In a haplotype network, how to determine   which one is the root or where is the origin of the spp. and where does it   invaded from.

Coalescent theory predicts that ancestral   haplotypes will be the haplotypes most frequently sampled.  They are usually more broadly distributed   geographically, and more likely to have a larger number of connections or   descendant nodes/haplotypes.  If I   recall correctly, TCS calculates the haplotype that has the highest outgroup   probability (potentially the most ancestral haplotype) and displays it as a   square, whereas other haplotypes are displayed as ovals.

Regarding from where the species invaded:

Additional geographic, molecular dating,   and natural history data would be helpful in determining the answer to that   question.  You might consider the   geographic locality/region of the haplotype with the highest outgroup   probability.  if that haplotype is   concentrated in a certain geographic area, it may indicate a glacial refugium   or point of invasion.  This would   depend on the scale of your sampling, mobility of organism, etc.

在一个单倍型网络中，如何确定哪一个单倍型是根，或者物种的起源在哪里，以及它从哪里入侵。

根据溯祖理论预测，祖先的单倍型将是最常被抽样到的单倍型。它们通常在地理上分布更广，并具具有更多的连接或后代节点/单倍型。如果我记得正确的话，TCS计算出具有最高外群（连接）概率的单倍型（可能是最原始的单倍型），并将其显示为一个正方形，而其他单倍型则显示为椭圆形。

关于物种入侵的来源：

额外的地理、分子年代测定和自然历史数据将有助于确定这个问题的答案。您可以考虑具有最高的外群概率单倍型的地理位置/区域。如果这种单倍型集中在某个地理区域，可能表明是冰川避难所或入侵点。这将取决于你的取样规模、生物体的流动性等。