-rich in cod (*Gadus morhua*). A boat that came here to fish never left
+have learned some bitter lessons that this is not the case. One significant lesson dates back to 1992. The Gulf off Newfoundland had always been
+rich in cod (*Gadus morhua*, Atlantic cod). A boat that came to fish there never left
without a rich catch. But over time, the situation began to change. In
-the late 1980s, biologists called for the need to cut the fishery in
-half to avoid plundering the fishery. However, because a reduction in
-hunting would dragg the area into recession, the government did not
-deceide to limit hunting. Unfortunately, nature floows its own
-laws. Gradually, the situation reached the point where a halt to
-hunting was inevitable. Cod stocks have fallen to just one per cent of
-their original levels. A moratorium on fishing was therefore
-declared. The moratorium was initially two years long. However, the
-small cod stocks did no recover substantially. Therefore, the
+the late 1980s, biologists called for a 50% reduction in fishing to avoid plundering the fishery. However, because a reduction in
+fishing would drag the area into recession, the government did not
+decide to impose limits. Unfortunately, nature follows its own
+laws. Gradually, the situation reached the point where halting fishing was inevitable. The cod population fell to just one percent of its original level. A moratorium on fishing was therefore
+declared. Initially, the moratorium was to last two years. However, the
+small cod population did not recover substantially. Therefore, the
restrictions have lasted much longer than originally
-anticipated. After some hope of a release in 2015, the allowable
-harvest rate was reduced again in 2018 after the stock collapsed
-again. The moratorium on hunting resulted in job losses for 35,000
+anticipated. Despite some hope of easing restrictions in 2015, the allowable
+harvest rate was reduced again in 2018 after the population collapsed
+again. The moratorium on fishing resulted in job losses for 35,000
fishermen and fish processing factory workers. This had huge economic and
sociological impacts on the entire region.
+<-- Navržené změny jsou ve smyslu snadnějšího porozumění textu a zachování konzistence také v kontextu s následujícími příklady, kde se modeluje růst populace “= population” ne “stock” (“hunting” je nahrazeno “fishing”, “stock” je nahrazeno “population”)
-
+
It should be added that the case described above is not
unique. Simultaneously with the collapse of the Newfoundland
fisheries, a similar situation occurred in five other Canadian
-fisheries where a moratorium on hunting was issued in 1993 (Southern
-Grand Bank, St. Pierre Bank, Northen Gulf of St. Lawrence, Southern
+fisheries where a moratorium on fishing was issued in 1993 (Southern
+Grand Bank, St. Pierre Bank, Northern Gulf of St. Lawrence, Southern
Gulf of St. Lawrence, Eastern Scotian Shelf). And have you read
-Steinbeck's 1945 novel Cannery Row? It describes life around a
+Steinbeck's 1945 novel *Cannery Row*? It describes life around a
sardine factory in California. Shortly after the novel was published,
-the fishery began to collapse due to unsustainable hunting, and
-commercial hunting had to be banned in 1967.
+the fishery began to collapse due to unsustainable fishing, and
+commercial fishing had to be banned in 1967.
-## Modeling population growth
+## Modeling Population Growth
In order to prevent fisheries collapses and to be able to
-realistically and effectively model the growth of stocks in nature,
-effective and well tested mathematical models have been developed. One
-simple but reasonably accurate model describes the population growth rates
-using a quadratic function
+realistically and effectively model population growth in nature,
+effective and time-tested mathematical models have been developed. One
+simple yet reasonably accurate model describes the population growth rate
+using a quadratic function:
$$ f(N) = r N \left(1-\frac NK\right), $$
where $N$ is the population size, $f(N)$ is the population growth
rate, and $r$ and $K$ are constants. The constant $K$ is called the
carrying capacity of the environment. The constants $r$ and $K$
-determine the reproductive capacity of the population and the effect
+determine the reproductive capabilities of the population and the impact
of the environment on the population. These constants have also given
-names to the *r*/*K* selection theory which describes the life strategies
-of organism in nature. Populations that qualify as *r*-strategists are
+names to the *r*/*K* selection theory which describes two basic life strategies that help populations in nature to establish and thrive successfully. <!-- Tento překlad více odpovídá české verzi a myslím je i smysluplnější -->
+ Populations that qualify as *r*-strategists are
able to reproduce rapidly. They do not care much for their offspring
and compensate for care by abundance. These populations have a large
value of the constant $r$. In contrast, *K*-strategists have few
offspring, but care for them and can cope better with environmental
changes. Therefore, their population sizes are closer to the carrying
capacity of the environment than is the case for *r*-strategists.
