In the version of this article initially published, there were errors in equations and notations in the Methods “Model development” subsection which arose during manuscript preparation; the errors affect presentation of the study but not the analysis, results, or code provided with the article. Clarifications to text and equations follow.
In Equation (1), “N” replaces “Normal”; in Equations (2), (3), (7) and in text directly below Equations (3), (5) and (7), “ys,i,z” now replaces “Δxs,t1, t2.” In the two paragraphs below Equation (2), “t2 = 2016” and “t1 = 2001” now replace “2016” and “2001” in five instances. Further, Equations (5)–(7) have been revised as follows:
$$begin{array}{ll}fleft( {x_{s,t}} right) = {{{mathrm{exp}}}} & left( {beta _0 + mathop {sum }limits_{i = 1}^{I = 5} beta _{1,i} x_{s,i,t} + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = i}^{K = 5} beta _{2,i,k}x_{s,i,t}x_{k,s,t}}right. & quad quad left. {+ mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = 1, k neq i}^{K = 5} beta _{3,i,k}x_{s,i,t}x_{k,s,t}} right)end{array} {rm{Revised}} {rm{Eq}}. (5)$$
$$begin{array}{ll}fleft( {x_{s,t}} right) = expleft( {beta _0 + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{j = 1}^{J = 2} beta _{0,i,j,}x_{i,s,t}^j + mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{k = i + 1}^{K = 6} beta _{1,i,k}x_{i,s,t}x_{k,s,t}} right) {mathrm{Original}} {rm{Eq}}. (5)end{array}$$
$$y_{s,i,z} = left{ {begin{array}{*{20}{l}} {y_{s,i,1} = left| {Delta x_{s,i}} right|,} hfill & {y_{s,i,2} = 0,} hfill & {{{{mathrm{if}}}},Delta x_{s,i} < 0} hfill {y_{s,i,1} = 0,} hfill & {y_{s,i,2} = Delta x_{s,i}} hfill & {{{{mathrm{otherwise}}}}} hfill end{array}} right. {rm{Revised}} {rm{Eq}}. (6)$$
$$x_{i,s,} = left{ {begin{array}{*{20}{l}} {x_{1,i,s} = left| {Delta x_{i,s}} right|,} hfill & {x_{2,i,s} = 0,} hfill & {if,Delta x_{i,s} < 0} hfill {x_{1,i,s} = 0,} hfill & {x_{2,i,s} = Delta x_{i,s},} hfill & {otherwise} hfill end{array}} right. {rm{Original}} {rm{Eq}}. (6)$$
$$omega left( {y_{s,i,z};gamma } right) = {{{mathrm{exp}}}}left( {mathop {sum }limits_{i = 1}^{I = 5} mathop {sum }limits_{z = 1}^{Z = 2} – gamma _{i,z} y_{s,i,z}} right) {rm{Revised}} {rm{Eq}}. (7)$$
$$omega left( {Delta x_{s,t_1,t_2};gamma } right) = expleft( {mathop {sum }limits_{i = 1}^{I = 5} – gamma _{i,z}Delta x_{z,s,i}} right) {rm{Original}} {rm{Eq}}. (7)$$
All changes have been made in the HTML and PDF versions of the article.
Source: Ecology - nature.com