+<!-- V tomto odstavci postrádám vysvětlení významu konstanty r. O dynamických systémech toho moc nevím, ale funkce f(N) by měla být funkcí času (rate of change f(N)=dN/dt) a čas (jednotka času) je myslím obsažen právě v “konstantě” r. Aby se daly dělat správné závěry i v příkladech, tak je přeci třeba vědět jaká je ta jednotka času ?? Je přeci rozdíl jestli se populace třeba zdvojnásobí za rok nebo jen za den. -->
@@ -70,122 +69,122 @@ The growth rate indicates how much the population size increases per
unit time. If it is zero, the population size does not change. If the
growth rate is positive and numerically large, the population size
grows rapidly. If the growth rate is negative, the population size
-decreases and the population dies out. The progression of the function
-modelling growth is shown in the figure. This model captures the
+decreases and the population dies out. The graph of the function
+modelling growth rate is shown in the figure. This model captures the
well-known facts that a population of small size reproduces slowly (a
small population has few individuals and hence few individuals capable
of reproduction). The model also captures the fact that a larger
population reproduces faster, but only to a certain extent that the
carrying capacity of the environment allows.
-
## Problems
Consider a hypothetical population exposed to harvesting. We will measure
the population size in appropriate units. This can be in numbers of
individuals, in thousands of individuals, in tons, and so on. For
-example, consider the parameters $K=1000$ and $r=0{,}1$. That is, the
+example, consider the parameters $K=1000$ and $r=0.1$. That is, the
size of the population that can sustain in the environment is
1000, and a small population that does not suffer from intraspecific
competition grows at 10% of its current size per unit time.
> **Problem 1.** Determine the population size $N_*$ which guaranties
-> the maximum growth rate. Find the maximal growthe rate. We will
-> henceforth denote this value by $h_*$, because it is also the
-> maximum theoretical possible harvesting rate. The value $N_*$ is the
-> population size at this maximum intensity.
+> the maximum growth rate. Find this maximum growth rate. We will
+> henceforth denote this value by $h_*$, as it is also the
+> maximum theoretical possible harvesting rate (also called harvesting intensity). The value $N_*$ is the
+> population size at this maximum rate.
+<!-- Termín “intensity” není odborně špatně, ale pro středoškolské studenty myslím nebude zřejmé, že je to to same jako “rate”. Nové termíny je třeba zavádět opatrně, tak aby text byl, pokud možno samostatně, srozumitelný. V dalším textu je používáno také “hunting effort” ve stejném významu jako “harvesting intensity”. Nechávám jen “harvesting intensity”.-->
*Solution.* Function
$$f(N) = r N \left(1-\frac NK\right),$$
-which describes growth is a quadratic fuction and its graph is a parabola. Here we suppose $N\geq0$.
+which describes growth is a quadratic function and its graph is a parabola. This graph is only meaningful for $N\geq0$.
+<!-- nahrazuji větičkou více odpovídající české verzi -->
-
+
-Since the function is given in the form of the product of the root
-factors we see that the roots are $N=0$ and $N=K$. The function takes
-its maximum at the vertex of the parabola, i.e. for $N_*=\frac
+Since the function is given in the form of a product of the root
+Factors, we see that the roots are $N=0$ and $N=K$. The function takes
+its maximum at the vertex of the parabola, i.e., for $N_*=\frac
{K}{2}=500$. The function value is
$$h_* = f(N_*) = r \frac{K}2 \left(1-\frac{\frac K2}{K}\right)=\frac{rK}4$$
-and for the given values we get
+and for the given values of the constants $K$ and $r$ we get
-$$h_* = \frac{0{,}1 \times 1000}{4} = 25.$$
+$$h_* = \frac{0.1 \cdot 1000}{4} = 25.$$
-Comparing this with the carrying capacity of the environment (1000),
+Comparing this to the carrying capacity of the environment ($K=1000$),
we see that this value is 2.5 percent of the carrying capacity of the
-environment. Since such a hunt stabilizes the population size at half
-of the carrying capacity, this means that the hunt proceeds at such a
+environment. Since the population stabilizes at half
+of the carrying capacity when harvesting is at this rate, this means that the fishing proceeds at such a
rate that 5 percent of the current population is harvested per unit
time.
> **Problem 2.** Determine how many times the population growth rate
-> drops if the population size decreases from the size $N_*$ allowing
-> the maximum possible hunting effort, to one percent. This is the
-> value, to which the harvest would have to be reduced to avoid
-> overfishing. (In practice, however, we would want to rebuild stocks,
-> and therefore the limits specified in this step alone is not
+> decreases if the population size drops from the size $N_*$, which allows
+> the maximum possible harvesting intensity, to one percent.
+<!-- v předchozím textu byl definován termín “harvesting intensity” ne “hunting effort” a toho je třeba se držet, pro srozumitelnost a konzistentnost textu. -->
+This is the
+> value to which the harvest would have to be reduced to prevent further decline. <!-- “prevent overfishing” myslím nevystihuje dostatečně přesně situaci. Termín “overfishing” myslím neodpovídá zcela termínu “zastavení úbytku ryb = prevent further decline ”.--> (In practice, however, we would want population recovery,
+> and therefore, the restriction specified in this step alone is not
> sufficient.)
-*Solution.* Let $N_2$ be the size of the population after a decrease.
+*Solution.* Let $N_2$ be the size of the population after the decline.
Then
-$$N_2=0{,}01N_*=0{,}01 \frac K2$$
+$$N_2=0.01N_*=0.01 \frac K2$$
and we get
-$$f(N_2) = r \times 0{,}01 \frac K2 \left(1-\frac{0{,}01 \frac K2}{K}\right) = 0{,}004975 rK$$
+$$f(N_2) = r \cdot 0.01 \frac K2 \left(1-\frac{0.01 \frac K2}{K}\right) = 0.004975\cdot \,r\,K$$
and
-$$\frac{f(N_2)}{f(N_*)} = \frac{0{,}004975 rK}{0{,}25 rK} \approx 0{,}02.$$
-If the population size drops to one percent, the hunting effort must
-be reduced to two percent of the original effort to avoid further
-declines.
+$$\frac{f(N_2)}{f(N_*)} = \frac{0.004975 rK}{0.25 rK} \approx 0.02.$$
+If the population size drops to one percent, the harvesting intensity must
+be reduced to two percent of the original intensity to avoid further
+decline.
->**Problem 3.** Assume the careful hunt which is 80 percent of the
-> maximal sustainable harvest $h_*$. Even in this case a caution is
-> necessary. If the population stock is small, it cannot cope with the
-> hunt. Determine what the the minimal size of the population capable
-> to cope with with hunt equal to 80 percent of $h_*$.
+>**Problem 3.** Assume the careful fishing at 80 percent of the
+> maximum sustainable harvest $h_*$. Even in this case a caution is
+> necessary. If the population is too small, it cannot cope with fishing. Determine what is the minimum size of the population capable
+> of coping with fishing at the rate equal to 80 percent of $h_*$ without collapsing.
-*Solution.* According to the assignment, you have to solve the equation
+*Solution.* According to the assignment, we need to solve the equation
-$$ r N \left(1-\frac NK\right) = 0{,}8 \frac{rK}{4}.$$
+$$ r N \left(1-\frac NK\right) = 0.8 \frac{rK}{4}.$$
-We can multiply the parentheses and
-convert all terms to one side to the form
+We can expand the parentheses and
+move all terms to one side to obtain the form
$$ -\frac{r}{K} N^2 + rN - 0{,}8 \frac{rK}{4} = 0.$$
For $r=0.1$ and $K=1000$ we get
-$$ -0{,}0001 N^2 +0{,}1 N - 20 = 0$$
-
-and after adjustment
+$$ -0.0001 N^2 +0.1 N - 20 = 0$$
-$$N^2 - 1{,000 N + 200{,000 = 0$$
+which can be rewritten as
-The roots of this equation are
-$$N_{1,2}=\frac{1000\pm \sqrt{1000^2-4\times 200000}}{2}$$
-and hence $$N_1\approx 276$$ and $$N_2\approx 724$$
+$$N^2 – 1000 N + 200000 = 0$$
+The roots of this quadratic equation are
+$$N_{1,2}=\frac{1000\pm \sqrt{1000^2-4\cdot 200000}}{2}$$
+and hence $$N_1\approx 276$$ and $$N_2\approx 724.$$
-
+
The figure shows the parabola defining the growth rate, the horizontal
-line defining the harvesting rate and the intersections of $N_1$ and
-$N_2$. For population sizes smaller than $N_1$ hunting exceeds the
-growth. In this situation, population growth is not capable to
-compensate the harvesting rate. The population is overfished, dies out
-and collapses. In order to allow the harvest rate at 80 percent of the
-maximal sustainable harvest, it is necessary to wait until the
+line defining the harvesting rate and the intersections $N_1$ and
+$N_2$. For population sizes smaller than $N_1$ harvesting exceeds the
+growth. In this situation, population growth is not capable of
+compensating the harvesting rate. The population is overfished, declines,
+and collapses. To set fishing at 80 percent of the
+maximum sustainable harvest, it is necessary to wait until the
population grows to a size of $N_1=276$. This value is slightly
more than half of $N_*$, i.e., more than half the value at which the
-stock size will stabilize at maximum sustainable fishing effort.
+population stabilizes at the maximum sustainable harvesting intensity.
-This last part shows that after the population collapse it is not
-possible to set an earlier sustainable harvesting strategy and hope
-for a spontaneous recovery to return to its original state. The stock
-must have sufficient dynamics to cope with the harvesting rates. It is
-necessary to wait until the fish population returns to suficiently
+This last part shows that after a population collapse, it is not
+possible to set an earlier sustainable harvesting intensity and hope
+for a spontaneous recovery of the population. The population
+must have sufficient growth dynamics to cope with this level of harvesting. It is
+necessary to wait until the fish population returns to sufficiently
large stocks. It is possible to return to the previous harvesting
-strategy only if the stocks which prevent extinction are met.
+rate only if the population size, which prevents extinction, is achieved.
## References and literature
@@ -201,3 +200,4 @@ strategy only if the stocks which prevent extinction are met.
* Millennium Ecosystem Assessment: Ecosystems and Human Well-being: Opportunities and Challenges
for Business and Industry Ecosystems, <https://www.millenniumassessment.org/documents/document.353.aspx.pdf>, October 1,2023
+